TSTP Solution File: SEU165+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU165+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 12:38:57 EDT 2022
% Result : Theorem 0.80s 1.00s
% Output : CNFRefutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 42 ( 15 unt; 0 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 96 ( 44 ~; 20 |; 18 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 94 ( 4 sgn 72 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t106_zfmisc_1,conjecture,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(A,C)
& in(B,D) ) ) ).
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(subgoal_0,plain,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
=> in(A,C) ),
inference(strip,[],[t106_zfmisc_1]) ).
fof(subgoal_1,plain,
! [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(C,D))
& in(A,C) )
=> in(B,D) ),
inference(strip,[],[t106_zfmisc_1]) ).
fof(subgoal_2,plain,
! [A,B,C,D] :
( ( in(A,C)
& in(B,D) )
=> in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(strip,[],[t106_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
=> in(A,C) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C] :
( ~ in(A,C)
& ? [D] : in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
& ? [D] : in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,D)) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [D] : in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,D)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
in(ordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),
inference(skolemize,[],[normalize_0_2]) ).
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(canonicalize,[],[l55_zfmisc_1]) ).
fof(normalize_0_5,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( ~ in(A,C)
| ~ in(B,D) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,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_5]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(A,C) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
~ in(skolemFOFtoCNF_A_2,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_3]) ).
cnf(refute_0_1,plain,
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(A,C) ),
inference(canonicalize,[],[normalize_0_7]) ).
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(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) )],[refute_0_3,refute_0_4]) ).
fof(negate_1_0,plain,
~ ! [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(C,D))
& in(A,C) )
=> in(B,D) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A,B,C,D] :
( ~ in(B,D)
& in(A,C)
& in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ~ in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)
& in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1))
& in(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_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_1_4,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( ~ in(A,C)
| ~ in(B,D) ) ),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_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_1_4]) ).
fof(normalize_1_6,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(B,D) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
~ in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1),
inference(conjunct,[],[normalize_1_1]) ).
cnf(refute_1_0,plain,
in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(B,D) ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_2,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1))
| in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) ),
inference(subst,[],[refute_1_1:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_D_1))]]) ).
cnf(refute_1_3,plain,
in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)) )],[refute_1_0,refute_1_2]) ).
cnf(refute_1_4,plain,
~ in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_5,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) )],[refute_1_3,refute_1_4]) ).
fof(negate_2_0,plain,
~ ! [A,B,C,D] :
( ( in(A,C)
& in(B,D) )
=> in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
? [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
& in(A,C)
& in(B,D) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,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_2_2,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( ~ in(A,C)
| ~ in(B,D) ) ),
inference(specialize,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
$false,
inference(simplify,[],[normalize_2_0,normalize_2_2]) ).
cnf(refute_2_0,plain,
$false,
inference(canonicalize,[],[normalize_2_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU165+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n029.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 Jun 20 08:33:45 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.80/1.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.80/1.00
% 0.80/1.00 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.80/1.00
%------------------------------------------------------------------------------