%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET768+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n026.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 02:48:32 PM UTC 2026
% Result : Theorem 3.83s 11.22s
% Output : CNFRefutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 102 ( 10 unt; 0 def)
% Number of atoms : 367 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 436 ( 171 ~; 176 |; 60 &)
% ( 8 <=>; 19 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 220 ( 0 sgn 202 !; 18 ?; 84 :)
% 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(f15,axiom,
! [X0,X1,X2,X3] :
( member(X3,equivalence_class(X2,X1,X0))
<=> ( apply(X0,X2,X3)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',equivalence_class) ).
fof(f17,conjecture,
! [X0,X1,X2,X3] :
( ( member(X3,X0)
& member(X2,X0)
& equivalence(X1,X0) )
=> ( equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
<=> apply(X1,X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII04) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( member(X3,X0)
& member(X2,X0)
& equivalence(X1,X0) )
=> ( equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
<=> apply(X1,X2,X3) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,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(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(unused_predicate_definition_removal,[],[f19]) ).
fof(f21,plain,
? [X0,X1,X2,X3] :
( member(X3,X0)
& member(X2,X0)
& equivalence(X1,X0)
& ( equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
<~> apply(X1,X2,X3) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f22,plain,
? [X0,X1,X2,X3] :
( member(X3,X0)
& member(X2,X0)
& equivalence(X1,X0)
& ( equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
<~> apply(X1,X2,X3) ) ),
inference(flattening,[],[f21]) ).
fof(f23,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(ennf_transformation,[],[f20]) ).
fof(f24,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(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f26,plain,
? [X0,X1,X2,X3] :
( member(X3,X0)
& member(X2,X0)
& equivalence(X1,X0)
& ( equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
| apply(X1,X2,X3) )
& ( ~ equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
| ~ apply(X1,X2,X3) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f27,plain,
? [X0,X1,X2,X3] :
( member(X3,X0)
& member(X2,X0)
& equivalence(X1,X0)
& ( equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
| apply(X1,X2,X3) )
& ( ~ equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
| ~ apply(X1,X2,X3) ) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
( member(sK3,sK0)
& member(sK2,sK0)
& equivalence(sK1,sK0)
& ( equal_set(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| apply(sK1,sK2,sK3) )
& ( ~ equal_set(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| ~ apply(sK1,sK2,sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f27]) ).
fof(f29,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(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(flattening,[],[f29]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( ( ~ member(X3,equivalence_class(X2,X1,X0))
| ( apply(X0,X2,X3)
& member(X3,X1) ) )
& ( ~ apply(X0,X2,X3)
| ~ member(X3,X1)
| member(X3,equivalence_class(X2,X1,X0)) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( ( ~ member(X3,equivalence_class(X2,X1,X0))
| ( apply(X0,X2,X3)
& member(X3,X1) ) )
& ( ~ apply(X0,X2,X3)
| ~ member(X3,X1)
| member(X3,equivalence_class(X2,X1,X0)) ) ),
inference(flattening,[],[f31]) ).
fof(f33,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(f34,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,[],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK4(X0,X1),X0)
& ~ member(sK4(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f34]) ).
fof(f36,plain,
member(sK3,sK0),
inference(cnf_transformation,[],[f28]) ).
fof(f37,plain,
member(sK2,sK0),
inference(cnf_transformation,[],[f28]) ).
fof(f38,plain,
equivalence(sK1,sK0),
inference(cnf_transformation,[],[f28]) ).
fof(f39,plain,
( equal_set(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| apply(sK1,sK2,sK3) ),
inference(cnf_transformation,[],[f28]) ).
fof(f40,plain,
( ~ equal_set(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| ~ apply(sK1,sK2,sK3) ),
inference(cnf_transformation,[],[f28]) ).
fof(f41,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f42,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f43,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f44,plain,
! [X0,X1,X6,X7,X5] :
( ~ equivalence(X1,X0)
| ~ member(X7,X0)
| ~ member(X6,X0)
| ~ member(X5,X0)
| ~ apply(X1,X6,X7)
| ~ apply(X1,X5,X6)
| apply(X1,X5,X7) ),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
! [X3,X0,X1,X4] :
( ~ equivalence(X1,X0)
| ~ member(X4,X0)
| ~ member(X3,X0)
| ~ apply(X1,X3,X4)
| apply(X1,X4,X3) ),
inference(cnf_transformation,[],[f24]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ equivalence(X1,X0)
| ~ member(X2,X0)
| apply(X1,X2,X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,equivalence_class(X2,X1,X0))
| apply(X0,X2,X3) ),
inference(cnf_transformation,[],[f32]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,equivalence_class(X2,X1,X0))
| member(X3,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f49,plain,
! [X2,X3,X0,X1] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1)
| member(X3,equivalence_class(X2,X1,X0)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f50,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f51,plain,
! [X0,X1] :
( member(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f52,plain,
! [X0,X1] :
( ~ member(sK4(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_49,negated_conjecture,
( ~ apply(sK1,sK2,sK3)
| ~ equal_set(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_50,negated_conjecture,
( apply(sK1,sK2,sK3)
| equal_set(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_51,negated_conjecture,
equivalence(sK1,sK0),
inference(cnf_transformation,[],[f38]) ).
tcf(c_52,negated_conjecture,
member(sK2,sK0),
inference(cnf_transformation,[],[f37]) ).
tcf(c_53,negated_conjecture,
member(sK3,sK0),
inference(cnf_transformation,[],[f36]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ~ equivalence(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X2,X1)
| ~ member(X2,X3)
| ~ member(X1,X3)
| ~ equivalence(X0,X3)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X0,X1,X3)
| ~ member(X3,X4)
| ~ member(X2,X4)
| ~ member(X1,X4)
| ~ equivalence(X0,X4)
| ~ apply(X0,X2,X3)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X2,equivalence_class(X1,X3,X0))
| ~ member(X2,X3)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ member(X0,equivalence_class(X1,X2,X3)) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X3,X1,X0)
| ~ member(X0,equivalence_class(X1,X2,X3)) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_74,plain,
( ~ equal_set(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| ~ apply(sK1,sK2,sK3) ),
inference(prop_impl_just,[status(thm)],[c_49]) ).
tcf(c_75,plain,
( ~ apply(sK1,sK2,sK3)
| ~ equal_set(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)) ),
inference(renaming,[status(thm)],[c_74]) ).
tcf(c_76,plain,
( equal_set(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| apply(sK1,sK2,sK3) ),
inference(prop_impl_just,[status(thm)],[c_50]) ).
tcf(c_77,plain,
( apply(sK1,sK2,sK3)
| equal_set(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)) ),
inference(renaming,[status(thm)],[c_76]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ equal_set(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_55]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_56]) ).
tcf(c_225,plain,
! [X0: $i] :
( apply(sK1,X0,X0)
| ~ member(X0,sK0) ),
inference(resolution,[status(thm)],[c_51,c_57]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i] :
( apply(sK1,X1,X0)
| ~ member(X1,sK0)
| ~ member(X0,sK0)
| ~ apply(sK1,X0,X1) ),
inference(resolution,[status(thm)],[c_51,c_58]) ).
tcf(c_246,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(sK1,X0,X2)
| ~ member(X2,sK0)
| ~ member(X1,sK0)
| ~ member(X0,sK0)
| ~ apply(sK1,X1,X2)
| ~ apply(sK1,X0,X1) ),
inference(resolution,[status(thm)],[c_51,c_59]) ).
tcf(c_280,plain,
( apply(sK1,sK2,sK3)
| subset(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)) ),
inference(resolution,[status(thm)],[c_77,c_80]) ).
tcf(c_287,plain,
( apply(sK1,sK2,sK3)
| subset(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)) ),
inference(resolution,[status(thm)],[c_77,c_78]) ).
tcf(c_294,plain,
( ~ apply(sK1,sK2,sK3)
| ~ subset(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1))
| ~ subset(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)) ),
inference(resolution,[status(thm)],[c_75,c_54]) ).
tcf(c_382,plain,
( apply(sK1,sK3,sK3)
| ~ member(sK3,sK0) ),
inference(instantiation,[status(thm)],[c_225]) ).
tcf(c_387,plain,
! [X0: $i,X1: $i] :
( apply(sK1,sK2,X1)
| ~ member(sK2,sK0)
| ~ member(X1,sK0)
| ~ member(X0,sK0)
| ~ apply(sK1,sK2,X0)
| ~ apply(sK1,X0,X1) ),
inference(instantiation,[status(thm)],[c_246]) ).
tcf(c_390,plain,
( subset(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| member(sK4(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)),equivalence_class(sK2,sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_395,plain,
! [X0: $i,X1: $i] :
( member(sK3,equivalence_class(X1,sK0,X0))
| ~ member(sK3,sK0)
| ~ apply(X0,X1,sK3) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_407,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X2,X0,sK3)
| ~ member(sK3,equivalence_class(X0,X1,X2)) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_411,plain,
! [X0: $i,X1: $i] :
( member(sK3,X1)
| ~ member(sK3,X0)
| ~ subset(X0,X1) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_423,plain,
( member(sK3,equivalence_class(sK3,sK0,sK1))
| ~ member(sK3,sK0)
| ~ apply(sK1,sK3,sK3) ),
inference(instantiation,[status(thm)],[c_395]) ).
tcf(c_425,plain,
! [X0: $i] :
( apply(sK1,sK2,X0)
| ~ member(sK3,sK0)
| ~ member(sK2,sK0)
| ~ member(X0,sK0)
| ~ apply(sK1,sK2,sK3)
| ~ apply(sK1,sK3,X0) ),
inference(instantiation,[status(thm)],[c_387]) ).
tcf(c_434,plain,
( subset(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1))
| member(sK4(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)),equivalence_class(sK3,sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_435,plain,
( subset(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1))
| ~ member(sK4(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)),equivalence_class(sK2,sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK3,equivalence_class(X1,X2,X3))
| ~ member(sK3,X0)
| ~ subset(X0,equivalence_class(X1,X2,X3)) ),
inference(instantiation,[status(thm)],[c_411]) ).
tcf(c_491,plain,
( apply(sK1,sK2,sK3)
| ~ member(sK3,equivalence_class(sK2,sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_407]) ).
tcf(c_505,plain,
( apply(sK1,sK3,sK4(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)))
| ~ member(sK4(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)),equivalence_class(sK3,sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_506,plain,
( member(sK4(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)),sK0)
| ~ member(sK4(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)),equivalence_class(sK3,sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_564,plain,
! [X0: $i] :
( member(sK3,equivalence_class(sK2,sK0,sK1))
| ~ member(sK3,X0)
| ~ subset(X0,equivalence_class(sK2,sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_488]) ).
tcf(c_686,plain,
( member(sK3,equivalence_class(sK2,sK0,sK1))
| ~ member(sK3,equivalence_class(sK3,sK0,sK1))
| ~ subset(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_564]) ).
tcf(c_692,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(equivalence_class(X1,X2,X0),X3)
| apply(X0,X1,sK4(equivalence_class(X1,X2,X0),X3)) ),
inference(superposition,[status(thm)],[c_64,c_62]) ).
tcf(c_856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X2,equivalence_class(X1,X3,X0))
| ~ member(sK4(X2,equivalence_class(X1,X3,X0)),X3)
| ~ apply(X0,X1,sK4(X2,equivalence_class(X1,X3,X0))) ),
inference(superposition,[status(thm)],[c_60,c_63]) ).
tcf(c_1006,plain,
! [X0: $i,X1: $i] :
( member(sK4(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)),equivalence_class(X1,sK0,X0))
| ~ member(sK4(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)),sK0)
| ~ apply(X0,X1,sK4(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_1010,plain,
( apply(sK1,sK2,sK4(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)))
| ~ member(sK3,sK0)
| ~ member(sK2,sK0)
| ~ apply(sK1,sK2,sK3)
| ~ member(sK4(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)),sK0)
| ~ apply(sK1,sK3,sK4(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_425]) ).
tcf(c_1040,plain,
apply(sK1,sK2,sK3),
inference(global_subsumption_just,[status(thm)],[c_287,c_53,c_280,c_382,c_423,c_491,c_686]) ).
tcf(c_1043,plain,
( apply(sK1,sK3,sK2)
| ~ member(sK3,sK0)
| ~ member(sK2,sK0) ),
inference(superposition,[status(thm)],[c_1040,c_233]) ).
tcf(c_1044,plain,
apply(sK1,sK3,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_1043,c_53,c_52]) ).
tcf(c_1071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( member(sK4(equivalence_class(X0,X1,X2),equivalence_class(X3,X4,X5)),X1)
| ~ member(sK4(equivalence_class(X0,X1,X2),equivalence_class(X3,X4,X5)),equivalence_class(X0,X1,X2)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_1077,plain,
! [X0: $i] :
( apply(sK1,sK3,X0)
| ~ member(sK3,sK0)
| ~ member(sK2,sK0)
| ~ member(X0,sK0)
| ~ apply(sK1,sK2,X0) ),
inference(superposition,[status(thm)],[c_1044,c_246]) ).
tcf(c_1079,plain,
! [X0: $i] :
( apply(sK1,sK3,X0)
| ~ member(X0,sK0)
| ~ apply(sK1,sK2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1077,c_53,c_52]) ).
tcf(c_1325,plain,
! [X0: $i,X1: $i] :
( subset(equivalence_class(sK2,X0,sK1),X1)
| apply(sK1,sK3,sK4(equivalence_class(sK2,X0,sK1),X1))
| ~ member(sK4(equivalence_class(sK2,X0,sK1),X1),sK0) ),
inference(superposition,[status(thm)],[c_692,c_1079]) ).
tcf(c_1423,plain,
( member(sK4(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)),equivalence_class(sK2,sK0,sK1))
| ~ member(sK4(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)),sK0)
| ~ apply(sK1,sK2,sK4(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_1006]) ).
tcf(c_1517,plain,
~ subset(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)),
inference(global_subsumption_just,[status(thm)],[c_294,c_53,c_52,c_280,c_294,c_382,c_423,c_435,c_434,c_491,c_506,c_505,c_686,c_1010,c_1423]) ).
tcf(c_2319,plain,
( member(sK4(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)),sK0)
| ~ member(sK4(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)),equivalence_class(sK2,sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_1071]) ).
tcf(c_4080,plain,
! [X0: $i,X1: $i] :
( subset(equivalence_class(sK2,X0,sK1),equivalence_class(sK3,X1,sK1))
| ~ member(sK4(equivalence_class(sK2,X0,sK1),equivalence_class(sK3,X1,sK1)),sK0)
| ~ member(sK4(equivalence_class(sK2,X0,sK1),equivalence_class(sK3,X1,sK1)),X1) ),
inference(superposition,[status(thm)],[c_1325,c_856]) ).
tcf(c_4136,plain,
( subset(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| ~ member(sK4(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_4080]) ).
tcf(c_4137,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4136,c_2319,c_1517,c_390]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET768+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/10.39 % Computer : n026.cluster.edu
% 0.12/10.39 % Model : x86_64 x86_64
% 0.12/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.39 % Memory : 8046.5625MB
% 0.12/10.39 % OS : Linux 6.8.0-71-generic
% 0.12/10.39 % CPULimit : 300
% 0.12/10.39 % WCLimit : 300
% 0.12/10.39 % DateTime : Thu Sep 24 11:57:06 UTC 2026
% 0.12/10.39 % CPUTime :
% 0.12/10.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/10.43 Running first-order theorem proving
% 0.15/10.43 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
% 0.15/10.44
% 0.15/10.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.44
% 0.15/10.44 % Detected problem language: tptp
% 0.15/10.45 % Proving...
% 3.83/11.22 % SZS status Started for theBenchmark.p
% 3.83/11.22 % SZS status Theorem for theBenchmark.p
% 3.83/11.22
% 3.83/11.22 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.83/11.22
% 3.83/11.22 % ------ iProver source info
% 3.83/11.22
% 3.83/11.22 % git: date: 2026-07-19 20:42:38 +0200
% 3.83/11.22 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.83/11.22 % git: non_committed_changes: false
% 3.83/11.22
% 3.83/11.22 % ------ Parsing...
% 3.83/11.22 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.83/11.22
% 3.83/11.22 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.83/11.22
% 3.83/11.22 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.83/11.22 % ------ Proving...
% 3.83/11.22 % ------ Problem Properties
% 3.83/11.22
% 3.83/11.22 %
% 3.83/11.22 % clauses 14
% 3.83/11.22 % conjectures 2
% 3.83/11.22 % EPR 6
% 3.83/11.22 % Horn 11
% 3.83/11.22 % unary 2
% 3.83/11.22 % binary 7
% 3.83/11.22 % lits 35
% 3.83/11.22 % lits eq 0
% 3.83/11.22 % fd_pure 0
% 3.83/11.23 % fd_pseudo 0
% 3.83/11.23 % fd_cond 0
% 3.83/11.23 % fd_pseudo_cond 0
% 3.83/11.23 % AC symbols 0
% 3.83/11.23
% 3.83/11.23 % ------ Schedule dynamic 5 is on
% 3.83/11.23
% 3.83/11.23 % ------ no equalities: superposition off
% 3.83/11.23
% 3.83/11.23 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.83/11.23
% 3.83/11.23
% 3.83/11.23 % ------
% 3.83/11.23 % Current options:
% 3.83/11.23 % ------
% 3.83/11.23
% 3.83/11.23
% 3.83/11.23 %
% 3.83/11.23
% 3.83/11.23 % ------ Proving...
% 3.83/11.23 %
% 3.83/11.23
% 3.83/11.23 % SZS status Theorem for theBenchmark.p
% 3.83/11.23
% 3.83/11.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.83/11.23
% 3.83/11.23
%------------------------------------------------------------------------------