%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU214+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 : 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 02:55:56 PM UTC 2026
% Result : Theorem 10.28s 2.28s
% Output : CNFRefutation 10.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 89 ( 19 unt; 0 def)
% Number of atoms : 399 ( 67 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 530 ( 220 ~; 222 |; 59 &)
% ( 14 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 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 : 15 ( 15 usr; 4 con; 0-4 aty)
% Number of variables : 200 ( 0 sgn 176 !; 24 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
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(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(f33,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
=> apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_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)))
=> apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f42,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& ? [X2] :
( function(X2)
& relation(X2)
& in(X0,relation_dom(relation_composition(X2,X1)))
& apply(relation_composition(X2,X1),X0) != apply(X1,apply(X2,X0)) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f43,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& ? [X2] :
( function(X2)
& relation(X2)
& in(X0,relation_dom(relation_composition(X2,X1)))
& apply(relation_composition(X2,X1),X0) != apply(X1,apply(X2,X0)) ) ),
inference(flattening,[],[f42]) ).
fof(f53,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(f54,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(f55,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,[],[f54]) ).
fof(f56,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(f57,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
inference(flattening,[],[f56]) ).
fof(f64,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f65,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(flattening,[],[f64]) ).
fof(f66,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(f72,plain,
( function(sK1)
& relation(sK1)
& function(sK2)
& relation(sK2)
& in(sK0,relation_dom(relation_composition(sK2,sK1)))
& apply(relation_composition(sK2,sK1),sK0) != apply(sK1,apply(sK2,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f43]) ).
fof(f73,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,[],[f53]) ).
fof(f74,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,[],[f73]) ).
fof(f75,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(X5,sK5(X0,X5)),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK3(X0,X1),X1)
| in(ordered_pair(sK3(X0,X1),sK4(X0,X1)),X0) )
& ( ~ in(sK3(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(sK3(X0,X1),X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X2,sK3(X0,X1)),skolemize(X4,sK4(X0,X1)),skolemize(X7,sK5(X0,X5))],[f74]) ).
fof(f76,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,[],[f55]) ).
fof(f80,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,[],[f66]) ).
fof(f81,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,[],[f80]) ).
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)
| ( in(ordered_pair(sK12(X0,X1,X7,X8),X8),X1)
& in(ordered_pair(X7,sK12(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(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| ( in(ordered_pair(sK11(X0,X1,X2),sK10(X0,X1,X2)),X1)
& in(ordered_pair(sK9(X0,X1,X2),sK11(X0,X1,X2)),X0) ) )
& ( ~ in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,sK10(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK9(X0,X1,X2),X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12]),skolemize(X3,sK9(X0,X1,X2)),skolemize(X4,sK10(X0,X1,X2)),skolemize(X6,sK11(X0,X1,X2)),skolemize(X10,sK12(X0,X1,X7,X8))],[f81]) ).
fof(f88,plain,
function(sK1),
inference(cnf_transformation,[],[f72]) ).
fof(f89,plain,
relation(sK1),
inference(cnf_transformation,[],[f72]) ).
fof(f90,plain,
function(sK2),
inference(cnf_transformation,[],[f72]) ).
fof(f91,plain,
relation(sK2),
inference(cnf_transformation,[],[f72]) ).
fof(f92,plain,
in(sK0,relation_dom(relation_composition(sK2,sK1))),
inference(cnf_transformation,[],[f72]) ).
fof(f93,plain,
apply(relation_composition(sK2,sK1),sK0) != apply(sK1,apply(sK2,sK0)),
inference(cnf_transformation,[],[f72]) ).
fof(f102,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(X5,sK5(X0,X5)),X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f103,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f108,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,[],[f76]) ).
fof(f109,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,[],[f76]) ).
fof(f112,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| function(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f113,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f124,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f125,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(sK12(X0,X1,X7,X8),X8),X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f126,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,sK12(X0,X1,X7,X8)),X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f146,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,relation_dom(X0)) ),
inference(equality_resolution,[],[f103]) ).
fof(f147,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_dom(X0))
| in(ordered_pair(X5,sK5(X0,X5)),X0) ),
inference(equality_resolution,[],[f102]) ).
fof(f148,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| in(ordered_pair(X1,apply(X0,X1)),X0) ),
inference(equality_resolution,[],[f108]) ).
fof(f152,plain,
! [X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| in(ordered_pair(X7,sK12(X0,X1,X7,X8)),X0) ),
inference(equality_resolution,[],[f126]) ).
fof(f153,plain,
! [X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| in(ordered_pair(sK12(X0,X1,X7,X8),X8),X1) ),
inference(equality_resolution,[],[f125]) ).
tcf(c_49,negated_conjecture,
apply(relation_composition(sK2,sK1),sK0) != apply(sK1,apply(sK2,sK0)),
inference(cnf_transformation,[],[f93]) ).
tcf(c_50,negated_conjecture,
in(sK0,relation_dom(relation_composition(sK2,sK1))),
inference(cnf_transformation,[],[f92]) ).
tcf(c_51,negated_conjecture,
relation(sK2),
inference(cnf_transformation,[],[f91]) ).
tcf(c_52,negated_conjecture,
function(sK2),
inference(cnf_transformation,[],[f90]) ).
tcf(c_53,negated_conjecture,
relation(sK1),
inference(cnf_transformation,[],[f89]) ).
tcf(c_54,negated_conjecture,
function(sK1),
inference(cnf_transformation,[],[f88]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X0,sK5(X1,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,X0) = X1 )
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X2))
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X0,apply(X1,X0)),X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(X0,sK12(X2,X3,X0,X1)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_composition(X2,X3))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK12(X2,X3,X0,X1),X1),X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_composition(X2,X3))
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_85]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,X0) = X1 )
| ~ function(X2)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(global_subsumption_just,[status(thm)],[c_67,c_65,c_67]) ).
tcf(c_272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(sK12(X2,X3,X0,X1),X1),X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_91,c_136]) ).
tcf(c_273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(X0,sK12(X2,X3,X0,X1)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_90,c_136]) ).
tcf(c_1155,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1157,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK12(X2,X3,X0,X1) = apply(X2,X0) )
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),relation_composition(X2,X3)) ),
inference(superposition,[status(thm)],[c_273,c_138]) ).
tcf(c_2354,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,X0) = sK5(X1,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_66,c_138]) ).
tcf(c_2448,plain,
! [X0: $i] :
( ( apply(relation_composition(sK2,sK1),sK0) = apply(sK1,apply(sK2,sK0)) )
| ( apply(sK1,apply(sK2,sK0)) != X0 )
| ( apply(relation_composition(sK2,sK1),sK0) != X0 ) ),
inference(instantiation,[status(thm)],[c_1157]) ).
tcf(c_2450,plain,
( in(ordered_pair(sK0,sK5(relation_composition(sK2,sK1),sK0)),relation_composition(sK2,sK1))
| ~ relation(relation_composition(sK2,sK1))
| ~ in(sK0,relation_dom(relation_composition(sK2,sK1))) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_2451,plain,
( in(ordered_pair(sK0,apply(relation_composition(sK2,sK1),sK0)),relation_composition(sK2,sK1))
| ~ function(relation_composition(sK2,sK1))
| ~ relation(relation_composition(sK2,sK1))
| ~ in(sK0,relation_dom(relation_composition(sK2,sK1))) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_2969,plain,
( relation(relation_composition(sK2,sK1))
| ~ relation(sK1)
| ~ relation(sK2) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_3078,plain,
! [X0: $i] :
( ( apply(relation_composition(sK2,sK1),sK0) = X0 )
| ~ function(relation_composition(sK2,sK1))
| ~ relation(relation_composition(sK2,sK1))
| ~ in(ordered_pair(sK0,X0),relation_composition(sK2,sK1)) ),
inference(instantiation,[status(thm)],[c_138]) ).
tcf(c_3084,plain,
( ( apply(relation_composition(sK2,sK1),sK0) = apply(sK1,apply(sK2,sK0)) )
| ( apply(sK1,apply(sK2,sK0)) != apply(relation_composition(sK2,sK1),sK0) )
| ( apply(relation_composition(sK2,sK1),sK0) != apply(relation_composition(sK2,sK1),sK0) ) ),
inference(instantiation,[status(thm)],[c_2448]) ).
tcf(c_3085,plain,
apply(relation_composition(sK2,sK1),sK0) = apply(relation_composition(sK2,sK1),sK0),
inference(instantiation,[status(thm)],[c_1155]) ).
tcf(c_5241,plain,
( function(relation_composition(sK2,sK1))
| ~ function(sK1)
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_5424,plain,
! [X0: $i] :
( ( apply(sK1,apply(sK2,sK0)) = X0 )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(ordered_pair(apply(sK2,sK0),X0),sK1) ),
inference(instantiation,[status(thm)],[c_138]) ).
tcf(c_5962,plain,
( ( apply(relation_composition(sK2,sK1),sK0) = sK5(relation_composition(sK2,sK1),sK0) )
| ~ function(relation_composition(sK2,sK1))
| ~ relation(relation_composition(sK2,sK1))
| ~ in(ordered_pair(sK0,sK5(relation_composition(sK2,sK1),sK0)),relation_composition(sK2,sK1)) ),
inference(instantiation,[status(thm)],[c_3078]) ).
tcf(c_10602,plain,
( ( apply(sK1,apply(sK2,sK0)) = apply(relation_composition(sK2,sK1),sK0) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(ordered_pair(apply(sK2,sK0),apply(relation_composition(sK2,sK1),sK0)),sK1) ),
inference(instantiation,[status(thm)],[c_5424]) ).
tcf(c_15879,plain,
( ( apply(relation_composition(sK2,sK1),sK0) = sK5(relation_composition(sK2,sK1),sK0) )
| ~ function(relation_composition(sK2,sK1))
| ~ relation(relation_composition(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_50,c_2354]) ).
tcf(c_16858,plain,
apply(relation_composition(sK2,sK1),sK0) = sK5(relation_composition(sK2,sK1),sK0),
inference(global_subsumption_just,[status(thm)],[c_15879,c_54,c_53,c_52,c_51,c_50,c_2450,c_2969,c_5241,c_5962]) ).
tcf(c_16860,plain,
( in(ordered_pair(sK0,apply(relation_composition(sK2,sK1),sK0)),relation_composition(sK2,sK1))
| ~ relation(relation_composition(sK2,sK1))
| ~ in(sK0,relation_dom(relation_composition(sK2,sK1))) ),
inference(superposition,[status(thm)],[c_16858,c_66]) ).
tcf(c_16863,plain,
( in(ordered_pair(sK0,apply(relation_composition(sK2,sK1),sK0)),relation_composition(sK2,sK1))
| ~ relation(relation_composition(sK2,sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16860,c_50]) ).
tcf(c_16895,plain,
in(ordered_pair(sK0,apply(relation_composition(sK2,sK1),sK0)),relation_composition(sK2,sK1)),
inference(global_subsumption_just,[status(thm)],[c_16863,c_54,c_53,c_52,c_51,c_50,c_2451,c_2969,c_5241]) ).
tcf(c_16904,plain,
( ( sK12(sK2,sK1,sK0,apply(relation_composition(sK2,sK1),sK0)) = apply(sK2,sK0) )
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_16895,c_2269]) ).
tcf(c_16907,plain,
sK12(sK2,sK1,sK0,apply(relation_composition(sK2,sK1),sK0)) = apply(sK2,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_16904,c_52,c_53,c_51]) ).
tcf(c_16993,plain,
( in(ordered_pair(apply(sK2,sK0),apply(relation_composition(sK2,sK1),sK0)),sK1)
| ~ relation(sK1)
| ~ relation(sK2)
| ~ in(ordered_pair(sK0,apply(relation_composition(sK2,sK1),sK0)),relation_composition(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_16907,c_272]) ).
tcf(c_16998,plain,
in(ordered_pair(apply(sK2,sK0),apply(relation_composition(sK2,sK1),sK0)),sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_16993,c_53,c_51,c_16895]) ).
tcf(c_17005,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_16998,c_10602,c_3085,c_3084,c_49,c_53,c_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU214+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.35 % Computer : n002.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Thu Sep 24 13:15:49 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 10.28/2.28 % SZS status Started for theBenchmark.p
% 10.28/2.28 % SZS status Theorem for theBenchmark.p
% 10.28/2.28
% 10.28/2.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.28/2.28
% 10.28/2.28 % ------ iProver source info
% 10.28/2.28
% 10.28/2.28 % git: date: 2026-07-19 20:42:38 +0200
% 10.28/2.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.28/2.28 % git: non_committed_changes: false
% 10.28/2.28
% 10.28/2.28 % ------ Parsing...
% 10.28/2.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.28/2.28
% 10.28/2.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 10.28/2.28
% 10.28/2.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.28/2.28
% 10.28/2.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.28/2.28 % ------ Proving...
% 10.28/2.28 % ------ Problem Properties
% 10.28/2.28
% 10.28/2.28 %
% 10.28/2.28 % clauses 55
% 10.28/2.28 % conjectures 6
% 10.28/2.28 % EPR 22
% 10.28/2.28 % Horn 49
% 10.28/2.28 % unary 21
% 10.28/2.28 % binary 10
% 10.28/2.28 % lits 134
% 10.28/2.28 % lits eq 10
% 10.28/2.28 % fd_pure 0
% 10.28/2.28 % fd_pseudo 0
% 10.28/2.28 % fd_cond 1
% 10.28/2.28 % fd_pseudo_cond 7
% 10.28/2.28 % AC symbols 0
% 10.28/2.28
% 10.28/2.28 % ------ Schedule dynamic 5 is on
% 10.28/2.28
% 10.28/2.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.28/2.28
% 10.28/2.28
% 10.28/2.28 % ------
% 10.28/2.28 % Current options:
% 10.28/2.28 % ------
% 10.28/2.28
% 10.28/2.28
% 10.28/2.28 %
% 10.28/2.28
% 10.28/2.28 % ------ Proving...
% 10.28/2.28 %
% 10.28/2.28
% 10.28/2.28 % SZS status Theorem for theBenchmark.p
% 10.28/2.28
% 10.28/2.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.28/2.28
% 10.28/2.28
%------------------------------------------------------------------------------