%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU048+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n018.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 02:55:08 PM UTC 2026
% Result : Theorem 3.13s 1.08s
% Output : CNFRefutation 3.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 101 ( 23 unt; 3 def)
% Number of atoms : 513 ( 80 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 550 ( 221 ~; 227 |; 74 &)
% ( 14 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 181 ( 0 sgn 167 !; 14 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f6,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f12,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(f33,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) )
& ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_1) ).
fof(f35,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( one_to_one(X1)
=> one_to_one(relation_rng_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_funct_1) ).
fof(f36,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( one_to_one(X1)
=> one_to_one(relation_rng_restriction(X0,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f38,plain,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X4] :
( in(X4,relation_dom(X1))
=> apply(X2,X4) = apply(X1,X4) )
& ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) ) ) ) ) ),
inference(rectify,[],[f33]) ).
fof(f47,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( one_to_one(X0)
<=> ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f48,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( one_to_one(X0)
<=> ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) ) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f50,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f51,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) ) ),
inference(flattening,[],[f50]) ).
fof(f65,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X2,X4) = apply(X1,X4) )
& ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) ) ) ) ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f66,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X2,X4) = apply(X1,X4) )
& ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) ) ) ) ) ),
inference(flattening,[],[f65]) ).
fof(f68,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& one_to_one(X1)
& ~ one_to_one(relation_rng_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f36]) ).
fof(f69,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& one_to_one(X1)
& ~ one_to_one(relation_rng_restriction(X0,X1)) ),
inference(flattening,[],[f68]) ).
fof(f73,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) )
& ( ? [X1,X2] :
( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0))
& X1 != X2 )
| one_to_one(X0) ) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f74,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X3,X4] :
( apply(X0,X3) != apply(X0,X4)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ) )
& ( ? [X1,X2] :
( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0))
& X1 != X2 )
| one_to_one(X0) ) ) ),
inference(rectify,[],[f73]) ).
fof(f75,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X3,X4] :
( apply(X0,X3) != apply(X0,X4)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ) )
& ( ( apply(X0,sK2(X0)) = apply(X0,sK3(X0))
& in(sK3(X0),relation_dom(X0))
& in(sK2(X0),relation_dom(X0))
& sK2(X0) != sK3(X0) )
| one_to_one(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X1,sK2(X0)),skolemize(X2,sK3(X0))],[f74]) ).
fof(f87,plain,
! [X1,X0,X2] :
( ~ sP1(X1,X0,X2)
| ( ( relation_rng_restriction(X0,X2) != X1
| sP0(X2,X0,X1) )
& ( ~ sP0(X2,X0,X1)
| X1 = relation_rng_restriction(X0,X2) ) ) ),
inference(nnf_transformation,[],[f71]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ~ sP1(X0,X1,X2)
| ( ( relation_rng_restriction(X1,X2) != X0
| sP0(X2,X1,X0) )
& ( ~ sP0(X2,X1,X0)
| relation_rng_restriction(X1,X2) = X0 ) ) ),
inference(rectify,[],[f87]) ).
fof(f93,plain,
( function(sK18)
& relation(sK18)
& one_to_one(sK18)
& ~ one_to_one(relation_rng_restriction(sK17,sK18)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18]),skolemize(X0,sK17),skolemize(X1,sK18)],[f69]) ).
fof(f100,plain,
! [X3,X0,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| apply(X0,X3) != apply(X0,X4)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ),
inference(cnf_transformation,[],[f75]) ).
fof(f101,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| apply(X0,sK2(X0)) = apply(X0,sK3(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f102,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK3(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f103,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK2(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f104,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| sK2(X0) != sK3(X0)
| one_to_one(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f105,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f113,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| function(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f114,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f145,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| relation_rng_restriction(X1,X2) != X0
| sP0(X2,X1,X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f157,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| sP1(X1,X0,X2) ),
inference(cnf_transformation,[],[f72]) ).
fof(f159,plain,
function(sK18),
inference(cnf_transformation,[],[f93]) ).
fof(f160,plain,
relation(sK18),
inference(cnf_transformation,[],[f93]) ).
fof(f161,plain,
one_to_one(sK18),
inference(cnf_transformation,[],[f93]) ).
fof(f162,plain,
~ one_to_one(relation_rng_restriction(sK17,sK18)),
inference(cnf_transformation,[],[f93]) ).
fof(f163,plain,
! [X2,X1] :
( ~ sP1(relation_rng_restriction(X1,X2),X1,X2)
| sP0(X2,X1,relation_rng_restriction(X1,X2)) ),
inference(equality_resolution,[],[f145]) ).
tcf(c_53,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| ( sK2(X0) != sK3(X0) ) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_54,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK2(X0),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_55,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK3(X0),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_56,plain,
! [X0: $i] :
( one_to_one(X0)
| ( apply(X0,sK2(X0)) = apply(X0,sK3(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| ( apply(X0,X1) != apply(X0,X2) ) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( function(relation_rng_restriction(X1,X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( sP0(X1,X0,relation_rng_restriction(X0,X1))
| ~ sP1(relation_rng_restriction(X0,X1),X0,X1) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X0,X2,X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_112,negated_conjecture,
~ one_to_one(relation_rng_restriction(sK17,sK18)),
inference(cnf_transformation,[],[f162]) ).
tcf(c_113,negated_conjecture,
one_to_one(sK18),
inference(cnf_transformation,[],[f161]) ).
tcf(c_114,negated_conjecture,
relation(sK18),
inference(cnf_transformation,[],[f160]) ).
tcf(c_115,negated_conjecture,
function(sK18),
inference(cnf_transformation,[],[f159]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_66,c_58]) ).
tcf(c_708,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP0(X1,X0,relation_rng_restriction(X0,X1))
| ~ relation(X4)
| ~ relation(X2)
| ~ function(X4)
| ~ function(X2)
| ( X1 != X4 )
| ( X0 != X3 )
| ( relation_rng_restriction(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_99,c_110]) ).
tcf(c_709,plain,
! [X0: $i,X1: $i] :
( sP0(X1,X0,relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ function(relation_rng_restriction(X0,X1)) ),
inference(unflattening,[status(thm)],[c_708]) ).
tcf(c_721,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1,relation_rng_restriction(X1,X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_709,c_148,c_67]) ).
tcf(c_3540,definition,
iPr_def_10 = relation_rng_restriction(sK17,sK18),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3541,negated_conjecture,
function(sK18),
inference(demodulation,[status(thm)],[c_115]) ).
tcf(c_3542,negated_conjecture,
relation(sK18),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_3543,negated_conjecture,
one_to_one(sK18),
inference(demodulation,[status(thm)],[c_113]) ).
tcf(c_3544,negated_conjecture,
~ one_to_one(iPr_def_10),
inference(demodulation,[status(thm)],[c_112,c_3540]) ).
tcf(c_3547,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_4312,plain,
( relation(iPr_def_10)
| ~ relation(sK18) ),
inference(superposition,[status(thm)],[c_3540,c_58]) ).
tcf(c_4313,plain,
relation(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_4312,c_3542]) ).
tcf(c_4406,plain,
( function(iPr_def_10)
| ~ relation(sK18)
| ~ function(sK18) ),
inference(superposition,[status(thm)],[c_3540,c_67]) ).
tcf(c_4407,plain,
function(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_4406,c_3542,c_3541]) ).
tcf(c_4719,plain,
( one_to_one(iPr_def_10)
| ( apply(iPr_def_10,sK2(iPr_def_10)) = apply(iPr_def_10,sK3(iPr_def_10)) )
| ~ relation(iPr_def_10) ),
inference(superposition,[status(thm)],[c_4407,c_56]) ).
tcf(c_4721,plain,
apply(iPr_def_10,sK2(iPr_def_10)) = apply(iPr_def_10,sK3(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_4719,c_3544,c_4313]) ).
tcf(c_4914,plain,
( one_to_one(iPr_def_10)
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10)
| ( sK2(iPr_def_10) != sK3(iPr_def_10) ) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_5186,plain,
! [X0: $i] :
( ( sK2(iPr_def_10) = sK3(iPr_def_10) )
| ( sK3(iPr_def_10) != X0 )
| ( sK2(iPr_def_10) != X0 ) ),
inference(instantiation,[status(thm)],[c_3547]) ).
tcf(c_6478,plain,
( sP0(sK18,sK17,iPr_def_10)
| ~ relation(sK18)
| ~ function(sK18) ),
inference(superposition,[status(thm)],[c_3540,c_721]) ).
tcf(c_6483,plain,
sP0(sK18,sK17,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_6478,c_3542,c_3541]) ).
fof(f70,definition,
! [X2,X0,X1] :
( sP0(X2,X0,X1)
<=> ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X2,X4) = apply(X1,X4) )
& ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f71,definition,
! [X1,X0,X2] :
( ~ sP1(X1,X0,X2)
| ( X1 = relation_rng_restriction(X0,X2)
<=> sP0(X2,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f72,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| sP1(X1,X0,X2) ) ),
inference(definition_folding,[],[f66,f71,f70]) ).
fof(f89,plain,
! [X2,X0,X1] :
( ( ~ sP0(X2,X0,X1)
| ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X2,X4) = apply(X1,X4) )
& ! [X3] :
( ( ~ in(X3,relation_dom(X1))
| ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) )
& ( ~ in(apply(X2,X3),X0)
| ~ in(X3,relation_dom(X2))
| in(X3,relation_dom(X1)) ) ) ) )
& ( ? [X4] :
( in(X4,relation_dom(X1))
& apply(X2,X4) != apply(X1,X4) )
| ? [X3] :
( ( in(X3,relation_dom(X1))
| ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) )
& ( ~ in(X3,relation_dom(X1))
| ~ in(apply(X2,X3),X0)
| ~ in(X3,relation_dom(X2)) ) )
| sP0(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f70]) ).
fof(f90,plain,
! [X2,X0,X1] :
( ( ~ sP0(X2,X0,X1)
| ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X2,X4) = apply(X1,X4) )
& ! [X3] :
( ( ~ in(X3,relation_dom(X1))
| ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) )
& ( ~ in(apply(X2,X3),X0)
| ~ in(X3,relation_dom(X2))
| in(X3,relation_dom(X1)) ) ) ) )
& ( ? [X4] :
( in(X4,relation_dom(X1))
& apply(X2,X4) != apply(X1,X4) )
| ? [X3] :
( ( in(X3,relation_dom(X1))
| ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) )
& ( ~ in(X3,relation_dom(X1))
| ~ in(apply(X2,X3),X0)
| ~ in(X3,relation_dom(X2)) ) )
| sP0(X2,X0,X1) ) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ( ! [X6] :
( ~ in(X6,relation_dom(X2))
| apply(X0,X6) = apply(X2,X6) )
& ! [X5] :
( ( ~ in(X5,relation_dom(X2))
| ( in(apply(X0,X5),X1)
& in(X5,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X5),X1)
| ~ in(X5,relation_dom(X0))
| in(X5,relation_dom(X2)) ) ) ) )
& ( ? [X4] :
( in(X4,relation_dom(X2))
& apply(X2,X4) != apply(X0,X4) )
| ? [X3] :
( ( in(X3,relation_dom(X2))
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,relation_dom(X2))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| sP0(X0,X1,X2) ) ),
inference(rectify,[],[f90]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ( ! [X6] :
( ~ in(X6,relation_dom(X2))
| apply(X0,X6) = apply(X2,X6) )
& ! [X5] :
( ( ~ in(X5,relation_dom(X2))
| ( in(apply(X0,X5),X1)
& in(X5,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X5),X1)
| ~ in(X5,relation_dom(X0))
| in(X5,relation_dom(X2)) ) ) ) )
& ( ( in(sK16(X0,X2),relation_dom(X2))
& apply(X2,sK16(X0,X2)) != apply(X0,sK16(X0,X2)) )
| ( ( in(sK15(X0,X1,X2),relation_dom(X2))
| ( in(apply(X0,sK15(X0,X1,X2)),X1)
& in(sK15(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK15(X0,X1,X2),relation_dom(X2))
| ~ in(apply(X0,sK15(X0,X1,X2)),X1)
| ~ in(sK15(X0,X1,X2),relation_dom(X0)) ) )
| sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16]),skolemize(X3,sK15(X0,X1,X2)),skolemize(X4,sK16(X0,X2))],[f91]) ).
fof(f147,plain,
! [X2,X0,X1,X6] :
( ~ sP0(X0,X1,X2)
| ~ in(X6,relation_dom(X2))
| apply(X0,X6) = apply(X2,X6) ),
inference(cnf_transformation,[],[f92]) ).
fof(f149,plain,
! [X2,X0,X1,X5] :
( ~ sP0(X0,X1,X2)
| ~ in(X5,relation_dom(X2))
| in(X5,relation_dom(X0)) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,relation_dom(X0))
| ~ in(X3,relation_dom(X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X0,X3) = apply(X2,X3) )
| ~ in(X3,relation_dom(X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_6526,plain,
! [X0: $i] :
( ( apply(sK18,X0) = apply(iPr_def_10,X0) )
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_6483,c_109]) ).
tcf(c_6528,plain,
! [X0: $i] :
( in(X0,relation_dom(sK18))
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_6483,c_107]) ).
tcf(c_6549,plain,
( one_to_one(iPr_def_10)
| in(sK2(iPr_def_10),relation_dom(sK18))
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_54,c_6528]) ).
tcf(c_6550,plain,
( one_to_one(iPr_def_10)
| in(sK3(iPr_def_10),relation_dom(sK18))
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_55,c_6528]) ).
tcf(c_6570,plain,
in(sK3(iPr_def_10),relation_dom(sK18)),
inference(forward_subsumption_resolution,[status(thm)],[c_6550,c_3544,c_4313,c_4407]) ).
tcf(c_6571,plain,
in(sK2(iPr_def_10),relation_dom(sK18)),
inference(forward_subsumption_resolution,[status(thm)],[c_6549,c_3544,c_4313,c_4407]) ).
tcf(c_6927,plain,
( one_to_one(iPr_def_10)
| ( apply(sK18,sK2(iPr_def_10)) = apply(iPr_def_10,sK2(iPr_def_10)) )
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_54,c_6526]) ).
tcf(c_6928,plain,
( one_to_one(iPr_def_10)
| ( apply(sK18,sK3(iPr_def_10)) = apply(iPr_def_10,sK3(iPr_def_10)) )
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_55,c_6526]) ).
tcf(c_6945,plain,
( one_to_one(iPr_def_10)
| ( apply(sK18,sK3(iPr_def_10)) = apply(iPr_def_10,sK2(iPr_def_10)) )
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_6928,c_4721]) ).
tcf(c_6946,plain,
apply(sK18,sK3(iPr_def_10)) = apply(iPr_def_10,sK2(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_6945,c_3544,c_4313,c_4407]) ).
tcf(c_6947,plain,
apply(sK18,sK2(iPr_def_10)) = apply(iPr_def_10,sK2(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_6927,c_3544,c_4313,c_4407]) ).
tcf(c_7005,plain,
! [X0: $i] :
( ( sK3(iPr_def_10) = X0 )
| ~ one_to_one(sK18)
| ~ relation(sK18)
| ~ function(sK18)
| ~ in(X0,relation_dom(sK18))
| ~ in(sK3(iPr_def_10),relation_dom(sK18))
| ( apply(iPr_def_10,sK2(iPr_def_10)) != apply(sK18,X0) ) ),
inference(superposition,[status(thm)],[c_6946,c_57]) ).
tcf(c_7013,plain,
! [X0: $i] :
( ( sK3(iPr_def_10) = X0 )
| ~ in(X0,relation_dom(sK18))
| ( apply(iPr_def_10,sK2(iPr_def_10)) != apply(sK18,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7005,c_3543,c_3542,c_3541,c_6570]) ).
tcf(c_7021,plain,
! [X0: $i] :
( ( sK2(iPr_def_10) = X0 )
| ~ one_to_one(sK18)
| ~ relation(sK18)
| ~ function(sK18)
| ~ in(X0,relation_dom(sK18))
| ~ in(sK2(iPr_def_10),relation_dom(sK18))
| ( apply(iPr_def_10,sK2(iPr_def_10)) != apply(sK18,X0) ) ),
inference(superposition,[status(thm)],[c_6947,c_57]) ).
tcf(c_7029,plain,
! [X0: $i] :
( ( sK2(iPr_def_10) = X0 )
| ~ in(X0,relation_dom(sK18))
| ( apply(iPr_def_10,sK2(iPr_def_10)) != apply(sK18,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7021,c_3543,c_3542,c_3541,c_6571]) ).
tcf(c_7035,plain,
! [X0: $i] :
( ( apply(iPr_def_10,sK2(iPr_def_10)) != apply(sK18,X0) )
| ~ in(X0,relation_dom(sK18)) ),
inference(global_subsumption_just,[status(thm)],[c_7013,c_3544,c_4313,c_4407,c_4914,c_5186,c_7013,c_7029]) ).
tcf(c_7036,plain,
! [X0: $i] :
( ~ in(X0,relation_dom(sK18))
| ( apply(iPr_def_10,sK2(iPr_def_10)) != apply(sK18,X0) ) ),
inference(renaming,[status(thm)],[c_7035]) ).
tcf(c_7043,plain,
~ in(sK3(iPr_def_10),relation_dom(sK18)),
inference(superposition,[status(thm)],[c_6946,c_7036]) ).
tcf(c_7044,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7043,c_6570]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU048+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/0.36 % Computer : n018.cluster.edu
% 0.04/0.36 % Model : x86_64 x86_64
% 0.04/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.36 % Memory : 8046.5625MB
% 0.04/0.36 % OS : Linux 6.8.0-71-generic
% 0.04/0.36 % CPULimit : 300
% 0.04/0.36 % WCLimit : 300
% 0.04/0.36 % DateTime : Thu Sep 24 12:40:33 UTC 2026
% 0.04/0.36 % CPUTime :
% 0.04/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/0.40 Running first-order theorem proving
% 0.04/0.40 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
% 0.04/0.41
% 0.04/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.04/0.41
% 0.04/0.41 % Detected problem language: tptp
% 0.04/0.43 % Proving...
% 3.13/1.08 % SZS status Started for theBenchmark.p
% 3.13/1.08 % SZS status Theorem for theBenchmark.p
% 3.13/1.08
% 3.13/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.13/1.08
% 3.13/1.08 % ------ iProver source info
% 3.13/1.08
% 3.13/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 3.13/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.13/1.08 % git: non_committed_changes: false
% 3.13/1.08
% 3.13/1.08 % ------ Parsing...
% 3.13/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.13/1.08
% 3.13/1.08 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.13/1.08
% 3.13/1.08 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.13/1.08
% 3.13/1.08 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.13/1.08 % ------ Proving...
% 3.13/1.08 % ------ Problem Properties
% 3.13/1.08
% 3.13/1.08 %
% 3.13/1.08 % clauses 62
% 3.13/1.08 % conjectures 4
% 3.13/1.08 % EPR 30
% 3.13/1.08 % Horn 52
% 3.13/1.08 % unary 27
% 3.13/1.08 % binary 12
% 3.13/1.08 % lits 140
% 3.13/1.08 % lits eq 12
% 3.13/1.08 % fd_pure 0
% 3.13/1.08 % fd_pseudo 0
% 3.13/1.08 % fd_cond 1
% 3.13/1.08 % fd_pseudo_cond 3
% 3.13/1.08 % AC symbols 0
% 3.13/1.08
% 3.13/1.08 % ------ Schedule dynamic 5 is on
% 3.13/1.08
% 3.13/1.08 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.13/1.08
% 3.13/1.08
% 3.13/1.08 % ------
% 3.13/1.08 % Current options:
% 3.13/1.08 % ------
% 3.13/1.08
% 3.13/1.08
% 3.13/1.08 %
% 3.13/1.08
% 3.13/1.08 % ------ Proving...
% 3.13/1.08 %
% 3.13/1.08
% 3.13/1.08 % SZS status Theorem for theBenchmark.p
% 3.13/1.08
% 3.13/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.13/1.08
%------------------------------------------------------------------------------