%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU213+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 : n002.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 02:55:55 PM UTC 2026
% Result : Theorem 51.57s 14.85s
% Output : CNFRefutation 51.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 150 ( 15 unt; 0 def)
% Number of atoms : 612 ( 74 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 796 ( 334 ~; 348 |; 78 &)
% ( 16 <=>; 18 =>; 0 <=; 2 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-4 aty)
% Number of variables : 320 ( 0 sgn 290 !; 30 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( ( ~ in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f6,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(f7,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(f8,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(f15,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f18,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
fof(f26,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f27,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f35,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f36,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f40,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f41,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f46,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f47,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( ~ in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f48,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( ~ in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f50,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,[],[f8]) ).
fof(f51,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(ennf_transformation,[],[f15]) ).
fof(f52,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f54,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
inference(flattening,[],[f53]) ).
fof(f57,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(ennf_transformation,[],[f26]) ).
fof(f58,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f62,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f63,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& ? [X2] :
( function(X2)
& relation(X2)
& ( in(X0,relation_dom(relation_composition(X2,X1)))
<~> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f64,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& ? [X2] :
( function(X2)
& relation(X2)
& ( in(X0,relation_dom(relation_composition(X2,X1)))
<~> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ) ) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f66,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f65]) ).
fof(f68,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f69,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f70,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( ( apply(X0,X1) != X2
| X2 = empty_set )
& ( empty_set != X2
| X2 = apply(X0,X1) ) ) )
& ( ~ in(X1,relation_dom(X0))
| ( ( apply(X0,X1) != X2
| in(ordered_pair(X1,X2),X0) )
& ( ~ in(ordered_pair(X1,X2),X0)
| X2 = apply(X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f71,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,[],[f49]) ).
fof(f72,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,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(X5,sK2(X0,X5)),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0) )
& ( ~ in(sK0(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(sK0(X0,X1),X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X4,sK1(X0,X1)),skolemize(X7,sK2(X0,X5))],[f72]) ).
fof(f74,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,[],[f50]) ).
fof(f75,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,[],[f74]) ).
fof(f76,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(sK6(X0,X1,X7,X8),X8),X1)
& in(ordered_pair(X7,sK6(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(sK3(X0,X1,X2),sK4(X0,X1,X2)),X2)
| ( in(ordered_pair(sK5(X0,X1,X2),sK4(X0,X1,X2)),X1)
& in(ordered_pair(sK3(X0,X1,X2),sK5(X0,X1,X2)),X0) ) )
& ( ~ in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,sK4(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK3(X0,X1,X2),X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X3,sK3(X0,X1,X2)),skolemize(X4,sK4(X0,X1,X2)),skolemize(X6,sK5(X0,X1,X2)),skolemize(X10,sK6(X0,X1,X7,X8))],[f75]) ).
fof(f84,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& ? [X2] :
( function(X2)
& relation(X2)
& ( in(X0,relation_dom(relation_composition(X2,X1)))
| ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
& ( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2)) ) ) ),
inference(nnf_transformation,[],[f64]) ).
fof(f85,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& ? [X2] :
( function(X2)
& relation(X2)
& ( in(X0,relation_dom(relation_composition(X2,X1)))
| ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
& ( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2)) ) ) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
( function(sK15)
& relation(sK15)
& function(sK16)
& relation(sK16)
& ( in(sK14,relation_dom(relation_composition(sK16,sK15)))
| ( in(apply(sK16,sK14),relation_dom(sK15))
& in(sK14,relation_dom(sK16)) ) )
& ( ~ in(sK14,relation_dom(relation_composition(sK16,sK15)))
| ~ in(apply(sK16,sK14),relation_dom(sK15))
| ~ in(sK14,relation_dom(sK16)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X0,sK14),skolemize(X1,sK15),skolemize(X2,sK16)],[f85]) ).
fof(f89,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f93,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| apply(X0,X1) != X2
| in(ordered_pair(X1,X2),X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f94,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(ordered_pair(X1,X2),X0)
| apply(X0,X1) = X2 ),
inference(cnf_transformation,[],[f70]) ).
fof(f95,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(X5,sK2(X0,X5)),X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f96,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f97,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK0(X0,X1),X1)
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| relation_dom(X0) = X1 ),
inference(cnf_transformation,[],[f73]) ).
fof(f99,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f100,plain,
! [X2,X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(ordered_pair(X7,X8),X2)
| in(ordered_pair(sK6(X0,X1,X7,X8),X8),X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f101,plain,
! [X2,X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(ordered_pair(X7,X8),X2)
| in(ordered_pair(X7,sK6(X0,X1,X7,X8)),X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f102,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,[],[f76]) ).
fof(f106,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f109,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| empty(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f120,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f122,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f134,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f135,plain,
function(sK15),
inference(cnf_transformation,[],[f86]) ).
fof(f136,plain,
relation(sK15),
inference(cnf_transformation,[],[f86]) ).
fof(f137,plain,
function(sK16),
inference(cnf_transformation,[],[f86]) ).
fof(f138,plain,
relation(sK16),
inference(cnf_transformation,[],[f86]) ).
fof(f139,plain,
( in(sK14,relation_dom(relation_composition(sK16,sK15)))
| in(apply(sK16,sK14),relation_dom(sK15)) ),
inference(cnf_transformation,[],[f86]) ).
fof(f140,plain,
( in(sK14,relation_dom(relation_composition(sK16,sK15)))
| in(sK14,relation_dom(sK16)) ),
inference(cnf_transformation,[],[f86]) ).
fof(f141,plain,
( ~ in(sK14,relation_dom(relation_composition(sK16,sK15)))
| ~ in(apply(sK16,sK14),relation_dom(sK15))
| ~ in(sK14,relation_dom(sK16)) ),
inference(cnf_transformation,[],[f86]) ).
fof(f142,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f144,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f145,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f146,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| apply(X0,X1) = X2 ),
inference(definition_unfolding,[],[f94,f99]) ).
fof(f147,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| apply(X0,X1) != X2
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0) ),
inference(definition_unfolding,[],[f93,f99]) ).
fof(f149,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK0(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X0)
| relation_dom(X0) = X1 ),
inference(definition_unfolding,[],[f97,f99]) ).
fof(f150,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| in(X5,X1) ),
inference(definition_unfolding,[],[f96,f99]) ).
fof(f151,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,sK2(X0,X5)),singleton(X5)),X0) ),
inference(definition_unfolding,[],[f95,f99]) ).
fof(f155,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,[],[f102,f99,f99,f99]) ).
fof(f156,plain,
! [X2,X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),X2)
| in(unordered_pair(unordered_pair(X7,sK6(X0,X1,X7,X8)),singleton(X7)),X0) ),
inference(definition_unfolding,[],[f101,f99,f99]) ).
fof(f157,plain,
! [X2,X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),X2)
| in(unordered_pair(unordered_pair(sK6(X0,X1,X7,X8),X8),singleton(sK6(X0,X1,X7,X8))),X1) ),
inference(definition_unfolding,[],[f100,f99,f99]) ).
fof(f159,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| in(unordered_pair(unordered_pair(X1,apply(X0,X1)),singleton(X1)),X0) ),
inference(equality_resolution,[],[f147]) ).
fof(f162,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| in(X5,relation_dom(X0)) ),
inference(equality_resolution,[],[f150]) ).
fof(f163,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_dom(X0))
| in(unordered_pair(unordered_pair(X5,sK2(X0,X5)),singleton(X5)),X0) ),
inference(equality_resolution,[],[f151]) ).
fof(f164,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,[],[f155]) ).
fof(f165,plain,
! [X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1))
| in(unordered_pair(unordered_pair(X7,sK6(X0,X1,X7,X8)),singleton(X7)),X0) ),
inference(equality_resolution,[],[f156]) ).
fof(f166,plain,
! [X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1))
| in(unordered_pair(unordered_pair(sK6(X0,X1,X7,X8),X8),singleton(sK6(X0,X1,X7,X8))),X1) ),
inference(equality_resolution,[],[f157]) ).
tcf(c_51,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,X0) = X1 )
| ~ relation(X2)
| ~ function(X2)
| ~ in(X0,relation_dom(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,apply(X1,X0)),singleton(X0)),X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X0)
| ( relation_dom(X0) = X1 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,sK2(X1,X0)),singleton(X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_64,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,[],[f164]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,sK6(X2,X3,X0,X1)),singleton(X0)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_composition(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(X2,X3)) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(sK6(X2,X3,X0,X1),X1),singleton(sK6(X2,X3,X0,X1))),X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_composition(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(X2,X3)) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_81,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_82,plain,
! [X0: $i] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_96,negated_conjecture,
( ~ in(sK14,relation_dom(sK16))
| ~ in(sK14,relation_dom(relation_composition(sK16,sK15)))
| ~ in(apply(sK16,sK14),relation_dom(sK15)) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_97,negated_conjecture,
( in(sK14,relation_dom(sK16))
| in(sK14,relation_dom(relation_composition(sK16,sK15))) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_98,negated_conjecture,
( in(sK14,relation_dom(relation_composition(sK16,sK15)))
| in(apply(sK16,sK14),relation_dom(sK15)) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_99,negated_conjecture,
relation(sK16),
inference(cnf_transformation,[],[f138]) ).
tcf(c_100,negated_conjecture,
function(sK16),
inference(cnf_transformation,[],[f137]) ).
tcf(c_101,negated_conjecture,
relation(sK15),
inference(cnf_transformation,[],[f136]) ).
tcf(c_102,negated_conjecture,
function(sK15),
inference(cnf_transformation,[],[f135]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,X0) = X1 )
| ~ relation(X2)
| ~ function(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(global_subsumption_just,[status(thm)],[c_53,c_59,c_53]) ).
tcf(c_170,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_180,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X0) = relation_dom(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_182,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ element(X1,X2)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_215,plain,
( in(unordered_pair(unordered_pair(sK14,sK2(relation_composition(sK16,sK15),sK14)),singleton(sK14)),relation_composition(sK16,sK15))
| ~ relation(relation_composition(sK16,sK15))
| ~ in(sK14,relation_dom(relation_composition(sK16,sK15))) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_250,plain,
( in(unordered_pair(unordered_pair(sK14,apply(sK16,sK14)),singleton(sK14)),sK16)
| ~ relation(sK16)
| ~ function(sK16)
| ~ in(sK14,relation_dom(sK16)) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_256,plain,
( in(unordered_pair(unordered_pair(apply(sK16,sK14),apply(sK15,apply(sK16,sK14))),singleton(apply(sK16,sK14))),sK15)
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(apply(sK16,sK14),relation_dom(sK15)) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_372,plain,
( relation(relation_composition(sK16,sK15))
| ~ relation(sK15)
| ~ relation(sK16) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_652,plain,
( in(sK14,relation_dom(relation_composition(sK16,sK15)))
| ~ empty(relation_dom(sK15)) ),
inference(superposition,[status(thm)],[c_98,c_105]) ).
tcf(c_726,plain,
( ~ empty(relation_dom(sK15))
| ~ empty(relation_dom(relation_composition(sK16,sK15))) ),
inference(superposition,[status(thm)],[c_652,c_105]) ).
tcf(c_780,plain,
( ~ empty(relation_dom(sK15))
| ~ empty(relation_composition(sK16,sK15)) ),
inference(superposition,[status(thm)],[c_82,c_726]) ).
tcf(c_876,plain,
( in(unordered_pair(unordered_pair(sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14)),sK2(relation_composition(sK16,sK15),sK14)),singleton(sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14)))),sK15)
| ~ relation(sK15)
| ~ relation(sK16)
| ~ relation(relation_composition(sK16,sK15))
| ~ in(unordered_pair(unordered_pair(sK14,sK2(relation_composition(sK16,sK15),sK14)),singleton(sK14)),relation_composition(sK16,sK15)) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_877,plain,
( in(unordered_pair(unordered_pair(sK14,sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14))),singleton(sK14)),sK16)
| ~ relation(sK15)
| ~ relation(sK16)
| ~ relation(relation_composition(sK16,sK15))
| ~ in(unordered_pair(unordered_pair(sK14,sK2(relation_composition(sK16,sK15),sK14)),singleton(sK14)),relation_composition(sK16,sK15)) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_881,plain,
( ~ relation(sK16)
| ~ empty(sK15)
| ~ empty(relation_dom(sK15)) ),
inference(superposition,[status(thm)],[c_69,c_780]) ).
tcf(c_882,plain,
( ~ empty(relation_dom(sK15))
| ~ empty(sK15) ),
inference(global_subsumption_just,[status(thm)],[c_881,c_99,c_881]) ).
tcf(c_883,plain,
( ~ empty(sK15)
| ~ empty(relation_dom(sK15)) ),
inference(renaming,[status(thm)],[c_882]) ).
tcf(c_886,plain,
~ empty(sK15),
inference(forward_subsumption_resolution,[status(thm)],[c_883,c_82]) ).
tcf(c_1071,plain,
( empty(relation_dom(sK15))
| in(apply(sK16,sK14),relation_dom(sK15))
| ~ element(apply(sK16,sK14),relation_dom(sK15)) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_1079,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,apply(sK15,apply(sK16,sK14))),singleton(X0)),relation_composition(X1,sK15))
| ~ relation(sK15)
| ~ relation(X1)
| ~ relation(relation_composition(X1,sK15))
| ~ in(unordered_pair(unordered_pair(X0,apply(sK16,sK14)),singleton(X0)),X1)
| ~ in(unordered_pair(unordered_pair(apply(sK16,sK14),apply(sK15,apply(sK16,sK14))),singleton(apply(sK16,sK14))),sK15) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_1585,plain,
! [X0: $i,X1: $i] :
( element(X0,relation_dom(X1))
| ~ in(X0,relation_dom(X1)) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_2166,plain,
( in(sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14)),relation_dom(sK15))
| ~ relation(sK15)
| ~ in(unordered_pair(unordered_pair(sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14)),sK2(relation_composition(sK16,sK15),sK14)),singleton(sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14)))),sK15) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_2174,plain,
( ( apply(sK16,sK14) = sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14)) )
| ~ relation(sK16)
| ~ function(sK16)
| ~ in(unordered_pair(unordered_pair(sK14,sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14))),singleton(sK14)),sK16) ),
inference(instantiation,[status(thm)],[c_141]) ).
tcf(c_2175,plain,
( in(sK14,relation_dom(sK16))
| ~ relation(sK16)
| ~ in(unordered_pair(unordered_pair(sK14,sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14))),singleton(sK14)),sK16) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_2263,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X1,X2)
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_173,c_170]) ).
tcf(c_2265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,relation_dom(X2))
| ~ in(X1,relation_dom(X3))
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_173,c_180]) ).
tcf(c_2529,plain,
( in(unordered_pair(unordered_pair(sK14,apply(sK15,apply(sK16,sK14))),singleton(sK14)),relation_composition(sK16,sK15))
| ~ relation(sK15)
| ~ relation(sK16)
| ~ relation(relation_composition(sK16,sK15))
| ~ in(unordered_pair(unordered_pair(sK14,apply(sK16,sK14)),singleton(sK14)),sK16)
| ~ in(unordered_pair(unordered_pair(apply(sK16,sK14),apply(sK15,apply(sK16,sK14))),singleton(apply(sK16,sK14))),sK15) ),
inference(instantiation,[status(thm)],[c_1079]) ).
tcf(c_2575,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ~ empty(X2)
| ~ empty(X0)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[c_2263,c_106]) ).
tcf(c_2759,plain,
! [X0: $i] :
( in(sK14,relation_dom(sK16))
| in(X0,relation_dom(relation_composition(sK16,sK15)))
| ~ empty(sK14)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[c_2575,c_97]) ).
tcf(c_2808,plain,
in(sK14,relation_dom(sK16)),
inference(global_subsumption_just,[status(thm)],[c_2759,c_101,c_99,c_97,c_215,c_372,c_877,c_2175]) ).
tcf(c_3719,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1),X1)
| ( relation_dom(X0) = X1 )
| ~ relation(X0)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[c_58,c_105]) ).
tcf(c_5991,plain,
! [X0: $i,X1: $i] :
( ~ empty(X0)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X0) ),
inference(instantiation,[status(thm)],[c_105]) ).
tcf(c_8468,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1),X1)
| ( relation_dom(X0) = X1 )
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3719,c_51,c_58,c_5991]) ).
tcf(c_11888,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(X1))
| in(sK14,relation_dom(relation_composition(sK16,sK15)))
| ( X1 != sK15 )
| ( X0 != apply(sK16,sK14) ) ),
inference(resolution,[status(thm)],[c_2265,c_98]) ).
tcf(c_12242,plain,
! [X0: $i,X1: $i] :
( in(relation_dom(X1),relation_dom(X0))
| in(sK14,relation_dom(relation_composition(sK16,sK15)))
| in(sK0(X1,apply(sK16,sK14)),apply(sK16,sK14))
| ~ empty(X1)
| ( X0 != sK15 ) ),
inference(resolution,[status(thm)],[c_11888,c_8468]) ).
tcf(c_13211,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,apply(sK16,sK14))
| in(relation_dom(X1),relation_dom(X0))
| in(sK14,relation_dom(relation_composition(sK16,sK15)))
| ~ empty(X2)
| ~ empty(X1)
| ~ empty(sK0(X1,apply(sK16,sK14)))
| ( X0 != sK15 ) ),
inference(resolution,[status(thm)],[c_12242,c_2575]) ).
tcf(c_16853,plain,
( in(sK14,relation_dom(relation_composition(sK16,sK15)))
| ~ relation(relation_composition(sK16,sK15))
| ~ in(unordered_pair(unordered_pair(sK14,apply(sK15,apply(sK16,sK14))),singleton(sK14)),relation_composition(sK16,sK15)) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_16883,plain,
in(sK14,relation_dom(relation_composition(sK16,sK15))),
inference(global_subsumption_just,[status(thm)],[c_13211,c_102,c_101,c_100,c_99,c_98,c_250,c_256,c_372,c_2529,c_2808,c_16853]) ).
tcf(c_17320,plain,
( element(sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14)),relation_dom(sK15))
| ~ in(sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14)),relation_dom(sK15)) ),
inference(instantiation,[status(thm)],[c_1585]) ).
tcf(c_23634,plain,
( empty(sK15)
| ~ relation(sK15)
| ~ empty(relation_dom(sK15)) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_109689,plain,
! [X0: $i] :
( element(X0,relation_dom(sK15))
| ~ element(sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14)),relation_dom(sK15))
| ( X0 != sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14)) ) ),
inference(instantiation,[status(thm)],[c_182]) ).
tcf(c_114043,plain,
( element(apply(sK16,sK14),relation_dom(sK15))
| ~ element(sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14)),relation_dom(sK15))
| ( apply(sK16,sK14) != sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14)) ) ),
inference(instantiation,[status(thm)],[c_109689]) ).
tcf(c_114044,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_114043,c_23634,c_17320,c_16883,c_2808,c_2174,c_2166,c_1071,c_886,c_876,c_877,c_372,c_215,c_96,c_99,c_100,c_101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU213+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.77 % Computer : n002.cluster.edu
% 0.11/0.77 % Model : x86_64 x86_64
% 0.11/0.77 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.77 % Memory : 8046.5625MB
% 0.11/0.77 % OS : Linux 6.8.0-71-generic
% 0.11/0.78 % CPULimit : 300
% 0.11/0.78 % WCLimit : 300
% 0.11/0.78 % DateTime : Thu Sep 24 13:15:21 UTC 2026
% 0.11/0.78 % CPUTime :
% 0.11/0.78 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.82 Running first-order theorem proving
% 0.14/0.82 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
% 0.14/0.83
% 0.14/0.83 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.83
% 0.14/0.83 % Detected problem language: tptp
% 0.14/0.84 % Proving...
% 51.57/14.85 % SZS status Started for theBenchmark.p
% 51.57/14.85 % SZS status Theorem for theBenchmark.p
% 51.57/14.85
% 51.57/14.85 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 51.57/14.85
% 51.57/14.85 % ------ iProver source info
% 51.57/14.85
% 51.57/14.85 % git: date: 2026-07-19 20:42:38 +0200
% 51.57/14.85 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 51.57/14.85 % git: non_committed_changes: false
% 51.57/14.85
% 51.57/14.85 % ------ Parsing...
% 51.57/14.85 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 51.57/14.85
% 51.57/14.85 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 1 0s sf_e %
% 51.57/14.85
% 51.57/14.85 % ------ Preprocessing...%
% 51.57/14.85
% 51.57/14.85 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 51.57/14.85 % ------ Proving...
% 51.57/14.85 % ------ Problem Properties
% 51.57/14.85
% 51.57/14.85 %
% 51.57/14.85 % clauses 53
% 51.57/14.85 % conjectures 7
% 51.57/14.85 % EPR 23
% 51.57/14.85 % Horn 46
% 51.57/14.85 % unary 20
% 51.57/14.85 % binary 10
% 51.57/14.85 % lits 133
% 51.57/14.85 % lits eq 10
% 51.57/14.85 % fd_pure 0
% 51.57/14.85 % fd_pseudo 0
% 51.57/14.85 % fd_cond 1
% 51.57/14.85 % fd_pseudo_cond 7
% 51.57/14.85 % AC symbols 0
% 51.57/14.85
% 51.57/14.85 % ------ Input Options Time Limit: Unbounded
% 51.57/14.85
% 51.57/14.85
% 51.57/14.85 % ------
% 51.57/14.85 % Current options:
% 51.57/14.85 % ------
% 51.57/14.85
% 51.57/14.85
% 51.57/14.85 %
% 51.57/14.85
% 51.57/14.85 % ------ Proving...
% 51.57/14.85 %
% 51.57/14.85
% 51.57/14.85 % SZS status Theorem for theBenchmark.p
% 51.57/14.85
% 51.57/14.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 51.57/14.85
% 51.57/14.85
%------------------------------------------------------------------------------