%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET765+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 : n010.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 02:48:31 PM UTC 2026
% Result : Theorem 0.70s 1.29s
% Output : CNFRefutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 108 ( 10 unt; 2 def)
% Number of atoms : 488 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 550 ( 212 ~; 242 |; 73 &)
% ( 8 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 233 ( 0 sgn 212 !; 21 ?; 67 :)
% 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(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/sandbox/benchmark/Axioms/SET006+2.ax',equivalence) ).
fof(f17,conjecture,
! [X0,X1,X2] :
( ( subset(X2,X0)
& equivalence(X1,X0) )
=> equivalence(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIII01) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X2,X0)
& equivalence(X1,X0) )
=> equivalence(X1,X2) ),
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] :
( subset(X0,X1)
=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f21,plain,
? [X0,X1,X2] :
( subset(X2,X0)
& equivalence(X1,X0)
& ~ equivalence(X1,X2) ),
inference(ennf_transformation,[],[f18]) ).
fof(f22,plain,
? [X0,X1,X2] :
( subset(X2,X0)
& equivalence(X1,X0)
& ~ equivalence(X1,X2) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
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(ennf_transformation,[],[f19]) ).
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(f29,plain,
( subset(sK4,sK2)
& equivalence(sK3,sK2)
& ~ equivalence(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f22]) ).
fof(f30,plain,
! [X1,X0] :
( ( ~ sP1(X1,X0)
| ( 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) ) ) )
& ( ~ 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) )
| sP1(X1,X0) ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f31,plain,
! [X1,X0] :
( ( ~ sP1(X1,X0)
| ( 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) ) ) )
& ( ~ 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) )
| sP1(X1,X0) ) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ( ~ sP1(X0,X1)
| ( sP0(X0,X1)
& ! [X6,X7] :
( ~ member(X7,X1)
| ~ member(X6,X1)
| ~ apply(X0,X6,X7)
| apply(X0,X7,X6) )
& ! [X5] :
( ~ member(X5,X1)
| apply(X0,X5,X5) ) ) )
& ( ~ sP0(X0,X1)
| ? [X3,X4] :
( member(X4,X1)
& member(X3,X1)
& apply(X0,X3,X4)
& ~ apply(X0,X4,X3) )
| ? [X2] :
( member(X2,X1)
& ~ apply(X0,X2,X2) )
| sP1(X0,X1) ) ),
inference(rectify,[],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( ( ~ sP1(X0,X1)
| ( sP0(X0,X1)
& ! [X6,X7] :
( ~ member(X7,X1)
| ~ member(X6,X1)
| ~ apply(X0,X6,X7)
| apply(X0,X7,X6) )
& ! [X5] :
( ~ member(X5,X1)
| apply(X0,X5,X5) ) ) )
& ( ~ sP0(X0,X1)
| ( member(sK7(X0,X1),X1)
& member(sK6(X0,X1),X1)
& apply(X0,sK6(X0,X1),sK7(X0,X1))
& ~ apply(X0,sK7(X0,X1),sK6(X0,X1)) )
| ( member(sK5(X0,X1),X1)
& ~ apply(X0,sK5(X0,X1),sK5(X0,X1)) )
| sP1(X0,X1) ) ),
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))],[f32]) ).
fof(f37,plain,
! [X0,X1] :
( ( ~ equivalence(X1,X0)
| sP1(X1,X0) )
& ( ~ sP1(X1,X0)
| equivalence(X1,X0) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f38,plain,
subset(sK4,sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f39,plain,
equivalence(sK3,sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f40,plain,
~ equivalence(sK3,sK4),
inference(cnf_transformation,[],[f29]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f43,plain,
! [X0,X1,X6,X7] :
( ~ sP1(X0,X1)
| ~ member(X7,X1)
| ~ member(X6,X1)
| ~ apply(X0,X6,X7)
| apply(X0,X7,X6) ),
inference(cnf_transformation,[],[f33]) ).
fof(f44,plain,
! [X0,X1,X5] :
( ~ sP1(X0,X1)
| ~ member(X5,X1)
| apply(X0,X5,X5) ),
inference(cnf_transformation,[],[f33]) ).
fof(f45,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| member(sK7(X0,X1),X1)
| member(sK5(X0,X1),X1)
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f46,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| member(sK6(X0,X1),X1)
| member(sK5(X0,X1),X1)
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f47,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| apply(X0,sK6(X0,X1),sK7(X0,X1))
| member(sK5(X0,X1),X1)
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f48,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ~ apply(X0,sK7(X0,X1),sK6(X0,X1))
| member(sK5(X0,X1),X1)
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f49,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| member(sK7(X0,X1),X1)
| ~ apply(X0,sK5(X0,X1),sK5(X0,X1))
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f50,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| member(sK6(X0,X1),X1)
| ~ apply(X0,sK5(X0,X1),sK5(X0,X1))
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f51,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| apply(X0,sK6(X0,X1),sK7(X0,X1))
| ~ apply(X0,sK5(X0,X1),sK5(X0,X1))
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f52,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ~ apply(X0,sK7(X0,X1),sK6(X0,X1))
| ~ apply(X0,sK5(X0,X1),sK5(X0,X1))
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f60,plain,
! [X0,X1] :
( ~ equivalence(X1,X0)
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f61,plain,
! [X0,X1] :
( ~ sP1(X1,X0)
| equivalence(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_49,negated_conjecture,
~ equivalence(sK3,sK4),
inference(cnf_transformation,[],[f40]) ).
tcf(c_50,negated_conjecture,
equivalence(sK3,sK2),
inference(cnf_transformation,[],[f39]) ).
tcf(c_51,negated_conjecture,
subset(sK4,sK2),
inference(cnf_transformation,[],[f38]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| ~ sP0(X0,X1)
| ~ apply(X0,sK7(X0,X1),sK6(X0,X1))
| ~ apply(X0,sK5(X0,X1),sK5(X0,X1)) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| apply(X0,sK6(X0,X1),sK7(X0,X1))
| ~ sP0(X0,X1)
| ~ apply(X0,sK5(X0,X1),sK5(X0,X1)) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| member(sK6(X0,X1),X1)
| ~ sP0(X0,X1)
| ~ apply(X0,sK5(X0,X1),sK5(X0,X1)) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| member(sK7(X0,X1),X1)
| ~ sP0(X0,X1)
| ~ apply(X0,sK5(X0,X1),sK5(X0,X1)) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| member(sK5(X0,X1),X1)
| ~ sP0(X0,X1)
| ~ apply(X0,sK7(X0,X1),sK6(X0,X1)) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| member(sK5(X0,X1),X1)
| apply(X0,sK6(X0,X1),sK7(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| member(sK6(X0,X1),X1)
| member(sK5(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| member(sK7(X0,X1),X1)
| member(sK5(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X2,X0,X0)
| ~ sP1(X2,X1)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X2,X1)
| ~ sP1(X0,X3)
| ~ member(X2,X3)
| ~ member(X1,X3)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( equivalence(X0,X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| ~ equivalence(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( ~ equivalence(X0,X1)
| sP1(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_72]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| ~ equivalence(X0,X1) ),
inference(renaming,[status(thm)],[c_91]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( equivalence(X0,X1)
| ~ sP1(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_71]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( ~ sP1(X0,X1)
| sP0(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_63]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| ~ sP1(X0,X1) ),
inference(renaming,[status(thm)],[c_95]) ).
tcf(c_305,plain,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,sK4) ),
inference(resolution,[status(thm)],[c_51,c_52]) ).
tcf(c_316,plain,
~ sP1(sK3,sK4),
inference(resolution,[status(thm)],[c_49,c_93]) ).
tcf(c_320,plain,
sP1(sK3,sK2),
inference(resolution,[status(thm)],[c_50,c_92]) ).
tcf(c_654,plain,
( member(sK7(sK3,sK4),sK4)
| member(sK5(sK3,sK4),sK4)
| ~ sP0(sK3,sK4) ),
inference(resolution,[status(thm)],[c_60,c_316]) ).
tcf(c_664,plain,
( member(sK6(sK3,sK4),sK4)
| member(sK5(sK3,sK4),sK4)
| ~ sP0(sK3,sK4) ),
inference(resolution,[status(thm)],[c_59,c_316]) ).
tcf(c_674,plain,
( member(sK5(sK3,sK4),sK4)
| apply(sK3,sK6(sK3,sK4),sK7(sK3,sK4))
| ~ sP0(sK3,sK4) ),
inference(resolution,[status(thm)],[c_58,c_316]) ).
tcf(c_684,plain,
( member(sK5(sK3,sK4),sK4)
| ~ sP0(sK3,sK4)
| ~ apply(sK3,sK7(sK3,sK4),sK6(sK3,sK4)) ),
inference(resolution,[status(thm)],[c_57,c_316]) ).
tcf(c_694,plain,
( member(sK7(sK3,sK4),sK4)
| ~ sP0(sK3,sK4)
| ~ apply(sK3,sK5(sK3,sK4),sK5(sK3,sK4)) ),
inference(resolution,[status(thm)],[c_56,c_316]) ).
tcf(c_704,plain,
( member(sK6(sK3,sK4),sK4)
| ~ sP0(sK3,sK4)
| ~ apply(sK3,sK5(sK3,sK4),sK5(sK3,sK4)) ),
inference(resolution,[status(thm)],[c_55,c_316]) ).
tcf(c_714,plain,
( apply(sK3,sK6(sK3,sK4),sK7(sK3,sK4))
| ~ sP0(sK3,sK4)
| ~ apply(sK3,sK5(sK3,sK4),sK5(sK3,sK4)) ),
inference(resolution,[status(thm)],[c_54,c_316]) ).
tcf(c_724,plain,
( ~ sP0(sK3,sK4)
| ~ apply(sK3,sK7(sK3,sK4),sK6(sK3,sK4))
| ~ apply(sK3,sK5(sK3,sK4),sK5(sK3,sK4)) ),
inference(resolution,[status(thm)],[c_53,c_316]) ).
tcf(c_734,plain,
sP0(sK3,sK2),
inference(resolution,[status(thm)],[c_96,c_320]) ).
tcf(c_3722,plain,
( member(sK5(sK3,sK4),sK2)
| ~ member(sK5(sK3,sK4),sK4) ),
inference(instantiation,[status(thm)],[c_305]) ).
tcf(c_3735,plain,
! [X0: $i] :
( apply(X0,sK5(sK3,sK4),sK5(sK3,sK4))
| ~ sP1(X0,sK2)
| ~ member(sK5(sK3,sK4),sK2) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_3744,plain,
( apply(sK3,sK5(sK3,sK4),sK5(sK3,sK4))
| ~ sP1(sK3,sK2)
| ~ member(sK5(sK3,sK4),sK2) ),
inference(instantiation,[status(thm)],[c_3735]) ).
tcf(c_3750,plain,
( member(sK6(sK3,sK4),sK2)
| ~ member(sK6(sK3,sK4),sK4) ),
inference(instantiation,[status(thm)],[c_305]) ).
tcf(c_3756,plain,
( member(sK7(sK3,sK4),sK2)
| ~ member(sK7(sK3,sK4),sK4) ),
inference(instantiation,[status(thm)],[c_305]) ).
tcf(c_3759,plain,
! [X0: $i,X1: $i] :
( apply(X0,X1,sK6(sK3,sK4))
| ~ sP1(X0,sK2)
| ~ member(X1,sK2)
| ~ member(sK6(sK3,sK4),sK2)
| ~ apply(X0,sK6(sK3,sK4),X1) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_3772,plain,
( apply(sK3,sK7(sK3,sK4),sK6(sK3,sK4))
| ~ sP1(sK3,sK2)
| ~ member(sK6(sK3,sK4),sK2)
| ~ member(sK7(sK3,sK4),sK2)
| ~ apply(sK3,sK6(sK3,sK4),sK7(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_3759]) ).
tcf(c_3788,plain,
( member(sK10(sK3,sK4),sK2)
| ~ member(sK10(sK3,sK4),sK4) ),
inference(instantiation,[status(thm)],[c_305]) ).
tcf(c_3795,plain,
( member(sK9(sK3,sK4),sK2)
| ~ member(sK9(sK3,sK4),sK4) ),
inference(instantiation,[status(thm)],[c_305]) ).
tcf(c_3802,plain,
( member(sK8(sK3,sK4),sK2)
| ~ member(sK8(sK3,sK4),sK4) ),
inference(instantiation,[status(thm)],[c_305]) ).
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,definition,
! [X1,X0] :
( sP1(X1,X0)
<=> ( 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) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f28,plain,
! [X0,X1] :
( equivalence(X1,X0)
<=> sP1(X1,X0) ),
inference(definition_folding,[],[f25,f27,f26]) ).
fof(f34,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) ) )
& ( ? [X5,X6,X7] :
( member(X7,X0)
& member(X6,X0)
& member(X5,X0)
& apply(X1,X6,X7)
& apply(X1,X5,X6)
& ~ apply(X1,X5,X7) )
| sP0(X1,X0) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f35,plain,
! [X0,X1] :
( ( ~ sP0(X0,X1)
| ! [X5,X6,X7] :
( ~ member(X7,X1)
| ~ member(X6,X1)
| ~ member(X5,X1)
| ~ apply(X0,X6,X7)
| ~ apply(X0,X5,X6)
| apply(X0,X5,X7) ) )
& ( ? [X2,X3,X4] :
( member(X4,X1)
& member(X3,X1)
& member(X2,X1)
& apply(X0,X3,X4)
& apply(X0,X2,X3)
& ~ apply(X0,X2,X4) )
| sP0(X0,X1) ) ),
inference(rectify,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ( ~ sP0(X0,X1)
| ! [X5,X6,X7] :
( ~ member(X7,X1)
| ~ member(X6,X1)
| ~ member(X5,X1)
| ~ apply(X0,X6,X7)
| ~ apply(X0,X5,X6)
| apply(X0,X5,X7) ) )
& ( ( member(sK10(X0,X1),X1)
& member(sK9(X0,X1),X1)
& member(sK8(X0,X1),X1)
& apply(X0,sK9(X0,X1),sK10(X0,X1))
& apply(X0,sK8(X0,X1),sK9(X0,X1))
& ~ apply(X0,sK8(X0,X1),sK10(X0,X1)) )
| sP0(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X2,sK8(X0,X1)),skolemize(X3,sK9(X0,X1)),skolemize(X4,sK10(X0,X1))],[f35]) ).
fof(f53,plain,
! [X0,X1,X6,X7,X5] :
( ~ sP0(X0,X1)
| ~ member(X7,X1)
| ~ member(X6,X1)
| ~ member(X5,X1)
| ~ apply(X0,X6,X7)
| ~ apply(X0,X5,X6)
| apply(X0,X5,X7) ),
inference(cnf_transformation,[],[f36]) ).
fof(f54,plain,
! [X0,X1] :
( member(sK10(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f55,plain,
! [X0,X1] :
( member(sK9(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f56,plain,
! [X0,X1] :
( member(sK8(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f57,plain,
! [X0,X1] :
( apply(X0,sK9(X0,X1),sK10(X0,X1))
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f58,plain,
! [X0,X1] :
( apply(X0,sK8(X0,X1),sK9(X0,X1))
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f59,plain,
! [X0,X1] :
( ~ apply(X0,sK8(X0,X1),sK10(X0,X1))
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| ~ apply(X0,sK8(X0,X1),sK10(X0,X1)) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| apply(X0,sK8(X0,X1),sK9(X0,X1)) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| apply(X0,sK9(X0,X1),sK10(X0,X1)) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| member(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| member(sK9(X0,X1),X1) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| member(sK10(X0,X1),X1) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X0,X1,X3)
| ~ sP0(X0,X4)
| ~ member(X3,X4)
| ~ member(X2,X4)
| ~ member(X1,X4)
| ~ apply(X0,X2,X3)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_3661,plain,
( sP0(sK3,sK4)
| apply(sK3,sK9(sK3,sK4),sK10(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_3662,plain,
( sP0(sK3,sK4)
| apply(sK3,sK8(sK3,sK4),sK9(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_3663,plain,
( sP0(sK3,sK4)
| ~ apply(sK3,sK8(sK3,sK4),sK10(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_3664,plain,
( sP0(sK3,sK4)
| member(sK10(sK3,sK4),sK4) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_3665,plain,
( sP0(sK3,sK4)
| member(sK9(sK3,sK4),sK4) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_3666,plain,
( sP0(sK3,sK4)
| member(sK8(sK3,sK4),sK4) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_3838,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,sK8(sK3,sK4),X2)
| ~ sP0(X0,sK2)
| ~ member(X2,sK2)
| ~ member(X1,sK2)
| ~ apply(X0,X1,X2)
| ~ member(sK8(sK3,sK4),sK2)
| ~ apply(X0,sK8(sK3,sK4),X1) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_3850,plain,
! [X0: $i] :
( apply(sK3,sK8(sK3,sK4),sK10(sK3,sK4))
| ~ sP0(sK3,sK2)
| ~ member(X0,sK2)
| ~ member(sK10(sK3,sK4),sK2)
| ~ member(sK8(sK3,sK4),sK2)
| ~ apply(sK3,X0,sK10(sK3,sK4))
| ~ apply(sK3,sK8(sK3,sK4),X0) ),
inference(instantiation,[status(thm)],[c_3838]) ).
tcf(c_3865,plain,
( apply(sK3,sK8(sK3,sK4),sK10(sK3,sK4))
| ~ sP0(sK3,sK2)
| ~ member(sK9(sK3,sK4),sK2)
| ~ member(sK10(sK3,sK4),sK2)
| ~ member(sK8(sK3,sK4),sK2)
| ~ apply(sK3,sK9(sK3,sK4),sK10(sK3,sK4))
| ~ apply(sK3,sK8(sK3,sK4),sK9(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_3850]) ).
tcf(c_3866,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3865,c_3802,c_3795,c_3788,c_3772,c_3756,c_3750,c_3744,c_3722,c_3661,c_3662,c_3663,c_3664,c_3665,c_3666,c_734,c_724,c_714,c_704,c_694,c_684,c_674,c_664,c_654,c_320]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET765+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n010.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 11:53:43 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.38 Running first-order theorem proving
% 0.14/0.38 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
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.41 % Proving...
% 0.70/1.29 % SZS status Started for theBenchmark.p
% 0.70/1.29 % SZS status Theorem for theBenchmark.p
% 0.70/1.29
% 0.70/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.70/1.29
% 0.70/1.29 % ------ iProver source info
% 0.70/1.29
% 0.70/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.70/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.70/1.29 % git: non_committed_changes: false
% 0.70/1.29
% 0.70/1.29 % ------ Parsing...
% 0.70/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.70/1.29
% 0.70/1.29 % ------ 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 %
% 0.70/1.29
% 0.70/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.70/1.29 % ------ Proving...
% 0.70/1.29 % ------ Problem Properties
% 0.70/1.29
% 0.70/1.29 %
% 0.70/1.29 % clauses 21
% 0.70/1.29 % conjectures 0
% 0.70/1.29 % EPR 7
% 0.70/1.29 % Horn 9
% 0.70/1.29 % unary 2
% 0.70/1.29 % binary 8
% 0.70/1.29 % lits 65
% 0.70/1.29 % lits eq 0
% 0.70/1.29 % fd_pure 0
% 0.70/1.29 % fd_pseudo 0
% 0.70/1.29 % fd_cond 0
% 0.70/1.29 % fd_pseudo_cond 0
% 0.70/1.29 % AC symbols 0
% 0.70/1.29
% 0.70/1.29 % ------ Schedule dynamic 5 is on
% 0.70/1.29
% 0.70/1.29 % ------ no conjectures: strip conj schedule
% 0.70/1.29
% 0.70/1.29 % ------ no equalities: superposition off
% 0.70/1.29
% 0.70/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.70/1.29
% 0.70/1.29
% 0.70/1.29 % ------
% 0.70/1.29 % Current options:
% 0.70/1.29 % ------
% 0.70/1.29
% 0.70/1.29
% 0.70/1.29 %
% 0.70/1.29
% 0.70/1.29 % ------ Proving...
% 0.70/1.29 %
% 0.70/1.29
% 0.70/1.29 % SZS status Theorem for theBenchmark.p
% 0.70/1.29
% 0.70/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.70/1.29
% 0.70/1.29
%------------------------------------------------------------------------------