%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET707+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:10:30 PM UTC 2026
% Result : Theorem 0.16s 0.51s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 110 ( 6 unt; 8 def)
% Number of atoms : 341 ( 83 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 413 ( 182 ~; 194 |; 21 &)
% ( 13 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 97 ( 91 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,A] :
( member(X,singleton(A))
<=> X = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,A,B] :
( member(X,unordered_pair(A,B))
<=> ( X = B
| X = A ) ),
file('/export/starexec/sandbox2/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)))
=> ( B = V
& A = U ) ),
file('/export/starexec/sandbox2/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)))
=> ( B = V
& A = U ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,B)
| ~ member(X,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
( ! [A,B] :
( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f17,plain,
( ! [A,B] :
( ( ~ member(sK0_skl(B,A),B)
& member(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f22,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f46,plain,
! [X,A] :
( ( X != A
| member(X,singleton(A)) )
& ( X = A
| ~ member(X,singleton(A)) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f47,plain,
( ! [X,A] :
( X != A
| member(X,singleton(A)) )
& ! [X,A] :
( X = A
| ~ member(X,singleton(A)) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( X0 != X1
| member(X0,singleton(X1)) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
! [X,A,B] :
( ( ( X != B
& X != A )
| member(X,unordered_pair(A,B)) )
& ( X = B
| X = A
| ~ member(X,unordered_pair(A,B)) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f51,plain,
( ! [X,A,B] :
( ( X != B
& X != A )
| member(X,unordered_pair(A,B)) )
& ! [X,A,B] :
( X = B
| X = A
| ~ member(X,unordered_pair(A,B)) ) ),
inference(miniscoping,[status(thm)],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0,X1,X2] :
( X0 != X1
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f54,plain,
! [X0,X1,X2] :
( X0 != X2
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f68,plain,
? [A,B,U,V] :
( ( B != V
| A != U )
& equal_set(unordered_pair(singleton(A),unordered_pair(A,B)),unordered_pair(singleton(U),unordered_pair(U,V))) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
( ( sK4_skl != sK6_skl
| sK3_skl != sK5_skl )
& equal_set(unordered_pair(singleton(sK3_skl),unordered_pair(sK3_skl,sK4_skl)),unordered_pair(singleton(sK5_skl),unordered_pair(sK5_skl,sK6_skl))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl),skolemize(U,sK5_skl),skolemize(V,sK6_skl)],[f68]) ).
fof(f70,plain,
equal_set(unordered_pair(singleton(sK3_skl),unordered_pair(sK3_skl,sK4_skl)),unordered_pair(singleton(sK5_skl),unordered_pair(sK5_skl,sK6_skl))),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
( sK4_skl != sK6_skl
| sK3_skl != sK5_skl ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f72,definition,
( sQ0_spl
<=> sK3_skl = sK5_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f73,plain,
( ~ sQ0_spl
| sK3_skl = sK5_skl ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f74,plain,
( sQ0_spl
| sK3_skl != sK5_skl ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f75,definition,
( sQ1_spl
<=> sK4_skl = sK6_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( sQ1_spl
| sK4_skl != sK6_skl ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f71,f72,f75]) ).
fof(f79,plain,
! [X0] : member(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f49]) ).
fof(f80,plain,
! [X0,X1] : member(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f53]) ).
fof(f81,plain,
! [X0,X1] : member(X0,unordered_pair(X1,X0)),
inference(destructive_equality_resolution,[status(thm)],[f54]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ~ equal_set(X2,X1)
| member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f18,f24]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ~ equal_set(X1,X2)
| member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f18,f23]) ).
fof(f88,plain,
! [X0] :
( member(X0,unordered_pair(singleton(sK3_skl),unordered_pair(sK3_skl,sK4_skl)))
| ~ member(X0,unordered_pair(singleton(sK5_skl),unordered_pair(sK5_skl,sK6_skl))) ),
inference(resolution,[status(thm)],[f86,f70]) ).
fof(f94,plain,
! [X0] :
( member(X0,unordered_pair(singleton(sK5_skl),unordered_pair(sK5_skl,sK6_skl)))
| ~ member(X0,unordered_pair(singleton(sK3_skl),unordered_pair(sK3_skl,sK4_skl))) ),
inference(resolution,[status(thm)],[f87,f70]) ).
fof(f106,plain,
! [X0] :
( X0 = unordered_pair(sK3_skl,sK4_skl)
| X0 = singleton(sK3_skl)
| ~ member(X0,unordered_pair(singleton(sK5_skl),unordered_pair(sK5_skl,sK6_skl))) ),
inference(resolution,[status(thm)],[f88,f52]) ).
fof(f107,plain,
( unordered_pair(sK5_skl,sK6_skl) = unordered_pair(sK3_skl,sK4_skl)
| unordered_pair(sK5_skl,sK6_skl) = singleton(sK3_skl) ),
inference(resolution,[status(thm)],[f106,f81]) ).
fof(f108,plain,
( singleton(sK5_skl) = unordered_pair(sK3_skl,sK4_skl)
| singleton(sK5_skl) = singleton(sK3_skl) ),
inference(resolution,[status(thm)],[f106,f80]) ).
fof(f109,definition,
( sQ2_spl
<=> unordered_pair(sK5_skl,sK6_skl) = singleton(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ2_spl
| unordered_pair(sK5_skl,sK6_skl) = singleton(sK3_skl) ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,definition,
( sQ3_spl
<=> unordered_pair(sK5_skl,sK6_skl) = unordered_pair(sK3_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f113,plain,
( ~ sQ3_spl
| unordered_pair(sK5_skl,sK6_skl) = unordered_pair(sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f112]) ).
fof(f115,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f107,f109,f112]) ).
fof(f116,definition,
( sQ4_spl
<=> singleton(sK5_skl) = singleton(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f117,plain,
( ~ sQ4_spl
| singleton(sK5_skl) = singleton(sK3_skl) ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f118,plain,
( sQ4_spl
| singleton(sK5_skl) != singleton(sK3_skl) ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f119,definition,
( sQ5_spl
<=> singleton(sK5_skl) = unordered_pair(sK3_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f120,plain,
( ~ sQ5_spl
| singleton(sK5_skl) = unordered_pair(sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f121,plain,
( sQ5_spl
| singleton(sK5_skl) != unordered_pair(sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,plain,
( sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f108,f116,f119]) ).
fof(f127,plain,
( ~ sQ4_spl
| member(sK3_skl,singleton(sK5_skl)) ),
inference(paramodulation,[status(thm)],[f117,f79]) ).
fof(f128,plain,
( ~ sQ4_spl
| sK3_skl = sK5_skl ),
inference(resolution,[status(thm)],[f127,f48]) ).
fof(f129,plain,
( ~ sQ4_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f128,f74]) ).
fof(f130,plain,
( ~ sQ4_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f129]) ).
fof(f131,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| unordered_pair(sK5_skl,sK6_skl) = singleton(sK5_skl) ),
inference(forward_demodulation,[status(thm)],[f73,f110]) ).
fof(f133,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| member(sK6_skl,singleton(sK5_skl)) ),
inference(paramodulation,[status(thm)],[f131,f81]) ).
fof(f135,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| sK6_skl = sK5_skl ),
inference(resolution,[status(thm)],[f133,f48]) ).
fof(f137,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| unordered_pair(sK5_skl,sK6_skl) = singleton(sK6_skl) ),
inference(backward_demodulation,[status(thm)],[f135,f131]) ).
fof(f138,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| sK3_skl = sK6_skl ),
inference(backward_demodulation,[status(thm)],[f135,f73]) ).
fof(f139,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| unordered_pair(sK6_skl,sK6_skl) = singleton(sK6_skl) ),
inference(forward_demodulation,[status(thm)],[f135,f137]) ).
fof(f140,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ0_spl
| singleton(sK6_skl) = unordered_pair(sK3_skl,sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f135,f120]) ).
fof(f141,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ0_spl
| singleton(sK6_skl) = unordered_pair(sK6_skl,sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f138,f140]) ).
fof(f143,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ0_spl
| member(sK4_skl,singleton(sK6_skl)) ),
inference(paramodulation,[status(thm)],[f141,f81]) ).
fof(f145,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sK4_skl = sK6_skl ),
inference(resolution,[status(thm)],[f143,f48]) ).
fof(f146,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f145,f77]) ).
fof(f147,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f146]) ).
fof(f150,plain,
member(unordered_pair(sK3_skl,sK4_skl),unordered_pair(singleton(sK5_skl),unordered_pair(sK5_skl,sK6_skl))),
inference(resolution,[status(thm)],[f94,f81]) ).
fof(f156,plain,
( ~ sQ5_spl
| member(sK3_skl,singleton(sK5_skl)) ),
inference(paramodulation,[status(thm)],[f120,f80]) ).
fof(f160,plain,
( ~ sQ5_spl
| sK3_skl = sK5_skl ),
inference(resolution,[status(thm)],[f156,f48]) ).
fof(f161,plain,
( ~ sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f160,f72,f119]) ).
fof(f163,plain,
( sQ5_spl
| ~ sQ4_spl
| singleton(sK5_skl) != unordered_pair(sK5_skl,sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f128,f121]) ).
fof(f169,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| unordered_pair(sK5_skl,sK6_skl) = unordered_pair(sK5_skl,sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f128,f113]) ).
fof(f171,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| member(sK4_skl,unordered_pair(sK5_skl,sK6_skl)) ),
inference(paramodulation,[status(thm)],[f169,f81]) ).
fof(f173,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sK4_skl = sK6_skl
| sK4_skl = sK5_skl ),
inference(resolution,[status(thm)],[f171,f52]) ).
fof(f174,definition,
( sQ6_spl
<=> sK4_skl = sK5_skl ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( ~ sQ6_spl
| sK4_skl = sK5_skl ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f173,f174,f75,f116,f112]) ).
fof(f180,plain,
( sQ1_spl
| ~ sQ6_spl
| sK5_skl != sK6_skl ),
inference(backward_demodulation,[status(thm)],[f175,f77]) ).
fof(f193,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sK6_skl != sK6_skl ),
inference(forward_demodulation,[status(thm)],[f135,f180]) ).
fof(f194,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f193]) ).
fof(f195,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f194]) ).
fof(f203,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| unordered_pair(sK5_skl,sK6_skl) = unordered_pair(sK5_skl,sK5_skl) ),
inference(forward_demodulation,[status(thm)],[f175,f169]) ).
fof(f204,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| X0 = sK5_skl
| X0 = sK5_skl
| ~ member(X0,unordered_pair(sK5_skl,sK6_skl)) ),
inference(paramodulation,[status(thm)],[f203,f52]) ).
fof(f207,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| X0 = sK5_skl
| ~ member(X0,unordered_pair(sK5_skl,sK6_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f204]) ).
fof(f208,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| sK6_skl = sK5_skl ),
inference(resolution,[status(thm)],[f207,f81]) ).
fof(f210,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f208,f180]) ).
fof(f211,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f210]) ).
fof(f214,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sK3_skl = sK6_skl ),
inference(backward_demodulation,[status(thm)],[f135,f128]) ).
fof(f222,plain,
( sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| singleton(sK6_skl) != unordered_pair(sK5_skl,sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f135,f163]) ).
fof(f223,plain,
( sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| singleton(sK6_skl) != unordered_pair(sK6_skl,sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f135,f222]) ).
fof(f255,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| member(unordered_pair(sK6_skl,sK4_skl),unordered_pair(singleton(sK5_skl),unordered_pair(sK5_skl,sK6_skl))) ),
inference(forward_demodulation,[status(thm)],[f214,f150]) ).
fof(f256,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| member(unordered_pair(sK6_skl,sK4_skl),unordered_pair(singleton(sK6_skl),unordered_pair(sK5_skl,sK6_skl))) ),
inference(forward_demodulation,[status(thm)],[f135,f255]) ).
fof(f257,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| member(unordered_pair(sK6_skl,sK4_skl),unordered_pair(singleton(sK6_skl),unordered_pair(sK6_skl,sK6_skl))) ),
inference(forward_demodulation,[status(thm)],[f135,f256]) ).
fof(f258,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| member(unordered_pair(sK6_skl,sK4_skl),unordered_pair(singleton(sK6_skl),singleton(sK6_skl))) ),
inference(forward_demodulation,[status(thm)],[f139,f257]) ).
fof(f259,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| unordered_pair(sK6_skl,sK4_skl) = singleton(sK6_skl)
| unordered_pair(sK6_skl,sK4_skl) = singleton(sK6_skl) ),
inference(resolution,[status(thm)],[f258,f52]) ).
fof(f261,definition,
( sQ7_spl
<=> unordered_pair(sK6_skl,sK4_skl) = singleton(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f262,plain,
( ~ sQ7_spl
| unordered_pair(sK6_skl,sK4_skl) = singleton(sK6_skl) ),
inference(component_clause,[status(thm)],[f261]) ).
fof(f264,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f259,f261,f72,f109,f116]) ).
fof(f265,plain,
( ~ sQ7_spl
| sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f262,f223]) ).
fof(f266,plain,
( ~ sQ7_spl
| sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f265]) ).
fof(f273,plain,
( sQ4_spl
| ~ sQ0_spl
| singleton(sK5_skl) != singleton(sK5_skl) ),
inference(forward_demodulation,[status(thm)],[f73,f118]) ).
fof(f274,plain,
( sQ4_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f273]) ).
fof(f275,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f274]) ).
fof(f276,plain,
$false,
inference(sat_refutation,[status(thm)],[f78,f115,f122,f130,f147,f161,f177,f195,f211,f264,f266,f275]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET707+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n007.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 05:31:06 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.45 % Drodi V4.1.1
% 0.16/0.51 % Refutation found
% 0.16/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.56 % Elapsed time: 0.115846 seconds
% 0.16/0.56 % CPU time: 0.388084 seconds
% 0.16/0.56 % Total memory used: 47.520 MB
% 0.16/0.56 % Net memory used: 47.208 MB
%------------------------------------------------------------------------------