%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU213+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.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 45.29s 10.06s
% Output : CNFRefutation 45.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 10
% Syntax : Number of formulae : 165 ( 28 unt; 0 def)
% Number of atoms : 651 ( 86 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 849 ( 363 ~; 379 |; 75 &)
% ( 16 <=>; 14 =>; 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 : 318 ( 0 sgn 288 !; 30 ?; 97 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
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(f9,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f13,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1)
& function(X0)
& relation(X0) )
=> ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f32,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f33,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(f34,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)],[f33]) ).
fof(f40,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f49,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(f50,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,[],[f49]) ).
fof(f51,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(f52,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(f53,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f54,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(flattening,[],[f53]) ).
fof(f57,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f58,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
inference(flattening,[],[f57]) ).
fof(f65,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f66,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,[],[f34]) ).
fof(f67,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,[],[f66]) ).
fof(f75,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f77,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,[],[f50]) ).
fof(f78,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,[],[f51]) ).
fof(f79,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,[],[f78]) ).
fof(f80,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))],[f79]) ).
fof(f81,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,[],[f52]) ).
fof(f82,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,[],[f81]) ).
fof(f83,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))],[f82]) ).
fof(f93,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,[],[f67]) ).
fof(f94,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,[],[f93]) ).
fof(f95,plain,
( function(sK17)
& relation(sK17)
& function(sK18)
& relation(sK18)
& ( in(sK16,relation_dom(relation_composition(sK18,sK17)))
| ( in(apply(sK18,sK16),relation_dom(sK17))
& in(sK16,relation_dom(sK18)) ) )
& ( ~ in(sK16,relation_dom(relation_composition(sK18,sK17)))
| ~ in(apply(sK18,sK16),relation_dom(sK17))
| ~ in(sK16,relation_dom(sK18)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18]),skolemize(X0,sK16),skolemize(X1,sK17),skolemize(X2,sK18)],[f94]) ).
fof(f99,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(X0))
| apply(X0,X1) != X2
| empty_set = X2 ),
inference(cnf_transformation,[],[f77]) ).
fof(f102,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,[],[f77]) ).
fof(f103,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,[],[f77]) ).
fof(f104,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(X5,sK2(X0,X5)),X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f105,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f108,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f109,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,[],[f83]) ).
fof(f110,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,[],[f83]) ).
fof(f111,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,[],[f83]) ).
fof(f115,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f121,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| function(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f122,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f149,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f150,plain,
function(sK17),
inference(cnf_transformation,[],[f95]) ).
fof(f151,plain,
relation(sK17),
inference(cnf_transformation,[],[f95]) ).
fof(f152,plain,
function(sK18),
inference(cnf_transformation,[],[f95]) ).
fof(f153,plain,
relation(sK18),
inference(cnf_transformation,[],[f95]) ).
fof(f154,plain,
( in(sK16,relation_dom(relation_composition(sK18,sK17)))
| in(apply(sK18,sK16),relation_dom(sK17)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f155,plain,
( in(sK16,relation_dom(relation_composition(sK18,sK17)))
| in(sK16,relation_dom(sK18)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f156,plain,
( ~ in(sK16,relation_dom(relation_composition(sK18,sK17)))
| ~ in(apply(sK18,sK16),relation_dom(sK17))
| ~ in(sK16,relation_dom(sK18)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f162,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f164,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,[],[f103,f108]) ).
fof(f165,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,[],[f102,f108]) ).
fof(f168,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,[],[f105,f108]) ).
fof(f169,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,[],[f104,f108]) ).
fof(f173,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,[],[f111,f108,f108,f108]) ).
fof(f174,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,[],[f110,f108,f108]) ).
fof(f175,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,[],[f109,f108,f108]) ).
fof(f177,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,[],[f165]) ).
fof(f179,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(X0))
| apply(X0,X1) = empty_set ),
inference(equality_resolution,[],[f100]) ).
fof(f180,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| in(X5,relation_dom(X0)) ),
inference(equality_resolution,[],[f168]) ).
fof(f181,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,[],[f169]) ).
fof(f182,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,[],[f173]) ).
fof(f183,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,[],[f174]) ).
fof(f184,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,[],[f175]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f99]) ).
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,[],[f164]) ).
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,[],[f177]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_dom(X0))
| ( apply(X0,X1) = empty_set )
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f179]) ).
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,[],[f180]) ).
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,[],[f181]) ).
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,[],[f182]) ).
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,[],[f183]) ).
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,[],[f184]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( function(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_102,negated_conjecture,
( ~ in(sK16,relation_dom(sK18))
| ~ in(sK16,relation_dom(relation_composition(sK18,sK17)))
| ~ in(apply(sK18,sK16),relation_dom(sK17)) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_103,negated_conjecture,
( in(sK16,relation_dom(sK18))
| in(sK16,relation_dom(relation_composition(sK18,sK17))) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_104,negated_conjecture,
( in(sK16,relation_dom(relation_composition(sK18,sK17)))
| in(apply(sK18,sK16),relation_dom(sK17)) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_105,negated_conjecture,
relation(sK18),
inference(cnf_transformation,[],[f153]) ).
tcf(c_106,negated_conjecture,
function(sK18),
inference(cnf_transformation,[],[f152]) ).
tcf(c_107,negated_conjecture,
relation(sK17),
inference(cnf_transformation,[],[f151]) ).
tcf(c_108,negated_conjecture,
function(sK17),
inference(cnf_transformation,[],[f150]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_67]) ).
tcf(c_157,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_306,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)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X4)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_64,c_155]) ).
tcf(c_307,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)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_65,c_155]) ).
tcf(c_308,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)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_66,c_155]) ).
tcf(c_576,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_59,c_52]) ).
tcf(c_594,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(demodulation,[status(thm)],[c_60,c_52]) ).
tcf(c_610,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,X0) = X1 )
| ~ relation(X2)
| ~ function(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_157,c_52]) ).
tcf(c_623,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,apply(X1,X0))),X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(demodulation,[status(thm)],[c_54,c_52]) ).
tcf(c_662,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X0,X1))),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_composition(X2,X3)) ),
inference(demodulation,[status(thm)],[c_307,c_52]) ).
tcf(c_675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(sK6(X2,X3,X0,X1)),unordered_pair(X1,sK6(X2,X3,X0,X1))),X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_composition(X2,X3)) ),
inference(demodulation,[status(thm)],[c_308,c_52]) ).
tcf(c_688,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),relation_composition(X2,X4))
| ~ relation(X4)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X4)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_306,c_52]) ).
tcf(c_2084,plain,
( in(unordered_pair(singleton(sK16),unordered_pair(sK16,sK2(relation_composition(sK18,sK17),sK16))),relation_composition(sK18,sK17))
| ~ relation(relation_composition(sK18,sK17))
| ~ in(sK16,relation_dom(relation_composition(sK18,sK17))) ),
inference(instantiation,[status(thm)],[c_594]) ).
tcf(c_2087,plain,
( in(unordered_pair(singleton(sK16),unordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16))),relation_composition(sK18,sK17))
| ~ relation(relation_composition(sK18,sK17))
| ~ function(relation_composition(sK18,sK17))
| ~ in(sK16,relation_dom(relation_composition(sK18,sK17))) ),
inference(instantiation,[status(thm)],[c_623]) ).
tcf(c_2200,plain,
( relation(relation_composition(sK18,sK17))
| ~ relation(sK17)
| ~ relation(sK18) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_2273,plain,
( function(relation_composition(sK18,sK17))
| ~ relation(sK17)
| ~ relation(sK18)
| ~ function(sK17)
| ~ function(sK18) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_3802,plain,
( ( apply(relation_composition(sK18,sK17),sK16) = sK2(relation_composition(sK18,sK17),sK16) )
| ~ relation(relation_composition(sK18,sK17))
| ~ function(relation_composition(sK18,sK17))
| ~ in(unordered_pair(singleton(sK16),unordered_pair(sK16,sK2(relation_composition(sK18,sK17),sK16))),relation_composition(sK18,sK17)) ),
inference(instantiation,[status(thm)],[c_610]) ).
tcf(c_3805,plain,
( in(unordered_pair(singleton(sK16),unordered_pair(sK16,sK6(sK18,sK17,sK16,sK2(relation_composition(sK18,sK17),sK16)))),sK18)
| ~ relation(sK17)
| ~ relation(sK18)
| ~ in(unordered_pair(singleton(sK16),unordered_pair(sK16,sK2(relation_composition(sK18,sK17),sK16))),relation_composition(sK18,sK17)) ),
inference(instantiation,[status(thm)],[c_662]) ).
tcf(c_10390,plain,
( in(apply(sK18,sK16),relation_dom(sK17))
| ( apply(sK17,apply(sK18,sK16)) = empty_set )
| ~ relation(sK17)
| ~ function(sK17) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_10423,plain,
( in(sK16,relation_dom(sK18))
| ~ relation(sK18)
| ~ in(unordered_pair(singleton(sK16),unordered_pair(sK16,sK6(sK18,sK17,sK16,sK2(relation_composition(sK18,sK17),sK16)))),sK18) ),
inference(instantiation,[status(thm)],[c_576]) ).
tcf(c_11543,negated_conjecture,
in(sK16,relation_dom(sK18)),
inference(global_subsumption_just,[status(thm)],[c_103,c_107,c_105,c_103,c_2084,c_2200,c_3805,c_10423]) ).
tcf(c_11545,plain,
( ~ in(sK16,relation_dom(relation_composition(sK18,sK17)))
| ~ in(apply(sK18,sK16),relation_dom(sK17)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_102,c_11543]) ).
tcf(c_11800,plain,
( ( apply(sK17,apply(sK18,sK16)) = empty_set )
| ~ relation(sK17)
| ~ function(sK17)
| ~ in(sK16,relation_dom(relation_composition(sK18,sK17))) ),
inference(superposition,[status(thm)],[c_56,c_11545]) ).
tcf(c_11803,plain,
( ( apply(sK17,apply(sK18,sK16)) = empty_set )
| ~ in(sK16,relation_dom(relation_composition(sK18,sK17))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11800,c_107,c_108]) ).
tcf(c_11866,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2) ),
inference(superposition,[status(thm)],[c_52,c_576]) ).
tcf(c_11873,plain,
! [X0: $i,X1: $i] :
( element(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_594,c_101]) ).
tcf(c_11882,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,X0) = sK2(X1,X0) )
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_594,c_610]) ).
tcf(c_13019,plain,
( ( apply(sK18,sK16) = sK2(sK18,sK16) )
| ~ relation(sK18)
| ~ function(sK18) ),
inference(superposition,[status(thm)],[c_11543,c_11882]) ).
tcf(c_13020,plain,
( in(sK16,relation_dom(relation_composition(sK18,sK17)))
| ( apply(sK17,apply(sK18,sK16)) = sK2(sK17,apply(sK18,sK16)) )
| ~ relation(sK17)
| ~ function(sK17) ),
inference(superposition,[status(thm)],[c_104,c_11882]) ).
tcf(c_13040,plain,
apply(sK18,sK16) = sK2(sK18,sK16),
inference(forward_subsumption_resolution,[status(thm)],[c_13019,c_105,c_106]) ).
tcf(c_13041,plain,
( in(sK16,relation_dom(relation_composition(sK18,sK17)))
| ( apply(sK17,apply(sK18,sK16)) = sK2(sK17,apply(sK18,sK16)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13020,c_107,c_108]) ).
tcf(c_13139,plain,
( in(unordered_pair(singleton(sK16),unordered_pair(sK16,apply(sK18,sK16))),sK18)
| ~ relation(sK18)
| ~ in(sK16,relation_dom(sK18)) ),
inference(superposition,[status(thm)],[c_13040,c_594]) ).
tcf(c_13141,plain,
in(unordered_pair(singleton(sK16),unordered_pair(sK16,apply(sK18,sK16))),sK18),
inference(forward_subsumption_resolution,[status(thm)],[c_13139,c_105,c_11543]) ).
tcf(c_13147,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(sK16),unordered_pair(sK16,X0)),relation_composition(sK18,X1))
| ~ relation(sK18)
| ~ relation(X1)
| ~ in(unordered_pair(singleton(apply(sK18,sK16)),unordered_pair(apply(sK18,sK16),X0)),X1) ),
inference(superposition,[status(thm)],[c_13141,c_688]) ).
tcf(c_13150,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(sK16),unordered_pair(sK16,X0)),relation_composition(sK18,X1))
| ~ relation(X1)
| ~ in(unordered_pair(singleton(apply(sK18,sK16)),unordered_pair(apply(sK18,sK16),X0)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13147,c_105]) ).
tcf(c_13158,plain,
( ( apply(sK17,apply(sK18,sK16)) = sK2(sK17,apply(sK18,sK16)) )
| ( apply(relation_composition(sK18,sK17),sK16) = sK2(relation_composition(sK18,sK17),sK16) )
| ~ relation(relation_composition(sK18,sK17))
| ~ function(relation_composition(sK18,sK17)) ),
inference(superposition,[status(thm)],[c_13041,c_11882]) ).
tcf(c_13160,plain,
( ( apply(sK17,apply(sK18,sK16)) = empty_set )
| ( apply(sK17,apply(sK18,sK16)) = sK2(sK17,apply(sK18,sK16)) ) ),
inference(superposition,[status(thm)],[c_13041,c_11803]) ).
tcf(c_13170,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(sK16),unordered_pair(sK16,X0)),relation_composition(sK18,X1))
| ~ relation(X1)
| ~ in(unordered_pair(singleton(apply(sK18,sK16)),unordered_pair(X0,apply(sK18,sK16))),X1) ),
inference(superposition,[status(thm)],[c_52,c_13150]) ).
tcf(c_13347,plain,
( element(unordered_pair(singleton(apply(sK18,sK16)),unordered_pair(apply(sK18,sK16),apply(sK17,apply(sK18,sK16)))),sK17)
| ( apply(sK17,apply(sK18,sK16)) = empty_set )
| ~ relation(sK17)
| ~ in(apply(sK18,sK16),relation_dom(sK17)) ),
inference(superposition,[status(thm)],[c_13160,c_11873]) ).
tcf(c_13348,plain,
( in(unordered_pair(singleton(apply(sK18,sK16)),unordered_pair(apply(sK18,sK16),apply(sK17,apply(sK18,sK16)))),sK17)
| ( apply(sK17,apply(sK18,sK16)) = empty_set )
| ~ relation(sK17)
| ~ in(apply(sK18,sK16),relation_dom(sK17)) ),
inference(superposition,[status(thm)],[c_13160,c_594]) ).
tcf(c_13350,plain,
( in(unordered_pair(singleton(apply(sK18,sK16)),unordered_pair(apply(sK18,sK16),apply(sK17,apply(sK18,sK16)))),sK17)
| ( apply(sK17,apply(sK18,sK16)) = empty_set )
| ~ in(apply(sK18,sK16),relation_dom(sK17)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13348,c_107]) ).
tcf(c_13351,plain,
( element(unordered_pair(singleton(apply(sK18,sK16)),unordered_pair(apply(sK18,sK16),apply(sK17,apply(sK18,sK16)))),sK17)
| ( apply(sK17,apply(sK18,sK16)) = empty_set )
| ~ in(apply(sK18,sK16),relation_dom(sK17)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13347,c_107]) ).
tcf(c_13440,plain,
( in(unordered_pair(singleton(apply(sK18,sK16)),unordered_pair(apply(sK18,sK16),apply(sK17,apply(sK18,sK16)))),sK17)
| ( apply(sK17,apply(sK18,sK16)) = empty_set ) ),
inference(global_subsumption_just,[status(thm)],[c_13350,c_108,c_107,c_10390,c_13350]) ).
tcf(c_13450,plain,
( in(unordered_pair(singleton(sK16),unordered_pair(sK16,apply(sK17,apply(sK18,sK16)))),relation_composition(sK18,sK17))
| ( apply(sK17,apply(sK18,sK16)) = empty_set )
| ~ relation(sK17) ),
inference(superposition,[status(thm)],[c_13440,c_13150]) ).
tcf(c_13452,plain,
( in(unordered_pair(singleton(sK16),unordered_pair(sK16,apply(sK17,apply(sK18,sK16)))),relation_composition(sK18,sK17))
| ( apply(sK17,apply(sK18,sK16)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13450,c_107]) ).
tcf(c_13470,plain,
( in(sK16,relation_dom(relation_composition(sK18,sK17)))
| ( apply(sK17,apply(sK18,sK16)) = empty_set )
| ~ relation(relation_composition(sK18,sK17)) ),
inference(superposition,[status(thm)],[c_13452,c_576]) ).
tcf(c_13474,plain,
apply(sK17,apply(sK18,sK16)) = empty_set,
inference(global_subsumption_just,[status(thm)],[c_13351,c_107,c_105,c_2200,c_11803,c_13470]) ).
tcf(c_13486,plain,
( in(unordered_pair(singleton(apply(sK18,sK16)),unordered_pair(apply(sK18,sK16),empty_set)),sK17)
| ~ relation(sK17)
| ~ function(sK17)
| ~ in(apply(sK18,sK16),relation_dom(sK17)) ),
inference(superposition,[status(thm)],[c_13474,c_623]) ).
tcf(c_13487,plain,
( in(unordered_pair(singleton(apply(sK18,sK16)),unordered_pair(apply(sK18,sK16),empty_set)),sK17)
| ~ in(apply(sK18,sK16),relation_dom(sK17)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13486,c_107,c_108]) ).
tcf(c_13489,plain,
( in(unordered_pair(singleton(apply(sK18,sK16)),unordered_pair(empty_set,apply(sK18,sK16))),sK17)
| ~ in(apply(sK18,sK16),relation_dom(sK17)) ),
inference(demodulation,[status(thm)],[c_13487,c_52]) ).
tcf(c_13932,plain,
( in(unordered_pair(singleton(sK16),unordered_pair(sK16,empty_set)),relation_composition(sK18,sK17))
| ~ relation(sK17)
| ~ in(apply(sK18,sK16),relation_dom(sK17)) ),
inference(superposition,[status(thm)],[c_13489,c_13170]) ).
tcf(c_13935,plain,
( in(unordered_pair(singleton(sK16),unordered_pair(sK16,empty_set)),relation_composition(sK18,sK17))
| ~ in(apply(sK18,sK16),relation_dom(sK17)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13932,c_107]) ).
tcf(c_13939,plain,
( in(unordered_pair(singleton(sK16),unordered_pair(empty_set,sK16)),relation_composition(sK18,sK17))
| ~ in(apply(sK18,sK16),relation_dom(sK17)) ),
inference(demodulation,[status(thm)],[c_13935,c_52]) ).
tcf(c_13945,plain,
( ~ empty(relation_composition(sK18,sK17))
| ~ in(apply(sK18,sK16),relation_dom(sK17)) ),
inference(superposition,[status(thm)],[c_13939,c_114]) ).
tcf(c_13948,plain,
( in(sK16,relation_dom(relation_composition(sK18,sK17)))
| ~ relation(relation_composition(sK18,sK17))
| ~ in(apply(sK18,sK16),relation_dom(sK17)) ),
inference(superposition,[status(thm)],[c_13939,c_11866]) ).
tcf(c_14079,plain,
apply(relation_composition(sK18,sK17),sK16) = sK2(relation_composition(sK18,sK17),sK16),
inference(global_subsumption_just,[status(thm)],[c_13158,c_108,c_107,c_106,c_105,c_104,c_2084,c_2200,c_2273,c_3802,c_11545,c_13948]) ).
tcf(c_14288,plain,
~ in(apply(sK18,sK16),relation_dom(sK17)),
inference(global_subsumption_just,[status(thm)],[c_13945,c_107,c_105,c_2200,c_11545,c_13948]) ).
tcf(c_42969,negated_conjecture,
in(sK16,relation_dom(sK18)),
inference(global_subsumption_just,[status(thm)],[c_103,c_107,c_105,c_103,c_2084,c_2200,c_3805,c_10423]) ).
tcf(c_42971,plain,
( ~ in(sK16,relation_dom(relation_composition(sK18,sK17)))
| ~ in(apply(sK18,sK16),relation_dom(sK17)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_102,c_42969]) ).
tcf(c_42972,negated_conjecture,
in(sK16,relation_dom(relation_composition(sK18,sK17))),
inference(global_subsumption_just,[status(thm)],[c_104,c_104,c_14288]) ).
tcf(c_42974,plain,
~ in(apply(sK18,sK16),relation_dom(sK17)),
inference(backward_subsumption_resolution,[status(thm)],[c_42971,c_42972]) ).
tcf(c_43303,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,X0) = sK2(X1,X0) )
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_594,c_610]) ).
tcf(c_43442,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK6(X2,X3,X0,X1) = apply(X2,X0) )
| ~ relation(X3)
| ~ relation(X2)
| ~ function(X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_662,c_610]) ).
tcf(c_44293,plain,
( ( apply(relation_composition(sK18,sK17),sK16) = sK2(relation_composition(sK18,sK17),sK16) )
| ~ relation(relation_composition(sK18,sK17))
| ~ function(relation_composition(sK18,sK17)) ),
inference(superposition,[status(thm)],[c_42972,c_43303]) ).
tcf(c_44327,plain,
apply(relation_composition(sK18,sK17),sK16) = sK2(relation_composition(sK18,sK17),sK16),
inference(global_subsumption_just,[status(thm)],[c_44293,c_14079]) ).
tcf(c_44330,plain,
( in(unordered_pair(singleton(sK16),unordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16))),relation_composition(sK18,sK17))
| ~ relation(relation_composition(sK18,sK17))
| ~ in(sK16,relation_dom(relation_composition(sK18,sK17))) ),
inference(superposition,[status(thm)],[c_44327,c_594]) ).
tcf(c_44332,plain,
( in(unordered_pair(singleton(sK16),unordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16))),relation_composition(sK18,sK17))
| ~ relation(relation_composition(sK18,sK17)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_44330,c_42972]) ).
tcf(c_44335,plain,
in(unordered_pair(singleton(sK16),unordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16))),relation_composition(sK18,sK17)),
inference(global_subsumption_just,[status(thm)],[c_44332,c_108,c_107,c_106,c_105,c_104,c_2087,c_2200,c_2273,c_14288]) ).
tcf(c_49035,plain,
( ( sK6(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16)) = apply(sK18,sK16) )
| ~ relation(sK17)
| ~ relation(sK18)
| ~ function(sK18) ),
inference(superposition,[status(thm)],[c_44335,c_43442]) ).
tcf(c_49126,plain,
sK6(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16)) = apply(sK18,sK16),
inference(forward_subsumption_resolution,[status(thm)],[c_49035,c_107,c_105,c_106]) ).
tcf(c_49188,plain,
( in(unordered_pair(singleton(apply(sK18,sK16)),unordered_pair(apply(relation_composition(sK18,sK17),sK16),apply(sK18,sK16))),sK17)
| ~ relation(sK17)
| ~ relation(sK18)
| ~ in(unordered_pair(singleton(sK16),unordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16))),relation_composition(sK18,sK17)) ),
inference(superposition,[status(thm)],[c_49126,c_675]) ).
tcf(c_49191,plain,
in(unordered_pair(singleton(apply(sK18,sK16)),unordered_pair(apply(relation_composition(sK18,sK17),sK16),apply(sK18,sK16))),sK17),
inference(forward_subsumption_resolution,[status(thm)],[c_49188,c_107,c_105,c_44335]) ).
tcf(c_49192,plain,
in(unordered_pair(singleton(apply(sK18,sK16)),unordered_pair(apply(sK18,sK16),apply(relation_composition(sK18,sK17),sK16))),sK17),
inference(demodulation,[status(thm)],[c_49191,c_52]) ).
tcf(c_49199,plain,
( in(apply(sK18,sK16),relation_dom(sK17))
| ~ relation(sK17) ),
inference(superposition,[status(thm)],[c_49192,c_576]) ).
tcf(c_49201,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_49199,c_42974,c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU213+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.56 % Computer : n001.cluster.edu
% 0.08/0.56 % Model : x86_64 x86_64
% 0.08/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.56 % Memory : 8046.5625MB
% 0.08/0.56 % OS : Linux 6.8.0-71-generic
% 0.08/0.56 % CPULimit : 300
% 0.08/0.56 % WCLimit : 300
% 0.08/0.56 % DateTime : Thu Sep 24 13:18:08 UTC 2026
% 0.08/0.57 % CPUTime :
% 0.08/0.57 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.60 Running first-order theorem proving
% 0.08/0.60 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
% 0.08/0.62
% 0.08/0.62 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.62
% 0.08/0.62 % Detected problem language: tptp
% 0.12/0.63 % Proving...
% 45.29/10.06 % SZS status Started for theBenchmark.p
% 45.29/10.06 % SZS status Theorem for theBenchmark.p
% 45.29/10.06
% 45.29/10.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 45.29/10.06
% 45.29/10.06 % ------ iProver source info
% 45.29/10.06
% 45.29/10.06 % git: date: 2026-07-19 20:42:38 +0200
% 45.29/10.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 45.29/10.06 % git: non_committed_changes: false
% 45.29/10.06
% 45.29/10.06 % ------ Parsing...
% 45.29/10.06 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 45.29/10.06
% 45.29/10.06 % ------ Preprocessing... sup_sim: 12 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 %
% 45.29/10.06
% 45.29/10.06 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 45.29/10.06
% 45.29/10.06 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 45.29/10.06 % ------ Proving...
% 45.29/10.06 % ------ Problem Properties
% 45.29/10.06
% 45.29/10.06 %
% 45.29/10.06 % clauses 60
% 45.29/10.06 % conjectures 7
% 45.29/10.06 % EPR 23
% 45.29/10.06 % Horn 52
% 45.29/10.06 % unary 23
% 45.29/10.06 % binary 12
% 45.29/10.06 % lits 143
% 45.29/10.06 % lits eq 10
% 45.29/10.06 % fd_pure 0
% 45.29/10.06 % fd_pseudo 0
% 45.29/10.06 % fd_cond 1
% 45.29/10.06 % fd_pseudo_cond 7
% 45.29/10.06 % AC symbols 0
% 45.29/10.06
% 45.29/10.06 % ------ Input Options Time Limit: Unbounded
% 45.29/10.06
% 45.29/10.06
% 45.29/10.06 % ------
% 45.29/10.06 % Current options:
% 45.29/10.06 % ------
% 45.29/10.06
% 45.29/10.06
% 45.29/10.06 %
% 45.29/10.06
% 45.29/10.06 % ------ Proving...
% 45.29/10.06 %
% 45.29/10.06
% 45.29/10.06 % SZS status Theorem for theBenchmark.p
% 45.29/10.06
% 45.29/10.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 45.29/10.07
% 45.29/10.07
%------------------------------------------------------------------------------