TSTP Solution File: SEU089+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU089+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 12:38:23 EDT 2022
% Result : Theorem 19.46s 19.65s
% Output : CNFRefutation 19.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 19 unt; 0 def)
% Number of atoms : 80 ( 15 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 66 ( 26 ~; 21 |; 14 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 49 ( 0 sgn 26 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_zfmisc_1,axiom,
! [A,B,C] : cartesian_product3(A,B,C) = cartesian_product2(cartesian_product2(A,B),C) ).
fof(fc14_finset_1,axiom,
! [A,B] :
( ( finite(A)
& finite(B) )
=> finite(cartesian_product2(A,B)) ) ).
fof(t19_finset_1,axiom,
! [A,B] :
( ( finite(A)
& finite(B) )
=> finite(cartesian_product2(A,B)) ) ).
fof(t20_finset_1,conjecture,
! [A,B,C] :
( ( finite(A)
& finite(B)
& finite(C) )
=> finite(cartesian_product3(A,B,C)) ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( ( finite(A)
& finite(B)
& finite(C) )
=> finite(cartesian_product3(A,B,C)) ),
inference(strip,[],[t20_finset_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( ( finite(A)
& finite(B)
& finite(C) )
=> finite(cartesian_product3(A,B,C)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C] :
( ~ finite(cartesian_product3(A,B,C))
& finite(A)
& finite(B)
& finite(C) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ finite(cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C))
& finite(skolemFOFtoCNF_A_21)
& finite(skolemFOFtoCNF_B_5)
& finite(skolemFOFtoCNF_C) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
finite(skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ finite(A)
| ~ finite(B)
| finite(cartesian_product2(A,B)) ),
inference(canonicalize,[],[t19_finset_1]) ).
fof(normalize_0_4,plain,
! [A,B] :
( ~ finite(A)
| ~ finite(B)
| finite(cartesian_product2(A,B)) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
finite(skolemFOFtoCNF_B_5),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_6,plain,
finite(skolemFOFtoCNF_A_21),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_7,plain,
! [A,B,C] : cartesian_product3(A,B,C) = cartesian_product2(cartesian_product2(A,B),C),
inference(canonicalize,[],[d3_zfmisc_1]) ).
fof(normalize_0_8,plain,
! [A,B,C] : cartesian_product3(A,B,C) = cartesian_product2(cartesian_product2(A,B),C),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
~ finite(cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C)),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
finite(skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ finite(A)
| ~ finite(B)
| finite(cartesian_product2(A,B)) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ finite(X_111)
| ~ finite(skolemFOFtoCNF_C)
| finite(cartesian_product2(X_111,skolemFOFtoCNF_C)) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_111)),bind(B,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_3,plain,
( ~ finite(X_111)
| finite(cartesian_product2(X_111,skolemFOFtoCNF_C)) ),
inference(resolve,[$cnf( finite(skolemFOFtoCNF_C) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ finite(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5))
| finite(cartesian_product2(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5),skolemFOFtoCNF_C)) ),
inference(subst,[],[refute_0_3:[bind(X_111,$fot(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5)))]]) ).
cnf(refute_0_5,plain,
finite(skolemFOFtoCNF_B_5),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_6,plain,
finite(skolemFOFtoCNF_A_21),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_7,plain,
( ~ finite(X_112)
| ~ finite(skolemFOFtoCNF_A_21)
| finite(cartesian_product2(skolemFOFtoCNF_A_21,X_112)) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_A_21)),bind(B,$fot(X_112))]]) ).
cnf(refute_0_8,plain,
( ~ finite(X_112)
| finite(cartesian_product2(skolemFOFtoCNF_A_21,X_112)) ),
inference(resolve,[$cnf( finite(skolemFOFtoCNF_A_21) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ finite(skolemFOFtoCNF_B_5)
| finite(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5)) ),
inference(subst,[],[refute_0_8:[bind(X_112,$fot(skolemFOFtoCNF_B_5))]]) ).
cnf(refute_0_10,plain,
finite(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5)),
inference(resolve,[$cnf( finite(skolemFOFtoCNF_B_5) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
finite(cartesian_product2(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5),skolemFOFtoCNF_C)),
inference(resolve,[$cnf( finite(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5)) )],[refute_0_10,refute_0_4]) ).
cnf(refute_0_12,plain,
cartesian_product3(A,B,C) = cartesian_product2(cartesian_product2(A,B),C),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_13,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_14,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_15,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( cartesian_product3(A,B,C) != cartesian_product2(cartesian_product2(A,B),C)
| cartesian_product2(cartesian_product2(A,B),C) = cartesian_product3(A,B,C) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(cartesian_product3(A,B,C))),bind(Y,$fot(cartesian_product2(cartesian_product2(A,B),C)))]]) ).
cnf(refute_0_17,plain,
cartesian_product2(cartesian_product2(A,B),C) = cartesian_product3(A,B,C),
inference(resolve,[$cnf( $equal(cartesian_product3(A,B,C),cartesian_product2(cartesian_product2(A,B),C)) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
cartesian_product2(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5),skolemFOFtoCNF_C) = cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C),
inference(subst,[],[refute_0_17:[bind(A,$fot(skolemFOFtoCNF_A_21)),bind(B,$fot(skolemFOFtoCNF_B_5)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_19,plain,
( cartesian_product2(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5),skolemFOFtoCNF_C) != cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C)
| ~ finite(cartesian_product2(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5),skolemFOFtoCNF_C))
| finite(cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C)) ),
introduced(tautology,[equality,[$cnf( finite(cartesian_product2(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5),skolemFOFtoCNF_C)) ),[0],$fot(cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C))]]) ).
cnf(refute_0_20,plain,
( ~ finite(cartesian_product2(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5),skolemFOFtoCNF_C))
| finite(cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C)) ),
inference(resolve,[$cnf( $equal(cartesian_product2(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5),skolemFOFtoCNF_C),cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
finite(cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C)),
inference(resolve,[$cnf( finite(cartesian_product2(cartesian_product2(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5),skolemFOFtoCNF_C)) )],[refute_0_11,refute_0_20]) ).
cnf(refute_0_22,plain,
~ finite(cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( finite(cartesian_product3(skolemFOFtoCNF_A_21,skolemFOFtoCNF_B_5,skolemFOFtoCNF_C)) )],[refute_0_21,refute_0_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU089+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n024.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 : Sun Jun 19 04:18:47 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 19.46/19.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.46/19.65
% 19.46/19.65 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.46/19.66
%------------------------------------------------------------------------------