%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET805+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n008.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 4.13s 1.28s
% Output : CNFRefutation 4.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 100 ( 9 unt; 2 def)
% Number of atoms : 427 ( 23 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 530 ( 203 ~; 229 |; 73 &)
% ( 8 <=>; 17 =>; 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 : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 248 ( 0 sgn 232 !; 16 ?; 89 :)
% 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(f12,axiom,
! [X0,X1] :
( order(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) ) )
& ! [X2,X3] :
( ( member(X3,X1)
& member(X2,X1) )
=> ( ( apply(X0,X3,X2)
& apply(X0,X2,X3) )
=> X2 = X3 ) )
& ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',order) ).
fof(f22,conjecture,
! [X0,X1] :
( order(X0,X1)
=> ! [X2] :
( subset(X2,X1)
=> order(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV17) ).
fof(f23,negated_conjecture,
~ ! [X0,X1] :
( order(X0,X1)
=> ! [X2] :
( subset(X2,X1)
=> order(X0,X2) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( order(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) ) )
& ! [X3,X4] :
( ( member(X4,X1)
& member(X3,X1) )
=> ( ( apply(X0,X4,X3)
& apply(X0,X3,X4) )
=> X3 = X4 ) )
& ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ) ),
inference(rectify,[],[f12]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f26,plain,
? [X0,X1] :
( order(X0,X1)
& ? [X2] :
( subset(X2,X1)
& ~ order(X0,X2) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f27,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f28,plain,
! [X0,X1] :
( order(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) )
& ! [X3,X4] :
( ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X3)
| ~ apply(X0,X3,X4)
| X3 = X4 )
& ! [X2] :
( ~ member(X2,X1)
| apply(X0,X2,X2) ) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f29,plain,
! [X0,X1] :
( order(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) )
& ! [X3,X4] :
( ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X3)
| ~ apply(X0,X3,X4)
| X3 = X4 )
& ! [X2] :
( ~ member(X2,X1)
| apply(X0,X2,X2) ) ) ),
inference(flattening,[],[f28]) ).
fof(f33,plain,
( order(sK2,sK3)
& subset(sK4,sK3)
& ~ order(sK2,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f26]) ).
fof(f34,plain,
! [X0,X1] :
( ( ~ sP1(X0,X1)
| ! [X3,X4] :
( ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X3)
| ~ apply(X0,X3,X4)
| X3 = X4 ) )
& ( ? [X3,X4] :
( member(X4,X1)
& member(X3,X1)
& apply(X0,X4,X3)
& apply(X0,X3,X4)
& X3 != X4 )
| sP1(X0,X1) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f35,plain,
! [X0,X1] :
( ( ~ sP1(X0,X1)
| ! [X4,X5] :
( ~ member(X5,X1)
| ~ member(X4,X1)
| ~ apply(X0,X5,X4)
| ~ apply(X0,X4,X5)
| X4 = X5 ) )
& ( ? [X2,X3] :
( member(X3,X1)
& member(X2,X1)
& apply(X0,X3,X2)
& apply(X0,X2,X3)
& X2 != X3 )
| sP1(X0,X1) ) ),
inference(rectify,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ( ~ sP1(X0,X1)
| ! [X4,X5] :
( ~ member(X5,X1)
| ~ member(X4,X1)
| ~ apply(X0,X5,X4)
| ~ apply(X0,X4,X5)
| X4 = X5 ) )
& ( ( member(sK6(X0,X1),X1)
& member(sK5(X0,X1),X1)
& apply(X0,sK6(X0,X1),sK5(X0,X1))
& apply(X0,sK5(X0,X1),sK6(X0,X1))
& sK5(X0,X1) != sK6(X0,X1) )
| sP1(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X2,sK5(X0,X1)),skolemize(X3,sK6(X0,X1))],[f35]) ).
fof(f40,plain,
! [X0,X1] :
( ( ~ order(X0,X1)
| ( sP0(X0,X1)
& sP1(X0,X1)
& ! [X2] :
( ~ member(X2,X1)
| apply(X0,X2,X2) ) ) )
& ( ~ sP0(X0,X1)
| ~ sP1(X0,X1)
| ? [X2] :
( member(X2,X1)
& ~ apply(X0,X2,X2) )
| order(X0,X1) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f41,plain,
! [X0,X1] :
( ( ~ order(X0,X1)
| ( sP0(X0,X1)
& sP1(X0,X1)
& ! [X2] :
( ~ member(X2,X1)
| apply(X0,X2,X2) ) ) )
& ( ~ sP0(X0,X1)
| ~ sP1(X0,X1)
| ? [X2] :
( member(X2,X1)
& ~ apply(X0,X2,X2) )
| order(X0,X1) ) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ( ~ order(X0,X1)
| ( sP0(X0,X1)
& sP1(X0,X1)
& ! [X3] :
( ~ member(X3,X1)
| apply(X0,X3,X3) ) ) )
& ( ~ sP0(X0,X1)
| ~ sP1(X0,X1)
| ? [X2] :
( member(X2,X1)
& ~ apply(X0,X2,X2) )
| order(X0,X1) ) ),
inference(rectify,[],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ( ~ order(X0,X1)
| ( sP0(X0,X1)
& sP1(X0,X1)
& ! [X3] :
( ~ member(X3,X1)
| apply(X0,X3,X3) ) ) )
& ( ~ sP0(X0,X1)
| ~ sP1(X0,X1)
| ( member(sK10(X0,X1),X1)
& ~ apply(X0,sK10(X0,X1),sK10(X0,X1)) )
| order(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f42]) ).
fof(f44,plain,
order(sK2,sK3),
inference(cnf_transformation,[],[f33]) ).
fof(f45,plain,
subset(sK4,sK3),
inference(cnf_transformation,[],[f33]) ).
fof(f46,plain,
~ order(sK2,sK4),
inference(cnf_transformation,[],[f33]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f48,plain,
! [X0,X1,X4,X5] :
( ~ sP1(X0,X1)
| ~ member(X5,X1)
| ~ member(X4,X1)
| ~ apply(X0,X5,X4)
| ~ apply(X0,X4,X5)
| X4 = X5 ),
inference(cnf_transformation,[],[f36]) ).
fof(f49,plain,
! [X0,X1] :
( member(sK6(X0,X1),X1)
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f50,plain,
! [X0,X1] :
( member(sK5(X0,X1),X1)
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f51,plain,
! [X0,X1] :
( apply(X0,sK6(X0,X1),sK5(X0,X1))
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f52,plain,
! [X0,X1] :
( apply(X0,sK5(X0,X1),sK6(X0,X1))
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f53,plain,
! [X0,X1] :
( sK5(X0,X1) != sK6(X0,X1)
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f61,plain,
! [X0,X1] :
( ~ order(X0,X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f62,plain,
! [X0,X1] :
( ~ order(X0,X1)
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f63,plain,
! [X3,X0,X1] :
( ~ order(X0,X1)
| ~ member(X3,X1)
| apply(X0,X3,X3) ),
inference(cnf_transformation,[],[f43]) ).
fof(f64,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ~ sP1(X0,X1)
| member(sK10(X0,X1),X1)
| order(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f65,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ~ sP1(X0,X1)
| ~ apply(X0,sK10(X0,X1),sK10(X0,X1))
| order(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_49,negated_conjecture,
~ order(sK2,sK4),
inference(cnf_transformation,[],[f46]) ).
tcf(c_50,negated_conjecture,
subset(sK4,sK3),
inference(cnf_transformation,[],[f45]) ).
tcf(c_51,negated_conjecture,
order(sK2,sK3),
inference(cnf_transformation,[],[f44]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| ( sK5(X0,X1) != sK6(X0,X1) ) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| apply(X0,sK5(X0,X1),sK6(X0,X1)) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| apply(X0,sK6(X0,X1),sK5(X0,X1)) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| member(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| member(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ~ sP1(X0,X3)
| ~ member(X2,X3)
| ~ member(X1,X3)
| ~ apply(X0,X2,X1)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( order(X0,X1)
| ~ sP0(X0,X1)
| ~ sP1(X0,X1)
| ~ apply(X0,sK10(X0,X1),sK10(X0,X1)) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( order(X0,X1)
| member(sK10(X0,X1),X1)
| ~ sP0(X0,X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ~ order(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| ~ order(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| ~ order(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_311,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ( X1 != sK3 )
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_52]) ).
tcf(c_312,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,sK4) ),
inference(unflattening,[status(thm)],[c_311]) ).
tcf(c_395,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| ( X1 != sK3 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_70]) ).
tcf(c_396,plain,
sP0(sK2,sK3),
inference(unflattening,[status(thm)],[c_395]) ).
tcf(c_400,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| ( X1 != sK3 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_69]) ).
tcf(c_401,plain,
sP1(sK2,sK3),
inference(unflattening,[status(thm)],[c_400]) ).
tcf(c_2637,plain,
! [X0: $i] :
( sP1(X0,sK4)
| member(sK5(X0,sK4),sK3) ),
inference(superposition,[status(thm)],[c_56,c_312]) ).
tcf(c_2649,plain,
! [X0: $i] :
( order(X0,sK4)
| member(sK10(X0,sK4),sK3)
| ~ sP0(X0,sK4)
| ~ sP1(X0,sK4) ),
inference(superposition,[status(thm)],[c_67,c_312]) ).
tcf(c_2659,plain,
! [X0: $i] :
( sP1(X0,sK4)
| member(sK6(X0,sK4),sK3) ),
inference(superposition,[status(thm)],[c_57,c_312]) ).
tcf(c_2745,plain,
! [X0: $i] :
( apply(sK2,X0,X0)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_51,c_68]) ).
tcf(c_2768,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X0,X1)
| ( sK5(X0,X1) = sK6(X0,X1) )
| ~ sP1(X0,X2)
| ~ member(sK6(X0,X1),X2)
| ~ member(sK5(X0,X1),X2)
| ~ apply(X0,sK6(X0,X1),sK5(X0,X1)) ),
inference(superposition,[status(thm)],[c_54,c_58]) ).
tcf(c_2769,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X0,X1)
| ( sK5(X0,X1) = sK6(X0,X1) )
| ~ sP1(X0,X2)
| ~ member(sK6(X0,X1),X2)
| ~ member(sK5(X0,X1),X2)
| ~ apply(X0,sK5(X0,X1),sK6(X0,X1)) ),
inference(superposition,[status(thm)],[c_55,c_58]) ).
tcf(c_2852,plain,
! [X0: $i] :
( order(sK2,X0)
| ~ sP0(sK2,X0)
| ~ sP1(sK2,X0)
| ~ member(sK10(sK2,X0),sK3) ),
inference(superposition,[status(thm)],[c_2745,c_66]) ).
tcf(c_2867,plain,
( order(sK2,sK4)
| ~ sP0(sK2,sK4)
| ~ sP1(sK2,sK4) ),
inference(superposition,[status(thm)],[c_2649,c_2852]) ).
tcf(c_2868,plain,
( ~ sP0(sK2,sK4)
| ~ sP1(sK2,sK4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2867,c_49]) ).
tcf(c_2875,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X0,X1)
| ~ member(sK5(X0,X1),X2)
| ~ member(sK6(X0,X1),X2)
| ~ sP1(X0,X2) ),
inference(global_subsumption_just,[status(thm)],[c_2768,c_54,c_53,c_2769]) ).
tcf(c_2876,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X0,X1)
| ~ sP1(X0,X2)
| ~ member(sK6(X0,X1),X2)
| ~ member(sK5(X0,X1),X2) ),
inference(renaming,[status(thm)],[c_2875]) ).
tcf(c_2886,plain,
! [X0: $i] :
( sP1(X0,sK4)
| ~ sP1(X0,sK3)
| ~ member(sK6(X0,sK4),sK3) ),
inference(superposition,[status(thm)],[c_2637,c_2876]) ).
tcf(c_2891,plain,
! [X0: $i] :
( sP1(X0,sK4)
| ~ sP1(X0,sK3) ),
inference(global_subsumption_just,[status(thm)],[c_2886,c_2659,c_2886]) ).
tcf(c_2893,plain,
( sP1(sK2,sK4)
| ~ sP1(sK2,sK3) ),
inference(instantiation,[status(thm)],[c_2891]) ).
fof(f30,definition,
! [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) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f31,definition,
! [X0,X1] :
( sP1(X0,X1)
<=> ! [X3,X4] :
( ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X3)
| ~ apply(X0,X3,X4)
| X3 = X4 ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f32,plain,
! [X0,X1] :
( order(X0,X1)
<=> ( sP0(X0,X1)
& sP1(X0,X1)
& ! [X2] :
( ~ member(X2,X1)
| apply(X0,X2,X2) ) ) ),
inference(definition_folding,[],[f29,f31,f30]) ).
fof(f37,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) ) )
& ( ? [X5,X6,X7] :
( member(X7,X1)
& member(X6,X1)
& member(X5,X1)
& apply(X0,X6,X7)
& apply(X0,X5,X6)
& ~ apply(X0,X5,X7) )
| sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f38,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,[],[f37]) ).
fof(f39,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(sK9(X0,X1),X1)
& member(sK8(X0,X1),X1)
& member(sK7(X0,X1),X1)
& apply(X0,sK8(X0,X1),sK9(X0,X1))
& apply(X0,sK7(X0,X1),sK8(X0,X1))
& ~ apply(X0,sK7(X0,X1),sK9(X0,X1)) )
| sP0(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X2,sK7(X0,X1)),skolemize(X3,sK8(X0,X1)),skolemize(X4,sK9(X0,X1))],[f38]) ).
fof(f54,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,[],[f39]) ).
fof(f55,plain,
! [X0,X1] :
( member(sK9(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f56,plain,
! [X0,X1] :
( member(sK8(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f57,plain,
! [X0,X1] :
( member(sK7(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f58,plain,
! [X0,X1] :
( apply(X0,sK8(X0,X1),sK9(X0,X1))
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f59,plain,
! [X0,X1] :
( apply(X0,sK7(X0,X1),sK8(X0,X1))
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f60,plain,
! [X0,X1] :
( ~ apply(X0,sK7(X0,X1),sK9(X0,X1))
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| ~ apply(X0,sK7(X0,X1),sK9(X0,X1)) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| apply(X0,sK7(X0,X1),sK8(X0,X1)) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| apply(X0,sK8(X0,X1),sK9(X0,X1)) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| member(sK7(X0,X1),X1) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| member(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| member(sK9(X0,X1),X1) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_65,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,[],[f54]) ).
tcf(c_2667,plain,
! [X0: $i] :
( sP0(X0,sK4)
| member(sK7(X0,sK4),sK3) ),
inference(superposition,[status(thm)],[c_62,c_312]) ).
tcf(c_2675,plain,
! [X0: $i] :
( sP0(X0,sK4)
| member(sK8(X0,sK4),sK3) ),
inference(superposition,[status(thm)],[c_63,c_312]) ).
tcf(c_2678,plain,
( sP0(sK2,sK4)
| member(sK8(sK2,sK4),sK3) ),
inference(instantiation,[status(thm)],[c_2675]) ).
tcf(c_2683,plain,
! [X0: $i] :
( sP0(X0,sK4)
| member(sK9(X0,sK4),sK3) ),
inference(superposition,[status(thm)],[c_64,c_312]) ).
tcf(c_2686,plain,
( sP0(sK2,sK4)
| member(sK9(sK2,sK4),sK3) ),
inference(instantiation,[status(thm)],[c_2683]) ).
tcf(c_2814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP0(X0,X1)
| apply(X0,sK7(X0,X1),X2)
| ~ sP0(X0,X3)
| ~ member(X2,X3)
| ~ member(sK8(X0,X1),X3)
| ~ member(sK7(X0,X1),X3)
| ~ apply(X0,sK8(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_60,c_65]) ).
tcf(c_3109,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1)
| apply(X0,sK7(X0,X1),sK9(X0,X1))
| ~ sP0(X0,X2)
| ~ member(sK8(X0,X1),X2)
| ~ member(sK9(X0,X1),X2)
| ~ member(sK7(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_61,c_2814]) ).
tcf(c_3123,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1)
| ~ member(sK7(X0,X1),X2)
| ~ member(sK9(X0,X1),X2)
| ~ member(sK8(X0,X1),X2)
| ~ sP0(X0,X2) ),
inference(global_subsumption_just,[status(thm)],[c_3109,c_59,c_3109]) ).
tcf(c_3124,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1)
| ~ sP0(X0,X2)
| ~ member(sK8(X0,X1),X2)
| ~ member(sK9(X0,X1),X2)
| ~ member(sK7(X0,X1),X2) ),
inference(renaming,[status(thm)],[c_3123]) ).
tcf(c_3136,plain,
! [X0: $i] :
( sP0(X0,sK4)
| ~ sP0(X0,sK3)
| ~ member(sK8(X0,sK4),sK3)
| ~ member(sK9(X0,sK4),sK3) ),
inference(superposition,[status(thm)],[c_2667,c_3124]) ).
tcf(c_3141,plain,
( sP0(sK2,sK4)
| ~ sP0(sK2,sK3)
| ~ member(sK8(sK2,sK4),sK3)
| ~ member(sK9(sK2,sK4),sK3) ),
inference(instantiation,[status(thm)],[c_3136]) ).
tcf(c_3142,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3141,c_2893,c_2868,c_2686,c_2678,c_401,c_396]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET805+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n008.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 12:00:55 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 4.13/1.28 % SZS status Started for theBenchmark.p
% 4.13/1.28 % SZS status Theorem for theBenchmark.p
% 4.13/1.28
% 4.13/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.13/1.28
% 4.13/1.28 % ------ iProver source info
% 4.13/1.28
% 4.13/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.13/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.13/1.28 % git: non_committed_changes: false
% 4.13/1.28
% 4.13/1.28 % ------ Parsing...
% 4.13/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.13/1.28
% 4.13/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 4.13/1.28
% 4.13/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.13/1.28
% 4.13/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.13/1.28 % ------ Proving...
% 4.13/1.28 % ------ Problem Properties
% 4.13/1.28
% 4.13/1.28 %
% 4.13/1.28 % clauses 21
% 4.13/1.28 % conjectures 2
% 4.13/1.28 % EPR 8
% 4.13/1.28 % Horn 11
% 4.13/1.28 % unary 2
% 4.13/1.28 % binary 14
% 4.13/1.28 % lits 54
% 4.13/1.28 % lits eq 2
% 4.13/1.28 % fd_pure 0
% 4.13/1.28 % fd_pseudo 0
% 4.13/1.28 % fd_cond 0
% 4.13/1.28 % fd_pseudo_cond 1
% 4.13/1.28 % AC symbols 0
% 4.13/1.28
% 4.13/1.28 % ------ Schedule dynamic 5 is on
% 4.13/1.28
% 4.13/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.13/1.28
% 4.13/1.28
% 4.13/1.28 % ------
% 4.13/1.28 % Current options:
% 4.13/1.28 % ------
% 4.13/1.28
% 4.13/1.28
% 4.13/1.28 %
% 4.13/1.28
% 4.13/1.28 % ------ Proving...
% 4.13/1.28 %
% 4.13/1.28
% 4.13/1.28 % SZS status Theorem for theBenchmark.p
% 4.13/1.28
% 4.13/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.13/1.29
% 4.13/1.29
%------------------------------------------------------------------------------