TSTP Solution File: SEU167+3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU167+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 12:38:59 EDT 2022
% Result : Theorem 0.19s 0.43s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 11 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 62 ( 25 ~; 20 |; 12 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 41 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t118_zfmisc_1,axiom,
! [A,B,C] :
( subset(A,B)
=> ( subset(cartesian_product2(A,C),cartesian_product2(B,C))
& subset(cartesian_product2(C,A),cartesian_product2(C,B)) ) ) ).
fof(t119_zfmisc_1,conjecture,
! [A,B,C,D] :
( ( subset(A,B)
& subset(C,D) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ) ).
fof(t1_xboole_1,axiom,
! [A,B,C] :
( ( subset(A,B)
& subset(B,C) )
=> subset(A,C) ) ).
fof(subgoal_0,plain,
! [A,B,C,D] :
( ( subset(A,B)
& subset(C,D) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
inference(strip,[],[t119_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,D] :
( ( subset(A,B)
& subset(C,D) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C,D] :
( ~ subset(cartesian_product2(A,C),cartesian_product2(B,D))
& subset(A,B)
& subset(C,D) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ subset(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))
& subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
& subset(skolemFOFtoCNF_C,skolemFOFtoCNF_D) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
subset(skolemFOFtoCNF_C,skolemFOFtoCNF_D),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ subset(A,B)
| ( ! [C] : subset(cartesian_product2(A,C),cartesian_product2(B,C))
& ! [C] : subset(cartesian_product2(C,A),cartesian_product2(C,B)) ) ),
inference(canonicalize,[],[t118_zfmisc_1]) ).
fof(normalize_0_4,plain,
! [A,B] :
( ~ subset(A,B)
| ( ! [C] : subset(cartesian_product2(A,C),cartesian_product2(B,C))
& ! [C] : subset(cartesian_product2(C,A),cartesian_product2(C,B)) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C] :
( ( ~ subset(A,B)
| subset(cartesian_product2(A,C),cartesian_product2(B,C)) )
& ( ~ subset(A,B)
| subset(cartesian_product2(C,A),cartesian_product2(C,B)) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C] :
( ~ subset(A,B)
| subset(cartesian_product2(C,A),cartesian_product2(C,B)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_8,plain,
! [A,B,C] :
( ~ subset(A,B)
| subset(cartesian_product2(A,C),cartesian_product2(B,C)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_9,plain,
! [A,B,C] :
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
inference(canonicalize,[],[t1_xboole_1]) ).
fof(normalize_0_10,plain,
! [A,B,C] :
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
~ subset(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
subset(skolemFOFtoCNF_C,skolemFOFtoCNF_D),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ subset(A,B)
| subset(cartesian_product2(C,A),cartesian_product2(C,B)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ subset(skolemFOFtoCNF_C,skolemFOFtoCNF_D)
| subset(cartesian_product2(X_19,skolemFOFtoCNF_C),cartesian_product2(X_19,skolemFOFtoCNF_D)) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_C)),bind(B,$fot(skolemFOFtoCNF_D)),bind(C,$fot(X_19))]]) ).
cnf(refute_0_3,plain,
subset(cartesian_product2(X_19,skolemFOFtoCNF_C),cartesian_product2(X_19,skolemFOFtoCNF_D)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C,skolemFOFtoCNF_D) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
subset(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)),
inference(subst,[],[refute_0_3:[bind(X_19,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_5,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
( ~ subset(A,B)
| subset(cartesian_product2(A,C),cartesian_product2(B,C)) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_7,plain,
( ~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| subset(cartesian_product2(skolemFOFtoCNF_A_2,X_3),cartesian_product2(skolemFOFtoCNF_B,X_3)) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(X_3))]]) ).
cnf(refute_0_8,plain,
subset(cartesian_product2(skolemFOFtoCNF_A_2,X_3),cartesian_product2(skolemFOFtoCNF_B,X_3)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_10,plain,
( ~ subset(cartesian_product2(skolemFOFtoCNF_A_2,X_3),cartesian_product2(skolemFOFtoCNF_B,X_3))
| ~ subset(cartesian_product2(skolemFOFtoCNF_B,X_3),X_56)
| subset(cartesian_product2(skolemFOFtoCNF_A_2,X_3),X_56) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(cartesian_product2(skolemFOFtoCNF_A_2,X_3))),bind(B,$fot(cartesian_product2(skolemFOFtoCNF_B,X_3))),bind(C,$fot(X_56))]]) ).
cnf(refute_0_11,plain,
( ~ subset(cartesian_product2(skolemFOFtoCNF_B,X_3),X_56)
| subset(cartesian_product2(skolemFOFtoCNF_A_2,X_3),X_56) ),
inference(resolve,[$cnf( subset(cartesian_product2(skolemFOFtoCNF_A_2,X_3),cartesian_product2(skolemFOFtoCNF_B,X_3)) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ subset(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))
| subset(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) ),
inference(subst,[],[refute_0_11:[bind(X_3,$fot(skolemFOFtoCNF_C)),bind(X_56,$fot(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))]]) ).
cnf(refute_0_13,plain,
subset(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)),
inference(resolve,[$cnf( subset(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
~ subset(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_15,plain,
$false,
inference(resolve,[$cnf( subset(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) )],[refute_0_13,refute_0_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU167+3 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n016.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 : Sun Jun 19 07:31:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43
% 0.19/0.43 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.44
%------------------------------------------------------------------------------