%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU168+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n014.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 02:55:44 PM UTC 2026
% Result : Theorem 10.56s 7.23s
% Output : CNFRefutation 10.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 99 ( 5 unt; 1 def)
% Number of atoms : 402 ( 11 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 511 ( 208 ~; 203 |; 85 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 211 ( 0 sgn 181 !; 30 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f7,conjecture,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X2] :
( in(X2,X1)
=> in(powerset(X2),X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X2] :
( in(X2,X1)
=> in(powerset(X2),X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X2] :
~ ( ! [X3] :
~ ( ! [X4] :
( subset(X4,X2)
=> in(X4,X3) )
& in(X3,X1) )
& in(X2,X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
fof(f11,plain,
~ ! [X0] :
? [X1] :
( ! [X5] :
~ ( ~ in(X5,X1)
& ~ are_equipotent(X5,X1)
& subset(X5,X1) )
& ! [X4] :
( in(X4,X1)
=> in(powerset(X4),X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
inference(rectify,[],[f8]) ).
fof(f12,plain,
! [X0] :
? [X1] :
( ! [X7] :
~ ( ~ in(X7,X1)
& ~ are_equipotent(X7,X1)
& subset(X7,X1) )
& ! [X4] :
~ ( ! [X5] :
~ ( ! [X6] :
( subset(X6,X4)
=> in(X6,X5) )
& in(X5,X1) )
& in(X4,X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
inference(rectify,[],[f9]) ).
fof(f14,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f15,plain,
? [X0] :
! [X1] :
( ? [X5] :
( ~ in(X5,X1)
& ~ are_equipotent(X5,X1)
& subset(X5,X1) )
| ? [X4] :
( in(X4,X1)
& ~ in(powerset(X4),X1) )
| ? [X2,X3] :
( subset(X3,X2)
& in(X2,X1)
& ~ in(X3,X1) )
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f16,plain,
? [X0] :
! [X1] :
( ? [X5] :
( ~ in(X5,X1)
& ~ are_equipotent(X5,X1)
& subset(X5,X1) )
| ? [X4] :
( in(X4,X1)
& ~ in(powerset(X4),X1) )
| ? [X2,X3] :
( subset(X3,X2)
& in(X2,X1)
& ~ in(X3,X1) )
| ~ in(X0,X1) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0] :
? [X1] :
( ! [X7] :
( in(X7,X1)
| are_equipotent(X7,X1)
| ~ subset(X7,X1) )
& ! [X4] :
( ? [X5] :
( ! [X6] :
( ~ subset(X6,X4)
| in(X6,X5) )
& in(X5,X1) )
| ~ in(X4,X1) )
& ! [X2,X3] :
( ~ subset(X3,X2)
| ~ in(X2,X1)
| in(X3,X1) )
& in(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f18,plain,
! [X0] :
? [X1] :
( ! [X7] :
( in(X7,X1)
| are_equipotent(X7,X1)
| ~ subset(X7,X1) )
& ! [X4] :
( ? [X5] :
( ! [X6] :
( ~ subset(X6,X4)
| in(X6,X5) )
& in(X5,X1) )
| ~ in(X4,X1) )
& ! [X2,X3] :
( ~ subset(X3,X2)
| ~ in(X2,X1)
| in(X3,X1) )
& in(X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f21,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| subset(X2,X0) )
& ( ~ subset(X2,X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f22,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(rectify,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ( ( in(sK1(X0,X1),X1)
| subset(sK1(X0,X1),X0) )
& ( ~ in(sK1(X0,X1),X1)
| ~ subset(sK1(X0,X1),X0) ) )
| X1 = powerset(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK2(X0,X1),X0)
& ~ in(sK2(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f25]) ).
fof(f32,plain,
! [X1] :
( sP0(X1)
| ( in(sK9(X1),X1)
& ~ in(powerset(sK9(X1)),X1) )
| ( subset(sK8(X1),sK7(X1))
& in(sK7(X1),X1)
& ~ in(sK8(X1),X1) )
| ~ in(sK6,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9]),skolemize(X0,sK6),skolemize(X2,sK7(X1)),skolemize(X3,sK8(X1)),skolemize(X4,sK9(X1))],[f20]) ).
fof(f33,plain,
! [X0] :
( ! [X7] :
( in(X7,sK10(X0))
| are_equipotent(X7,sK10(X0))
| ~ subset(X7,sK10(X0)) )
& ! [X4] :
( ( ! [X6] :
( ~ subset(X6,X4)
| in(X6,sK11(X0,X4)) )
& in(sK11(X0,X4),sK10(X0)) )
| ~ in(X4,sK10(X0)) )
& ! [X2,X3] :
( ~ subset(X3,X2)
| ~ in(X2,sK10(X0))
| in(X3,sK10(X0)) )
& in(X0,sK10(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X1,sK10(X0)),skolemize(X5,sK11(X0,X4))],[f18]) ).
fof(f35,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
! [X0,X1] :
( in(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f41,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f48,plain,
! [X1] :
( sP0(X1)
| in(sK9(X1),X1)
| subset(sK8(X1),sK7(X1))
| ~ in(sK6,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f49,plain,
! [X1] :
( sP0(X1)
| ~ in(powerset(sK9(X1)),X1)
| subset(sK8(X1),sK7(X1))
| ~ in(sK6,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f50,plain,
! [X1] :
( sP0(X1)
| in(sK9(X1),X1)
| in(sK7(X1),X1)
| ~ in(sK6,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f51,plain,
! [X1] :
( sP0(X1)
| ~ in(powerset(sK9(X1)),X1)
| in(sK7(X1),X1)
| ~ in(sK6,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f52,plain,
! [X1] :
( sP0(X1)
| in(sK9(X1),X1)
| ~ in(sK8(X1),X1)
| ~ in(sK6,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f53,plain,
! [X1] :
( sP0(X1)
| ~ in(powerset(sK9(X1)),X1)
| ~ in(sK8(X1),X1)
| ~ in(sK6,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f54,plain,
! [X0,X7] :
( in(X7,sK10(X0))
| are_equipotent(X7,sK10(X0))
| ~ subset(X7,sK10(X0)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f55,plain,
! [X0,X6,X4] :
( ~ subset(X6,X4)
| in(X6,sK11(X0,X4))
| ~ in(X4,sK10(X0)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f56,plain,
! [X0,X4] :
( in(sK11(X0,X4),sK10(X0))
| ~ in(X4,sK10(X0)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f57,plain,
! [X2,X3,X0] :
( ~ subset(X3,X2)
| ~ in(X2,sK10(X0))
| in(X3,sK10(X0)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f58,plain,
! [X0] : in(X0,sK10(X0)),
inference(cnf_transformation,[],[f33]) ).
fof(f60,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f35]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_63,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| ~ in(sK6,X0)
| ~ in(sK8(X0),X0)
| ~ in(powerset(sK9(X0)),X0) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_64,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| in(sK9(X0),X0)
| ~ in(sK6,X0)
| ~ in(sK8(X0),X0) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_65,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| in(sK7(X0),X0)
| ~ in(sK6,X0)
| ~ in(powerset(sK9(X0)),X0) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_66,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| in(sK7(X0),X0)
| in(sK9(X0),X0)
| ~ in(sK6,X0) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_67,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| subset(sK8(X0),sK7(X0))
| ~ in(sK6,X0)
| ~ in(powerset(sK9(X0)),X0) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_68,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| in(sK9(X0),X0)
| subset(sK8(X0),sK7(X0))
| ~ in(sK6,X0) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_69,plain,
! [X0: $i] : in(X0,sK10(X0)),
inference(cnf_transformation,[],[f58]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK10(X1))
| ~ subset(X2,X0)
| ~ in(X0,sK10(X1)) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( in(sK11(X1,X0),sK10(X1))
| ~ in(X0,sK10(X1)) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK11(X1,X0))
| ~ subset(X2,X0)
| ~ in(X0,sK10(X1)) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( are_equipotent(X0,sK10(X1))
| in(X0,sK10(X1))
| ~ subset(X0,sK10(X1)) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_75,plain,
in(sK6,sK10(sK6)),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_2560,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| in(sK9(X0),X0)
| subset(sK8(X0),sK7(X0))
| ~ in(sK6,X0) ),
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_2561,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| subset(sK8(X0),sK7(X0))
| ~ in(sK6,X0)
| ~ in(powerset(sK9(X0)),X0) ),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_2562,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| in(sK7(X0),X0)
| in(sK9(X0),X0)
| ~ in(sK6,X0) ),
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_2563,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| in(sK7(X0),X0)
| ~ in(sK6,X0)
| ~ in(powerset(sK9(X0)),X0) ),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_2565,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| ~ in(sK6,X0)
| ~ in(sK8(X0),X0)
| ~ in(powerset(sK9(X0)),X0) ),
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_3148,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| subset(sK2(powerset(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_55,c_53]) ).
tcf(c_3595,plain,
! [X0: $i,X1: $i] :
( sP0(sK10(X1))
| in(X0,sK10(X1))
| in(sK9(sK10(X1)),sK10(X1))
| ~ in(sK6,sK10(X1))
| ~ subset(X0,sK7(sK10(X1))) ),
inference(superposition,[status(thm)],[c_2562,c_70]) ).
tcf(c_3597,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK10(X1))
| ~ in(X2,sK10(X1))
| ~ subset(X0,sK11(X1,X2)) ),
inference(superposition,[status(thm)],[c_71,c_70]) ).
tcf(c_3634,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,sK11(X1,X2))
| ~ in(X2,sK10(X1))
| ~ subset(sK2(X0,sK11(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_72,c_54]) ).
tcf(c_4164,plain,
! [X0: $i] :
( in(sK8(sK10(sK6)),sK10(sK6))
| ~ in(X0,sK10(sK6))
| ~ subset(sK8(sK10(sK6)),X0) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_12907,plain,
( in(sK8(sK10(sK6)),sK10(sK6))
| ~ in(sK7(sK10(sK6)),sK10(sK6))
| ~ subset(sK8(sK10(sK6)),sK7(sK10(sK6))) ),
inference(instantiation,[status(thm)],[c_4164]) ).
tcf(c_22758,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),sK11(X1,X0))
| ~ in(X0,sK10(X1)) ),
inference(superposition,[status(thm)],[c_3148,c_3634]) ).
tcf(c_23329,plain,
! [X0: $i,X1: $i] :
( in(powerset(X0),sK10(X1))
| ~ in(X0,sK10(X1)) ),
inference(superposition,[status(thm)],[c_22758,c_3597]) ).
tcf(c_23397,plain,
! [X0: $i] :
( sP0(sK10(X0))
| ~ in(sK6,sK10(X0))
| ~ in(sK9(sK10(X0)),sK10(X0))
| ~ in(sK8(sK10(X0)),sK10(X0)) ),
inference(superposition,[status(thm)],[c_23329,c_2565]) ).
tcf(c_23398,plain,
! [X0: $i] :
( sP0(sK10(X0))
| subset(sK8(sK10(X0)),sK7(sK10(X0)))
| ~ in(sK6,sK10(X0))
| ~ in(sK9(sK10(X0)),sK10(X0)) ),
inference(superposition,[status(thm)],[c_23329,c_2561]) ).
tcf(c_23399,plain,
! [X0: $i] :
( sP0(sK10(X0))
| in(sK7(sK10(X0)),sK10(X0))
| ~ in(sK6,sK10(X0))
| ~ in(sK9(sK10(X0)),sK10(X0)) ),
inference(superposition,[status(thm)],[c_23329,c_2563]) ).
fof(f19,definition,
! [X1] :
( ~ sP0(X1)
| ? [X5] :
( ~ in(X5,X1)
& ~ are_equipotent(X5,X1)
& subset(X5,X1) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f20,plain,
? [X0] :
! [X1] :
( sP0(X1)
| ? [X4] :
( in(X4,X1)
& ~ in(powerset(X4),X1) )
| ? [X2,X3] :
( subset(X3,X2)
& in(X2,X1)
& ~ in(X3,X1) )
| ~ in(X0,X1) ),
inference(definition_folding,[],[f16,f19]) ).
fof(f29,plain,
! [X1] :
( ~ sP0(X1)
| ? [X5] :
( ~ in(X5,X1)
& ~ are_equipotent(X5,X1)
& subset(X5,X1) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f30,plain,
! [X0] :
( ~ sP0(X0)
| ? [X1] :
( ~ in(X1,X0)
& ~ are_equipotent(X1,X0)
& subset(X1,X0) ) ),
inference(rectify,[],[f29]) ).
fof(f31,plain,
! [X0] :
( ~ sP0(X0)
| ( ~ in(sK5(X0),X0)
& ~ are_equipotent(sK5(X0),X0)
& subset(sK5(X0),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X1,sK5(X0))],[f30]) ).
fof(f45,plain,
! [X0] :
( ~ sP0(X0)
| ~ in(sK5(X0),X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f46,plain,
! [X0] :
( ~ sP0(X0)
| ~ are_equipotent(sK5(X0),X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f47,plain,
! [X0] :
( ~ sP0(X0)
| subset(sK5(X0),X0) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_60,plain,
! [X0: $i] :
( subset(sK5(X0),X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_61,plain,
! [X0: $i] :
( ~ sP0(X0)
| ~ are_equipotent(sK5(X0),X0) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_62,plain,
! [X0: $i] :
( ~ sP0(X0)
| ~ in(sK5(X0),X0) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_99,plain,
! [X0: $i] :
( subset(sK5(X0),X0)
| ~ sP0(X0) ),
inference(prop_impl_just,[status(thm)],[c_60]) ).
tcf(c_101,plain,
! [X0: $i] :
( ~ are_equipotent(sK5(X0),X0)
| ~ sP0(X0) ),
inference(prop_impl_just,[status(thm)],[c_61]) ).
tcf(c_102,plain,
! [X0: $i] :
( ~ sP0(X0)
| ~ are_equipotent(sK5(X0),X0) ),
inference(renaming,[status(thm)],[c_101]) ).
tcf(c_103,plain,
! [X0: $i] :
( ~ in(sK5(X0),X0)
| ~ sP0(X0) ),
inference(prop_impl_just,[status(thm)],[c_62]) ).
tcf(c_104,plain,
! [X0: $i] :
( ~ sP0(X0)
| ~ in(sK5(X0),X0) ),
inference(renaming,[status(thm)],[c_103]) ).
tcf(c_416,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,sK10(X2))
| ~ sP0(X0)
| ~ subset(X1,sK10(X2))
| ( sK10(X2) != X0 )
| ( sK5(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_102,c_73]) ).
tcf(c_417,plain,
! [X0: $i] :
( in(sK5(sK10(X0)),sK10(X0))
| ~ sP0(sK10(X0))
| ~ subset(sK5(sK10(X0)),sK10(X0)) ),
inference(unflattening,[status(thm)],[c_416]) ).
tcf(c_425,plain,
! [X0: $i] : ~ sP0(sK10(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_417,c_104,c_99]) ).
tcf(c_645,plain,
! [X0: $i,X1: $i] :
( in(sK9(X1),X1)
| ~ in(sK6,X1)
| ~ in(sK8(X1),X1)
| ( sK10(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_64,c_425]) ).
tcf(c_646,plain,
! [X0: $i] :
( in(sK9(sK10(X0)),sK10(X0))
| ~ in(sK6,sK10(X0))
| ~ in(sK8(sK10(X0)),sK10(X0)) ),
inference(unflattening,[status(thm)],[c_645]) ).
tcf(c_3613,plain,
! [X0: $i,X1: $i] :
( in(X0,sK10(X1))
| in(sK9(sK10(X1)),sK10(X1))
| ~ in(sK6,sK10(X1))
| ~ subset(X0,sK7(sK10(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3595,c_425]) ).
tcf(c_4455,plain,
! [X0: $i] :
( sP0(sK10(X0))
| in(sK9(sK10(X0)),sK10(X0))
| in(sK8(sK10(X0)),sK10(X0))
| ~ in(sK6,sK10(X0)) ),
inference(superposition,[status(thm)],[c_2560,c_3613]) ).
tcf(c_4462,plain,
! [X0: $i] :
( in(sK9(sK10(X0)),sK10(X0))
| in(sK8(sK10(X0)),sK10(X0))
| ~ in(sK6,sK10(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4455,c_425]) ).
tcf(c_4500,plain,
! [X0: $i] :
( in(sK9(sK10(X0)),sK10(X0))
| ~ in(sK6,sK10(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_4462,c_646,c_4462]) ).
tcf(c_4502,plain,
( in(sK9(sK10(sK6)),sK10(sK6))
| ~ in(sK6,sK10(sK6)) ),
inference(instantiation,[status(thm)],[c_4500]) ).
tcf(c_23418,plain,
! [X0: $i] :
( in(sK7(sK10(X0)),sK10(X0))
| ~ in(sK6,sK10(X0))
| ~ in(sK9(sK10(X0)),sK10(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23399,c_425]) ).
tcf(c_23422,plain,
! [X0: $i] :
( subset(sK8(sK10(X0)),sK7(sK10(X0)))
| ~ in(sK6,sK10(X0))
| ~ in(sK9(sK10(X0)),sK10(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23398,c_425]) ).
tcf(c_23426,plain,
! [X0: $i] :
( ~ in(sK6,sK10(X0))
| ~ in(sK9(sK10(X0)),sK10(X0))
| ~ in(sK8(sK10(X0)),sK10(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23397,c_425]) ).
tcf(c_23431,plain,
( in(sK7(sK10(sK6)),sK10(sK6))
| ~ in(sK6,sK10(sK6))
| ~ in(sK9(sK10(sK6)),sK10(sK6)) ),
inference(instantiation,[status(thm)],[c_23418]) ).
tcf(c_23432,plain,
( ~ in(sK6,sK10(sK6))
| ~ in(sK9(sK10(sK6)),sK10(sK6))
| ~ in(sK8(sK10(sK6)),sK10(sK6)) ),
inference(instantiation,[status(thm)],[c_23426]) ).
tcf(c_23433,plain,
( subset(sK8(sK10(sK6)),sK7(sK10(sK6)))
| ~ in(sK6,sK10(sK6))
| ~ in(sK9(sK10(sK6)),sK10(sK6)) ),
inference(instantiation,[status(thm)],[c_23422]) ).
tcf(c_23434,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_23433,c_23432,c_23431,c_12907,c_4502,c_75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU168+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.36 % Computer : n014.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Thu Sep 24 13:01:53 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.41 Running first-order theorem proving
% 0.13/5.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/5.42
% 0.13/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.42
% 0.13/5.42 % Detected problem language: tptp
% 0.13/5.43 % Proving...
% 10.56/7.23 % SZS status Started for theBenchmark.p
% 10.56/7.23 % SZS status Theorem for theBenchmark.p
% 10.56/7.23
% 10.56/7.23 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.56/7.23
% 10.56/7.23 % ------ iProver source info
% 10.56/7.23
% 10.56/7.23 % git: date: 2026-07-19 20:42:38 +0200
% 10.56/7.23 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.56/7.23 % git: non_committed_changes: false
% 10.56/7.23
% 10.56/7.23 % ------ Parsing...
% 10.56/7.23 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.56/7.23
% 10.56/7.23 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 10.56/7.23
% 10.56/7.23 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.56/7.23
% 10.56/7.23 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.56/7.23 % ------ Proving...
% 10.56/7.23 % ------ Problem Properties
% 10.56/7.23
% 10.56/7.23 %
% 10.56/7.23 % clauses 23
% 10.56/7.23 % conjectures 6
% 10.56/7.23 % EPR 4
% 10.56/7.23 % Horn 16
% 10.56/7.23 % unary 4
% 10.56/7.23 % binary 8
% 10.56/7.23 % lits 59
% 10.56/7.23 % lits eq 3
% 10.56/7.23 % fd_pure 0
% 10.56/7.23 % fd_pseudo 0
% 10.56/7.23 % fd_cond 0
% 10.56/7.23 % fd_pseudo_cond 2
% 10.56/7.23 % AC symbols 0
% 10.56/7.23
% 10.56/7.23 % ------ Schedule dynamic 5 is on
% 10.56/7.23
% 10.56/7.23 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.56/7.23
% 10.56/7.23
% 10.56/7.23 % ------
% 10.56/7.23 % Current options:
% 10.56/7.23 % ------
% 10.56/7.23
% 10.56/7.23
% 10.56/7.23 %
% 10.56/7.23
% 10.56/7.23 % ------ Proving...
% 10.56/7.23 %
% 10.56/7.23
% 10.56/7.23 % SZS status Theorem for theBenchmark.p
% 10.56/7.23
% 10.56/7.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.56/7.24
% 10.56/7.24
%------------------------------------------------------------------------------