TSTP Solution File: LAT270-2 by Twee---2.4.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Twee---2.4.1
% Problem  : LAT270-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof

% Computer : n026.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 : Sat Sep 17 18:24:55 EDT 2022

% Result   : Unsatisfiable 0.12s 0.39s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : LAT270-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34  % Computer : n026.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu Sep  1 13:10:22 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.39  % SZS status Unsatisfiable
% 0.12/0.39  
% 0.20/0.40  % SZS output start Proof
% 0.20/0.40  Take the following subset of the input axioms:
% 0.20/0.40    fof(cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0, axiom, ![V_b, V_a, V_S]: (~c_in(V_b, v_A, t_a) | (~c_in(V_a, v_A, t_a) | (~c_lessequals(V_S, c_Tarski_Ointerval(v_r, V_a, V_b, t_a), tc_set(t_a)) | c_lessequals(V_S, v_A, tc_set(t_a)))))).
% 0.20/0.40    fof(cls_conjecture_0, negated_conjecture, c_in(v_a, v_A, t_a)).
% 0.20/0.40    fof(cls_conjecture_1, negated_conjecture, c_in(v_b, v_A, t_a)).
% 0.20/0.40    fof(cls_conjecture_2, negated_conjecture, c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))).
% 0.20/0.40    fof(cls_conjecture_6, negated_conjecture, ~c_lessequals(v_S, v_A, tc_set(t_a))).
% 0.20/0.40  
% 0.20/0.40  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.40  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.40  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.40    fresh(y, y, x1...xn) = u
% 0.20/0.40    C => fresh(s, t, x1...xn) = v
% 0.20/0.40  where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.40  variables of u and v.
% 0.20/0.40  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.40  input problem has no model of domain size 1).
% 0.20/0.40  
% 0.20/0.40  The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.40  
% 0.20/0.40  Axiom 1 (cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0): fresh3(X, X, Y) = true.
% 0.20/0.40  Axiom 2 (cls_conjecture_0): c_in(v_a, v_A, t_a) = true.
% 0.20/0.40  Axiom 3 (cls_conjecture_1): c_in(v_b, v_A, t_a) = true.
% 0.20/0.40  Axiom 4 (cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0): fresh(X, X, Y, Z) = c_lessequals(Z, v_A, tc_set(t_a)).
% 0.20/0.40  Axiom 5 (cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0): fresh2(X, X, Y, Z, W) = fresh3(c_in(Y, v_A, t_a), true, W).
% 0.20/0.40  Axiom 6 (cls_conjecture_2): c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a)) = true.
% 0.20/0.40  Axiom 7 (cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0): fresh2(c_lessequals(X, c_Tarski_Ointerval(v_r, Y, Z, t_a), tc_set(t_a)), true, Z, Y, X) = fresh(c_in(Y, v_A, t_a), true, Z, X).
% 0.20/0.40  
% 0.20/0.40  Goal 1 (cls_conjecture_6): c_lessequals(v_S, v_A, tc_set(t_a)) = true.
% 0.20/0.40  Proof:
% 0.20/0.40    c_lessequals(v_S, v_A, tc_set(t_a))
% 0.20/0.40  = { by axiom 4 (cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0) R->L }
% 0.20/0.40    fresh(true, true, v_b, v_S)
% 0.20/0.40  = { by axiom 2 (cls_conjecture_0) R->L }
% 0.20/0.40    fresh(c_in(v_a, v_A, t_a), true, v_b, v_S)
% 0.20/0.40  = { by axiom 7 (cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0) R->L }
% 0.20/0.40    fresh2(c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a)), true, v_b, v_a, v_S)
% 0.20/0.40  = { by axiom 6 (cls_conjecture_2) }
% 0.20/0.40    fresh2(true, true, v_b, v_a, v_S)
% 0.20/0.40  = { by axiom 5 (cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0) }
% 0.20/0.40    fresh3(c_in(v_b, v_A, t_a), true, v_S)
% 0.20/0.40  = { by axiom 3 (cls_conjecture_1) }
% 0.20/0.40    fresh3(true, true, v_S)
% 0.20/0.40  = { by axiom 1 (cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0) }
% 0.20/0.40    true
% 0.20/0.40  % SZS output end Proof
% 0.20/0.40  
% 0.20/0.40  RESULT: Unsatisfiable (the axioms are contradictory).
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