TSTP Solution File: SET954+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET954+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 : Tue Jul 19 03:38:36 EDT 2022
% Result : Theorem 3.84s 4.00s
% Output : CNFRefutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 28 ( 8 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 60 ( 29 ~; 20 |; 5 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 4 sgn 40 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l55_zfmisc_1,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(A,C)
& in(B,D) ) ) ).
fof(t107_zfmisc_1,conjecture,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
=> in(ordered_pair(B,A),cartesian_product2(D,C)) ) ).
fof(subgoal_0,plain,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
=> in(ordered_pair(B,A),cartesian_product2(D,C)) ),
inference(strip,[],[t107_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
=> in(ordered_pair(B,A),cartesian_product2(D,C)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C,D] :
( ~ in(ordered_pair(B,A),cartesian_product2(D,C))
& in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),cartesian_product2(skolemFOFtoCNF_D,skolemFOFtoCNF_C))
& in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( ~ in(A,C)
| ~ in(B,D) ) ),
inference(canonicalize,[],[l55_zfmisc_1]) ).
fof(normalize_0_4,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( ~ in(A,C)
| ~ in(B,D) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C,D] :
( ( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(A,C) )
& ( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(B,D) )
& ( ~ in(A,C)
| ~ in(B,D)
| in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(A,C) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(B,D) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_8,plain,
! [A,B,C,D] :
( ~ in(A,C)
| ~ in(B,D)
| in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_9,plain,
~ in(ordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),cartesian_product2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(A,C) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_3,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(B,D) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| in(skolemFOFtoCNF_B,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_6,plain,
in(skolemFOFtoCNF_B,skolemFOFtoCNF_D),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ in(A,C)
| ~ in(B,D)
| in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_8,plain,
( ~ in(X_96,X_98)
| ~ in(skolemFOFtoCNF_B,skolemFOFtoCNF_D)
| in(ordered_pair(skolemFOFtoCNF_B,X_96),cartesian_product2(skolemFOFtoCNF_D,X_98)) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(X_96)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(X_98))]]) ).
cnf(refute_0_9,plain,
( ~ in(X_96,X_98)
| in(ordered_pair(skolemFOFtoCNF_B,X_96),cartesian_product2(skolemFOFtoCNF_D,X_98)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B,skolemFOFtoCNF_D) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| in(ordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),cartesian_product2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)) ),
inference(subst,[],[refute_0_9:[bind(X_96,$fot(skolemFOFtoCNF_A_2)),bind(X_98,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_11,plain,
in(ordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),cartesian_product2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) )],[refute_0_3,refute_0_10]) ).
cnf(refute_0_12,plain,
~ in(ordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),cartesian_product2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_13,plain,
$false,
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),cartesian_product2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)) )],[refute_0_11,refute_0_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET954+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 9 17:00:17 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.84/4.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.84/4.00
% 3.84/4.00 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.84/4.00
%------------------------------------------------------------------------------