%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU059+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 02:55:11 PM UTC 2026
% Result : Theorem 0.88s 6.64s
% Output : CNFRefutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 9
% Syntax : Number of formulae : 101 ( 19 unt; 5 def)
% Number of atoms : 512 ( 51 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 494 ( 203 ~; 222 |; 55 &)
% ( 9 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 5 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 : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 178 ( 0 sgn 164 !; 14 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f6,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f26,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> relation_inverse_image(X2,set_difference(X0,X1)) = set_difference(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_funct_1) ).
fof(f27,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> relation_inverse_image(X2,set_difference(X0,X1)) = set_difference(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f30,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f50,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f51,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f50]) ).
fof(f58,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& relation_inverse_image(X2,set_difference(X0,X1)) != set_difference(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(ennf_transformation,[],[f27]) ).
fof(f59,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& relation_inverse_image(X2,set_difference(X0,X1)) != set_difference(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(flattening,[],[f58]) ).
fof(f63,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f30]) ).
fof(f71,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f72,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(apply(X0,X4),X1)
& in(X4,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(apply(X0,X4),X1)
& in(X4,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| ( in(apply(X0,sK0(X0,X1,X2)),X1)
& in(sK0(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ~ in(apply(X0,sK0(X0,X1,X2)),X1)
| ~ in(sK0(X0,X1,X2),relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f73]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( ~ in(X4,X1)
& in(X4,X0) ) )
& ( in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(rectify,[],[f76]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( ~ in(X4,X1)
& in(X4,X0) ) )
& ( in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK1(X0,X1,X2),X2)
| ( ~ in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) ) )
& ( ~ in(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f77]) ).
fof(f90,plain,
( function(sK15)
& relation(sK15)
& relation_inverse_image(sK15,set_difference(sK13,sK14)) != set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15)],[f59]) ).
fof(f91,plain,
! [X0,X1] :
( ? [X2] :
( ( in(X2,X0)
| in(X2,X1) )
& ( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f63]) ).
fof(f92,plain,
! [X0,X1] :
( ( ( in(sK16(X0,X1),X0)
| in(sK16(X0,X1),X1) )
& ( ~ in(sK16(X0,X1),X0)
| ~ in(sK16(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X2,sK16(X0,X1))],[f91]) ).
fof(f98,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X4,X2)
| in(apply(X0,X4),X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f99,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,relation_dom(X0)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f100,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ),
inference(cnf_transformation,[],[f74]) ).
fof(f104,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| ~ in(X4,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f105,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f106,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f140,plain,
function(sK15),
inference(cnf_transformation,[],[f90]) ).
fof(f141,plain,
relation(sK15),
inference(cnf_transformation,[],[f90]) ).
fof(f142,plain,
relation_inverse_image(sK15,set_difference(sK13,sK14)) != set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)),
inference(cnf_transformation,[],[f90]) ).
fof(f145,plain,
! [X0,X1] :
( in(sK16(X0,X1),X0)
| in(sK16(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f92]) ).
fof(f146,plain,
! [X0,X1] :
( ~ in(sK16(X0,X1),X0)
| ~ in(sK16(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f92]) ).
fof(f155,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,relation_inverse_image(X0,X1)) ),
inference(equality_resolution,[],[f100]) ).
fof(f156,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(X4,relation_dom(X0)) ),
inference(equality_resolution,[],[f99]) ).
fof(f157,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(apply(X0,X4),X1) ),
inference(equality_resolution,[],[f98]) ).
fof(f158,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f106]) ).
fof(f159,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f105]) ).
fof(f160,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f104]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0)
| ~ function(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),X2) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,set_difference(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_94,negated_conjecture,
set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)) != relation_inverse_image(sK15,set_difference(sK13,sK14)),
inference(cnf_transformation,[],[f142]) ).
tcf(c_95,negated_conjecture,
relation(sK15),
inference(cnf_transformation,[],[f141]) ).
tcf(c_96,negated_conjecture,
function(sK15),
inference(cnf_transformation,[],[f140]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK16(X0,X1),X1)
| ~ in(sK16(X0,X1),X0) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( in(sK16(X0,X1),X1)
| in(sK16(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_2020,definition,
iPr_def_10 = relation_inverse_image(sK15,sK13),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2021,definition,
iPr_def_11 = relation_inverse_image(sK15,sK14),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2022,definition,
iPr_def_12 = set_difference(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2023,definition,
iPr_def_13 = set_difference(sK13,sK14),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2024,definition,
iPr_def_14 = relation_inverse_image(sK15,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_2025,negated_conjecture,
function(sK15),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_2026,negated_conjecture,
relation(sK15),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_2027,negated_conjecture,
iPr_def_12 != iPr_def_14,
inference(demodulation,[status(thm)],[c_94,c_2023,c_2024,c_2021,c_2020,c_2022]) ).
tcf(c_2756,plain,
! [X0: $i] :
( in(X0,sK13)
| ~ in(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_2023,c_62]) ).
tcf(c_2759,plain,
! [X0: $i] :
( in(X0,iPr_def_10)
| ~ in(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_2022,c_62]) ).
tcf(c_2888,plain,
! [X0: $i] :
( ~ in(X0,iPr_def_13)
| ~ in(X0,sK14) ),
inference(superposition,[status(thm)],[c_2023,c_63]) ).
tcf(c_2891,plain,
! [X0: $i] :
( ~ in(X0,iPr_def_12)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2022,c_63]) ).
tcf(c_3034,plain,
! [X0: $i] :
( in(X0,iPr_def_13)
| in(X0,sK14)
| ~ in(X0,sK13) ),
inference(superposition,[status(thm)],[c_2023,c_61]) ).
tcf(c_3037,plain,
! [X0: $i] :
( in(X0,iPr_def_12)
| in(X0,iPr_def_11)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2022,c_61]) ).
tcf(c_3462,plain,
! [X0: $i] :
( in(X0,relation_dom(sK15))
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2020,c_56]) ).
tcf(c_3464,plain,
! [X0: $i] :
( in(X0,relation_dom(sK15))
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_2024,c_56]) ).
tcf(c_3465,plain,
! [X0: $i] :
( in(X0,relation_dom(sK15))
| ~ in(X0,iPr_def_14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3464,c_2026,c_2025]) ).
tcf(c_3471,plain,
! [X0: $i] :
( in(X0,relation_dom(sK15))
| ~ in(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3462,c_2026,c_2025]) ).
tcf(c_3557,plain,
! [X0: $i] :
( in(apply(sK15,X0),sK13)
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2020,c_57]) ).
tcf(c_3558,plain,
! [X0: $i] :
( in(apply(sK15,X0),sK14)
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2021,c_57]) ).
tcf(c_3559,plain,
! [X0: $i] :
( in(apply(sK15,X0),iPr_def_13)
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_2024,c_57]) ).
tcf(c_3560,plain,
! [X0: $i] :
( in(apply(sK15,X0),iPr_def_13)
| ~ in(X0,iPr_def_14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3559,c_2026,c_2025]) ).
tcf(c_3563,plain,
! [X0: $i] :
( in(apply(sK15,X0),sK14)
| ~ in(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3558,c_2026,c_2025]) ).
tcf(c_3566,plain,
! [X0: $i] :
( in(apply(sK15,X0),sK13)
| ~ in(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3557,c_2026,c_2025]) ).
tcf(c_3736,plain,
! [X0: $i] :
( ~ in(X0,iPr_def_14)
| ~ in(apply(sK15,X0),sK14) ),
inference(superposition,[status(thm)],[c_3560,c_2888]) ).
tcf(c_3737,plain,
! [X0: $i] :
( in(apply(sK15,X0),sK13)
| ~ in(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_3560,c_2756]) ).
tcf(c_5083,plain,
! [X0: $i] :
( in(X0,relation_inverse_image(sK15,sK13))
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(X0,iPr_def_14)
| ~ in(X0,relation_dom(sK15)) ),
inference(superposition,[status(thm)],[c_3737,c_55]) ).
tcf(c_5088,plain,
! [X0: $i] :
( in(X0,iPr_def_10)
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(X0,iPr_def_14)
| ~ in(X0,relation_dom(sK15)) ),
inference(light_normalisation,[status(thm)],[c_5083,c_2020]) ).
tcf(c_5089,plain,
! [X0: $i] :
( in(X0,iPr_def_10)
| ~ in(X0,iPr_def_14)
| ~ in(X0,relation_dom(sK15)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5088,c_2026,c_2025]) ).
tcf(c_5103,plain,
! [X0: $i] :
( in(X0,iPr_def_10)
| ~ in(X0,iPr_def_14) ),
inference(global_subsumption_just,[status(thm)],[c_5089,c_3465,c_5089]) ).
tcf(c_5116,plain,
! [X0: $i] :
( in(sK16(iPr_def_14,X0),iPr_def_10)
| in(sK16(iPr_def_14,X0),X0)
| ( X0 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_100,c_5103]) ).
tcf(c_5474,plain,
! [X0: $i] :
( ~ in(X0,iPr_def_14)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3563,c_3736]) ).
tcf(c_7211,plain,
( in(sK16(iPr_def_14,iPr_def_12),iPr_def_10)
| ( iPr_def_12 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_5116,c_2759]) ).
tcf(c_7222,plain,
in(sK16(iPr_def_14,iPr_def_12),iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_7211,c_2027]) ).
tcf(c_7953,plain,
! [X0: $i] :
( in(apply(sK15,X0),iPr_def_13)
| in(apply(sK15,X0),sK14)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_3566,c_3034]) ).
tcf(c_8120,plain,
( in(sK16(iPr_def_14,iPr_def_12),iPr_def_12)
| in(sK16(iPr_def_14,iPr_def_12),iPr_def_11) ),
inference(superposition,[status(thm)],[c_7222,c_3037]) ).
tcf(c_8466,plain,
( in(sK16(iPr_def_14,iPr_def_12),iPr_def_11)
| ( iPr_def_12 = iPr_def_14 )
| ~ in(sK16(iPr_def_14,iPr_def_12),iPr_def_14) ),
inference(superposition,[status(thm)],[c_8120,c_99]) ).
tcf(c_8475,plain,
( in(sK16(iPr_def_14,iPr_def_12),iPr_def_11)
| ~ in(sK16(iPr_def_14,iPr_def_12),iPr_def_14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8466,c_2027]) ).
tcf(c_8480,plain,
~ in(sK16(iPr_def_14,iPr_def_12),iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_8475,c_5474]) ).
tcf(c_8481,plain,
( in(sK16(iPr_def_14,iPr_def_12),iPr_def_12)
| ( iPr_def_12 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_100,c_8480]) ).
tcf(c_8482,plain,
in(sK16(iPr_def_14,iPr_def_12),iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_8481,c_2027]) ).
tcf(c_8487,plain,
~ in(sK16(iPr_def_14,iPr_def_12),iPr_def_11),
inference(superposition,[status(thm)],[c_8482,c_2891]) ).
tcf(c_8842,plain,
! [X0: $i] :
( in(X0,relation_inverse_image(sK15,sK14))
| in(apply(sK15,X0),iPr_def_13)
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(X0,iPr_def_10)
| ~ in(X0,relation_dom(sK15)) ),
inference(superposition,[status(thm)],[c_7953,c_55]) ).
tcf(c_8853,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| in(apply(sK15,X0),iPr_def_13)
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(X0,iPr_def_10)
| ~ in(X0,relation_dom(sK15)) ),
inference(light_normalisation,[status(thm)],[c_8842,c_2021]) ).
tcf(c_8854,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| in(apply(sK15,X0),iPr_def_13)
| ~ in(X0,iPr_def_10)
| ~ in(X0,relation_dom(sK15)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8853,c_2026,c_2025]) ).
tcf(c_8871,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| in(apply(sK15,X0),iPr_def_13)
| ~ in(X0,iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_8854,c_3471,c_8854]) ).
tcf(c_8884,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| in(X0,relation_inverse_image(sK15,iPr_def_13))
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(X0,iPr_def_10)
| ~ in(X0,relation_dom(sK15)) ),
inference(superposition,[status(thm)],[c_8871,c_55]) ).
tcf(c_8899,plain,
! [X0: $i] :
( in(X0,iPr_def_14)
| in(X0,iPr_def_11)
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(X0,iPr_def_10)
| ~ in(X0,relation_dom(sK15)) ),
inference(light_normalisation,[status(thm)],[c_8884,c_2024]) ).
tcf(c_8900,plain,
! [X0: $i] :
( in(X0,iPr_def_14)
| in(X0,iPr_def_11)
| ~ in(X0,iPr_def_10)
| ~ in(X0,relation_dom(sK15)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8899,c_2026,c_2025]) ).
tcf(c_8943,plain,
! [X0: $i] :
( in(X0,iPr_def_14)
| in(X0,iPr_def_11)
| ~ in(X0,iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_8900,c_3471,c_8900]) ).
tcf(c_8981,plain,
( in(sK16(iPr_def_14,iPr_def_12),iPr_def_14)
| in(sK16(iPr_def_14,iPr_def_12),iPr_def_11) ),
inference(superposition,[status(thm)],[c_7222,c_8943]) ).
tcf(c_8984,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_8981,c_8480,c_8487]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU059+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n008.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 12:40:47 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.43
% 0.15/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.43
% 0.15/5.43 % Detected problem language: tptp
% 0.15/5.44 % Proving...
% 0.88/6.64 % SZS status Started for theBenchmark.p
% 0.88/6.64 % SZS status Theorem for theBenchmark.p
% 0.88/6.64
% 0.88/6.64 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.88/6.64
% 0.88/6.64 % ------ iProver source info
% 0.88/6.64
% 0.88/6.64 % git: date: 2026-07-19 20:42:38 +0200
% 0.88/6.64 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.88/6.64 % git: non_committed_changes: false
% 0.88/6.64
% 0.88/6.64 % ------ Parsing...
% 0.88/6.64 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.88/6.64
% 0.88/6.64 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.88/6.64
% 0.88/6.64 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.88/6.64
% 0.88/6.64 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.88/6.64 % ------ Proving...
% 0.88/6.64 % ------ Problem Properties
% 0.88/6.64
% 0.88/6.64 %
% 0.88/6.64 % clauses 61
% 0.88/6.64 % conjectures 3
% 0.88/6.64 % EPR 27
% 0.88/6.64 % Horn 52
% 0.88/6.64 % unary 31
% 0.88/6.64 % binary 12
% 0.88/6.64 % lits 121
% 0.88/6.64 % lits eq 18
% 0.88/6.64 % fd_pure 0
% 0.88/6.64 % fd_pseudo 0
% 0.88/6.64 % fd_cond 1
% 0.88/6.64 % fd_pseudo_cond 9
% 0.88/6.64 % AC symbols 0
% 0.88/6.64
% 0.88/6.64 % ------ Schedule dynamic 5 is on
% 0.88/6.64
% 0.88/6.64 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.88/6.64
% 0.88/6.64
% 0.88/6.64 % ------
% 0.88/6.64 % Current options:
% 0.88/6.64 % ------
% 0.88/6.64
% 0.88/6.64
% 0.88/6.64 %
% 0.88/6.64
% 0.88/6.64 % ------ Proving...
% 0.88/6.64 %
% 0.88/6.64
% 0.88/6.64 % SZS status Theorem for theBenchmark.p
% 0.88/6.64
% 0.88/6.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.88/6.64
% 0.88/6.64
%------------------------------------------------------------------------------