TSTP Solution File: SYN333+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN333+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 09:01:25 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 25 ( 10 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 99 ( 42 ~; 31 |; 20 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 61 ( 7 sgn 25 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_14_5,conjecture,
? [X,Y] :
! [Z] :
( big_f(X,Y)
=> ( big_f(Y,Z)
& big_f(Z,Z)
& ( ( big_f(X,Y)
& big_g(X,Y) )
=> ( big_g(X,Z)
& big_g(Z,Z) ) ) ) ) ).
fof(subgoal_0,plain,
? [X,Y] :
! [Z] :
( big_f(X,Y)
=> ( big_f(Y,Z)
& big_f(Z,Z)
& ( ( big_f(X,Y)
& big_g(X,Y) )
=> ( big_g(X,Z)
& big_g(Z,Z) ) ) ) ),
inference(strip,[],[church_46_14_5]) ).
fof(negate_0_0,plain,
~ ? [X,Y] :
! [Z] :
( big_f(X,Y)
=> ( big_f(Y,Z)
& big_f(Z,Z)
& ( ( big_f(X,Y)
& big_g(X,Y) )
=> ( big_g(X,Z)
& big_g(Z,Z) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ! [X,Y] : big_f(X,Y)
& ! [X,Y] :
( ( big_f(X,Y)
& big_g(X,Y)
& ( ? [Z] : ~ big_g(X,Z)
| ? [Z] : ~ big_g(Z,Z) ) )
| ? [Z] : ~ big_f(Y,Z)
| ? [Z] : ~ big_f(Z,Z) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ( big_f(X,Y)
& big_g(X,Y)
& ( ? [Z] : ~ big_g(X,Z)
| ? [Z] : ~ big_g(Z,Z) ) )
| ? [Z] : ~ big_f(Y,Z)
| ? [Z] : ~ big_f(Z,Z) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] : big_f(X,Y),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_3,plain,
! [X,Y] : big_f(X,Y),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [Y] :
( ( ( ? [Z] : ~ big_g(Z,Z)
| ! [X] :
? [Z] : ~ big_g(X,Z) )
& ! [X] : big_g(X,Y) )
| ? [Z] : ~ big_f(Y,Z)
| ? [Z] : ~ big_f(Z,Z) ),
inference(simplify,[],[normalize_0_1,normalize_0_3]) ).
fof(normalize_0_5,plain,
! [Y] :
( ( ( ? [Z] : ~ big_g(Z,Z)
| ! [X] :
? [Z] : ~ big_g(X,Z) )
& ! [X] : big_g(X,Y) )
| ? [Z] : ~ big_f(Y,Z)
| ? [Z] : ~ big_f(Z,Z) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ( ~ big_f(Y,skolemFOFtoCNF_Z_2(Y))
| ~ big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3)
| big_g(X,Y) )
& ( ~ big_f(Y,skolemFOFtoCNF_Z_2(Y))
| ~ big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3)
| ~ big_g(X,skolemFOFtoCNF_Z_1(X))
| ~ big_g(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ big_f(Y,skolemFOFtoCNF_Z_2(Y))
| ~ big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3)
| ~ big_g(X,skolemFOFtoCNF_Z_1(X))
| ~ big_g(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ big_f(Y,skolemFOFtoCNF_Z_2(Y))
| ~ big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3)
| big_g(X,Y) ),
inference(conjunct,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
( ~ big_f(Y,skolemFOFtoCNF_Z_2(Y))
| ~ big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3)
| ~ big_g(X,skolemFOFtoCNF_Z_1(X))
| ~ big_g(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_1,plain,
big_f(X,Y),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
big_f(Y,skolemFOFtoCNF_Z_2(Y)),
inference(subst,[],[refute_0_1:[bind(X,$fot(Y)),bind(Y,$fot(skolemFOFtoCNF_Z_2(Y)))]]) ).
cnf(refute_0_3,plain,
( ~ big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3)
| ~ big_g(X,skolemFOFtoCNF_Z_1(X))
| ~ big_g(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( big_f(Y,skolemFOFtoCNF_Z_2(Y)) )],[refute_0_2,refute_0_0]) ).
cnf(refute_0_4,plain,
big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_Z_3)),bind(Y,$fot(skolemFOFtoCNF_Z_3))]]) ).
cnf(refute_0_5,plain,
( ~ big_g(X,skolemFOFtoCNF_Z_1(X))
| ~ big_g(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ big_f(Y,skolemFOFtoCNF_Z_2(Y))
| ~ big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3)
| big_g(X,Y) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_7,plain,
( ~ big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3)
| big_g(X,Y) ),
inference(resolve,[$cnf( big_f(Y,skolemFOFtoCNF_Z_2(Y)) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
big_g(X,Y),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z_3,skolemFOFtoCNF_Z_3) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
big_g(X,skolemFOFtoCNF_Z_1(X)),
inference(subst,[],[refute_0_8:[bind(Y,$fot(skolemFOFtoCNF_Z_1(X)))]]) ).
cnf(refute_0_10,plain,
~ big_g(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z),
inference(resolve,[$cnf( big_g(X,skolemFOFtoCNF_Z_1(X)) )],[refute_0_9,refute_0_5]) ).
cnf(refute_0_11,plain,
big_g(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z),
inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_12,plain,
$false,
inference(resolve,[$cnf( big_g(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) )],[refute_0_11,refute_0_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYN333+1 : TPTP v8.1.0. Released v2.0.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jul 11 18:25:23 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36
%------------------------------------------------------------------------------