%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET698+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n001.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 : Fri Sep 25 02:47:49 PM UTC 2026
% Result : Theorem 5.91s 7.29s
% Output : CNFRefutation 5.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 96 ( 7 unt; 0 def)
% Number of atoms : 272 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 293 ( 117 ~; 129 |; 35 &)
% ( 7 <=>; 3 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 146 ( 0 sgn 132 !; 14 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(f5,axiom,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X2)
| member(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',union) ).
fof(f7,axiom,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( ~ member(X0,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',difference) ).
fof(f12,conjecture,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X2) )
=> ( subset(X0,X1)
<=> equal_set(union(difference(X2,X0),X1),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI32) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X2) )
=> ( subset(X0,X1)
<=> equal_set(union(difference(X2,X0),X1),X2) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0,X1,X2] :
( subset(X1,X2)
& subset(X0,X2)
& ( subset(X0,X1)
<~> equal_set(union(difference(X2,X0),X1),X2) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
? [X0,X1,X2] :
( subset(X1,X2)
& subset(X0,X2)
& ( subset(X0,X1)
<~> equal_set(union(difference(X2,X0),X1),X2) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f17,plain,
? [X0,X1,X2] :
( subset(X1,X2)
& subset(X0,X2)
& ( subset(X0,X1)
| equal_set(union(difference(X2,X0),X1),X2) )
& ( ~ subset(X0,X1)
| ~ equal_set(union(difference(X2,X0),X1),X2) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f18,plain,
? [X0,X1,X2] :
( subset(X1,X2)
& subset(X0,X2)
& ( subset(X0,X1)
| equal_set(union(difference(X2,X0),X1),X2) )
& ( ~ subset(X0,X1)
| ~ equal_set(union(difference(X2,X0),X1),X2) ) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
( subset(sK1,sK2)
& subset(sK0,sK2)
& ( subset(sK0,sK1)
| equal_set(union(difference(sK2,sK0),sK1),sK2) )
& ( ~ subset(sK0,sK1)
| ~ equal_set(union(difference(sK2,sK0),sK1),sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK3(X0,X1),X0)
& ~ member(sK3(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) )
& ( ( ~ member(X0,X2)
& ~ member(X0,X1) )
| member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) )
& ( ( ~ member(X0,X2)
& ~ member(X0,X1) )
| member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ( ~ equal_set(X0,X1)
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f26,plain,
! [X0,X1] :
( ( ~ equal_set(X0,X1)
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( ~ member(X0,difference(X2,X1))
| ( ~ member(X0,X1)
& member(X0,X2) ) )
& ( member(X0,X1)
| ~ member(X0,X2)
| member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( ~ member(X0,difference(X2,X1))
| ( ~ member(X0,X1)
& member(X0,X2) ) )
& ( member(X0,X1)
| ~ member(X0,X2)
| member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
subset(sK1,sK2),
inference(cnf_transformation,[],[f19]) ).
fof(f30,plain,
subset(sK0,sK2),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
( subset(sK0,sK1)
| equal_set(union(difference(sK2,sK0),sK1),sK2) ),
inference(cnf_transformation,[],[f19]) ).
fof(f32,plain,
( ~ subset(sK0,sK1)
| ~ equal_set(union(difference(sK2,sK0),sK1),sK2) ),
inference(cnf_transformation,[],[f19]) ).
fof(f33,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f34,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
! [X0,X1] :
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f39,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f40,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f41,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| member(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f44,plain,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,X2)
| member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_49,negated_conjecture,
( ~ subset(sK0,sK1)
| ~ equal_set(union(difference(sK2,sK0),sK1),sK2) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_50,negated_conjecture,
( subset(sK0,sK1)
| equal_set(union(difference(sK2,sK0),sK1),sK2) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_51,negated_conjecture,
subset(sK0,sK2),
inference(cnf_transformation,[],[f30]) ).
tcf(c_52,negated_conjecture,
subset(sK1,sK2),
inference(cnf_transformation,[],[f29]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_73,plain,
( ~ equal_set(union(difference(sK2,sK0),sK1),sK2)
| ~ subset(sK0,sK1) ),
inference(prop_impl_just,[status(thm)],[c_49]) ).
tcf(c_74,plain,
( ~ subset(sK0,sK1)
| ~ equal_set(union(difference(sK2,sK0),sK1),sK2) ),
inference(renaming,[status(thm)],[c_73]) ).
tcf(c_75,plain,
( equal_set(union(difference(sK2,sK0),sK1),sK2)
| subset(sK0,sK1) ),
inference(prop_impl_just,[status(thm)],[c_50]) ).
tcf(c_76,plain,
( subset(sK0,sK1)
| equal_set(union(difference(sK2,sK0),sK1),sK2) ),
inference(renaming,[status(thm)],[c_75]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( ~ equal_set(X0,X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_60]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ equal_set(X0,X1) ),
inference(renaming,[status(thm)],[c_83]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_61]) ).
tcf(c_207,plain,
( subset(sK0,sK1)
| subset(sK2,union(difference(sK2,sK0),sK1)) ),
inference(resolution,[status(thm)],[c_76,c_97]) ).
tcf(c_214,plain,
( subset(sK0,sK1)
| subset(union(difference(sK2,sK0),sK1),sK2) ),
inference(resolution,[status(thm)],[c_76,c_84]) ).
tcf(c_221,plain,
( ~ subset(sK0,sK1)
| ~ subset(sK2,union(difference(sK2,sK0),sK1))
| ~ subset(union(difference(sK2,sK0),sK1),sK2) ),
inference(resolution,[status(thm)],[c_74,c_59]) ).
tcf(c_298,plain,
( subset(union(difference(sK2,sK0),sK1),sK2)
| ~ member(sK3(union(difference(sK2,sK0),sK1),sK2),sK2) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_299,plain,
( subset(union(difference(sK2,sK0),sK1),sK2)
| member(sK3(union(difference(sK2,sK0),sK1),sK2),union(difference(sK2,sK0),sK1)) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_300,plain,
( subset(sK2,union(difference(sK2,sK0),sK1))
| member(sK3(sK2,union(difference(sK2,sK0),sK1)),sK2) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_301,plain,
( subset(sK2,union(difference(sK2,sK0),sK1))
| ~ member(sK3(sK2,union(difference(sK2,sK0),sK1)),union(difference(sK2,sK0),sK1)) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_303,plain,
! [X0: $i] :
( member(sK3(sK2,union(difference(sK2,sK0),sK1)),X0)
| member(sK3(sK2,union(difference(sK2,sK0),sK1)),difference(sK2,X0))
| ~ member(sK3(sK2,union(difference(sK2,sK0),sK1)),sK2) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_309,plain,
( subset(sK0,sK1)
| member(sK3(sK0,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_310,plain,
( subset(sK0,sK1)
| ~ member(sK3(sK0,sK1),sK1) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_311,plain,
! [X0: $i] :
( member(sK3(sK0,sK1),X0)
| ~ subset(sK0,X0)
| ~ member(sK3(sK0,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_312,plain,
( member(sK3(sK0,sK1),sK2)
| ~ subset(sK0,sK2)
| ~ member(sK3(sK0,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_311]) ).
tcf(c_319,plain,
! [X0: $i] :
( ~ member(sK3(sK0,sK1),sK0)
| ~ member(sK3(sK0,sK1),difference(X0,sK0)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_320,plain,
( ~ member(sK3(sK0,sK1),sK0)
| ~ member(sK3(sK0,sK1),difference(sK2,sK0)) ),
inference(instantiation,[status(thm)],[c_319]) ).
tcf(c_331,plain,
( member(sK3(union(difference(sK2,sK0),sK1),sK2),sK1)
| member(sK3(union(difference(sK2,sK0),sK1),sK2),difference(sK2,sK0))
| ~ member(sK3(union(difference(sK2,sK0),sK1),sK2),union(difference(sK2,sK0),sK1)) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_334,plain,
! [X0: $i] :
( member(sK3(union(difference(sK2,sK0),sK1),sK2),X0)
| ~ subset(sK1,X0)
| ~ member(sK3(union(difference(sK2,sK0),sK1),sK2),sK1) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_335,plain,
( member(sK3(union(difference(sK2,sK0),sK1),sK2),sK2)
| ~ subset(sK1,sK2)
| ~ member(sK3(union(difference(sK2,sK0),sK1),sK2),sK1) ),
inference(instantiation,[status(thm)],[c_334]) ).
tcf(c_454,plain,
! [X0: $i,X1: $i] :
( member(sK3(sK0,sK1),X1)
| ~ subset(X0,X1)
| ~ member(sK3(sK0,sK1),X0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_460,plain,
! [X0: $i,X1: $i] :
( member(sK3(sK0,sK1),X1)
| member(sK3(sK0,sK1),X0)
| ~ member(sK3(sK0,sK1),union(X0,X1)) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_570,plain,
( member(sK3(union(difference(sK2,sK0),sK1),sK2),sK2)
| ~ member(sK3(union(difference(sK2,sK0),sK1),sK2),difference(sK2,sK0)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_781,plain,
subset(union(difference(sK2,sK0),sK1),sK2),
inference(global_subsumption_just,[status(thm)],[c_214,c_52,c_298,c_299,c_331,c_335,c_570]) ).
tcf(c_876,plain,
! [X0: $i,X1: $i] :
( member(sK3(sK2,union(difference(sK2,sK0),sK1)),X1)
| ~ subset(X0,X1)
| ~ member(sK3(sK2,union(difference(sK2,sK0),sK1)),X0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_878,plain,
! [X0: $i,X1: $i] :
( member(sK3(sK2,union(difference(sK2,sK0),sK1)),union(X1,X0))
| ~ member(sK3(sK2,union(difference(sK2,sK0),sK1)),X0) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_879,plain,
! [X0: $i,X1: $i] :
( member(sK3(sK2,union(difference(sK2,sK0),sK1)),union(X0,X1))
| ~ member(sK3(sK2,union(difference(sK2,sK0),sK1)),X0) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_1559,plain,
! [X0: $i,X1: $i] :
( member(sK3(sK0,sK1),X1)
| member(sK3(sK0,sK1),difference(X0,sK0))
| ~ member(sK3(sK0,sK1),union(difference(X0,sK0),X1)) ),
inference(instantiation,[status(thm)],[c_460]) ).
tcf(c_1857,plain,
! [X0: $i] :
( member(sK3(sK0,sK1),sK1)
| member(sK3(sK0,sK1),difference(X0,sK0))
| ~ member(sK3(sK0,sK1),union(difference(X0,sK0),sK1)) ),
inference(instantiation,[status(thm)],[c_1559]) ).
tcf(c_1858,plain,
( member(sK3(sK0,sK1),sK1)
| member(sK3(sK0,sK1),difference(sK2,sK0))
| ~ member(sK3(sK0,sK1),union(difference(sK2,sK0),sK1)) ),
inference(instantiation,[status(thm)],[c_1857]) ).
tcf(c_2172,plain,
! [X0: $i] :
( member(sK3(sK0,sK1),union(difference(sK2,sK0),sK1))
| ~ member(sK3(sK0,sK1),X0)
| ~ subset(X0,union(difference(sK2,sK0),sK1)) ),
inference(instantiation,[status(thm)],[c_454]) ).
tcf(c_2173,plain,
( member(sK3(sK0,sK1),union(difference(sK2,sK0),sK1))
| ~ member(sK3(sK0,sK1),sK2)
| ~ subset(sK2,union(difference(sK2,sK0),sK1)) ),
inference(instantiation,[status(thm)],[c_2172]) ).
tcf(c_2499,plain,
( member(sK3(sK2,union(difference(sK2,sK0),sK1)),union(difference(sK2,sK0),sK1))
| ~ member(sK3(sK2,union(difference(sK2,sK0),sK1)),sK1) ),
inference(instantiation,[status(thm)],[c_878]) ).
tcf(c_2556,plain,
( member(sK3(sK2,union(difference(sK2,sK0),sK1)),union(difference(sK2,sK0),sK1))
| ~ member(sK3(sK2,union(difference(sK2,sK0),sK1)),difference(sK2,sK0)) ),
inference(instantiation,[status(thm)],[c_879]) ).
tcf(c_5032,plain,
! [X0: $i] :
( member(sK3(sK2,union(difference(sK2,sK0),sK1)),sK1)
| ~ subset(X0,sK1)
| ~ member(sK3(sK2,union(difference(sK2,sK0),sK1)),X0) ),
inference(instantiation,[status(thm)],[c_876]) ).
tcf(c_6887,plain,
subset(sK0,sK1),
inference(global_subsumption_just,[status(thm)],[c_207,c_51,c_207,c_310,c_309,c_312,c_320,c_1858,c_2173]) ).
tcf(c_14036,plain,
( member(sK3(sK2,union(difference(sK2,sK0),sK1)),sK1)
| ~ subset(sK0,sK1)
| ~ member(sK3(sK2,union(difference(sK2,sK0),sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_5032]) ).
tcf(c_21517,plain,
( member(sK3(sK2,union(difference(sK2,sK0),sK1)),sK0)
| member(sK3(sK2,union(difference(sK2,sK0),sK1)),difference(sK2,sK0))
| ~ member(sK3(sK2,union(difference(sK2,sK0),sK1)),sK2) ),
inference(instantiation,[status(thm)],[c_303]) ).
tcf(c_21519,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_21517,c_14036,c_6887,c_2556,c_2499,c_781,c_300,c_301,c_221]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET698+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n001.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 11:47:44 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.41 Running first-order theorem proving
% 0.15/5.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.42
% 0.15/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.42
% 0.15/5.43 % Detected problem language: tptp
% 0.15/5.44 % Proving...
% 5.91/7.29 % SZS status Started for theBenchmark.p
% 5.91/7.29 % SZS status Theorem for theBenchmark.p
% 5.91/7.29
% 5.91/7.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.91/7.29
% 5.91/7.29 % ------ iProver source info
% 5.91/7.29
% 5.91/7.29 % git: date: 2026-07-19 20:42:38 +0200
% 5.91/7.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.91/7.29 % git: non_committed_changes: false
% 5.91/7.29
% 5.91/7.29 % ------ Parsing...
% 5.91/7.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.91/7.29
% 5.91/7.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 5.91/7.29
% 5.91/7.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 5.91/7.29 % ------ Proving...
% 5.91/7.29 % ------ Problem Properties
% 5.91/7.29
% 5.91/7.29 %
% 5.91/7.29 % clauses 14
% 5.91/7.29 % conjectures 2
% 5.91/7.29 % EPR 3
% 5.91/7.29 % Horn 9
% 5.91/7.29 % unary 2
% 5.91/7.29 % binary 8
% 5.91/7.29 % lits 30
% 5.91/7.29 % lits eq 0
% 5.91/7.29 % fd_pure 0
% 5.91/7.29 % fd_pseudo 0
% 5.91/7.29 % fd_cond 0
% 5.91/7.29 % fd_pseudo_cond 0
% 5.91/7.29 % AC symbols 0
% 5.91/7.29
% 5.91/7.29 % ------ Schedule dynamic 5 is on
% 5.91/7.29
% 5.91/7.29 % ------ no equalities: superposition off
% 5.91/7.29
% 5.91/7.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 5.91/7.29
% 5.91/7.29
% 5.91/7.29 % ------
% 5.91/7.29 % Current options:
% 5.91/7.29 % ------
% 5.91/7.29
% 5.91/7.29
% 5.91/7.29 %
% 5.91/7.29
% 5.91/7.29 % ------ Proving...
% 5.91/7.29 %
% 5.91/7.29
% 5.91/7.29 % SZS status Theorem for theBenchmark.p
% 5.91/7.29
% 5.91/7.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.91/7.29
% 5.91/7.29
%------------------------------------------------------------------------------