TSTP Solution File: SYN321+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN321+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 09:01:15 EDT 2022
% Result : Theorem 0.12s 0.32s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 29 ( 7 unt; 0 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 64 ( 24 ~; 19 |; 3 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 81 ( 17 sgn 44 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_3_2,conjecture,
? [X,Y] :
( ( ? [Z] : big_f(X,Z)
=> ! [Z] : big_g(X,Z) )
=> ( ! [Z] :
( big_g(Z,Z)
=> big_f(Z,Y) )
=> ( big_f(X,Y)
<=> ! [Z] : big_g(X,Z) ) ) ) ).
fof(subgoal_0,plain,
? [X,Y] :
( ( ? [Z] : big_f(X,Z)
=> ! [Z] : big_g(X,Z) )
=> ( ! [Z] :
( big_g(Z,Z)
=> big_f(Z,Y) )
=> ( big_f(X,Y)
<=> ! [Z] : big_g(X,Z) ) ) ),
inference(strip,[],[church_46_3_2]) ).
fof(negate_0_0,plain,
~ ? [X,Y] :
( ( ? [Z] : big_f(X,Z)
=> ! [Z] : big_g(X,Z) )
=> ( ! [Z] :
( big_g(Z,Z)
=> big_f(Z,Y) )
=> ( big_f(X,Y)
<=> ! [Z] : big_g(X,Z) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ! [X] :
( ! [Z] : ~ big_f(X,Z)
| ! [Z] : big_g(X,Z) )
& ! [X,Y] :
( ~ big_f(X,Y)
<=> ! [Z] : big_g(X,Z) )
& ! [Y,Z] :
( ~ big_g(Z,Z)
| big_f(Z,Y) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ big_f(X,Y)
<=> ! [Z] : big_g(X,Z) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ~ big_f(X,Y)
<=> ! [Z] : big_g(X,Z) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y,Z] :
( ( ~ big_f(X,Y)
| ~ big_g(X,skolemFOFtoCNF_Z(X)) )
& ( big_f(X,Y)
| big_g(X,Z) ) ),
inference(clausify,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ big_f(X,Y)
| ~ big_g(X,skolemFOFtoCNF_Z(X)) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [Y,Z] :
( ~ big_g(Z,Z)
| big_f(Z,Y) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_6,plain,
! [Y,Z] :
( ~ big_g(Z,Z)
| big_f(Z,Y) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y,Z] :
( big_f(X,Y)
| big_g(X,Z) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_8,plain,
! [X] :
( ! [Z] : ~ big_f(X,Z)
| ! [Z] : big_g(X,Z) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_9,plain,
! [X] :
( ! [Z] : ~ big_f(X,Z)
| ! [Z] : big_g(X,Z) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Z,Z0] :
( ~ big_f(X,Z)
| big_g(X,Z0) ),
inference(clausify,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
( ~ big_f(X,Y)
| ~ big_g(X,skolemFOFtoCNF_Z(X)) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
( ~ big_f(X_8,X_7)
| ~ big_g(X_8,skolemFOFtoCNF_Z(X_8)) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(X_8)),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_2,plain,
( ~ big_g(Z,Z)
| big_f(Z,Y) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ big_g(X_6,X_6)
| big_f(X_6,Y) ),
inference(subst,[],[refute_0_2:[bind(Z,$fot(X_6))]]) ).
cnf(refute_0_4,plain,
( big_f(X,Y)
| big_g(X,Z) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( big_f(X_6,X_5)
| big_g(X_6,X_6) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_6)),bind(Y,$fot(X_5)),bind(Z,$fot(X_6))]]) ).
cnf(refute_0_6,plain,
( big_f(X_6,Y)
| big_f(X_6,X_5) ),
inference(resolve,[$cnf( big_g(X_6,X_6) )],[refute_0_5,refute_0_3]) ).
cnf(refute_0_7,plain,
big_f(X_8,X_7),
inference(subst,[],[refute_0_6:[bind(Y,$fot(X_7)),bind(X_5,$fot(X_7)),bind(X_6,$fot(X_8))]]) ).
cnf(refute_0_8,plain,
~ big_g(X_8,skolemFOFtoCNF_Z(X_8)),
inference(resolve,[$cnf( big_f(X_8,X_7) )],[refute_0_7,refute_0_1]) ).
cnf(refute_0_9,plain,
~ big_g(X_10,skolemFOFtoCNF_Z(X_10)),
inference(subst,[],[refute_0_8:[bind(X_8,$fot(X_10))]]) ).
cnf(refute_0_10,plain,
( ~ big_f(X,Z)
| big_g(X,Z0) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_11,plain,
big_f(X,Z),
inference(subst,[],[refute_0_6:[bind(Y,$fot(Z)),bind(X_5,$fot(Z)),bind(X_6,$fot(X))]]) ).
cnf(refute_0_12,plain,
big_g(X,Z0),
inference(resolve,[$cnf( big_f(X,Z) )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
big_g(X_10,skolemFOFtoCNF_Z(X_10)),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_10)),bind(Z0,$fot(skolemFOFtoCNF_Z(X_10)))]]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( big_g(X_10,skolemFOFtoCNF_Z(X_10)) )],[refute_0_13,refute_0_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN321+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.31 % Computer : n023.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 600
% 0.12/0.31 % DateTime : Tue Jul 12 02:51:39 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.32
% 0.12/0.32 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.33
%------------------------------------------------------------------------------