%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET703+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 02:10:29 PM UTC 2026
% Result : Theorem 8.07s 1.46s
% Output : CNFRefutation 8.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 26
% Syntax : Number of formulae : 146 ( 16 unt; 16 def)
% Number of atoms : 394 ( 43 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 404 ( 156 ~; 181 |; 39 &)
% ( 26 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 17 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 215 ( 206 !; 9 ?)
% 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(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,B)
| member(X,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( ~ member(B,A)
& member(B,E) ) ),
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 = B
| X = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,A] :
( member(X,sum(A))
<=> ? [Y] :
( member(X,Y)
& member(Y,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,A] :
( member(X,product(A))
<=> ! [Y] :
( member(Y,A)
=> member(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B] : equal_set(union(singleton(A),singleton(B)),unordered_pair(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B] : equal_set(union(singleton(A),singleton(B)),unordered_pair(A,B)),
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(f19,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| 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(f25,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f35,plain,
! [X,A,B] :
( ( ( ~ member(X,B)
& ~ member(X,A) )
| member(X,union(A,B)) )
& ( member(X,B)
| member(X,A)
| ~ member(X,union(A,B)) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f36,plain,
( ! [X,A,B] :
( ( ~ member(X,B)
& ~ member(X,A) )
| member(X,union(A,B)) )
& ! [X,A,B] :
( member(X,B)
| member(X,A)
| ~ member(X,union(A,B)) ) ),
inference(miniscoping,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f40,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
! [B,A,E] :
( ( member(B,A)
| ~ member(B,E)
| member(B,difference(E,A)) )
& ( ( ~ member(B,A)
& member(B,E) )
| ~ member(B,difference(E,A)) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( ! [B,A,E] :
( member(B,A)
| ~ member(B,E)
| member(B,difference(E,A)) )
& ! [B,A,E] :
( ( ~ member(B,A)
& member(B,E) )
| ~ member(B,difference(E,A)) ) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
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(f55,plain,
! [X,A] :
( ( ! [Y] :
( ~ member(X,Y)
| ~ member(Y,A) )
| member(X,sum(A)) )
& ( ? [Y] :
( member(X,Y)
& member(Y,A) )
| ~ member(X,sum(A)) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f56,plain,
( ! [X,A] :
( ! [Y] :
( ~ member(X,Y)
| ~ member(Y,A) )
| member(X,sum(A)) )
& ! [X,A] :
( ? [Y] :
( member(X,Y)
& member(Y,A) )
| ~ member(X,sum(A)) ) ),
inference(miniscoping,[status(thm)],[f55]) ).
fof(f57,plain,
( ! [X,A] :
( ! [Y] :
( ~ member(X,Y)
| ~ member(Y,A) )
| member(X,sum(A)) )
& ! [X,A] :
( ( member(X,sK1_skl(A,X))
& member(sK1_skl(A,X),A) )
| ~ member(X,sum(A)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y,sK1_skl(A,X))],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( member(sK1_skl(X1,X0),X1)
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X2,X1)
| member(X0,sum(X1)) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f61,plain,
! [X,A] :
( member(X,product(A))
<=> ! [Y] :
( member(X,Y)
| ~ member(Y,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f62,plain,
! [X,A] :
( ( ? [Y] :
( ~ member(X,Y)
& member(Y,A) )
| member(X,product(A)) )
& ( ! [Y] :
( member(X,Y)
| ~ member(Y,A) )
| ~ member(X,product(A)) ) ),
inference(NNF_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
( ! [X,A] :
( ? [Y] :
( ~ member(X,Y)
& member(Y,A) )
| member(X,product(A)) )
& ! [X,A] :
( ! [Y] :
( member(X,Y)
| ~ member(Y,A) )
| ~ member(X,product(A)) ) ),
inference(miniscoping,[status(thm)],[f62]) ).
fof(f64,plain,
( ! [X,A] :
( ( ~ member(X,sK2_skl(A,X))
& member(sK2_skl(A,X),A) )
| member(X,product(A)) )
& ! [X,A] :
( ! [Y] :
( member(X,Y)
| ~ member(Y,A) )
| ~ member(X,product(A)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y,sK2_skl(A,X))],[f63]) ).
fof(f65,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X2,X1)
| ~ member(X0,product(X1)) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( member(sK2_skl(X1,X0),X1)
| member(X0,product(X1)) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f68,plain,
? [A,B] : ~ equal_set(union(singleton(A),singleton(B)),unordered_pair(A,B)),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
~ equal_set(union(singleton(sK3_skl),singleton(sK4_skl)),unordered_pair(sK3_skl,sK4_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f68]) ).
fof(f70,plain,
~ equal_set(union(singleton(sK3_skl),singleton(sK4_skl)),unordered_pair(sK3_skl,sK4_skl)),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [X0] : member(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f49]) ).
fof(f72,plain,
! [X0,X1] : member(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f53]) ).
fof(f73,plain,
! [X0,X1] : member(X0,unordered_pair(X1,X0)),
inference(destructive_equality_resolution,[status(thm)],[f54]) ).
fof(f75,plain,
( ~ subset(unordered_pair(sK3_skl,sK4_skl),union(singleton(sK3_skl),singleton(sK4_skl)))
| ~ subset(union(singleton(sK3_skl),singleton(sK4_skl)),unordered_pair(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f25,f70]) ).
fof(f76,definition,
( sQ0_spl
<=> subset(union(singleton(sK3_skl),singleton(sK4_skl)),unordered_pair(sK3_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( sQ0_spl
| ~ subset(union(singleton(sK3_skl),singleton(sK4_skl)),unordered_pair(sK3_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f79,definition,
( sQ1_spl
<=> subset(unordered_pair(sK3_skl,sK4_skl),union(singleton(sK3_skl),singleton(sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( sQ1_spl
| ~ subset(unordered_pair(sK3_skl,sK4_skl),union(singleton(sK3_skl),singleton(sK4_skl))) ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f75,f76,f79]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ~ member(sK0_skl(X2,X1),X2)
| member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f18,f20]) ).
fof(f85,plain,
! [X0,X1,X2] :
( member(sK0_skl(X2,X1),X1)
| member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f18,f19]) ).
fof(f90,plain,
( sQ0_spl
| ~ member(sK0_skl(unordered_pair(sK3_skl,sK4_skl),union(singleton(sK3_skl),singleton(sK4_skl))),unordered_pair(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f78,f20]) ).
fof(f91,plain,
( sQ0_spl
| member(sK0_skl(unordered_pair(sK3_skl,sK4_skl),union(singleton(sK3_skl),singleton(sK4_skl))),union(singleton(sK3_skl),singleton(sK4_skl))) ),
inference(resolution,[status(thm)],[f78,f19]) ).
fof(f102,plain,
( sQ0_spl
| member(sK0_skl(unordered_pair(sK3_skl,sK4_skl),union(singleton(sK3_skl),singleton(sK4_skl))),singleton(sK4_skl))
| member(sK0_skl(unordered_pair(sK3_skl,sK4_skl),union(singleton(sK3_skl),singleton(sK4_skl))),singleton(sK3_skl)) ),
inference(resolution,[status(thm)],[f91,f37]) ).
fof(f103,definition,
( sQ2_spl
<=> member(sK0_skl(unordered_pair(sK3_skl,sK4_skl),union(singleton(sK3_skl),singleton(sK4_skl))),singleton(sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( ~ sQ2_spl
| member(sK0_skl(unordered_pair(sK3_skl,sK4_skl),union(singleton(sK3_skl),singleton(sK4_skl))),singleton(sK3_skl)) ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,definition,
( sQ3_spl
<=> member(sK0_skl(unordered_pair(sK3_skl,sK4_skl),union(singleton(sK3_skl),singleton(sK4_skl))),singleton(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ3_spl
| member(sK0_skl(unordered_pair(sK3_skl,sK4_skl),union(singleton(sK3_skl),singleton(sK4_skl))),singleton(sK4_skl)) ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,plain,
( sQ0_spl
| sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f102,f103,f106,f76]) ).
fof(f112,plain,
! [X0,X1,X2] :
( member(sK1_skl(X1,X2),X1)
| ~ member(X2,X0)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f60,f58]) ).
fof(f113,plain,
! [X0,X1,X2] :
( member(sK2_skl(X1,X2),X1)
| member(X2,X0)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f65,f66]) ).
fof(f114,plain,
( sQ1_spl
| ~ member(sK0_skl(union(singleton(sK3_skl),singleton(sK4_skl)),unordered_pair(sK3_skl,sK4_skl)),union(singleton(sK3_skl),singleton(sK4_skl))) ),
inference(resolution,[status(thm)],[f81,f20]) ).
fof(f115,plain,
( sQ1_spl
| member(sK0_skl(union(singleton(sK3_skl),singleton(sK4_skl)),unordered_pair(sK3_skl,sK4_skl)),unordered_pair(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f81,f19]) ).
fof(f120,plain,
( sQ1_spl
| ~ member(sK0_skl(union(singleton(sK3_skl),singleton(sK4_skl)),unordered_pair(sK3_skl,sK4_skl)),singleton(sK4_skl)) ),
inference(resolution,[status(thm)],[f114,f39]) ).
fof(f121,plain,
( sQ1_spl
| ~ member(sK0_skl(union(singleton(sK3_skl),singleton(sK4_skl)),unordered_pair(sK3_skl,sK4_skl)),singleton(sK3_skl)) ),
inference(resolution,[status(thm)],[f114,f38]) ).
fof(f122,plain,
( ~ sQ3_spl
| sK0_skl(unordered_pair(sK3_skl,sK4_skl),union(singleton(sK3_skl),singleton(sK4_skl))) = sK4_skl ),
inference(resolution,[status(thm)],[f107,f48]) ).
fof(f124,plain,
( sQ1_spl
| sK0_skl(union(singleton(sK3_skl),singleton(sK4_skl)),unordered_pair(sK3_skl,sK4_skl)) = sK4_skl
| sK0_skl(union(singleton(sK3_skl),singleton(sK4_skl)),unordered_pair(sK3_skl,sK4_skl)) = sK3_skl ),
inference(resolution,[status(thm)],[f115,f52]) ).
fof(f125,definition,
( sQ4_spl
<=> sK0_skl(union(singleton(sK3_skl),singleton(sK4_skl)),unordered_pair(sK3_skl,sK4_skl)) = sK3_skl ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ4_spl
| sK0_skl(union(singleton(sK3_skl),singleton(sK4_skl)),unordered_pair(sK3_skl,sK4_skl)) = sK3_skl ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,definition,
( sQ5_spl
<=> sK0_skl(union(singleton(sK3_skl),singleton(sK4_skl)),unordered_pair(sK3_skl,sK4_skl)) = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f129,plain,
( ~ sQ5_spl
| sK0_skl(union(singleton(sK3_skl),singleton(sK4_skl)),unordered_pair(sK3_skl,sK4_skl)) = sK4_skl ),
inference(component_clause,[status(thm)],[f128]) ).
fof(f131,plain,
( sQ1_spl
| sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f124,f125,f128,f79]) ).
fof(f153,plain,
! [X0,X1] :
( member(sK0_skl(X1,singleton(X0)),singleton(X0))
| member(X0,X1) ),
inference(resolution,[status(thm)],[f85,f71]) ).
fof(f164,plain,
! [X0,X1] :
( member(sK1_skl(X1,X0),X1)
| ~ member(singleton(X0),X1) ),
inference(resolution,[status(thm)],[f112,f71]) ).
fof(f175,plain,
! [X0] : member(sK1_skl(singleton(singleton(X0)),X0),singleton(singleton(X0))),
inference(resolution,[status(thm)],[f164,f71]) ).
fof(f208,plain,
! [X0,X1] :
( member(sK2_skl(singleton(X1),X0),singleton(X1))
| member(X0,X1) ),
inference(resolution,[status(thm)],[f113,f71]) ).
fof(f211,plain,
! [X0] :
( ~ sQ5_spl
| ~ member(sK4_skl,union(singleton(sK3_skl),singleton(sK4_skl)))
| member(X0,union(singleton(sK3_skl),singleton(sK4_skl)))
| ~ member(X0,unordered_pair(sK3_skl,sK4_skl)) ),
inference(paramodulation,[status(thm)],[f129,f84]) ).
fof(f212,definition,
! [X0] :
( sQ6_spl
<=> ( member(X0,union(singleton(sK3_skl),singleton(sK4_skl)))
| ~ member(X0,unordered_pair(sK3_skl,sK4_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f215,definition,
( sQ7_spl
<=> member(sK4_skl,union(singleton(sK3_skl),singleton(sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f216,plain,
( ~ sQ7_spl
| member(sK4_skl,union(singleton(sK3_skl),singleton(sK4_skl))) ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f217,plain,
( sQ7_spl
| ~ member(sK4_skl,union(singleton(sK3_skl),singleton(sK4_skl))) ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f211,f212,f215,f128]) ).
fof(f219,plain,
( sQ7_spl
| ~ member(sK4_skl,singleton(sK4_skl)) ),
inference(resolution,[status(thm)],[f217,f39]) ).
fof(f221,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f219,f71]) ).
fof(f222,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f221]) ).
fof(f228,plain,
( ~ sQ7_spl
| member(sK4_skl,singleton(sK4_skl))
| member(sK4_skl,singleton(sK3_skl)) ),
inference(resolution,[status(thm)],[f216,f37]) ).
fof(f230,plain,
! [X0] :
( ~ sQ7_spl
| member(sK1_skl(X0,sK4_skl),X0)
| ~ member(union(singleton(sK3_skl),singleton(sK4_skl)),X0) ),
inference(resolution,[status(thm)],[f216,f112]) ).
fof(f232,definition,
( sQ8_spl
<=> member(sK4_skl,singleton(sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( ~ sQ8_spl
| member(sK4_skl,singleton(sK3_skl)) ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f235,definition,
( sQ9_spl
<=> member(sK4_skl,singleton(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f238,plain,
( ~ sQ7_spl
| sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f228,f232,f235,f215]) ).
fof(f239,plain,
( ~ sQ8_spl
| sK4_skl = sK3_skl ),
inference(resolution,[status(thm)],[f233,f48]) ).
fof(f244,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| member(sK4_skl,union(singleton(sK4_skl),singleton(sK4_skl))) ),
inference(backward_demodulation,[status(thm)],[f239,f216]) ).
fof(f286,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| member(sK4_skl,singleton(sK4_skl))
| member(sK4_skl,singleton(sK4_skl)) ),
inference(resolution,[status(thm)],[f244,f37]) ).
fof(f290,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f286,f235,f232,f215]) ).
fof(f303,plain,
! [X0,X1] :
( sK0_skl(X1,singleton(X0)) = X0
| member(X0,X1) ),
inference(resolution,[status(thm)],[f153,f48]) ).
fof(f314,plain,
! [X0,X1,X2] :
( ~ member(X2,X1)
| sK0_skl(difference(X0,X1),singleton(X2)) = X2 ),
inference(resolution,[status(thm)],[f303,f44]) ).
fof(f315,plain,
! [X0,X1,X2] :
( member(X2,X0)
| sK0_skl(difference(X0,X1),singleton(X2)) = X2 ),
inference(resolution,[status(thm)],[f303,f43]) ).
fof(f368,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ member(sK4_skl,unordered_pair(sK3_skl,sK4_skl)) ),
inference(backward_demodulation,[status(thm)],[f122,f90]) ).
fof(f370,plain,
( sQ0_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f368,f73]) ).
fof(f371,plain,
( sQ0_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f370]) ).
fof(f374,plain,
( sQ1_spl
| ~ sQ4_spl
| ~ member(sK3_skl,singleton(sK3_skl)) ),
inference(forward_demodulation,[status(thm)],[f126,f121]) ).
fof(f375,plain,
( sQ1_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f374,f71]) ).
fof(f376,plain,
( sQ1_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f375]) ).
fof(f379,plain,
! [X0] :
( ~ sQ7_spl
| sK0_skl(difference(X0,union(singleton(sK3_skl),singleton(sK4_skl))),singleton(sK4_skl)) = sK4_skl ),
inference(resolution,[status(thm)],[f314,f216]) ).
fof(f433,plain,
! [X0,X1,X2] :
( X2 = X0
| sK0_skl(difference(singleton(X0),X1),singleton(X2)) = X2 ),
inference(resolution,[status(thm)],[f315,f48]) ).
fof(f554,plain,
! [X0] : sK1_skl(singleton(singleton(X0)),X0) = singleton(X0),
inference(resolution,[status(thm)],[f175,f48]) ).
fof(f566,plain,
! [X0,X1] :
( sK2_skl(singleton(X1),X0) = X1
| member(X0,X1) ),
inference(resolution,[status(thm)],[f208,f48]) ).
fof(f585,plain,
! [X0] : sK2_skl(singleton(empty_set),X0) = empty_set,
inference(resolution,[status(thm)],[f566,f40]) ).
fof(f592,plain,
! [X0] :
( member(empty_set,singleton(empty_set))
| member(X0,empty_set) ),
inference(paramodulation,[status(thm)],[f585,f208]) ).
fof(f594,definition,
! [X0] :
( sQ11_spl
<=> member(X0,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f595,plain,
! [X0] :
( ~ sQ11_spl
| member(X0,empty_set) ),
inference(component_clause,[status(thm)],[f594]) ).
fof(f597,definition,
( sQ12_spl
<=> member(empty_set,singleton(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f600,plain,
( sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f592,f594,f597]) ).
fof(f601,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f595,f40]) ).
fof(f602,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f601]) ).
fof(f639,plain,
( ~ sQ7_spl
| member(singleton(sK4_skl),singleton(singleton(sK4_skl)))
| ~ member(union(singleton(sK3_skl),singleton(sK4_skl)),singleton(singleton(sK4_skl))) ),
inference(paramodulation,[status(thm)],[f554,f230]) ).
fof(f640,definition,
( sQ13_spl
<=> member(union(singleton(sK3_skl),singleton(sK4_skl)),singleton(singleton(sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f643,definition,
( sQ14_spl
<=> member(singleton(sK4_skl),singleton(singleton(sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f646,plain,
( ~ sQ7_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f639,f640,f643,f215]) ).
fof(f764,plain,
! [X0] :
( ~ sQ7_spl
| sK4_skl = X0
| sK4_skl = sK4_skl ),
inference(paramodulation,[status(thm)],[f433,f379]) ).
fof(f770,definition,
( sQ15_spl
<=> sK4_skl = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f773,definition,
! [X0] :
( sQ16_spl
<=> sK4_skl = X0 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f776,plain,
( ~ sQ7_spl
| sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f764,f770,f773,f215]) ).
fof(f791,plain,
( ~ sQ2_spl
| sK0_skl(unordered_pair(sK3_skl,sK4_skl),union(singleton(sK3_skl),singleton(sK4_skl))) = sK3_skl ),
inference(resolution,[status(thm)],[f104,f48]) ).
fof(f798,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ member(sK3_skl,unordered_pair(sK3_skl,sK4_skl)) ),
inference(backward_demodulation,[status(thm)],[f791,f90]) ).
fof(f814,plain,
( sQ0_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f798,f72]) ).
fof(f815,plain,
( sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f814]) ).
fof(f818,plain,
( sQ1_spl
| ~ sQ5_spl
| ~ member(sK4_skl,singleton(sK4_skl)) ),
inference(backward_demodulation,[status(thm)],[f129,f120]) ).
fof(f822,plain,
( sQ1_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f818,f71]) ).
fof(f823,plain,
( sQ1_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f822]) ).
fof(f824,plain,
$false,
inference(sat_refutation,[status(thm)],[f82,f109,f131,f218,f222,f238,f290,f371,f376,f600,f602,f646,f776,f815,f823]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET703+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:33:07 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 8.07/1.46 % Refutation found
% 8.07/1.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 8.07/1.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.07/1.50 % Elapsed time: 1.134931 seconds
% 8.07/1.50 % CPU time: 8.815356 seconds
% 8.07/1.50 % Total memory used: 180.713 MB
% 8.07/1.50 % Net memory used: 167.000 MB
%------------------------------------------------------------------------------