%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET769+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 : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:48:32 PM UTC 2026
% Result : Theorem 49.11s 15.57s
% Output : CNFRefutation 49.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 164 ( 11 unt; 0 def)
% Number of atoms : 603 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 752 ( 313 ~; 341 |; 67 &)
% ( 10 <=>; 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 : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 364 ( 0 sgn 343 !; 21 ?; 206 :)
% 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(f12,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ~ ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',disjoint) ).
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))
<=> ~ disjoint(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII05) ).
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))
<=> ~ disjoint(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) ) ),
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))
<~> ~ disjoint(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) ) ),
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))
<~> ~ disjoint(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( disjoint(X0,X1)
<=> ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f12]) ).
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(ennf_transformation,[],[f20]) ).
fof(f25,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,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
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))
| ~ disjoint(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) )
& ( ~ equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
| disjoint(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f28,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))
| ~ disjoint(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) )
& ( ~ equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
| disjoint(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) ) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
( member(sK3,sK0)
& member(sK2,sK0)
& equivalence(sK1,sK0)
& ( equal_set(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| ~ disjoint(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)) )
& ( ~ equal_set(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| disjoint(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f28]) ).
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(f32,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) )
& ( ? [X2] :
( member(X2,X1)
& member(X2,X0) )
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f33,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] :
( ~ member(X3,X1)
| ~ member(X3,X0) ) )
& ( ? [X2] :
( member(X2,X1)
& member(X2,X0) )
| disjoint(X0,X1) ) ),
inference(rectify,[],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] :
( ~ member(X3,X1)
| ~ member(X3,X0) ) )
& ( ( member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) )
| disjoint(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f33]) ).
fof(f35,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(f36,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,[],[f35]) ).
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,[],[f26]) ).
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(sK5(X0,X1),X0)
& ~ member(sK5(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f38]) ).
fof(f40,plain,
member(sK3,sK0),
inference(cnf_transformation,[],[f29]) ).
fof(f41,plain,
member(sK2,sK0),
inference(cnf_transformation,[],[f29]) ).
fof(f42,plain,
equivalence(sK1,sK0),
inference(cnf_transformation,[],[f29]) ).
fof(f43,plain,
( equal_set(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| ~ disjoint(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f44,plain,
( ~ equal_set(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| disjoint(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f45,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f47,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f48,plain,
! [X3,X0,X1] :
( ~ disjoint(X0,X1)
| ~ member(X3,X1)
| ~ member(X3,X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f49,plain,
! [X0,X1] :
( member(sK4(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
! [X0,X1] :
( member(sK4(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f51,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,[],[f25]) ).
fof(f52,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,[],[f25]) ).
fof(f53,plain,
! [X2,X0,X1] :
( ~ equivalence(X1,X0)
| ~ member(X2,X0)
| apply(X1,X2,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,equivalence_class(X2,X1,X0))
| apply(X0,X2,X3) ),
inference(cnf_transformation,[],[f36]) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,equivalence_class(X2,X1,X0))
| member(X3,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1)
| member(X3,equivalence_class(X2,X1,X0)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f57,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f58,plain,
! [X0,X1] :
( member(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f59,plain,
! [X0,X1] :
( ~ member(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_49,negated_conjecture,
( disjoint(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| ~ equal_set(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_50,negated_conjecture,
( equal_set(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| ~ disjoint(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_51,negated_conjecture,
equivalence(sK1,sK0),
inference(cnf_transformation,[],[f42]) ).
tcf(c_52,negated_conjecture,
member(sK2,sK0),
inference(cnf_transformation,[],[f41]) ).
tcf(c_53,negated_conjecture,
member(sK3,sK0),
inference(cnf_transformation,[],[f40]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| member(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ~ equivalence(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_61,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,[],[f52]) ).
tcf(c_62,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,[],[f51]) ).
tcf(c_63,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,[],[f56]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ member(X0,equivalence_class(X1,X2,X3)) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X3,X1,X0)
| ~ member(X0,equivalence_class(X1,X2,X3)) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_79,plain,
( ~ disjoint(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| equal_set(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)) ),
inference(prop_impl_just,[status(thm)],[c_50]) ).
tcf(c_80,plain,
( equal_set(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| ~ disjoint(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)) ),
inference(renaming,[status(thm)],[c_79]) ).
tcf(c_81,plain,
( disjoint(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| ~ equal_set(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)) ),
inference(prop_impl_just,[status(thm)],[c_49]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_56]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( member(sK4(X0,X1),X0)
| disjoint(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_57]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| member(sK4(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_95]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( member(sK4(X0,X1),X1)
| disjoint(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_58]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| member(sK4(X0,X1),X1) ),
inference(renaming,[status(thm)],[c_97]) ).
tcf(c_257,plain,
! [X0: $i] :
( apply(sK1,X0,X0)
| ~ member(X0,sK0) ),
inference(resolution,[status(thm)],[c_51,c_60]) ).
tcf(c_265,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_61]) ).
tcf(c_278,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_62]) ).
tcf(c_342,plain,
( equal_set(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| member(sK4(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)),equivalence_class(sK3,sK0,sK1)) ),
inference(resolution,[status(thm)],[c_80,c_98]) ).
tcf(c_349,plain,
( equal_set(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(resolution,[status(thm)],[c_80,c_96]) ).
tcf(c_372,plain,
( subset(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1))
| ~ disjoint(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)) ),
inference(resolution,[status(thm)],[c_80,c_85]) ).
tcf(c_386,plain,
( disjoint(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| ~ 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_81,c_54]) ).
tcf(c_649,plain,
( apply(sK1,sK3,sK3)
| ~ member(sK3,sK0) ),
inference(instantiation,[status(thm)],[c_257]) ).
tcf(c_650,plain,
! [X0: $i] :
( apply(sK1,X0,sK2)
| ~ member(sK2,sK0)
| ~ member(X0,sK0)
| ~ apply(sK1,sK2,X0) ),
inference(instantiation,[status(thm)],[c_265]) ).
tcf(c_652,plain,
! [X0: $i] :
( apply(sK1,X0,sK3)
| ~ member(sK3,sK0)
| ~ member(X0,sK0)
| ~ apply(sK1,sK3,X0) ),
inference(instantiation,[status(thm)],[c_265]) ).
tcf(c_654,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_278]) ).
tcf(c_655,plain,
! [X0: $i,X1: $i] :
( apply(sK1,sK3,X1)
| ~ member(sK3,sK0)
| ~ member(X1,sK0)
| ~ member(X0,sK0)
| ~ apply(sK1,sK3,X0)
| ~ apply(sK1,X0,X1) ),
inference(instantiation,[status(thm)],[c_278]) ).
tcf(c_662,plain,
! [X0: $i] :
( disjoint(X0,sK0)
| member(sK4(X0,sK0),sK0) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_667,plain,
( subset(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| member(sK5(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)),equivalence_class(sK2,sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_669,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( disjoint(equivalence_class(X0,X1,X2),X3)
| member(sK4(equivalence_class(X0,X1,X2),X3),equivalence_class(X0,X1,X2)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_672,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK4(X0,equivalence_class(X1,X2,X3)),X2)
| ~ member(sK4(X0,equivalence_class(X1,X2,X3)),equivalence_class(X1,X2,X3)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_686,plain,
! [X0: $i,X1: $i] :
( member(sK3,equivalence_class(X1,sK0,X0))
| ~ member(sK3,sK0)
| ~ apply(X0,X1,sK3) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_697,plain,
! [X0: $i,X1: $i] :
( ~ member(sK3,X1)
| ~ member(sK3,X0)
| ~ disjoint(X0,X1) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_704,plain,
! [X0: $i,X1: $i] :
( member(sK3,X1)
| ~ member(sK3,X0)
| ~ subset(X0,X1) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_719,plain,
( apply(sK1,sK3,sK2)
| ~ member(sK3,sK0)
| ~ member(sK2,sK0)
| ~ apply(sK1,sK2,sK3) ),
inference(instantiation,[status(thm)],[c_650]) ).
tcf(c_735,plain,
( member(sK3,equivalence_class(sK3,sK0,sK1))
| ~ member(sK3,sK0)
| ~ apply(sK1,sK3,sK3) ),
inference(instantiation,[status(thm)],[c_686]) ).
tcf(c_745,plain,
! [X0: $i] :
( apply(sK1,sK3,X0)
| ~ member(sK3,sK0)
| ~ member(sK2,sK0)
| ~ member(X0,sK0)
| ~ apply(sK1,sK3,sK2)
| ~ apply(sK1,sK2,X0) ),
inference(instantiation,[status(thm)],[c_655]) ).
tcf(c_917,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X1)
| ~ disjoint(X1,X2)
| ~ member(sK4(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_58,c_59]) ).
tcf(c_946,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X2,X0,sK4(equivalence_class(X0,X1,X2),X3))
| ~ member(sK4(equivalence_class(X0,X1,X2),X3),equivalence_class(X0,X1,X2)) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X3,X1,sK4(X0,equivalence_class(X1,X2,X3)))
| ~ member(sK4(X0,equivalence_class(X1,X2,X3)),equivalence_class(X1,X2,X3)) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_970,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(sK1,sK4(equivalence_class(X0,sK0,X1),X2),sK3)
| ~ member(sK3,sK0)
| ~ member(sK4(equivalence_class(X0,sK0,X1),X2),sK0)
| ~ apply(sK1,sK3,sK4(equivalence_class(X0,sK0,X1),X2)) ),
inference(instantiation,[status(thm)],[c_652]) ).
tcf(c_993,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK4(X0,equivalence_class(X1,sK0,X2)),sK0)
| ~ member(sK4(X0,equivalence_class(X1,sK0,X2)),equivalence_class(X1,sK0,X2)) ),
inference(instantiation,[status(thm)],[c_672]) ).
tcf(c_1012,plain,
! [X0: $i] : subset(X0,X0),
inference(superposition,[status(thm)],[c_67,c_66]) ).
tcf(c_1013,plain,
subset(sK0,sK0),
inference(instantiation,[status(thm)],[c_1012]) ).
tcf(c_1025,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(equivalence_class(X0,X1,X2),X3)
| member(sK5(equivalence_class(X0,X1,X2),X3),X1) ),
inference(superposition,[status(thm)],[c_67,c_64]) ).
tcf(c_1039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( disjoint(equivalence_class(X0,X1,X2),X3)
| member(sK4(equivalence_class(X0,X1,X2),X3),X1) ),
inference(superposition,[status(thm)],[c_57,c_64]) ).
tcf(c_1059,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(sK1,sK2,X2)
| ~ member(sK2,sK0)
| ~ member(X2,sK0)
| ~ member(sK4(X0,X1),sK0)
| ~ apply(sK1,sK2,sK4(X0,X1))
| ~ apply(sK1,sK4(X0,X1),X2) ),
inference(instantiation,[status(thm)],[c_654]) ).
tcf(c_1070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( disjoint(equivalence_class(X1,X2,X0),X3)
| apply(X0,X1,sK4(equivalence_class(X1,X2,X0),X3)) ),
inference(superposition,[status(thm)],[c_57,c_65]) ).
tcf(c_1072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(equivalence_class(X1,X2,X0),X3)
| apply(X0,X1,sK5(equivalence_class(X1,X2,X0),X3)) ),
inference(superposition,[status(thm)],[c_67,c_65]) ).
tcf(c_1280,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_704]) ).
tcf(c_1674,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ member(sK3,X3)
| ~ member(sK3,equivalence_class(X0,X1,X2))
| ~ disjoint(equivalence_class(X0,X1,X2),X3) ),
inference(instantiation,[status(thm)],[c_697]) ).
tcf(c_1925,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_917]) ).
tcf(c_2109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X2,equivalence_class(X1,X3,X0))
| ~ member(sK5(X2,equivalence_class(X1,X3,X0)),X3)
| ~ apply(X0,X1,sK5(X2,equivalence_class(X1,X3,X0))) ),
inference(superposition,[status(thm)],[c_63,c_66]) ).
tcf(c_2438,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( disjoint(equivalence_class(X2,X1,X3),X0)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_1039,c_917]) ).
tcf(c_2499,plain,
! [X0: $i,X1: $i] :
( apply(sK1,sK2,sK3)
| ~ member(sK3,sK0)
| ~ member(sK2,sK0)
| ~ member(sK4(X0,X1),sK0)
| ~ apply(sK1,sK2,sK4(X0,X1))
| ~ apply(sK1,sK4(X0,X1),sK3) ),
inference(instantiation,[status(thm)],[c_1059]) ).
tcf(c_2702,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( disjoint(X0,equivalence_class(X2,X1,X3))
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_2438,c_1925]) ).
tcf(c_2964,plain,
( ~ member(sK3,equivalence_class(sK3,sK0,sK1))
| ~ member(sK3,equivalence_class(sK2,sK0,sK1))
| ~ disjoint(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_1674]) ).
tcf(c_3366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(equivalence_class(X2,X0,X3),X4)
| member(sK5(equivalence_class(X2,X0,X3),X4),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_1025,c_68]) ).
tcf(c_3525,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(sK1,X0,X3)
| disjoint(equivalence_class(X0,X1,sK1),X2)
| ~ member(X3,sK0)
| ~ member(X0,sK0)
| ~ member(sK4(equivalence_class(X0,X1,sK1),X2),sK0)
| ~ apply(sK1,sK4(equivalence_class(X0,X1,sK1),X2),X3) ),
inference(superposition,[status(thm)],[c_1070,c_278]) ).
tcf(c_3942,plain,
! [X0: $i] :
( apply(sK1,sK2,sK4(equivalence_class(sK2,X0,sK1),sK0))
| ~ member(sK4(equivalence_class(sK2,X0,sK1),sK0),equivalence_class(sK2,X0,sK1)) ),
inference(instantiation,[status(thm)],[c_946]) ).
tcf(c_3946,plain,
( apply(sK1,sK2,sK4(equivalence_class(sK2,sK0,sK1),sK0))
| ~ member(sK4(equivalence_class(sK2,sK0,sK1),sK0),equivalence_class(sK2,sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_3942]) ).
tcf(c_3980,plain,
! [X0: $i,X1: $i] :
( apply(sK1,sK2,sK4(equivalence_class(sK2,X0,sK1),X1))
| ~ member(sK4(equivalence_class(sK2,X0,sK1),X1),equivalence_class(sK2,X0,sK1)) ),
inference(instantiation,[status(thm)],[c_946]) ).
tcf(c_4295,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(sK1,sK4(equivalence_class(X0,sK0,X1),equivalence_class(sK3,X2,sK1)),sK3)
| ~ member(sK3,sK0)
| ~ member(sK4(equivalence_class(X0,sK0,X1),equivalence_class(sK3,X2,sK1)),sK0)
| ~ apply(sK1,sK3,sK4(equivalence_class(X0,sK0,X1),equivalence_class(sK3,X2,sK1))) ),
inference(instantiation,[status(thm)],[c_970]) ).
tcf(c_4314,plain,
! [X0: $i,X1: $i] :
( apply(sK1,sK3,sK4(X0,equivalence_class(sK3,X1,sK1)))
| ~ member(sK4(X0,equivalence_class(sK3,X1,sK1)),equivalence_class(sK3,X1,sK1)) ),
inference(instantiation,[status(thm)],[c_952]) ).
tcf(c_4759,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(equivalence_class(X0,X1,sK1),X2)
| apply(sK1,sK5(equivalence_class(X0,X1,sK1),X2),X0)
| ~ member(X0,sK0)
| ~ member(sK5(equivalence_class(X0,X1,sK1),X2),sK0) ),
inference(superposition,[status(thm)],[c_1072,c_265]) ).
tcf(c_5024,plain,
! [X0: $i,X1: $i] :
( member(sK3,equivalence_class(sK2,X1,sK1))
| ~ member(sK3,X0)
| ~ subset(X0,equivalence_class(sK2,X1,sK1)) ),
inference(instantiation,[status(thm)],[c_1280]) ).
tcf(c_5556,plain,
! [X0: $i] :
( disjoint(equivalence_class(sK2,sK0,sK1),X0)
| member(sK4(equivalence_class(sK2,sK0,sK1),X0),equivalence_class(sK2,sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_669]) ).
tcf(c_5557,plain,
( disjoint(equivalence_class(sK2,sK0,sK1),sK0)
| member(sK4(equivalence_class(sK2,sK0,sK1),sK0),equivalence_class(sK2,sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_5556]) ).
tcf(c_5664,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(equivalence_class(X0,X1,sK1),X2)
| apply(sK1,sK5(equivalence_class(X0,X1,sK1),X2),X3)
| ~ member(X3,sK0)
| ~ member(X0,sK0)
| ~ apply(sK1,X0,X3)
| ~ member(sK5(equivalence_class(X0,X1,sK1),X2),sK0) ),
inference(superposition,[status(thm)],[c_4759,c_278]) ).
tcf(c_6237,plain,
! [X0: $i] :
( disjoint(equivalence_class(sK2,X0,sK1),sK0)
| member(sK4(equivalence_class(sK2,X0,sK1),sK0),sK0) ),
inference(instantiation,[status(thm)],[c_662]) ).
tcf(c_6238,plain,
( disjoint(equivalence_class(sK2,sK0,sK1),sK0)
| member(sK4(equivalence_class(sK2,sK0,sK1),sK0),sK0) ),
inference(instantiation,[status(thm)],[c_6237]) ).
tcf(c_6357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(equivalence_class(X0,X1,sK1),X2)
| apply(sK1,X3,sK5(equivalence_class(X0,X1,sK1),X2))
| ~ member(X3,sK0)
| ~ member(X0,sK0)
| ~ apply(sK1,X0,X3)
| ~ member(sK5(equivalence_class(X0,X1,sK1),X2),sK0) ),
inference(superposition,[status(thm)],[c_5664,c_265]) ).
tcf(c_6694,plain,
! [X0: $i] :
( member(sK4(X0,equivalence_class(sK3,sK0,sK1)),sK0)
| ~ member(sK4(X0,equivalence_class(sK3,sK0,sK1)),equivalence_class(sK3,sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_993]) ).
tcf(c_7385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subset(equivalence_class(X0,X4,sK1),X5)
| disjoint(equivalence_class(X1,X2,sK1),X3)
| apply(sK1,X1,sK5(equivalence_class(X0,X4,sK1),X5))
| ~ member(X1,sK0)
| ~ member(X0,sK0)
| ~ member(sK5(equivalence_class(X0,X4,sK1),X5),sK0)
| ~ member(sK4(equivalence_class(X1,X2,sK1),X3),sK0)
| ~ apply(sK1,X0,sK4(equivalence_class(X1,X2,sK1),X3)) ),
inference(superposition,[status(thm)],[c_6357,c_3525]) ).
tcf(c_14707,plain,
! [X0: $i,X1: $i] :
( apply(sK1,sK2,sK3)
| ~ member(sK3,sK0)
| ~ member(sK2,sK0)
| ~ member(sK4(X0,equivalence_class(sK3,X1,sK1)),sK0)
| ~ apply(sK1,sK2,sK4(X0,equivalence_class(sK3,X1,sK1)))
| ~ apply(sK1,sK4(X0,equivalence_class(sK3,X1,sK1)),sK3) ),
inference(instantiation,[status(thm)],[c_2499]) ).
tcf(c_17886,plain,
! [X0: $i,X1: $i] :
( apply(sK1,sK3,sK4(equivalence_class(sK2,X0,sK1),equivalence_class(sK3,X1,sK1)))
| ~ member(sK4(equivalence_class(sK2,X0,sK1),equivalence_class(sK3,X1,sK1)),equivalence_class(sK3,X1,sK1)) ),
inference(instantiation,[status(thm)],[c_4314]) ).
tcf(c_17887,plain,
( apply(sK1,sK3,sK4(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)))
| ~ member(sK4(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)),equivalence_class(sK3,sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_17886]) ).
tcf(c_17975,plain,
! [X0: $i] :
( apply(sK1,sK2,sK3)
| ~ member(sK3,sK0)
| ~ member(sK2,sK0)
| ~ member(sK4(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,X0,sK1)),sK0)
| ~ apply(sK1,sK2,sK4(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,X0,sK1)))
| ~ apply(sK1,sK4(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,X0,sK1)),sK3) ),
inference(instantiation,[status(thm)],[c_14707]) ).
tcf(c_17978,plain,
( apply(sK1,sK2,sK3)
| ~ member(sK3,sK0)
| ~ member(sK2,sK0)
| ~ member(sK4(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)),sK0)
| ~ apply(sK1,sK2,sK4(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)))
| ~ apply(sK1,sK4(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)),sK3) ),
inference(instantiation,[status(thm)],[c_17975]) ).
tcf(c_17982,plain,
! [X0: $i,X1: $i] :
( apply(sK1,sK2,sK4(equivalence_class(sK2,X0,sK1),equivalence_class(sK3,X1,sK1)))
| ~ member(sK4(equivalence_class(sK2,X0,sK1),equivalence_class(sK3,X1,sK1)),equivalence_class(sK2,X0,sK1)) ),
inference(instantiation,[status(thm)],[c_3980]) ).
tcf(c_17983,plain,
( apply(sK1,sK2,sK4(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_17982]) ).
tcf(c_20218,plain,
! [X0: $i] :
( apply(sK1,sK4(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,X0,sK1)),sK3)
| ~ member(sK3,sK0)
| ~ member(sK4(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,X0,sK1)),sK0)
| ~ apply(sK1,sK3,sK4(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,X0,sK1))) ),
inference(instantiation,[status(thm)],[c_4295]) ).
tcf(c_20220,plain,
( apply(sK1,sK4(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)),sK3)
| ~ member(sK3,sK0)
| ~ member(sK4(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)),sK0)
| ~ apply(sK1,sK3,sK4(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_20218]) ).
tcf(c_20405,plain,
! [X0: $i] :
( member(sK4(equivalence_class(sK2,X0,sK1),equivalence_class(sK3,sK0,sK1)),sK0)
| ~ member(sK4(equivalence_class(sK2,X0,sK1),equivalence_class(sK3,sK0,sK1)),equivalence_class(sK3,sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_6694]) ).
tcf(c_20409,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(sK3,sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_20405]) ).
tcf(c_20961,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_5024]) ).
tcf(c_23544,plain,
~ disjoint(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)),
inference(global_subsumption_just,[status(thm)],[c_372,c_53,c_372,c_649,c_735,c_2964,c_20961]) ).
tcf(c_23547,plain,
~ disjoint(equivalence_class(sK2,sK0,sK1),sK0),
inference(superposition,[status(thm)],[c_2702,c_23544]) ).
tcf(c_32849,plain,
! [X0: $i] :
( apply(sK1,sK3,sK4(X0,sK0))
| ~ member(sK3,sK0)
| ~ member(sK2,sK0)
| ~ apply(sK1,sK3,sK2)
| ~ member(sK4(X0,sK0),sK0)
| ~ apply(sK1,sK2,sK4(X0,sK0)) ),
inference(instantiation,[status(thm)],[c_745]) ).
tcf(c_36310,plain,
( apply(sK1,sK2,sK5(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)))
| ~ member(sK5(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)),equivalence_class(sK2,sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_42684,plain,
! [X0: $i] :
( apply(sK1,sK3,sK4(equivalence_class(sK2,X0,sK1),sK0))
| ~ member(sK3,sK0)
| ~ member(sK2,sK0)
| ~ apply(sK1,sK3,sK2)
| ~ member(sK4(equivalence_class(sK2,X0,sK1),sK0),sK0)
| ~ apply(sK1,sK2,sK4(equivalence_class(sK2,X0,sK1),sK0)) ),
inference(instantiation,[status(thm)],[c_32849]) ).
tcf(c_42685,plain,
( apply(sK1,sK3,sK4(equivalence_class(sK2,sK0,sK1),sK0))
| ~ member(sK3,sK0)
| ~ member(sK2,sK0)
| ~ apply(sK1,sK3,sK2)
| ~ member(sK4(equivalence_class(sK2,sK0,sK1),sK0),sK0)
| ~ apply(sK1,sK2,sK4(equivalence_class(sK2,sK0,sK1),sK0)) ),
inference(instantiation,[status(thm)],[c_42684]) ).
tcf(c_44569,plain,
( apply(sK1,sK3,sK5(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)))
| ~ member(sK3,sK0)
| ~ member(sK2,sK0)
| ~ apply(sK1,sK3,sK2)
| ~ member(sK5(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)),sK0)
| ~ apply(sK1,sK2,sK5(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_745]) ).
tcf(c_136536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(equivalence_class(sK3,X3,sK1),X4)
| disjoint(equivalence_class(X0,X1,sK1),X2)
| apply(sK1,X0,sK5(equivalence_class(sK3,X3,sK1),X4))
| ~ member(sK3,sK0)
| ~ member(X0,sK0)
| ~ member(sK5(equivalence_class(sK3,X3,sK1),X4),sK0)
| ~ member(sK4(equivalence_class(X0,X1,sK1),X2),sK0)
| ~ apply(sK1,sK3,sK4(equivalence_class(X0,X1,sK1),X2)) ),
inference(instantiation,[status(thm)],[c_7385]) ).
tcf(c_137349,plain,
! [X0: $i] :
( subset(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1))
| member(sK5(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)),X0)
| ~ subset(sK0,X0) ),
inference(instantiation,[status(thm)],[c_3366]) ).
tcf(c_137350,plain,
( subset(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1))
| member(sK5(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)),sK0)
| ~ subset(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_137349]) ).
tcf(c_137511,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X1,equivalence_class(X0,X2,sK1))
| ~ member(sK5(X1,equivalence_class(X0,X2,sK1)),X2)
| ~ apply(sK1,X0,sK5(X1,equivalence_class(X0,X2,sK1))) ),
inference(instantiation,[status(thm)],[c_2109]) ).
tcf(c_138033,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(equivalence_class(X0,X1,sK1),X2)
| subset(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1))
| apply(sK1,X0,sK5(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)))
| ~ member(sK3,sK0)
| ~ member(X0,sK0)
| ~ member(sK4(equivalence_class(X0,X1,sK1),X2),sK0)
| ~ apply(sK1,sK3,sK4(equivalence_class(X0,X1,sK1),X2))
| ~ member(sK5(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_136536]) ).
tcf(c_139453,plain,
! [X0: $i] :
( subset(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| member(sK5(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)),X0)
| ~ subset(sK0,X0) ),
inference(instantiation,[status(thm)],[c_3366]) ).
tcf(c_139454,plain,
( subset(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| member(sK5(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)),sK0)
| ~ subset(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_139453]) ).
tcf(c_152354,plain,
( subset(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))
| ~ member(sK5(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1)),sK0)
| ~ apply(sK1,sK3,sK5(equivalence_class(sK2,sK0,sK1),equivalence_class(sK3,sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_137511]) ).
tcf(c_165529,plain,
( subset(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1))
| ~ member(sK5(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)),sK0)
| ~ apply(sK1,sK2,sK5(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_137511]) ).
tcf(c_212582,plain,
! [X0: $i,X1: $i] :
( disjoint(equivalence_class(sK2,X0,sK1),X1)
| subset(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1))
| apply(sK1,sK2,sK5(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)))
| ~ member(sK3,sK0)
| ~ member(sK2,sK0)
| ~ member(sK4(equivalence_class(sK2,X0,sK1),X1),sK0)
| ~ apply(sK1,sK3,sK4(equivalence_class(sK2,X0,sK1),X1))
| ~ member(sK5(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_138033]) ).
tcf(c_212583,plain,
( disjoint(equivalence_class(sK2,sK0,sK1),sK0)
| subset(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1))
| apply(sK1,sK2,sK5(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)))
| ~ member(sK3,sK0)
| ~ member(sK2,sK0)
| ~ member(sK4(equivalence_class(sK2,sK0,sK1),sK0),sK0)
| ~ apply(sK1,sK3,sK4(equivalence_class(sK2,sK0,sK1),sK0))
| ~ member(sK5(equivalence_class(sK3,sK0,sK1),equivalence_class(sK2,sK0,sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_212582]) ).
tcf(c_216957,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_212583,c_165529,c_152354,c_139454,c_137350,c_44569,c_42685,c_36310,c_23547,c_23544,c_20409,c_20220,c_17983,c_17978,c_17887,c_6238,c_5557,c_3946,c_1013,c_719,c_667,c_386,c_349,c_342,c_49,c_52,c_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET769+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/6.21 % Computer : n007.cluster.edu
% 0.10/6.21 % Model : x86_64 x86_64
% 0.10/6.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/6.21 % Memory : 8046.5625MB
% 0.10/6.21 % OS : Linux 6.8.0-71-generic
% 0.10/6.21 % CPULimit : 300
% 0.10/6.21 % WCLimit : 300
% 0.10/6.21 % DateTime : Thu Sep 24 11:52:59 UTC 2026
% 0.10/6.21 % CPUTime :
% 0.10/6.21 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/6.24 Running first-order theorem proving
% 0.10/6.24 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
% 0.10/6.25
% 0.10/6.25 % ======== iProver multi-core TPTP/SMT =========
% 0.10/6.25
% 0.10/6.26 % Detected problem language: tptp
% 0.10/6.27 % Proving...
% 49.11/15.57 % SZS status Started for theBenchmark.p
% 49.11/15.57 % SZS status Theorem for theBenchmark.p
% 49.11/15.57
% 49.11/15.57 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 49.11/15.57
% 49.11/15.57 % ------ iProver source info
% 49.11/15.57
% 49.11/15.57 % git: date: 2026-07-19 20:42:38 +0200
% 49.11/15.57 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 49.11/15.57 % git: non_committed_changes: false
% 49.11/15.57
% 49.11/15.57 % ------ Parsing...
% 49.11/15.57 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 49.11/15.57
% 49.11/15.57 % ------ 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 %
% 49.11/15.57
% 49.11/15.57 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 49.11/15.57 % ------ Proving...
% 49.11/15.57 % ------ Problem Properties
% 49.11/15.57
% 49.11/15.57 %
% 49.11/15.57 % clauses 17
% 49.11/15.57 % conjectures 2
% 49.11/15.57 % EPR 7
% 49.11/15.57 % Horn 14
% 49.11/15.57 % unary 2
% 49.11/15.57 % binary 9
% 49.11/15.57 % lits 42
% 49.11/15.57 % lits eq 0
% 49.11/15.57 % fd_pure 0
% 49.11/15.57 % fd_pseudo 0
% 49.11/15.57 % fd_cond 0
% 49.11/15.57 % fd_pseudo_cond 0
% 49.11/15.57 % AC symbols 0
% 49.11/15.57
% 49.11/15.57 % ------ Schedule dynamic 5 is on
% 49.11/15.57
% 49.11/15.57 % ------ no equalities: superposition off
% 49.11/15.57
% 49.11/15.57 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 49.11/15.57
% 49.11/15.57
% 49.11/15.57 % ------
% 49.11/15.57 % Current options:
% 49.11/15.57 % ------
% 49.11/15.57
% 49.11/15.57
% 49.11/15.57 %
% 49.11/15.57
% 49.11/15.57 % ------ Proving...
% 49.11/15.57 %
% 49.11/15.57
% 49.11/15.57 % SZS status Theorem for theBenchmark.p
% 49.11/15.57
% 49.11/15.57 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 49.11/15.57
% 49.11/15.57
%------------------------------------------------------------------------------