TSTP Solution File: SET016+4 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET016+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n020.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 12:33:33 EDT 2023
% Result : Theorem 0.14s 0.36s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 9 unt; 0 def)
% Number of atoms : 123 ( 34 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 125 ( 49 ~; 46 |; 20 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 84 (; 74 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,A] :
( member(X,singleton(A))
<=> X = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,A,B] :
( member(X,unordered_pair(A,B))
<=> ( X = A
| X = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B,U,V] :
( equal_set(unordered_pair(singleton(A),unordered_pair(A,B)),unordered_pair(singleton(U),unordered_pair(U,V)))
=> A = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B,U,V] :
( equal_set(unordered_pair(singleton(A),unordered_pair(A,B)),unordered_pair(singleton(U),unordered_pair(U,V)))
=> A = U ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( ~ member(X,A)
| member(X,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f15,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f14]) ).
fof(f16,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f17,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ( member(sk0_0(B,A),A)
& ~ member(sk0_0(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f21,plain,
! [A,B] :
( ( ~ equal_set(A,B)
| ( subset(A,B)
& subset(B,A) ) )
& ( equal_set(A,B)
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f22,plain,
( ! [A,B] :
( ~ equal_set(A,B)
| ( subset(A,B)
& subset(B,A) ) )
& ! [A,B] :
( equal_set(A,B)
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f24,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f46,plain,
! [X,A] :
( ( ~ member(X,singleton(A))
| X = A )
& ( member(X,singleton(A))
| X != A ) ),
inference(NNF_transformation,[status(esa)],[f8]) ).
fof(f47,plain,
( ! [X,A] :
( ~ member(X,singleton(A))
| X = A )
& ! [X,A] :
( member(X,singleton(A))
| X != A ) ),
inference(miniscoping,[status(esa)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( member(X0,singleton(X1))
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f50,plain,
! [X,A,B] :
( ( ~ member(X,unordered_pair(A,B))
| X = A
| X = B )
& ( member(X,unordered_pair(A,B))
| ( X != A
& X != B ) ) ),
inference(NNF_transformation,[status(esa)],[f9]) ).
fof(f51,plain,
( ! [X,A,B] :
( ~ member(X,unordered_pair(A,B))
| X = A
| X = B )
& ! [X,A,B] :
( member(X,unordered_pair(A,B))
| ( X != A
& X != B ) ) ),
inference(miniscoping,[status(esa)],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f53,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f68,plain,
? [A,B,U,V] :
( equal_set(unordered_pair(singleton(A),unordered_pair(A,B)),unordered_pair(singleton(U),unordered_pair(U,V)))
& A != U ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f69,plain,
? [A,U] :
( ? [B,V] : equal_set(unordered_pair(singleton(A),unordered_pair(A,B)),unordered_pair(singleton(U),unordered_pair(U,V)))
& A != U ),
inference(miniscoping,[status(esa)],[f68]) ).
fof(f70,plain,
( equal_set(unordered_pair(singleton(sk0_3),unordered_pair(sk0_3,sk0_5)),unordered_pair(singleton(sk0_4),unordered_pair(sk0_4,sk0_6)))
& sk0_3 != sk0_4 ),
inference(skolemization,[status(esa)],[f69]) ).
fof(f71,plain,
equal_set(unordered_pair(singleton(sk0_3),unordered_pair(sk0_3,sk0_5)),unordered_pair(singleton(sk0_4),unordered_pair(sk0_4,sk0_6))),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f72,plain,
sk0_3 != sk0_4,
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f73,plain,
! [X0] : member(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(esa)],[f49]) ).
fof(f74,plain,
! [X0,X1] : member(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(esa)],[f53]) ).
fof(f77,plain,
subset(unordered_pair(singleton(sk0_4),unordered_pair(sk0_4,sk0_6)),unordered_pair(singleton(sk0_3),unordered_pair(sk0_3,sk0_5))),
inference(resolution,[status(thm)],[f24,f71]) ).
fof(f119,plain,
! [X0] :
( ~ member(X0,unordered_pair(singleton(sk0_4),unordered_pair(sk0_4,sk0_6)))
| member(X0,unordered_pair(singleton(sk0_3),unordered_pair(sk0_3,sk0_5))) ),
inference(resolution,[status(thm)],[f18,f77]) ).
fof(f143,plain,
member(singleton(sk0_4),unordered_pair(singleton(sk0_3),unordered_pair(sk0_3,sk0_5))),
inference(resolution,[status(thm)],[f119,f74]) ).
fof(f144,plain,
( spl0_4
<=> singleton(sk0_4) = singleton(sk0_3) ),
introduced(split_symbol_definition) ).
fof(f145,plain,
( singleton(sk0_4) = singleton(sk0_3)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,plain,
( spl0_5
<=> singleton(sk0_4) = unordered_pair(sk0_3,sk0_5) ),
introduced(split_symbol_definition) ).
fof(f148,plain,
( singleton(sk0_4) = unordered_pair(sk0_3,sk0_5)
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,plain,
( singleton(sk0_4) = singleton(sk0_3)
| singleton(sk0_4) = unordered_pair(sk0_3,sk0_5) ),
inference(resolution,[status(thm)],[f143,f52]) ).
fof(f151,plain,
( spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f150,f144,f147]) ).
fof(f161,plain,
( member(sk0_4,singleton(sk0_3))
| ~ spl0_4 ),
inference(paramodulation,[status(thm)],[f145,f73]) ).
fof(f164,plain,
( sk0_4 = sk0_3
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f161,f48]) ).
fof(f165,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f164,f72]) ).
fof(f166,plain,
~ spl0_4,
inference(contradiction_clause,[status(thm)],[f165]) ).
fof(f172,plain,
( member(sk0_3,singleton(sk0_4))
| ~ spl0_5 ),
inference(paramodulation,[status(thm)],[f148,f74]) ).
fof(f176,plain,
( sk0_3 = sk0_4
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f172,f48]) ).
fof(f177,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f176,f72]) ).
fof(f178,plain,
~ spl0_5,
inference(contradiction_clause,[status(thm)],[f177]) ).
fof(f179,plain,
$false,
inference(sat_refutation,[status(thm)],[f151,f166,f178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET016+4 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue May 30 10:14:28 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Drodi V3.5.1
% 0.14/0.36 % Refutation found
% 0.14/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.37 % Elapsed time: 0.022675 seconds
% 0.14/0.37 % CPU time: 0.041555 seconds
% 0.14/0.37 % Memory used: 11.768 MB
%------------------------------------------------------------------------------