## TSTP Solution File: SYN367+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN367+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %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  : 600s
% DateTime : Thu Jul 21 09:01:50 EDT 2022

% Result   : Theorem 0.13s 0.34s
% Output   : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   22 (  10 unt;   0 def)
%            Number of atoms       :   58 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   56 (  20   ~;  15   |;  18   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   2 prp; 0-1 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   22 (   3 sgn  15   !;   4   ?)

%------------------------------------------------------------------------------
fof(x2118,conjecture,
( ! [X] :
( ( p
& big_q(X) )
| ( ~ p
& big_r(X) ) )
=> ( ! [X] : big_q(X)
| ! [X] : big_r(X) ) ) ).

fof(subgoal_0,plain,
( ( ! [X] :
( ( p
& big_q(X) )
| ( ~ p
& big_r(X) ) )
& ~ ! [X] : big_q(X) )
=> ! [X] : big_r(X) ),
inference(strip,[],[x2118]) ).

fof(negate_0_0,plain,
~ ( ( ! [X] :
( ( p
& big_q(X) )
| ( ~ p
& big_r(X) ) )
& ~ ! [X] : big_q(X) )
=> ! [X] : big_r(X) ),
inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
( ? [X] : ~ big_q(X)
& ? [X] : ~ big_r(X)
& ! [X] :
( ( ~ p
& big_r(X) )
| ( big_q(X)
& p ) ) ),
inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
? [X] : ~ big_q(X),
inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
~ big_q(skolemFOFtoCNF_X),
inference(skolemize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
! [X] :
( ( ~ p
& big_r(X) )
| ( big_q(X)
& p ) ),
inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_4,plain,
! [X] :
( ( ~ p
& big_r(X) )
| ( big_q(X)
& p ) ),
inference(specialize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
! [X] :
( ( ~ p
| big_q(X) )
& ( big_q(X)
| big_r(X) )
& ( big_r(X)
| p ) ),
inference(clausify,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
! [X] :
( ~ p
| big_q(X) ),
inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
? [X] : ~ big_r(X),
inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_8,plain,
~ big_r(skolemFOFtoCNF_X_1),
inference(skolemize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
! [X] :
( big_r(X)
| p ),
inference(conjunct,[],[normalize_0_5]) ).

cnf(refute_0_0,plain,
~ big_q(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
( ~ p
| big_q(X) ),
inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_2,plain,
~ big_r(skolemFOFtoCNF_X_1),
inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_3,plain,
( big_r(X)
| p ),
inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_4,plain,
( big_r(skolemFOFtoCNF_X_1)
| p ),
inference(subst,[],[refute_0_3:[bind(X,\$fot(skolemFOFtoCNF_X_1))]]) ).

cnf(refute_0_5,plain,
p,
inference(resolve,[\$cnf( big_r(skolemFOFtoCNF_X_1) )],[refute_0_4,refute_0_2]) ).

cnf(refute_0_6,plain,
big_q(X),
inference(resolve,[\$cnf( p )],[refute_0_5,refute_0_1]) ).

cnf(refute_0_7,plain,
big_q(skolemFOFtoCNF_X),
inference(subst,[],[refute_0_6:[bind(X,\$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_8,plain,
\$false,
inference(resolve,[\$cnf( big_q(skolemFOFtoCNF_X) )],[refute_0_7,refute_0_0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN367+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jul 11 14:51:55 EDT 2022
% 0.13/0.34  % CPUTime  :
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.34  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34
% 0.13/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35
%------------------------------------------------------------------------------