TSTP Solution File: GRP125-1.003 by CSE_E---1.4

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%------------------------------------------------------------------------------
% File     : CSE_E---1.4
% Problem  : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n022.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 16 20:52:43 EDT 2022

% Result   : Unsatisfiable 0.63s 0.70s
% Output   : CNFRefutation 0.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   45 (  23 unt;   7 nHn;  43 RR)
%            Number of literals    :   85 (   0 equ;  46 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   53 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(e_3_is_not_e_1,axiom,
    ~ equalish(e_3,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).

cnf(product_right_cancellation,axiom,
    ( equalish(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).

cnf(product_total_function1,axiom,
    ( product(X1,X2,e_1)
    | product(X1,X2,e_2)
    | product(X1,X2,e_3)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).

cnf(element_3,axiom,
    group_element(e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).

cnf(product_idempotence,axiom,
    product(X1,X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).

cnf(e_3_is_not_e_2,axiom,
    ~ equalish(e_3,e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).

cnf(product_left_cancellation,axiom,
    ( equalish(X1,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).

cnf(element_1,axiom,
    group_element(e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).

cnf(e_2_is_not_e_1,axiom,
    ~ equalish(e_2,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).

cnf(element_2,axiom,
    group_element(e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).

cnf(product_total_function2,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).

cnf(qg3,negated_conjecture,
    ( product(X3,X4,X1)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X1,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).

cnf(c_0_12,axiom,
    ~ equalish(e_3,e_1),
    e_3_is_not_e_1 ).

cnf(c_0_13,axiom,
    ( equalish(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X3) ),
    product_right_cancellation ).

cnf(c_0_14,axiom,
    ( product(X1,X2,e_1)
    | product(X1,X2,e_2)
    | product(X1,X2,e_3)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    product_total_function1 ).

cnf(c_0_15,axiom,
    group_element(e_3),
    element_3 ).

cnf(c_0_16,plain,
    ( ~ product(X1,e_1,X2)
    | ~ product(X1,e_3,X2) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,axiom,
    product(X1,X1,X1),
    product_idempotence ).

cnf(c_0_18,axiom,
    ~ equalish(e_3,e_2),
    e_3_is_not_e_2 ).

cnf(c_0_19,axiom,
    ( equalish(X1,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X3) ),
    product_left_cancellation ).

cnf(c_0_20,plain,
    ( product(X1,e_3,e_3)
    | product(X1,e_3,e_2)
    | product(X1,e_3,e_1)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_21,axiom,
    group_element(e_1),
    element_1 ).

cnf(c_0_22,plain,
    ~ product(e_1,e_3,e_1),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_23,plain,
    ( ~ product(e_2,X1,X2)
    | ~ product(e_3,X1,X2) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_24,axiom,
    ~ equalish(e_2,e_1),
    e_2_is_not_e_1 ).

cnf(c_0_25,plain,
    ( ~ product(e_1,X1,X2)
    | ~ product(e_3,X1,X2) ),
    inference(spm,[status(thm)],[c_0_12,c_0_19]) ).

cnf(c_0_26,plain,
    ( product(e_1,e_3,e_2)
    | product(e_1,e_3,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).

cnf(c_0_27,axiom,
    group_element(e_2),
    element_2 ).

cnf(c_0_28,plain,
    ~ product(e_2,e_3,e_3),
    inference(spm,[status(thm)],[c_0_23,c_0_17]) ).

cnf(c_0_29,plain,
    ( ~ product(e_1,X1,X2)
    | ~ product(e_2,X1,X2) ),
    inference(spm,[status(thm)],[c_0_24,c_0_19]) ).

cnf(c_0_30,plain,
    product(e_1,e_3,e_2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_17])]) ).

cnf(c_0_31,plain,
    ( product(e_2,e_3,e_1)
    | product(e_2,e_3,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_27]),c_0_28]) ).

cnf(c_0_32,plain,
    ~ product(e_2,e_3,e_2),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_33,plain,
    ( ~ product(X1,e_2,X2)
    | ~ product(X1,e_3,X2) ),
    inference(spm,[status(thm)],[c_0_18,c_0_13]) ).

cnf(c_0_34,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    product_total_function2 ).

cnf(c_0_35,negated_conjecture,
    ( product(X3,X4,X1)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X1,X4) ),
    qg3 ).

cnf(c_0_36,plain,
    product(e_2,e_3,e_1),
    inference(sr,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_37,plain,
    ( product(X1,e_2,e_3)
    | product(X1,e_2,e_2)
    | product(X1,e_2,e_1)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_27]) ).

cnf(c_0_38,plain,
    ~ product(e_3,e_2,e_3),
    inference(spm,[status(thm)],[c_0_33,c_0_17]) ).

cnf(c_0_39,plain,
    ( ~ product(X1,X2,e_1)
    | ~ product(X1,X2,e_3) ),
    inference(spm,[status(thm)],[c_0_12,c_0_34]) ).

cnf(c_0_40,negated_conjecture,
    ( product(X1,e_1,e_3)
    | ~ product(e_3,e_2,X1) ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_41,plain,
    ( product(e_3,e_2,e_1)
    | product(e_3,e_2,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_15]),c_0_38]) ).

cnf(c_0_42,plain,
    ~ product(e_1,e_1,e_3),
    inference(spm,[status(thm)],[c_0_39,c_0_17]) ).

cnf(c_0_43,negated_conjecture,
    product(e_3,e_2,e_2),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).

cnf(c_0_44,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_43]),c_0_17])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.06/0.12  % Command   : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n022.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Aug 31 14:57:55 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.44  openjdk version "1.8.0_171"
% 0.18/0.44  OpenJDK Runtime Environment (build 1.8.0_171-b10)
% 0.18/0.44  OpenJDK 64-Bit Server VM (build 25.171-b10, mixed mode)
% 0.18/0.45  file=/export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.54/0.66  start to proof: theBenchmark
% 0.63/0.70  % Version  : CSE_E---1.4
% 0.63/0.70  % Problem  : theBenchmark.p
% 0.63/0.70  % Proof found
% 0.63/0.70  % SZS status Theorem for theBenchmark.p
% 0.63/0.70  % SZS output start Proof
% See solution above
% 0.63/0.71  % Total time : 0.033000 s
%------------------------------------------------------------------------------