TSTP Solution File: SEU154+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU154+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n010.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 12:36:01 EDT 2023
% Result : Theorem 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 60 ( 8 unt; 0 def)
% Number of atoms : 214 ( 50 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 246 ( 92 ~; 103 |; 40 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 168 (; 160 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( A = B
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f19,axiom,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,plain,
! [A,B] :
( ( A != B
| ( subset(A,B)
& subset(B,A) ) )
& ( A = B
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f24,plain,
( ! [A,B] :
( A != B
| ( subset(A,B)
& subset(B,A) ) )
& ! [A,B] :
( A = B
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(miniscoping,[status(esa)],[f23]) ).
fof(f27,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f28,plain,
! [A,B] :
( ( B != singleton(A)
| ! [C] :
( ( ~ in(C,B)
| C = A )
& ( in(C,B)
| C != A ) ) )
& ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
| C != A )
& ( in(C,B)
| C = A ) ) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f29,plain,
( ! [A,B] :
( B != singleton(A)
| ( ! [C] :
( ~ in(C,B)
| C = A )
& ! [C] :
( in(C,B)
| C != A ) ) )
& ! [A,B] :
( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
| C != A )
& ( in(C,B)
| C = A ) ) ) ),
inference(miniscoping,[status(esa)],[f28]) ).
fof(f30,plain,
( ! [A,B] :
( B != singleton(A)
| ( ! [C] :
( ~ in(C,B)
| C = A )
& ! [C] :
( in(C,B)
| C != A ) ) )
& ! [A,B] :
( B = singleton(A)
| ( ( ~ in(sk0_0(B,A),B)
| sk0_0(B,A) != A )
& ( in(sk0_0(B,A),B)
| sk0_0(B,A) = A ) ) ) ),
inference(skolemization,[status(esa)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( X0 != singleton(X1)
| ~ in(X2,X0)
| X2 = X1 ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( X0 != singleton(X1)
| in(X2,X0)
| X2 != X1 ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f35,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f36,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)],[f35]) ).
fof(f37,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)],[f36]) ).
fof(f38,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ( in(sk0_1(B,A),A)
& ~ in(sk0_1(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f40,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_1(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f41,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_1(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f42,plain,
! [A,B,C] :
( ( C != set_intersection2(A,B)
| ! [D] :
( ( ~ in(D,C)
| ( in(D,A)
& in(D,B) ) )
& ( in(D,C)
| ~ in(D,A)
| ~ in(D,B) ) ) )
& ( C = set_intersection2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ~ in(D,A)
| ~ in(D,B) )
& ( in(D,C)
| ( in(D,A)
& in(D,B) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f6]) ).
fof(f43,plain,
( ! [A,B,C] :
( C != set_intersection2(A,B)
| ( ! [D] :
( ~ in(D,C)
| ( in(D,A)
& in(D,B) ) )
& ! [D] :
( in(D,C)
| ~ in(D,A)
| ~ in(D,B) ) ) )
& ! [A,B,C] :
( C = set_intersection2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ~ in(D,A)
| ~ in(D,B) )
& ( in(D,C)
| ( in(D,A)
& in(D,B) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f42]) ).
fof(f44,plain,
( ! [A,B,C] :
( C != set_intersection2(A,B)
| ( ! [D] :
( ~ in(D,C)
| ( in(D,A)
& in(D,B) ) )
& ! [D] :
( in(D,C)
| ~ in(D,A)
| ~ in(D,B) ) ) )
& ! [A,B,C] :
( C = set_intersection2(A,B)
| ( ( ~ in(sk0_2(C,B,A),C)
| ~ in(sk0_2(C,B,A),A)
| ~ in(sk0_2(C,B,A),B) )
& ( in(sk0_2(C,B,A),C)
| ( in(sk0_2(C,B,A),A)
& in(sk0_2(C,B,A),B) ) ) ) ) ),
inference(skolemization,[status(esa)],[f43]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( X0 != set_intersection2(X1,X2)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( X0 != set_intersection2(X1,X2)
| ~ in(X3,X0)
| in(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f51,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set )
& ( disjoint(A,B)
| set_intersection2(A,B) != empty_set ) ),
inference(NNF_transformation,[status(esa)],[f7]) ).
fof(f52,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set )
& ! [A,B] :
( disjoint(A,B)
| set_intersection2(A,B) != empty_set ) ),
inference(miniscoping,[status(esa)],[f51]) ).
fof(f54,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f58,plain,
? [A,B] :
( ~ in(A,B)
& ~ disjoint(singleton(A),B) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f59,plain,
( ~ in(sk0_3,sk0_4)
& ~ disjoint(singleton(sk0_3),sk0_4) ),
inference(skolemization,[status(esa)],[f58]) ).
fof(f60,plain,
~ in(sk0_3,sk0_4),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f61,plain,
~ disjoint(singleton(sk0_3),sk0_4),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f70,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f73,plain,
! [X0,X1] :
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(destructive_equality_resolution,[status(esa)],[f31]) ).
fof(f74,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(esa)],[f32]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f45]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f46]) ).
fof(f79,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(resolution,[status(thm)],[f27,f70]) ).
fof(f99,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| sk0_1(X1,singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[f40,f73]) ).
fof(f103,plain,
! [X0,X1,X2] :
( in(sk0_1(X0,set_intersection2(X1,X2)),X1)
| subset(set_intersection2(X1,X2),X0) ),
inference(resolution,[status(thm)],[f75,f40]) ).
fof(f121,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(paramodulation,[status(thm)],[f99,f41]) ).
fof(f122,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(duplicate_literals_removal,[status(esa)],[f121]) ).
fof(f126,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| ~ in(X2,singleton(X0))
| in(X2,X1) ),
inference(resolution,[status(thm)],[f122,f39]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| in(sk0_1(X2,singleton(X0)),X1)
| subset(singleton(X0),X2) ),
inference(resolution,[status(thm)],[f126,f40]) ).
fof(f168,plain,
! [X0,X1,X2,X3] :
( ~ in(X0,set_intersection2(X1,X2))
| subset(singleton(X0),X3)
| in(sk0_1(X3,singleton(X0)),X2) ),
inference(resolution,[status(thm)],[f131,f76]) ).
fof(f282,plain,
! [X0,X1,X2] :
( ~ in(X0,set_intersection2(X1,X2))
| subset(singleton(X0),X2)
| subset(singleton(X0),X2) ),
inference(resolution,[status(thm)],[f168,f41]) ).
fof(f283,plain,
! [X0,X1,X2] :
( ~ in(X0,set_intersection2(X1,X2))
| subset(singleton(X0),X2) ),
inference(duplicate_literals_removal,[status(esa)],[f282]) ).
fof(f302,plain,
! [X0,X1,X2] :
( subset(singleton(sk0_1(X0,set_intersection2(X1,X2))),X2)
| subset(set_intersection2(X1,X2),X0) ),
inference(resolution,[status(thm)],[f283,f40]) ).
fof(f508,plain,
! [X0,X1,X2] :
( subset(set_intersection2(singleton(X0),X1),X2)
| sk0_1(X2,set_intersection2(singleton(X0),X1)) = X0 ),
inference(resolution,[status(thm)],[f103,f73]) ).
fof(f953,plain,
! [X0,X1,X2] :
( subset(singleton(X0),X1)
| subset(set_intersection2(singleton(X0),X1),X2)
| subset(set_intersection2(singleton(X0),X1),X2) ),
inference(paramodulation,[status(thm)],[f508,f302]) ).
fof(f954,plain,
! [X0,X1,X2] :
( subset(singleton(X0),X1)
| subset(set_intersection2(singleton(X0),X1),X2) ),
inference(duplicate_literals_removal,[status(esa)],[f953]) ).
fof(f1065,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| set_intersection2(singleton(X0),X1) = empty_set ),
inference(resolution,[status(thm)],[f954,f79]) ).
fof(f1078,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| disjoint(singleton(X0),X1) ),
inference(resolution,[status(thm)],[f1065,f54]) ).
fof(f1179,plain,
subset(singleton(sk0_3),sk0_4),
inference(resolution,[status(thm)],[f1078,f61]) ).
fof(f1275,plain,
! [X0] :
( ~ in(X0,singleton(sk0_3))
| in(X0,sk0_4) ),
inference(resolution,[status(thm)],[f1179,f39]) ).
fof(f1336,plain,
in(sk0_3,sk0_4),
inference(resolution,[status(thm)],[f1275,f74]) ).
fof(f1337,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1336,f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SEU154+1 : TPTP v8.1.2. Released v3.3.0.
% 0.05/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n010.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 09:01:37 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.30 % Drodi V3.5.1
% 0.14/0.38 % Refutation found
% 0.14/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.40 % Elapsed time: 0.095307 seconds
% 0.14/0.40 % CPU time: 0.428375 seconds
% 0.14/0.40 % Memory used: 51.537 MB
%------------------------------------------------------------------------------