%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU079+1 : 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 : n006.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 02:55:20 PM UTC 2026
% Result : Theorem 51.73s 11.95s
% Output : CNFRefutation 51.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 99 ( 11 unt; 0 def)
% Number of atoms : 508 ( 55 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 684 ( 275 ~; 287 |; 85 &)
% ( 22 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 3 con; 0-4 aty)
% Number of variables : 337 ( 0 sgn 287 !; 50 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f7,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f8,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f10,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f11,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f12,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f13,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f40,conjecture,
! [X0,X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_rng(X1),relation_dom(X2))
=> subset(relation_inverse_image(X1,X0),relation_inverse_image(relation_composition(X1,X2),relation_image(X2,X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_funct_1) ).
fof(f41,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_rng(X1),relation_dom(X2))
=> subset(relation_inverse_image(X1,X0),relation_inverse_image(relation_composition(X1,X2),relation_image(X2,X0))) ) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f60,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f61,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f62,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f63,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f64,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f65,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) ) ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f66,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f67,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(flattening,[],[f66]) ).
fof(f81,plain,
? [X0,X1] :
( relation(X1)
& ? [X2] :
( relation(X2)
& subset(relation_rng(X1),relation_dom(X2))
& ~ subset(relation_inverse_image(X1,X0),relation_inverse_image(relation_composition(X1,X2),relation_image(X2,X0))) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f82,plain,
? [X0,X1] :
( relation(X1)
& ? [X2] :
( relation(X2)
& subset(relation_rng(X1),relation_dom(X2))
& ~ subset(relation_inverse_image(X1,X0),relation_inverse_image(relation_composition(X1,X2),relation_image(X2,X0))) ) ),
inference(flattening,[],[f81]) ).
fof(f92,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) )
& ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f60]) ).
fof(f93,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ? [X8] :
( in(X8,X1)
& in(ordered_pair(X8,X6),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) )
| in(X6,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,X3),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(rectify,[],[f92]) ).
fof(f94,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( in(sK2(X0,X1,X6),X1)
& in(ordered_pair(sK2(X0,X1,X6),X6),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) )
| in(X6,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| ( in(sK1(X0,X1,X2),X1)
& in(ordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),X0) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,sK0(X0,X1,X2)),X0) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X5,sK1(X0,X1,X2)),skolemize(X8,sK2(X0,X1,X6))],[f93]) ).
fof(f95,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) )
& ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f96,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ? [X8] :
( in(X8,X1)
& in(ordered_pair(X6,X8),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) )
| in(X6,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X5] :
( in(X5,X1)
& in(ordered_pair(X3,X5),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(rectify,[],[f95]) ).
fof(f97,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( in(sK5(X0,X1,X6),X1)
& in(ordered_pair(X6,sK5(X0,X1,X6)),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) )
| in(X6,X2) ) ) )
& ( ( ( in(sK3(X0,X1,X2),X2)
| ( in(sK4(X0,X1,X2),X1)
& in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X0) ) )
& ( ~ in(sK3(X0,X1,X2),X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(sK3(X0,X1,X2),X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X3,sK3(X0,X1,X2)),skolemize(X5,sK4(X0,X1,X2)),skolemize(X8,sK5(X0,X1,X6))],[f96]) ).
fof(f98,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,[],[f62]) ).
fof(f99,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,[],[f98]) ).
fof(f100,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK6(X0,X1),X0)
& ~ in(sK6(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f99]) ).
fof(f101,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] : in(ordered_pair(X2,X3),X0) )
& ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] : in(ordered_pair(X2,X3),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f102,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] : in(ordered_pair(X5,X7),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] : in(ordered_pair(X2,X4),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(rectify,[],[f101]) ).
fof(f103,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(X5,sK9(X0,X5)),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK7(X0,X1),X1)
| in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0) )
& ( ~ in(sK7(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(sK7(X0,X1),X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X2,sK7(X0,X1)),skolemize(X4,sK8(X0,X1)),skolemize(X7,sK9(X0,X5))],[f102]) ).
fof(f104,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(nnf_transformation,[],[f64]) ).
fof(f105,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] : in(ordered_pair(X7,X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] : in(ordered_pair(X4,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(rectify,[],[f104]) ).
fof(f106,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(sK12(X0,X5),X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK10(X0,X1),X1)
| in(ordered_pair(sK11(X0,X1),sK10(X0,X1)),X0) )
& ( ~ in(sK10(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK10(X0,X1)),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X2,sK10(X0,X1)),skolemize(X4,sK11(X0,X1)),skolemize(X7,sK12(X0,X5))],[f105]) ).
fof(f107,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_composition(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) )
& ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f65]) ).
fof(f108,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_composition(X0,X1) != X2
| ! [X7,X8] :
( ( ~ in(ordered_pair(X7,X8),X2)
| ? [X10] :
( in(ordered_pair(X10,X8),X1)
& in(ordered_pair(X7,X10),X0) ) )
& ( ! [X9] :
( ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0) )
| in(ordered_pair(X7,X8),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ? [X6] :
( in(ordered_pair(X6,X4),X1)
& in(ordered_pair(X3,X6),X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(rectify,[],[f107]) ).
fof(f109,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_composition(X0,X1) != X2
| ! [X7,X8] :
( ( ~ in(ordered_pair(X7,X8),X2)
| ( in(ordered_pair(sK16(X0,X1,X7,X8),X8),X1)
& in(ordered_pair(X7,sK16(X0,X1,X7,X8)),X0) ) )
& ( ! [X9] :
( ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0) )
| in(ordered_pair(X7,X8),X2) ) ) )
& ( ( ( in(ordered_pair(sK13(X0,X1,X2),sK14(X0,X1,X2)),X2)
| ( in(ordered_pair(sK15(X0,X1,X2),sK14(X0,X1,X2)),X1)
& in(ordered_pair(sK13(X0,X1,X2),sK15(X0,X1,X2)),X0) ) )
& ( ~ in(ordered_pair(sK13(X0,X1,X2),sK14(X0,X1,X2)),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,sK14(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK13(X0,X1,X2),X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16]),skolemize(X3,sK13(X0,X1,X2)),skolemize(X4,sK14(X0,X1,X2)),skolemize(X6,sK15(X0,X1,X2)),skolemize(X10,sK16(X0,X1,X7,X8))],[f108]) ).
fof(f121,plain,
( relation(sK29)
& relation(sK30)
& subset(relation_rng(sK29),relation_dom(sK30))
& ~ subset(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28,sK29,sK30]),skolemize(X0,sK28),skolemize(X1,sK29),skolemize(X2,sK30)],[f82]) ).
fof(f131,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0)
| in(X6,X2) ),
inference(cnf_transformation,[],[f94]) ).
fof(f135,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK5(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f136,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(ordered_pair(X6,sK5(X0,X1,X6)),X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f137,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0)
| in(X6,X2) ),
inference(cnf_transformation,[],[f97]) ).
fof(f141,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f142,plain,
! [X0,X1] :
( in(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f143,plain,
! [X0,X1] :
( ~ in(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f144,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(X5,sK9(X0,X5)),X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f149,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f152,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f155,plain,
! [X2,X0,X1,X8,X9,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0)
| in(ordered_pair(X7,X8),X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f159,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f201,plain,
relation(sK29),
inference(cnf_transformation,[],[f121]) ).
fof(f202,plain,
relation(sK30),
inference(cnf_transformation,[],[f121]) ).
fof(f203,plain,
subset(relation_rng(sK29),relation_dom(sK30)),
inference(cnf_transformation,[],[f121]) ).
fof(f204,plain,
~ subset(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),
inference(cnf_transformation,[],[f121]) ).
fof(f216,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X7,X6),singleton(X7)),X0)
| in(X6,X2) ),
inference(definition_unfolding,[],[f131,f152]) ).
fof(f220,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| in(X6,X2) ),
inference(definition_unfolding,[],[f137,f152]) ).
fof(f221,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(unordered_pair(unordered_pair(X6,sK5(X0,X1,X6)),singleton(X6)),X0) ),
inference(definition_unfolding,[],[f136,f152]) ).
fof(f225,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,sK9(X0,X5)),singleton(X5)),X0) ),
inference(definition_unfolding,[],[f144,f152]) ).
fof(f228,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| in(X5,X1) ),
inference(definition_unfolding,[],[f149,f152]) ).
fof(f233,plain,
! [X2,X0,X1,X8,X9,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X9,X8),singleton(X9)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X9),singleton(X7)),X0)
| in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),X2) ),
inference(definition_unfolding,[],[f155,f152,f152,f152]) ).
fof(f237,plain,
! [X0,X1,X6,X7] :
( ~ relation(X0)
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X7,X6),singleton(X7)),X0)
| in(X6,relation_image(X0,X1)) ),
inference(equality_resolution,[],[f216]) ).
fof(f240,plain,
! [X0,X1,X6,X7] :
( ~ relation(X0)
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| in(X6,relation_inverse_image(X0,X1)) ),
inference(equality_resolution,[],[f220]) ).
fof(f241,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| in(unordered_pair(unordered_pair(X6,sK5(X0,X1,X6)),singleton(X6)),X0) ),
inference(equality_resolution,[],[f221]) ).
fof(f242,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| in(sK5(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f135]) ).
fof(f244,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_dom(X0))
| in(unordered_pair(unordered_pair(X5,sK9(X0,X5)),singleton(X5)),X0) ),
inference(equality_resolution,[],[f225]) ).
fof(f245,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| in(X5,relation_rng(X0)) ),
inference(equality_resolution,[],[f228]) ).
fof(f247,plain,
! [X0,X1,X8,X9,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(unordered_pair(unordered_pair(X9,X8),singleton(X9)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X9),singleton(X7)),X0)
| in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1)) ),
inference(equality_resolution,[],[f233]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,relation_image(X2,X3))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f237]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f240]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK5(X1,X2,X0)),singleton(X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f241]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(X1,X2,X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f242]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,sK9(X1,X0)),singleton(X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f244]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f245]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X0,X3),singleton(X0)),relation_composition(X2,X4))
| ~ relation(X4)
| ~ relation(X2)
| ~ relation(relation_composition(X2,X4))
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X4)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f247]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_124,negated_conjecture,
~ subset(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),
inference(cnf_transformation,[],[f204]) ).
tcf(c_125,negated_conjecture,
subset(relation_rng(sK29),relation_dom(sK30)),
inference(cnf_transformation,[],[f203]) ).
tcf(c_126,negated_conjecture,
relation(sK30),
inference(cnf_transformation,[],[f202]) ).
tcf(c_127,negated_conjecture,
relation(sK29),
inference(cnf_transformation,[],[f201]) ).
tcf(c_264,plain,
( subset(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))
| in(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),relation_inverse_image(sK29,sK28)) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_506,plain,
( in(unordered_pair(unordered_pair(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),singleton(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),sK29)
| ~ relation(sK29)
| ~ in(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),relation_inverse_image(sK29,sK28)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_507,plain,
( in(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),sK28)
| ~ relation(sK29)
| ~ in(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),relation_inverse_image(sK29,sK28)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_1060,plain,
( in(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),relation_rng(sK29))
| ~ relation(sK29)
| ~ in(unordered_pair(unordered_pair(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),singleton(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),sK29) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_1095,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_image(X1,sK28))
| ~ relation(X1)
| ~ in(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),sK28)
| ~ in(unordered_pair(unordered_pair(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),X0),singleton(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),X1) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_2621,plain,
( relation(relation_composition(sK29,sK30))
| ~ relation(sK30)
| ~ relation(sK29) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_2927,plain,
! [X0: $i] :
( in(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),X0)
| ~ subset(relation_rng(sK29),X0)
| ~ in(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),relation_rng(sK29)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_12169,plain,
( in(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),relation_dom(sK30))
| ~ subset(relation_rng(sK29),relation_dom(sK30))
| ~ in(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),relation_rng(sK29)) ),
inference(instantiation,[status(thm)],[c_2927]) ).
tcf(c_13814,plain,
( in(unordered_pair(unordered_pair(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),singleton(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),sK30)
| ~ relation(sK30)
| ~ in(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),relation_dom(sK30)) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_22821,plain,
( in(sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),relation_image(sK30,sK28))
| ~ relation(sK30)
| ~ in(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),sK28)
| ~ in(unordered_pair(unordered_pair(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),singleton(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),sK30) ),
inference(instantiation,[status(thm)],[c_1095]) ).
tcf(c_66020,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),singleton(X0)),relation_composition(X1,sK30))
| ~ relation(sK30)
| ~ relation(X1)
| ~ relation(relation_composition(X1,sK30))
| ~ in(unordered_pair(unordered_pair(X0,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),singleton(X0)),X1)
| ~ in(unordered_pair(unordered_pair(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),singleton(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),sK30) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_70620,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_inverse_image(X1,relation_image(sK30,sK28)))
| ~ relation(X1)
| ~ in(sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),relation_image(sK30,sK28))
| ~ in(unordered_pair(unordered_pair(X0,sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),singleton(X0)),X1) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_73670,plain,
( in(unordered_pair(unordered_pair(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),singleton(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),relation_composition(sK29,sK30))
| ~ relation(sK30)
| ~ relation(sK29)
| ~ relation(relation_composition(sK29,sK30))
| ~ in(unordered_pair(unordered_pair(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),singleton(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),sK29)
| ~ in(unordered_pair(unordered_pair(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),singleton(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),sK30) ),
inference(instantiation,[status(thm)],[c_66020]) ).
tcf(c_98038,plain,
( in(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))
| ~ relation(relation_composition(sK29,sK30))
| ~ in(sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),relation_image(sK30,sK28))
| ~ in(unordered_pair(unordered_pair(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),singleton(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),relation_composition(sK29,sK30)) ),
inference(instantiation,[status(thm)],[c_70620]) ).
tcf(c_100981,plain,
( subset(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))
| ~ in(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_100982,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_100981,c_98038,c_73670,c_22821,c_13814,c_12169,c_2621,c_1060,c_506,c_507,c_264,c_124,c_125,c_126,c_127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU079+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 12:42:41 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 51.73/11.95 % SZS status Started for theBenchmark.p
% 51.73/11.95 % SZS status Theorem for theBenchmark.p
% 51.73/11.95
% 51.73/11.95 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 51.73/11.95
% 51.73/11.95 % ------ iProver source info
% 51.73/11.95
% 51.73/11.95 % git: date: 2026-07-19 20:42:38 +0200
% 51.73/11.95 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 51.73/11.95 % git: non_committed_changes: false
% 51.73/11.95
% 51.73/11.95 % ------ Parsing...
% 51.73/11.95 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 51.73/11.95
% 51.73/11.95 % ------ Preprocessing... sf_s rm: 7 0s sf_e sf_s rm: 2 0s sf_e %
% 51.73/11.95
% 51.73/11.95 % ------ Preprocessing...%
% 51.73/11.95
% 51.73/11.95 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 51.73/11.95 % ------ Proving...
% 51.73/11.95 % ------ Problem Properties
% 51.73/11.95
% 51.73/11.95 %
% 51.73/11.95 % clauses 79
% 51.73/11.95 % conjectures 4
% 51.73/11.95 % EPR 24
% 51.73/11.95 % Horn 68
% 51.73/11.95 % unary 26
% 51.73/11.95 % binary 15
% 51.73/11.95 % lits 201
% 51.73/11.95 % lits eq 16
% 51.73/11.95 % fd_pure 0
% 51.73/11.95 % fd_pseudo 0
% 51.73/11.95 % fd_cond 1
% 51.73/11.95 % fd_pseudo_cond 14
% 51.73/11.95 % AC symbols 0
% 51.73/11.95
% 51.73/11.95 % ------ Input Options Time Limit: Unbounded
% 51.73/11.95
% 51.73/11.95
% 51.73/11.95 % ------
% 51.73/11.95 % Current options:
% 51.73/11.95 % ------
% 51.73/11.95
% 51.73/11.95
% 51.73/11.95 %
% 51.73/11.95
% 51.73/11.95 % ------ Proving...
% 51.73/11.95 %
% 51.73/11.95
% 51.73/11.95 % SZS status Theorem for theBenchmark.p
% 51.73/11.95
% 51.73/11.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 51.73/11.96
% 51.73/11.96
%------------------------------------------------------------------------------