TSTP Solution File: SEU166+3 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU166+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n022.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 : 300s
% DateTime : Wed May 31 12:36:05 EDT 2023
% Result : Theorem 4.54s 1.02s
% Output : CNFRefutation 4.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 65 ( 4 unt; 0 def)
% Number of atoms : 243 ( 60 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 312 ( 134 ~; 136 |; 30 &)
% ( 9 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-5 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-4 aty)
% Number of variables : 240 (; 217 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,conjecture,
! [A,B,C] :
( subset(A,B)
=> ( subset(cartesian_product2(A,C),cartesian_product2(B,C))
& subset(cartesian_product2(C,A),cartesian_product2(C,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ! [A,B,C] :
( subset(A,B)
=> ( subset(cartesian_product2(A,C),cartesian_product2(B,C))
& subset(cartesian_product2(C,A),cartesian_product2(C,B)) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f15,plain,
! [A,B,D,E,F] :
( pd0_0(F,E,D,B,A)
<=> ( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) ),
introduced(predicate_definition,[f3]) ).
fof(f16,plain,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] : pd0_0(F,E,D,B,A) ) ),
inference(formula_renaming,[status(thm)],[f3,f15]) ).
fof(f17,plain,
! [A,B,C] :
( ( C != cartesian_product2(A,B)
| ! [D] :
( ( ~ in(D,C)
| ? [E,F] : pd0_0(F,E,D,B,A) )
& ( in(D,C)
| ! [E,F] : ~ pd0_0(F,E,D,B,A) ) ) )
& ( C = cartesian_product2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ! [E,F] : ~ pd0_0(F,E,D,B,A) )
& ( in(D,C)
| ? [E,F] : pd0_0(F,E,D,B,A) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f16]) ).
fof(f18,plain,
( ! [A,B,C] :
( C != cartesian_product2(A,B)
| ( ! [D] :
( ~ in(D,C)
| ? [E,F] : pd0_0(F,E,D,B,A) )
& ! [D] :
( in(D,C)
| ! [E,F] : ~ pd0_0(F,E,D,B,A) ) ) )
& ! [A,B,C] :
( C = cartesian_product2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ! [E,F] : ~ pd0_0(F,E,D,B,A) )
& ( in(D,C)
| ? [E,F] : pd0_0(F,E,D,B,A) ) ) ) ),
inference(miniscoping,[status(esa)],[f17]) ).
fof(f19,plain,
( ! [A,B,C] :
( C != cartesian_product2(A,B)
| ( ! [D] :
( ~ in(D,C)
| pd0_0(sk0_1(D,C,B,A),sk0_0(D,C,B,A),D,B,A) )
& ! [D] :
( in(D,C)
| ! [E,F] : ~ pd0_0(F,E,D,B,A) ) ) )
& ! [A,B,C] :
( C = cartesian_product2(A,B)
| ( ( ~ in(sk0_2(C,B,A),C)
| ! [E,F] : ~ pd0_0(F,E,sk0_2(C,B,A),B,A) )
& ( in(sk0_2(C,B,A),C)
| pd0_0(sk0_4(C,B,A),sk0_3(C,B,A),sk0_2(C,B,A),B,A) ) ) ) ),
inference(skolemization,[status(esa)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( X0 != cartesian_product2(X1,X2)
| ~ in(X3,X0)
| pd0_0(sk0_1(X3,X0,X2,X1),sk0_0(X3,X0,X2,X1),X3,X2,X1) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f21,plain,
! [X0,X1,X2,X3,X4,X5] :
( X0 != cartesian_product2(X1,X2)
| in(X3,X0)
| ~ pd0_0(X4,X5,X3,X2,X1) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f24,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f25,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f24]) ).
fof(f26,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(miniscoping,[status(esa)],[f25]) ).
fof(f27,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ( in(sk0_5(B,A),A)
& ~ in(sk0_5(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_5(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f30,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_5(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f39,plain,
? [A,B,C] :
( subset(A,B)
& ( ~ subset(cartesian_product2(A,C),cartesian_product2(B,C))
| ~ subset(cartesian_product2(C,A),cartesian_product2(C,B)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f40,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(miniscoping,[status(esa)],[f39]) ).
fof(f41,plain,
( subset(sk0_8,sk0_9)
& ( ~ subset(cartesian_product2(sk0_8,sk0_10),cartesian_product2(sk0_9,sk0_10))
| ~ subset(cartesian_product2(sk0_11,sk0_8),cartesian_product2(sk0_11,sk0_9)) ) ),
inference(skolemization,[status(esa)],[f40]) ).
fof(f42,plain,
subset(sk0_8,sk0_9),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f43,plain,
( ~ subset(cartesian_product2(sk0_8,sk0_10),cartesian_product2(sk0_9,sk0_10))
| ~ subset(cartesian_product2(sk0_11,sk0_8),cartesian_product2(sk0_11,sk0_9)) ),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f44,plain,
! [A,B,D,E,F] :
( ( ~ pd0_0(F,E,D,B,A)
| ( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) )
& ( pd0_0(F,E,D,B,A)
| ~ in(E,A)
| ~ in(F,B)
| D != ordered_pair(E,F) ) ),
inference(NNF_transformation,[status(esa)],[f15]) ).
fof(f45,plain,
( ! [A,B,D,E,F] :
( ~ pd0_0(F,E,D,B,A)
| ( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) )
& ! [A,B,D,E,F] :
( pd0_0(F,E,D,B,A)
| ~ in(E,A)
| ~ in(F,B)
| D != ordered_pair(E,F) ) ),
inference(miniscoping,[status(esa)],[f44]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4] :
( ~ pd0_0(X0,X1,X2,X3,X4)
| in(X1,X4) ),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f47,plain,
! [X0,X1,X2,X3,X4] :
( ~ pd0_0(X0,X1,X2,X3,X4)
| in(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f48,plain,
! [X0,X1,X2,X3,X4] :
( ~ pd0_0(X0,X1,X2,X3,X4)
| X2 = ordered_pair(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4] :
( pd0_0(X0,X1,X2,X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X3)
| X2 != ordered_pair(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f50,plain,
( spl0_0
<=> subset(cartesian_product2(sk0_8,sk0_10),cartesian_product2(sk0_9,sk0_10)) ),
introduced(split_symbol_definition) ).
fof(f52,plain,
( ~ subset(cartesian_product2(sk0_8,sk0_10),cartesian_product2(sk0_9,sk0_10))
| spl0_0 ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,plain,
( spl0_1
<=> subset(cartesian_product2(sk0_11,sk0_8),cartesian_product2(sk0_11,sk0_9)) ),
introduced(split_symbol_definition) ).
fof(f55,plain,
( ~ subset(cartesian_product2(sk0_11,sk0_8),cartesian_product2(sk0_11,sk0_9))
| spl0_1 ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f43,f50,f53]) ).
fof(f57,plain,
! [X0] :
( ~ in(X0,sk0_8)
| in(X0,sk0_9) ),
inference(resolution,[status(thm)],[f28,f42]) ).
fof(f73,plain,
! [X0,X1,X2,X3] :
( X0 != cartesian_product2(X1,X2)
| ~ in(X3,X0)
| in(sk0_1(X3,X0,X2,X1),X2) ),
inference(resolution,[status(thm)],[f20,f47]) ).
fof(f74,plain,
! [X0,X1,X2,X3] :
( X0 != cartesian_product2(X1,X2)
| ~ in(X3,X0)
| in(sk0_0(X3,X0,X2,X1),X1) ),
inference(resolution,[status(thm)],[f20,f46]) ).
fof(f77,plain,
! [X0,X1,X2,X3] :
( X0 = ordered_pair(sk0_0(X0,X1,X2,X3),sk0_1(X0,X1,X2,X3))
| X1 != cartesian_product2(X3,X2)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f48,f20]) ).
fof(f117,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ in(X0,X1)
| ~ in(X2,X3)
| X4 != ordered_pair(X0,X2)
| X5 != cartesian_product2(X1,X3)
| in(X4,X5) ),
inference(resolution,[status(thm)],[f49,f21]) ).
fof(f159,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ in(sk0_0(X0,X1,X2,X3),X4)
| ~ in(sk0_1(X0,X1,X2,X3),X5)
| X6 != cartesian_product2(X4,X5)
| in(X0,X6)
| X1 != cartesian_product2(X3,X2)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f117,f77]) ).
fof(f329,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ in(sk0_0(X0,X1,X2,X3),X4)
| X5 != cartesian_product2(X4,X2)
| in(X0,X5)
| X1 != cartesian_product2(X3,X2)
| ~ in(X0,X1)
| X1 != cartesian_product2(X3,X2)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f159,f73]) ).
fof(f330,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ in(sk0_0(X0,X1,X2,X3),X4)
| X5 != cartesian_product2(X4,X2)
| in(X0,X5)
| X1 != cartesian_product2(X3,X2)
| ~ in(X0,X1) ),
inference(duplicate_literals_removal,[status(esa)],[f329]) ).
fof(f334,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ in(sk0_0(X0,X1,X2,X3),X4)
| X5 != cartesian_product2(X4,sk0_9)
| in(X0,X5)
| X1 != cartesian_product2(X3,X2)
| ~ in(X0,X1)
| ~ in(sk0_1(X0,X1,X2,X3),sk0_8) ),
inference(resolution,[status(thm)],[f159,f57]) ).
fof(f1043,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(sk0_0(X0,X1,sk0_8,X2),X3)
| X4 != cartesian_product2(X3,sk0_9)
| in(X0,X4)
| X1 != cartesian_product2(X2,sk0_8)
| ~ in(X0,X1)
| X1 != cartesian_product2(X2,sk0_8)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f334,f73]) ).
fof(f1044,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(sk0_0(X0,X1,sk0_8,X2),X3)
| X4 != cartesian_product2(X3,sk0_9)
| in(X0,X4)
| X1 != cartesian_product2(X2,sk0_8)
| ~ in(X0,X1) ),
inference(duplicate_literals_removal,[status(esa)],[f1043]) ).
fof(f1045,plain,
! [X0,X1,X2,X3] :
( X0 != cartesian_product2(X1,sk0_9)
| in(X2,X0)
| X3 != cartesian_product2(X1,sk0_8)
| ~ in(X2,X3)
| X3 != cartesian_product2(X1,sk0_8)
| ~ in(X2,X3) ),
inference(resolution,[status(thm)],[f1044,f74]) ).
fof(f1046,plain,
! [X0,X1,X2,X3] :
( X0 != cartesian_product2(X1,sk0_9)
| in(X2,X0)
| X3 != cartesian_product2(X1,sk0_8)
| ~ in(X2,X3) ),
inference(duplicate_literals_removal,[status(esa)],[f1045]) ).
fof(f1055,plain,
! [X0,X1,X2] :
( in(X0,cartesian_product2(X1,sk0_9))
| X2 != cartesian_product2(X1,sk0_8)
| ~ in(X0,X2) ),
inference(equality_resolution,[status(esa)],[f1046]) ).
fof(f1074,plain,
! [X0,X1,X2] :
( X0 != cartesian_product2(X1,sk0_8)
| ~ in(sk0_5(cartesian_product2(X1,sk0_9),X2),X0)
| subset(X2,cartesian_product2(X1,sk0_9)) ),
inference(resolution,[status(thm)],[f1055,f30]) ).
fof(f1081,plain,
! [X0,X1] :
( X0 != cartesian_product2(X1,sk0_8)
| subset(X0,cartesian_product2(X1,sk0_9))
| subset(X0,cartesian_product2(X1,sk0_9)) ),
inference(resolution,[status(thm)],[f1074,f29]) ).
fof(f1082,plain,
! [X0,X1] :
( X0 != cartesian_product2(X1,sk0_8)
| subset(X0,cartesian_product2(X1,sk0_9)) ),
inference(duplicate_literals_removal,[status(esa)],[f1081]) ).
fof(f1086,plain,
( cartesian_product2(sk0_11,sk0_8) != cartesian_product2(sk0_11,sk0_8)
| spl0_1 ),
inference(resolution,[status(thm)],[f1082,f55]) ).
fof(f1087,plain,
( $false
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f1086]) ).
fof(f1088,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f1087]) ).
fof(f1374,plain,
! [X0,X1,X2,X3,X4] :
( X0 != cartesian_product2(sk0_9,X1)
| in(X2,X0)
| X3 != cartesian_product2(X4,X1)
| ~ in(X2,X3)
| ~ in(sk0_0(X2,X3,X1,X4),sk0_8) ),
inference(resolution,[status(thm)],[f330,f57]) ).
fof(f2397,plain,
! [X0,X1,X2,X3] :
( X0 != cartesian_product2(sk0_9,X1)
| in(X2,X0)
| X3 != cartesian_product2(sk0_8,X1)
| ~ in(X2,X3)
| X3 != cartesian_product2(sk0_8,X1)
| ~ in(X2,X3) ),
inference(resolution,[status(thm)],[f1374,f74]) ).
fof(f2398,plain,
! [X0,X1,X2,X3] :
( X0 != cartesian_product2(sk0_9,X1)
| in(X2,X0)
| X3 != cartesian_product2(sk0_8,X1)
| ~ in(X2,X3) ),
inference(duplicate_literals_removal,[status(esa)],[f2397]) ).
fof(f2400,plain,
! [X0,X1,X2] :
( in(X0,cartesian_product2(sk0_9,X1))
| X2 != cartesian_product2(sk0_8,X1)
| ~ in(X0,X2) ),
inference(equality_resolution,[status(esa)],[f2398]) ).
fof(f2436,plain,
! [X0,X1,X2] :
( X0 != cartesian_product2(sk0_8,X1)
| ~ in(sk0_5(cartesian_product2(sk0_9,X1),X2),X0)
| subset(X2,cartesian_product2(sk0_9,X1)) ),
inference(resolution,[status(thm)],[f2400,f30]) ).
fof(f2448,plain,
! [X0,X1] :
( X0 != cartesian_product2(sk0_8,X1)
| subset(X0,cartesian_product2(sk0_9,X1))
| subset(X0,cartesian_product2(sk0_9,X1)) ),
inference(resolution,[status(thm)],[f2436,f29]) ).
fof(f2449,plain,
! [X0,X1] :
( X0 != cartesian_product2(sk0_8,X1)
| subset(X0,cartesian_product2(sk0_9,X1)) ),
inference(duplicate_literals_removal,[status(esa)],[f2448]) ).
fof(f2459,plain,
( cartesian_product2(sk0_8,sk0_10) != cartesian_product2(sk0_8,sk0_10)
| spl0_0 ),
inference(resolution,[status(thm)],[f2449,f52]) ).
fof(f2460,plain,
( $false
| spl0_0 ),
inference(trivial_equality_resolution,[status(esa)],[f2459]) ).
fof(f2461,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f2460]) ).
fof(f2462,plain,
$false,
inference(sat_refutation,[status(thm)],[f56,f1088,f2461]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU166+3 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n022.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 : 300
% 0.13/0.35 % DateTime : Tue May 30 09:13:27 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.5.1
% 4.54/1.02 % Refutation found
% 4.54/1.02 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.54/1.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.54/1.05 % Elapsed time: 0.681183 seconds
% 4.54/1.05 % CPU time: 5.299604 seconds
% 4.54/1.05 % Memory used: 115.723 MB
%------------------------------------------------------------------------------