%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU214+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n010.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 8.61s 2.17s
% Output : CNFRefutation 8.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 88 ( 19 unt; 0 def)
% Number of atoms : 395 ( 66 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 524 ( 217 ~; 219 |; 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 : 199 ( 0 sgn 175 !; 24 ?; 49 :)
% 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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f15,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f20,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1)
& function(X0)
& relation(X0) )
=> ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f36,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/sandbox/benchmark/theBenchmark.p',t22_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)))
=> apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
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,[],[f37]) ).
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(f50,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(f51,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(f52,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,[],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f54,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
inference(flattening,[],[f53]) ).
fof(f61,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(ennf_transformation,[],[f15]) ).
fof(f62,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(flattening,[],[f61]) ).
fof(f63,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(f65,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(f66,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,[],[f50]) ).
fof(f67,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,[],[f66]) ).
fof(f68,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))],[f67]) ).
fof(f69,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,[],[f52]) ).
fof(f73,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,[],[f63]) ).
fof(f74,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,[],[f73]) ).
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)
| ( 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))],[f74]) ).
fof(f78,plain,
function(sK1),
inference(cnf_transformation,[],[f65]) ).
fof(f79,plain,
relation(sK1),
inference(cnf_transformation,[],[f65]) ).
fof(f80,plain,
function(sK2),
inference(cnf_transformation,[],[f65]) ).
fof(f81,plain,
relation(sK2),
inference(cnf_transformation,[],[f65]) ).
fof(f82,plain,
in(sK0,relation_dom(relation_composition(sK2,sK1))),
inference(cnf_transformation,[],[f65]) ).
fof(f83,plain,
apply(relation_composition(sK2,sK1),sK0) != apply(sK1,apply(sK2,sK0)),
inference(cnf_transformation,[],[f65]) ).
fof(f90,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(X5,sK5(X0,X5)),X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f91,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f96,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,[],[f69]) ).
fof(f97,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,[],[f69]) ).
fof(f100,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| function(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f101,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f112,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f113,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,[],[f75]) ).
fof(f114,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,[],[f75]) ).
fof(f126,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,relation_dom(X0)) ),
inference(equality_resolution,[],[f91]) ).
fof(f127,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_dom(X0))
| in(ordered_pair(X5,sK5(X0,X5)),X0) ),
inference(equality_resolution,[],[f90]) ).
fof(f128,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| in(ordered_pair(X1,apply(X0,X1)),X0) ),
inference(equality_resolution,[],[f96]) ).
fof(f132,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,[],[f114]) ).
fof(f133,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,[],[f113]) ).
tcf(c_49,negated_conjecture,
apply(relation_composition(sK2,sK1),sK0) != apply(sK1,apply(sK2,sK0)),
inference(cnf_transformation,[],[f83]) ).
tcf(c_50,negated_conjecture,
in(sK0,relation_dom(relation_composition(sK2,sK1))),
inference(cnf_transformation,[],[f82]) ).
tcf(c_51,negated_conjecture,
relation(sK2),
inference(cnf_transformation,[],[f81]) ).
tcf(c_52,negated_conjecture,
function(sK2),
inference(cnf_transformation,[],[f80]) ).
tcf(c_53,negated_conjecture,
relation(sK1),
inference(cnf_transformation,[],[f79]) ).
tcf(c_54,negated_conjecture,
function(sK1),
inference(cnf_transformation,[],[f78]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X0,sK5(X1,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_65,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,[],[f97]) ).
tcf(c_66,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,[],[f128]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_88,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,[],[f132]) ).
tcf(c_89,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,[],[f133]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_71,c_83]) ).
tcf(c_123,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_65,c_63,c_65]) ).
tcf(c_230,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_89,c_121]) ).
tcf(c_231,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_88,c_121]) ).
tcf(c_1002,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1004,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1768,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_231,c_123]) ).
tcf(c_2013,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_64,c_123]) ).
tcf(c_2029,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_1004]) ).
tcf(c_2071,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_64]) ).
tcf(c_2072,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_66]) ).
tcf(c_2282,plain,
( relation(relation_composition(sK2,sK1))
| ~ relation(sK1)
| ~ relation(sK2) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_2391,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_123]) ).
tcf(c_2397,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_2029]) ).
tcf(c_2398,plain,
apply(relation_composition(sK2,sK1),sK0) = apply(relation_composition(sK2,sK1),sK0),
inference(instantiation,[status(thm)],[c_1002]) ).
tcf(c_3112,plain,
( function(relation_composition(sK2,sK1))
| ~ function(sK1)
| ~ function(sK2)
| ~ relation(sK1)
| ~ relation(sK2) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_3296,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_123]) ).
tcf(c_4530,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_2391]) ).
tcf(c_16799,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_2013]) ).
tcf(c_17254,plain,
apply(relation_composition(sK2,sK1),sK0) = sK5(relation_composition(sK2,sK1),sK0),
inference(global_subsumption_just,[status(thm)],[c_16799,c_54,c_53,c_52,c_51,c_50,c_2071,c_2282,c_3112,c_4530]) ).
tcf(c_17256,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_17254,c_64]) ).
tcf(c_17258,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_17256,c_50]) ).
tcf(c_17294,plain,
in(ordered_pair(sK0,apply(relation_composition(sK2,sK1),sK0)),relation_composition(sK2,sK1)),
inference(global_subsumption_just,[status(thm)],[c_17258,c_54,c_53,c_52,c_51,c_50,c_2072,c_2282,c_3112]) ).
tcf(c_17302,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_17294,c_1768]) ).
tcf(c_17305,plain,
sK12(sK2,sK1,sK0,apply(relation_composition(sK2,sK1),sK0)) = apply(sK2,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_17302,c_52,c_53,c_51]) ).
tcf(c_17362,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_17305,c_230]) ).
tcf(c_17366,plain,
in(ordered_pair(apply(sK2,sK0),apply(relation_composition(sK2,sK1),sK0)),sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_17362,c_53,c_51,c_17294]) ).
tcf(c_17368,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_17366,c_3296,c_2398,c_2397,c_49,c_53,c_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU214+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.78 % Computer : n010.cluster.edu
% 0.10/0.78 % Model : x86_64 x86_64
% 0.10/0.78 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.78 % Memory : 8046.5625MB
% 0.10/0.78 % OS : Linux 6.8.0-71-generic
% 0.10/0.78 % CPULimit : 300
% 0.10/0.78 % WCLimit : 300
% 0.10/0.79 % DateTime : Thu Sep 24 13:12:30 UTC 2026
% 0.10/0.79 % CPUTime :
% 0.10/0.79 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.83 Running first-order theorem proving
% 0.14/0.83 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.84
% 0.14/0.84 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.84
% 0.14/0.84 % Detected problem language: tptp
% 0.14/0.85 % Proving...
% 8.61/2.17 % SZS status Started for theBenchmark.p
% 8.61/2.17 % SZS status Theorem for theBenchmark.p
% 8.61/2.17
% 8.61/2.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.61/2.17
% 8.61/2.17 % ------ iProver source info
% 8.61/2.17
% 8.61/2.17 % git: date: 2026-07-19 20:42:38 +0200
% 8.61/2.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.61/2.17 % git: non_committed_changes: false
% 8.61/2.17
% 8.61/2.17 % ------ Parsing...
% 8.61/2.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.61/2.17
% 8.61/2.17 % ------ 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 %
% 8.61/2.17
% 8.61/2.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.61/2.17
% 8.61/2.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.61/2.17 % ------ Proving...
% 8.61/2.17 % ------ Problem Properties
% 8.61/2.17
% 8.61/2.17 %
% 8.61/2.17 % clauses 45
% 8.61/2.17 % conjectures 6
% 8.61/2.17 % EPR 20
% 8.61/2.17 % Horn 41
% 8.61/2.17 % unary 17
% 8.61/2.17 % binary 7
% 8.61/2.17 % lits 115
% 8.61/2.17 % lits eq 10
% 8.61/2.17 % fd_pure 0
% 8.61/2.17 % fd_pseudo 0
% 8.61/2.17 % fd_cond 1
% 8.61/2.17 % fd_pseudo_cond 7
% 8.61/2.17 % AC symbols 0
% 8.61/2.17
% 8.61/2.17 % ------ Schedule dynamic 5 is on
% 8.61/2.17
% 8.61/2.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.61/2.17
% 8.61/2.17
% 8.61/2.17 % ------
% 8.61/2.17 % Current options:
% 8.61/2.17 % ------
% 8.61/2.17
% 8.61/2.17
% 8.61/2.17 %
% 8.61/2.17
% 8.61/2.17 % ------ Proving...
% 8.61/2.17 %
% 8.61/2.17
% 8.61/2.17 % SZS status Theorem for theBenchmark.p
% 8.61/2.17
% 8.61/2.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.61/2.17
% 8.61/2.17
%------------------------------------------------------------------------------