%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU168+1 : TPTP v9.3.1. Released v3.3.0.
% 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 02:55:43 PM UTC 2026
% Result : Theorem 7.05s 1.97s
% Output : CNFRefutation 7.05s
% 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(f6,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(f7,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)],[f6]) ).
fof(f8,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(f10,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,[],[f7]) ).
fof(f11,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,[],[f8]) ).
fof(f13,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f14,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,[],[f10]) ).
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(flattening,[],[f14]) ).
fof(f16,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,[],[f11]) ).
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(flattening,[],[f16]) ).
fof(f20,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(f21,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,[],[f20]) ).
fof(f22,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))],[f21]) ).
fof(f23,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,[],[f13]) ).
fof(f24,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,[],[f23]) ).
fof(f25,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))],[f24]) ).
fof(f29,plain,
! [X1] :
( sP0(X1)
| ( in(sK7(X1),X1)
& ~ in(powerset(sK7(X1)),X1) )
| ( subset(sK6(X1),sK5(X1))
& in(sK5(X1),X1)
& ~ in(sK6(X1),X1) )
| ~ in(sK4,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X2,sK5(X1)),skolemize(X3,sK6(X1)),skolemize(X4,sK7(X1))],[f19]) ).
fof(f30,plain,
! [X0] :
( ! [X7] :
( in(X7,sK8(X0))
| are_equipotent(X7,sK8(X0))
| ~ subset(X7,sK8(X0)) )
& ! [X4] :
( ( ! [X6] :
( ~ subset(X6,X4)
| in(X6,sK9(X0,X4)) )
& in(sK9(X0,X4),sK8(X0)) )
| ~ in(X4,sK8(X0)) )
& ! [X2,X3] :
( ~ subset(X3,X2)
| ~ in(X2,sK8(X0))
| in(X3,sK8(X0)) )
& in(X0,sK8(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X1,sK8(X0)),skolemize(X5,sK9(X0,X4))],[f17]) ).
fof(f32,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
! [X0,X1] :
( in(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f38,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f43,plain,
! [X1] :
( sP0(X1)
| in(sK7(X1),X1)
| subset(sK6(X1),sK5(X1))
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f44,plain,
! [X1] :
( sP0(X1)
| ~ in(powerset(sK7(X1)),X1)
| subset(sK6(X1),sK5(X1))
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f45,plain,
! [X1] :
( sP0(X1)
| in(sK7(X1),X1)
| in(sK5(X1),X1)
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f46,plain,
! [X1] :
( sP0(X1)
| ~ in(powerset(sK7(X1)),X1)
| in(sK5(X1),X1)
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f47,plain,
! [X1] :
( sP0(X1)
| in(sK7(X1),X1)
| ~ in(sK6(X1),X1)
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f48,plain,
! [X1] :
( sP0(X1)
| ~ in(powerset(sK7(X1)),X1)
| ~ in(sK6(X1),X1)
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f49,plain,
! [X0,X7] :
( in(X7,sK8(X0))
| are_equipotent(X7,sK8(X0))
| ~ subset(X7,sK8(X0)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f50,plain,
! [X0,X6,X4] :
( ~ subset(X6,X4)
| in(X6,sK9(X0,X4))
| ~ in(X4,sK8(X0)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f51,plain,
! [X0,X4] :
( in(sK9(X0,X4),sK8(X0))
| ~ in(X4,sK8(X0)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f52,plain,
! [X2,X3,X0] :
( ~ subset(X3,X2)
| ~ in(X2,sK8(X0))
| in(X3,sK8(X0)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f53,plain,
! [X0] : in(X0,sK8(X0)),
inference(cnf_transformation,[],[f30]) ).
fof(f55,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f32]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_61,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| ~ in(sK4,X0)
| ~ in(sK6(X0),X0)
| ~ in(powerset(sK7(X0)),X0) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_62,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| in(sK7(X0),X0)
| ~ in(sK4,X0)
| ~ in(sK6(X0),X0) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_63,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| in(sK5(X0),X0)
| ~ in(sK4,X0)
| ~ in(powerset(sK7(X0)),X0) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_64,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| in(sK5(X0),X0)
| in(sK7(X0),X0)
| ~ in(sK4,X0) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_65,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| subset(sK6(X0),sK5(X0))
| ~ in(sK4,X0)
| ~ in(powerset(sK7(X0)),X0) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_66,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| in(sK7(X0),X0)
| subset(sK6(X0),sK5(X0))
| ~ in(sK4,X0) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_67,plain,
! [X0: $i] : in(X0,sK8(X0)),
inference(cnf_transformation,[],[f53]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK8(X1))
| ~ subset(X2,X0)
| ~ in(X0,sK8(X1)) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( in(sK9(X1,X0),sK8(X1))
| ~ in(X0,sK8(X1)) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK9(X1,X0))
| ~ subset(X2,X0)
| ~ in(X0,sK8(X1)) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( are_equipotent(X0,sK8(X1))
| in(X0,sK8(X1))
| ~ subset(X0,sK8(X1)) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_73,plain,
in(sK4,sK8(sK4)),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_2543,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| in(sK7(X0),X0)
| subset(sK6(X0),sK5(X0))
| ~ in(sK4,X0) ),
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_2544,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| subset(sK6(X0),sK5(X0))
| ~ in(sK4,X0)
| ~ in(powerset(sK7(X0)),X0) ),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_2545,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| in(sK5(X0),X0)
| in(sK7(X0),X0)
| ~ in(sK4,X0) ),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_2546,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| in(sK5(X0),X0)
| ~ in(sK4,X0)
| ~ in(powerset(sK7(X0)),X0) ),
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_2548,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| ~ in(sK4,X0)
| ~ in(sK6(X0),X0)
| ~ in(powerset(sK7(X0)),X0) ),
inference(demodulation,[status(thm)],[c_61]) ).
tcf(c_3125,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_3301,plain,
! [X0: $i,X1: $i] :
( sP0(sK8(X1))
| in(X0,sK8(X1))
| in(sK7(sK8(X1)),sK8(X1))
| ~ in(sK4,sK8(X1))
| ~ subset(X0,sK5(sK8(X1))) ),
inference(superposition,[status(thm)],[c_2545,c_68]) ).
tcf(c_3303,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK8(X1))
| ~ in(X2,sK8(X1))
| ~ subset(X0,sK9(X1,X2)) ),
inference(superposition,[status(thm)],[c_69,c_68]) ).
tcf(c_3618,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,sK9(X1,X2))
| ~ in(X2,sK8(X1))
| ~ subset(sK2(X0,sK9(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_70,c_54]) ).
tcf(c_4022,plain,
! [X0: $i] :
( in(sK6(sK8(sK4)),sK8(sK4))
| ~ in(X0,sK8(sK4))
| ~ subset(sK6(sK8(sK4)),X0) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_13817,plain,
( in(sK6(sK8(sK4)),sK8(sK4))
| ~ in(sK5(sK8(sK4)),sK8(sK4))
| ~ subset(sK6(sK8(sK4)),sK5(sK8(sK4))) ),
inference(instantiation,[status(thm)],[c_4022]) ).
tcf(c_16508,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),sK9(X1,X0))
| ~ in(X0,sK8(X1)) ),
inference(superposition,[status(thm)],[c_3125,c_3618]) ).
tcf(c_16907,plain,
! [X0: $i,X1: $i] :
( in(powerset(X0),sK8(X1))
| ~ in(X0,sK8(X1)) ),
inference(superposition,[status(thm)],[c_16508,c_3303]) ).
tcf(c_16995,plain,
! [X0: $i] :
( sP0(sK8(X0))
| ~ in(sK4,sK8(X0))
| ~ in(sK7(sK8(X0)),sK8(X0))
| ~ in(sK6(sK8(X0)),sK8(X0)) ),
inference(superposition,[status(thm)],[c_16907,c_2548]) ).
tcf(c_16996,plain,
! [X0: $i] :
( sP0(sK8(X0))
| subset(sK6(sK8(X0)),sK5(sK8(X0)))
| ~ in(sK4,sK8(X0))
| ~ in(sK7(sK8(X0)),sK8(X0)) ),
inference(superposition,[status(thm)],[c_16907,c_2544]) ).
tcf(c_16997,plain,
! [X0: $i] :
( sP0(sK8(X0))
| in(sK5(sK8(X0)),sK8(X0))
| ~ in(sK4,sK8(X0))
| ~ in(sK7(sK8(X0)),sK8(X0)) ),
inference(superposition,[status(thm)],[c_16907,c_2546]) ).
fof(f18,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(f19,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,[],[f15,f18]) ).
fof(f26,plain,
! [X1] :
( ~ sP0(X1)
| ? [X5] :
( ~ in(X5,X1)
& ~ are_equipotent(X5,X1)
& subset(X5,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f27,plain,
! [X0] :
( ~ sP0(X0)
| ? [X1] :
( ~ in(X1,X0)
& ~ are_equipotent(X1,X0)
& subset(X1,X0) ) ),
inference(rectify,[],[f26]) ).
fof(f28,plain,
! [X0] :
( ~ sP0(X0)
| ( ~ in(sK3(X0),X0)
& ~ are_equipotent(sK3(X0),X0)
& subset(sK3(X0),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f27]) ).
fof(f40,plain,
! [X0] :
( ~ sP0(X0)
| ~ in(sK3(X0),X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f41,plain,
! [X0] :
( ~ sP0(X0)
| ~ are_equipotent(sK3(X0),X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f42,plain,
! [X0] :
( ~ sP0(X0)
| subset(sK3(X0),X0) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_58,plain,
! [X0: $i] :
( subset(sK3(X0),X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_59,plain,
! [X0: $i] :
( ~ sP0(X0)
| ~ are_equipotent(sK3(X0),X0) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_60,plain,
! [X0: $i] :
( ~ sP0(X0)
| ~ in(sK3(X0),X0) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_97,plain,
! [X0: $i] :
( subset(sK3(X0),X0)
| ~ sP0(X0) ),
inference(prop_impl_just,[status(thm)],[c_58]) ).
tcf(c_99,plain,
! [X0: $i] :
( ~ are_equipotent(sK3(X0),X0)
| ~ sP0(X0) ),
inference(prop_impl_just,[status(thm)],[c_59]) ).
tcf(c_100,plain,
! [X0: $i] :
( ~ sP0(X0)
| ~ are_equipotent(sK3(X0),X0) ),
inference(renaming,[status(thm)],[c_99]) ).
tcf(c_101,plain,
! [X0: $i] :
( ~ in(sK3(X0),X0)
| ~ sP0(X0) ),
inference(prop_impl_just,[status(thm)],[c_60]) ).
tcf(c_102,plain,
! [X0: $i] :
( ~ sP0(X0)
| ~ in(sK3(X0),X0) ),
inference(renaming,[status(thm)],[c_101]) ).
tcf(c_402,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,sK8(X2))
| ~ sP0(X0)
| ~ subset(X1,sK8(X2))
| ( sK8(X2) != X0 )
| ( sK3(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_100,c_71]) ).
tcf(c_403,plain,
! [X0: $i] :
( in(sK3(sK8(X0)),sK8(X0))
| ~ sP0(sK8(X0))
| ~ subset(sK3(sK8(X0)),sK8(X0)) ),
inference(unflattening,[status(thm)],[c_402]) ).
tcf(c_411,plain,
! [X0: $i] : ~ sP0(sK8(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_403,c_102,c_97]) ).
tcf(c_631,plain,
! [X0: $i,X1: $i] :
( in(sK7(X1),X1)
| ~ in(sK4,X1)
| ~ in(sK6(X1),X1)
| ( sK8(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_62,c_411]) ).
tcf(c_632,plain,
! [X0: $i] :
( in(sK7(sK8(X0)),sK8(X0))
| ~ in(sK4,sK8(X0))
| ~ in(sK6(sK8(X0)),sK8(X0)) ),
inference(unflattening,[status(thm)],[c_631]) ).
tcf(c_3312,plain,
! [X0: $i,X1: $i] :
( in(X0,sK8(X1))
| in(sK7(sK8(X1)),sK8(X1))
| ~ in(sK4,sK8(X1))
| ~ subset(X0,sK5(sK8(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3301,c_411]) ).
tcf(c_3978,plain,
! [X0: $i] :
( sP0(sK8(X0))
| in(sK7(sK8(X0)),sK8(X0))
| in(sK6(sK8(X0)),sK8(X0))
| ~ in(sK4,sK8(X0)) ),
inference(superposition,[status(thm)],[c_2543,c_3312]) ).
tcf(c_3985,plain,
! [X0: $i] :
( in(sK7(sK8(X0)),sK8(X0))
| in(sK6(sK8(X0)),sK8(X0))
| ~ in(sK4,sK8(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3978,c_411]) ).
tcf(c_4024,plain,
! [X0: $i] :
( in(sK7(sK8(X0)),sK8(X0))
| ~ in(sK4,sK8(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_3985,c_632,c_3985]) ).
tcf(c_4026,plain,
( in(sK7(sK8(sK4)),sK8(sK4))
| ~ in(sK4,sK8(sK4)) ),
inference(instantiation,[status(thm)],[c_4024]) ).
tcf(c_17016,plain,
! [X0: $i] :
( in(sK5(sK8(X0)),sK8(X0))
| ~ in(sK4,sK8(X0))
| ~ in(sK7(sK8(X0)),sK8(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16997,c_411]) ).
tcf(c_17020,plain,
! [X0: $i] :
( subset(sK6(sK8(X0)),sK5(sK8(X0)))
| ~ in(sK4,sK8(X0))
| ~ in(sK7(sK8(X0)),sK8(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16996,c_411]) ).
tcf(c_17024,plain,
! [X0: $i] :
( ~ in(sK4,sK8(X0))
| ~ in(sK7(sK8(X0)),sK8(X0))
| ~ in(sK6(sK8(X0)),sK8(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16995,c_411]) ).
tcf(c_17029,plain,
( in(sK5(sK8(sK4)),sK8(sK4))
| ~ in(sK4,sK8(sK4))
| ~ in(sK7(sK8(sK4)),sK8(sK4)) ),
inference(instantiation,[status(thm)],[c_17016]) ).
tcf(c_17030,plain,
( ~ in(sK4,sK8(sK4))
| ~ in(sK7(sK8(sK4)),sK8(sK4))
| ~ in(sK6(sK8(sK4)),sK8(sK4)) ),
inference(instantiation,[status(thm)],[c_17024]) ).
tcf(c_17031,plain,
( subset(sK6(sK8(sK4)),sK5(sK8(sK4)))
| ~ in(sK4,sK8(sK4))
| ~ in(sK7(sK8(sK4)),sK8(sK4)) ),
inference(instantiation,[status(thm)],[c_17020]) ).
tcf(c_17032,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_17031,c_17030,c_17029,c_13817,c_4026,c_73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU168+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.60 % Computer : n014.cluster.edu
% 0.10/0.60 % Model : x86_64 x86_64
% 0.10/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.60 % Memory : 8046.5625MB
% 0.10/0.60 % OS : Linux 6.8.0-71-generic
% 0.10/0.60 % CPULimit : 300
% 0.10/0.60 % WCLimit : 300
% 0.10/0.60 % DateTime : Thu Sep 24 13:02:03 UTC 2026
% 0.10/0.60 % CPUTime :
% 0.10/0.60 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.64 Running first-order theorem proving
% 0.15/0.64 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.65
% 0.15/0.65 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.65
% 0.15/0.65 % Detected problem language: tptp
% 0.15/0.66 % Proving...
% 7.05/1.97 % SZS status Started for theBenchmark.p
% 7.05/1.97 % SZS status Theorem for theBenchmark.p
% 7.05/1.97
% 7.05/1.97 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.05/1.97
% 7.05/1.97 % ------ iProver source info
% 7.05/1.97
% 7.05/1.97 % git: date: 2026-07-19 20:42:38 +0200
% 7.05/1.97 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.05/1.97 % git: non_committed_changes: false
% 7.05/1.97
% 7.05/1.97 % ------ Parsing...
% 7.05/1.97 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.05/1.97
% 7.05/1.97 % ------ 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 %
% 7.05/1.97
% 7.05/1.97 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.05/1.97
% 7.05/1.97 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.05/1.97 % ------ Proving...
% 7.05/1.97 % ------ Problem Properties
% 7.05/1.97
% 7.05/1.97 %
% 7.05/1.97 % clauses 22
% 7.05/1.97 % conjectures 6
% 7.05/1.97 % EPR 3
% 7.05/1.97 % Horn 15
% 7.05/1.97 % unary 3
% 7.05/1.97 % binary 8
% 7.05/1.97 % lits 58
% 7.05/1.97 % lits eq 2
% 7.05/1.97 % fd_pure 0
% 7.05/1.97 % fd_pseudo 0
% 7.05/1.97 % fd_cond 0
% 7.05/1.97 % fd_pseudo_cond 2
% 7.05/1.97 % AC symbols 0
% 7.05/1.97
% 7.05/1.97 % ------ Schedule dynamic 5 is on
% 7.05/1.97
% 7.05/1.97 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.05/1.97
% 7.05/1.97
% 7.05/1.97 % ------
% 7.05/1.97 % Current options:
% 7.05/1.97 % ------
% 7.05/1.97
% 7.05/1.97
% 7.05/1.97 %
% 7.05/1.97
% 7.05/1.97 % ------ Proving...
% 7.05/1.97 %
% 7.05/1.97
% 7.05/1.97 % SZS status Theorem for theBenchmark.p
% 7.05/1.97
% 7.05/1.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.05/1.97
% 7.05/1.97
%------------------------------------------------------------------------------