%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET806+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.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 02:48:37 PM UTC 2026
% Result : Theorem 4.40s 1.32s
% Output : CNFRefutation 4.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 104 ( 17 unt; 1 def)
% Number of atoms : 326 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 341 ( 119 ~; 123 |; 76 &)
% ( 6 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 178 ( 0 sgn 151 !; 27 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(f14,axiom,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X2,X3,X4] :
( ( member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X2,X3) )
=> apply(X1,X2,X4) ) )
& ! [X2,X3] :
( ( member(X3,X0)
& member(X2,X0) )
=> ( apply(X1,X2,X3)
=> apply(X1,X3,X2) ) )
& ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',equivalence) ).
fof(f17,axiom,
! [X0,X1] :
( apply(equal_set_predicate,X0,X1)
<=> equal_set(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rel_equal_set) ).
fof(f18,conjecture,
! [X0] : equivalence(equal_set_predicate,power_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII13) ).
fof(f19,negated_conjecture,
~ ! [X0] : equivalence(equal_set_predicate,power_set(X0)),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X5,X6,X7] :
( ( member(X7,X0)
& member(X6,X0)
& member(X5,X0) )
=> ( ( apply(X1,X6,X7)
& apply(X1,X5,X6) )
=> apply(X1,X5,X7) ) )
& ! [X3,X4] :
( ( member(X4,X0)
& member(X3,X0) )
=> ( apply(X1,X3,X4)
=> apply(X1,X4,X3) ) )
& ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) ) ) ),
inference(rectify,[],[f14]) ).
fof(f21,plain,
! [X0,X1] :
( ( ! [X5,X6,X7] :
( ( member(X7,X0)
& member(X6,X0)
& member(X5,X0) )
=> ( ( apply(X1,X6,X7)
& apply(X1,X5,X6) )
=> apply(X1,X5,X7) ) )
& ! [X3,X4] :
( ( member(X4,X0)
& member(X3,X0) )
=> ( apply(X1,X3,X4)
=> apply(X1,X4,X3) ) )
& ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) ) )
=> equivalence(X1,X0) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f22,plain,
? [X0] : ~ equivalence(equal_set_predicate,power_set(X0)),
inference(ennf_transformation,[],[f19]) ).
fof(f23,plain,
! [X0,X1] :
( ? [X5,X6,X7] :
( member(X7,X0)
& member(X6,X0)
& member(X5,X0)
& apply(X1,X6,X7)
& apply(X1,X5,X6)
& ~ apply(X1,X5,X7) )
| ? [X3,X4] :
( member(X4,X0)
& member(X3,X0)
& apply(X1,X3,X4)
& ~ apply(X1,X4,X3) )
| ? [X2] :
( member(X2,X0)
& ~ apply(X1,X2,X2) )
| equivalence(X1,X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f24,plain,
! [X0,X1] :
( ? [X5,X6,X7] :
( member(X7,X0)
& member(X6,X0)
& member(X5,X0)
& apply(X1,X6,X7)
& apply(X1,X5,X6)
& ~ apply(X1,X5,X7) )
| ? [X3,X4] :
( member(X4,X0)
& member(X3,X0)
& apply(X1,X3,X4)
& ~ apply(X1,X4,X3) )
| ? [X2] :
( member(X2,X0)
& ~ apply(X1,X2,X2) )
| equivalence(X1,X0) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f28,plain,
! [X0,X1] :
( ( ~ apply(equal_set_predicate,X0,X1)
| equal_set(X0,X1) )
& ( ~ equal_set(X0,X1)
| apply(equal_set_predicate,X0,X1) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f29,plain,
~ equivalence(equal_set_predicate,power_set(sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f22]) ).
fof(f30,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(f31,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,[],[f30]) ).
fof(f36,plain,
! [X0,X1] :
( sP0(X1,X0)
| ( member(sK7(X0,X1),X0)
& member(sK6(X0,X1),X0)
& apply(X1,sK6(X0,X1),sK7(X0,X1))
& ~ apply(X1,sK7(X0,X1),sK6(X0,X1)) )
| ( member(sK5(X0,X1),X0)
& ~ apply(X1,sK5(X0,X1),sK5(X0,X1)) )
| equivalence(X1,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X2,sK5(X0,X1)),skolemize(X3,sK6(X0,X1)),skolemize(X4,sK7(X0,X1))],[f27]) ).
fof(f37,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,[],[f25]) ).
fof(f38,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,[],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK8(X0,X1),X0)
& ~ member(sK8(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X2,sK8(X0,X1))],[f38]) ).
fof(f40,plain,
! [X0,X1] :
( ~ apply(equal_set_predicate,X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f41,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| apply(equal_set_predicate,X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f42,plain,
~ equivalence(equal_set_predicate,power_set(sK1)),
inference(cnf_transformation,[],[f29]) ).
fof(f43,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f44,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f45,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f60,plain,
! [X0,X1] :
( sP0(X1,X0)
| apply(X1,sK6(X0,X1),sK7(X0,X1))
| ~ apply(X1,sK5(X0,X1),sK5(X0,X1))
| equivalence(X1,X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f61,plain,
! [X0,X1] :
( sP0(X1,X0)
| ~ apply(X1,sK7(X0,X1),sK6(X0,X1))
| ~ apply(X1,sK5(X0,X1),sK5(X0,X1))
| equivalence(X1,X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f62,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f63,plain,
! [X0,X1] :
( member(sK8(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f64,plain,
! [X0,X1] :
( ~ member(sK8(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( apply(equal_set_predicate,X0,X1)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ apply(equal_set_predicate,X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_51,negated_conjecture,
~ equivalence(equal_set_predicate,power_set(sK1)),
inference(cnf_transformation,[],[f42]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| equivalence(X0,X1)
| ~ apply(X0,sK7(X1,X0),sK6(X1,X0))
| ~ apply(X0,sK5(X1,X0),sK5(X1,X0)) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| equivalence(X0,X1)
| apply(X0,sK6(X1,X0),sK7(X1,X0))
| ~ apply(X0,sK5(X1,X0),sK5(X1,X0)) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK8(X0,X1),X0) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( ~ apply(equal_set_predicate,X0,X1)
| equal_set(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_50]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ apply(equal_set_predicate,X0,X1) ),
inference(renaming,[status(thm)],[c_96]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( apply(equal_set_predicate,X0,X1)
| ~ equal_set(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_49]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ equal_set(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_53]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_54]) ).
tcf(c_319,plain,
! [X0: $i,X1: $i] :
( apply(equal_set_predicate,X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[c_52,c_98]) ).
tcf(c_330,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ apply(equal_set_predicate,X0,X1) ),
inference(resolution,[status(thm)],[c_97,c_106]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ apply(equal_set_predicate,X0,X1) ),
inference(resolution,[status(thm)],[c_97,c_104]) ).
tcf(c_413,plain,
( sP0(equal_set_predicate,power_set(sK1))
| apply(equal_set_predicate,sK6(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate))
| ~ apply(equal_set_predicate,sK5(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate)) ),
inference(resolution,[status(thm)],[c_51,c_64]) ).
tcf(c_423,plain,
( sP0(equal_set_predicate,power_set(sK1))
| ~ apply(equal_set_predicate,sK7(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate))
| ~ apply(equal_set_predicate,sK5(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate)) ),
inference(resolution,[status(thm)],[c_51,c_63]) ).
tcf(c_1084,plain,
( apply(equal_set_predicate,sK5(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate))
| ~ subset(sK5(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate)) ),
inference(instantiation,[status(thm)],[c_319]) ).
tcf(c_1086,plain,
( subset(sK5(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate))
| ~ member(sK8(sK5(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate)),sK5(power_set(sK1),equal_set_predicate)) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_1087,plain,
( subset(sK5(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate))
| member(sK8(sK5(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate)),sK5(power_set(sK1),equal_set_predicate)) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_1106,plain,
( apply(equal_set_predicate,sK7(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate))
| ~ subset(sK6(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate))
| ~ subset(sK7(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate)) ),
inference(instantiation,[status(thm)],[c_319]) ).
tcf(c_1120,plain,
( subset(sK7(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate))
| ~ apply(equal_set_predicate,sK6(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate)) ),
inference(instantiation,[status(thm)],[c_330]) ).
tcf(c_1124,plain,
( subset(sK6(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate))
| ~ apply(equal_set_predicate,sK6(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate)) ),
inference(instantiation,[status(thm)],[c_338]) ).
fof(f26,definition,
! [X1,X0] :
( ~ sP0(X1,X0)
| ? [X5,X6,X7] :
( member(X7,X0)
& member(X6,X0)
& member(X5,X0)
& apply(X1,X6,X7)
& apply(X1,X5,X6)
& ~ apply(X1,X5,X7) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f27,plain,
! [X0,X1] :
( sP0(X1,X0)
| ? [X3,X4] :
( member(X4,X0)
& member(X3,X0)
& apply(X1,X3,X4)
& ~ apply(X1,X4,X3) )
| ? [X2] :
( member(X2,X0)
& ~ apply(X1,X2,X2) )
| equivalence(X1,X0) ),
inference(definition_folding,[],[f24,f26]) ).
fof(f33,plain,
! [X1,X0] :
( ~ sP0(X1,X0)
| ? [X5,X6,X7] :
( member(X7,X0)
& member(X6,X0)
& member(X5,X0)
& apply(X1,X6,X7)
& apply(X1,X5,X6)
& ~ apply(X1,X5,X7) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f34,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ? [X2,X3,X4] :
( member(X4,X1)
& member(X3,X1)
& member(X2,X1)
& apply(X0,X3,X4)
& apply(X0,X2,X3)
& ~ apply(X0,X2,X4) ) ),
inference(rectify,[],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ( member(sK4(X0,X1),X1)
& member(sK3(X0,X1),X1)
& member(sK2(X0,X1),X1)
& apply(X0,sK3(X0,X1),sK4(X0,X1))
& apply(X0,sK2(X0,X1),sK3(X0,X1))
& ~ apply(X0,sK2(X0,X1),sK4(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X2,sK2(X0,X1)),skolemize(X3,sK3(X0,X1)),skolemize(X4,sK4(X0,X1))],[f34]) ).
fof(f51,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| apply(X0,sK3(X0,X1),sK4(X0,X1)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f52,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| apply(X0,sK2(X0,X1),sK3(X0,X1)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f53,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ~ apply(X0,sK2(X0,X1),sK4(X0,X1)) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ~ sP0(X0,X1)
| ~ apply(X0,sK2(X0,X1),sK4(X0,X1)) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( apply(X0,sK2(X0,X1),sK3(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( apply(X0,sK3(X0,X1),sK4(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i] :
( ~ sP0(X0,X1)
| ~ apply(X0,sK2(X0,X1),sK4(X0,X1)) ),
inference(prop_impl_just,[status(thm)],[c_57]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i] :
( apply(X0,sK2(X0,X1),sK3(X0,X1))
| ~ sP0(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_58]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i] :
( apply(X0,sK3(X0,X1),sK4(X0,X1))
| ~ sP0(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_59]) ).
tcf(c_697,plain,
( apply(equal_set_predicate,sK3(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1)))
| ~ apply(equal_set_predicate,sK7(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate))
| ~ apply(equal_set_predicate,sK5(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate)) ),
inference(resolution,[status(thm)],[c_122,c_423]) ).
tcf(c_707,plain,
( apply(equal_set_predicate,sK6(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate))
| apply(equal_set_predicate,sK3(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1)))
| ~ apply(equal_set_predicate,sK5(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate)) ),
inference(resolution,[status(thm)],[c_122,c_413]) ).
tcf(c_777,plain,
( apply(equal_set_predicate,sK2(equal_set_predicate,power_set(sK1)),sK3(equal_set_predicate,power_set(sK1)))
| ~ apply(equal_set_predicate,sK7(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate))
| ~ apply(equal_set_predicate,sK5(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate)) ),
inference(resolution,[status(thm)],[c_120,c_423]) ).
tcf(c_787,plain,
( apply(equal_set_predicate,sK6(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate))
| apply(equal_set_predicate,sK2(equal_set_predicate,power_set(sK1)),sK3(equal_set_predicate,power_set(sK1)))
| ~ apply(equal_set_predicate,sK5(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate)) ),
inference(resolution,[status(thm)],[c_120,c_413]) ).
tcf(c_857,plain,
( ~ apply(equal_set_predicate,sK7(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate))
| ~ apply(equal_set_predicate,sK5(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate))
| ~ apply(equal_set_predicate,sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))) ),
inference(resolution,[status(thm)],[c_116,c_423]) ).
tcf(c_867,plain,
( apply(equal_set_predicate,sK6(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate))
| ~ apply(equal_set_predicate,sK5(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate))
| ~ apply(equal_set_predicate,sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))) ),
inference(resolution,[status(thm)],[c_116,c_413]) ).
tcf(c_3052,plain,
( apply(equal_set_predicate,sK3(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1)))
| ~ apply(equal_set_predicate,sK7(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate)) ),
inference(global_subsumption_just,[status(thm)],[c_697,c_697,c_1084,c_1087,c_1086]) ).
tcf(c_3058,plain,
( apply(equal_set_predicate,sK3(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1)))
| ~ subset(sK6(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate))
| ~ subset(sK7(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate)) ),
inference(superposition,[status(thm)],[c_319,c_3052]) ).
tcf(c_3465,plain,
( apply(equal_set_predicate,sK6(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate))
| apply(equal_set_predicate,sK3(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))) ),
inference(global_subsumption_just,[status(thm)],[c_707,c_707,c_1084,c_1087,c_1086,c_1120,c_1124,c_3058]) ).
tcf(c_3467,plain,
apply(equal_set_predicate,sK3(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))),
inference(global_subsumption_just,[status(thm)],[c_3465,c_1120,c_1124,c_3058,c_3465]) ).
tcf(c_3469,plain,
subset(sK3(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))),
inference(superposition,[status(thm)],[c_3467,c_338]) ).
tcf(c_3470,plain,
subset(sK4(equal_set_predicate,power_set(sK1)),sK3(equal_set_predicate,power_set(sK1))),
inference(superposition,[status(thm)],[c_3467,c_330]) ).
tcf(c_3542,plain,
! [X0: $i] :
( member(X0,sK4(equal_set_predicate,power_set(sK1)))
| ~ member(X0,sK3(equal_set_predicate,power_set(sK1))) ),
inference(superposition,[status(thm)],[c_3469,c_73]) ).
tcf(c_3549,plain,
! [X0: $i] :
( member(X0,sK3(equal_set_predicate,power_set(sK1)))
| ~ member(X0,sK4(equal_set_predicate,power_set(sK1))) ),
inference(superposition,[status(thm)],[c_3470,c_73]) ).
tcf(c_3685,plain,
( apply(equal_set_predicate,sK2(equal_set_predicate,power_set(sK1)),sK3(equal_set_predicate,power_set(sK1)))
| ~ apply(equal_set_predicate,sK7(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate)) ),
inference(global_subsumption_just,[status(thm)],[c_777,c_777,c_1084,c_1087,c_1086]) ).
tcf(c_3819,plain,
( apply(equal_set_predicate,sK6(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate))
| apply(equal_set_predicate,sK2(equal_set_predicate,power_set(sK1)),sK3(equal_set_predicate,power_set(sK1))) ),
inference(global_subsumption_just,[status(thm)],[c_787,c_787,c_1084,c_1087,c_1086,c_1106,c_1120,c_1124,c_3685]) ).
tcf(c_3821,plain,
apply(equal_set_predicate,sK2(equal_set_predicate,power_set(sK1)),sK3(equal_set_predicate,power_set(sK1))),
inference(global_subsumption_just,[status(thm)],[c_3819,c_1106,c_1120,c_1124,c_3685,c_3819]) ).
tcf(c_3823,plain,
subset(sK2(equal_set_predicate,power_set(sK1)),sK3(equal_set_predicate,power_set(sK1))),
inference(superposition,[status(thm)],[c_3821,c_338]) ).
tcf(c_3824,plain,
subset(sK3(equal_set_predicate,power_set(sK1)),sK2(equal_set_predicate,power_set(sK1))),
inference(superposition,[status(thm)],[c_3821,c_330]) ).
tcf(c_3860,plain,
! [X0: $i] :
( subset(sK4(equal_set_predicate,power_set(sK1)),X0)
| member(sK8(sK4(equal_set_predicate,power_set(sK1)),X0),sK3(equal_set_predicate,power_set(sK1))) ),
inference(superposition,[status(thm)],[c_72,c_3549]) ).
tcf(c_3891,plain,
! [X0: $i] :
( member(X0,sK3(equal_set_predicate,power_set(sK1)))
| ~ member(X0,sK2(equal_set_predicate,power_set(sK1))) ),
inference(superposition,[status(thm)],[c_3823,c_73]) ).
tcf(c_3898,plain,
! [X0: $i] :
( member(X0,sK2(equal_set_predicate,power_set(sK1)))
| ~ member(X0,sK3(equal_set_predicate,power_set(sK1))) ),
inference(superposition,[status(thm)],[c_3824,c_73]) ).
tcf(c_3909,plain,
! [X0: $i] :
( subset(sK2(equal_set_predicate,power_set(sK1)),X0)
| member(sK8(sK2(equal_set_predicate,power_set(sK1)),X0),sK3(equal_set_predicate,power_set(sK1))) ),
inference(superposition,[status(thm)],[c_72,c_3891]) ).
tcf(c_3939,plain,
( apply(equal_set_predicate,sK6(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate))
| ~ apply(equal_set_predicate,sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))) ),
inference(global_subsumption_just,[status(thm)],[c_867,c_857,c_867,c_1084,c_1087,c_1086,c_1106,c_1120,c_1124]) ).
tcf(c_3941,plain,
~ apply(equal_set_predicate,sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))),
inference(global_subsumption_just,[status(thm)],[c_3939,c_857,c_1084,c_1087,c_1086,c_1106,c_1120,c_1124,c_3939]) ).
tcf(c_3943,plain,
( ~ subset(sK4(equal_set_predicate,power_set(sK1)),sK2(equal_set_predicate,power_set(sK1)))
| ~ subset(sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))) ),
inference(superposition,[status(thm)],[c_319,c_3941]) ).
tcf(c_4045,plain,
! [X0: $i] :
( subset(sK4(equal_set_predicate,power_set(sK1)),X0)
| member(sK8(sK4(equal_set_predicate,power_set(sK1)),X0),sK2(equal_set_predicate,power_set(sK1))) ),
inference(superposition,[status(thm)],[c_3860,c_3898]) ).
tcf(c_4071,plain,
! [X0: $i] :
( subset(sK2(equal_set_predicate,power_set(sK1)),X0)
| member(sK8(sK2(equal_set_predicate,power_set(sK1)),X0),sK4(equal_set_predicate,power_set(sK1))) ),
inference(superposition,[status(thm)],[c_3909,c_3542]) ).
tcf(c_4108,plain,
subset(sK4(equal_set_predicate,power_set(sK1)),sK2(equal_set_predicate,power_set(sK1))),
inference(superposition,[status(thm)],[c_4045,c_71]) ).
tcf(c_4111,plain,
~ subset(sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))),
inference(backward_subsumption_resolution,[status(thm)],[c_3943,c_4108]) ).
tcf(c_4124,plain,
subset(sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))),
inference(superposition,[status(thm)],[c_4071,c_71]) ).
tcf(c_4127,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4124,c_4111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET806+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:04:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 4.40/1.32 % SZS status Started for theBenchmark.p
% 4.40/1.32 % SZS status Theorem for theBenchmark.p
% 4.40/1.32
% 4.40/1.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.40/1.32
% 4.40/1.32 % ------ iProver source info
% 4.40/1.32
% 4.40/1.32 % git: date: 2026-07-19 20:42:38 +0200
% 4.40/1.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.40/1.32 % git: non_committed_changes: false
% 4.40/1.32
% 4.40/1.32 % ------ Parsing...
% 4.40/1.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.40/1.32
% 4.40/1.32 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe_e %
% 4.40/1.32
% 4.40/1.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.40/1.32 % ------ Proving...
% 4.40/1.32 % ------ Problem Properties
% 4.40/1.32
% 4.40/1.32 %
% 4.40/1.32 % clauses 56
% 4.40/1.32 % conjectures 0
% 4.40/1.32 % EPR 4
% 4.40/1.32 % Horn 17
% 4.40/1.32 % unary 0
% 4.40/1.32 % binary 6
% 4.40/1.32 % lits 162
% 4.40/1.32 % lits eq 0
% 4.40/1.32 % fd_pure 0
% 4.40/1.32 % fd_pseudo 0
% 4.40/1.32 % fd_cond 0
% 4.40/1.32 % fd_pseudo_cond 0
% 4.40/1.32 % AC symbols 0
% 4.40/1.32
% 4.40/1.32 % ------ Schedule dynamic 5 is on
% 4.40/1.32
% 4.40/1.32 % ------ no conjectures: strip conj schedule
% 4.40/1.32
% 4.40/1.32 % ------ no equalities: superposition off
% 4.40/1.32
% 4.40/1.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 4.40/1.32
% 4.40/1.32
% 4.40/1.32 % ------
% 4.40/1.32 % Current options:
% 4.40/1.32 % ------
% 4.40/1.32
% 4.40/1.32
% 4.40/1.32 %
% 4.40/1.32
% 4.40/1.32 % ------ Proving...
% 4.40/1.32 %
% 4.40/1.32
% 4.40/1.32 % SZS status Theorem for theBenchmark.p
% 4.40/1.32
% 4.40/1.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.40/1.32
% 4.40/1.32
%------------------------------------------------------------------------------