%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU014+1 : 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 : n026.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 02:55:04 PM UTC 2026
% Result : Theorem 0.79s 6.49s
% Output : CNFRefutation 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 98 ( 34 unt; 3 def)
% Number of atoms : 384 ( 66 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 423 ( 178 ~; 178 |; 48 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 10 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 93 !; 8 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,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/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f5,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f9,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(f28,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f31,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_rng(X0),relation_dom(X1))
=> relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
fof(f32,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ( subset(relation_rng(X1),relation_dom(X0))
& one_to_one(relation_composition(X1,X0)) )
=> one_to_one(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_funct_1) ).
fof(f33,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ( subset(relation_rng(X1),relation_dom(X0))
& one_to_one(relation_composition(X1,X0)) )
=> one_to_one(X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f45,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,[],[f4]) ).
fof(f46,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,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f48,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(flattening,[],[f47]) ).
fof(f51,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f52,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
inference(flattening,[],[f51]) ).
fof(f63,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f64,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ),
inference(flattening,[],[f63]) ).
fof(f67,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ~ subset(relation_rng(X0),relation_dom(X1))
| relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f68,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ~ subset(relation_rng(X0),relation_dom(X1))
| relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
? [X0] :
( function(X0)
& relation(X0)
& ? [X1] :
( function(X1)
& relation(X1)
& subset(relation_rng(X1),relation_dom(X0))
& one_to_one(relation_composition(X1,X0))
& ~ one_to_one(X1) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f70,plain,
? [X0] :
( function(X0)
& relation(X0)
& ? [X1] :
( function(X1)
& relation(X1)
& subset(relation_rng(X1),relation_dom(X0))
& one_to_one(relation_composition(X1,X0))
& ~ one_to_one(X1) ) ),
inference(flattening,[],[f69]) ).
fof(f77,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,[],[f46]) ).
fof(f78,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,[],[f77]) ).
fof(f79,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,sK0(X0)) = apply(X0,sK1(X0))
& in(sK1(X0),relation_dom(X0))
& in(sK0(X0),relation_dom(X0))
& sK0(X0) != sK1(X0) )
| one_to_one(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0(X0)),skolemize(X2,sK1(X0))],[f78]) ).
fof(f90,plain,
( function(sK11)
& relation(sK11)
& function(sK12)
& relation(sK12)
& subset(relation_rng(sK12),relation_dom(sK11))
& one_to_one(relation_composition(sK12,sK11))
& ~ one_to_one(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X0,sK11),skolemize(X1,sK12)],[f70]) ).
fof(f94,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,[],[f79]) ).
fof(f95,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| apply(X0,sK0(X0)) = apply(X0,sK1(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f96,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK1(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f97,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK0(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f98,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| sK0(X0) != sK1(X0)
| one_to_one(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f99,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f48]) ).
fof(f105,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| function(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f134,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f138,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ subset(relation_rng(X0),relation_dom(X1))
| relation_dom(X0) = relation_dom(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f68]) ).
fof(f139,plain,
function(sK11),
inference(cnf_transformation,[],[f90]) ).
fof(f140,plain,
relation(sK11),
inference(cnf_transformation,[],[f90]) ).
fof(f141,plain,
function(sK12),
inference(cnf_transformation,[],[f90]) ).
fof(f142,plain,
relation(sK12),
inference(cnf_transformation,[],[f90]) ).
fof(f143,plain,
subset(relation_rng(sK12),relation_dom(sK11)),
inference(cnf_transformation,[],[f90]) ).
fof(f144,plain,
one_to_one(relation_composition(sK12,sK11)),
inference(cnf_transformation,[],[f90]) ).
fof(f145,plain,
~ one_to_one(sK12),
inference(cnf_transformation,[],[f90]) ).
tcf(c_52,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| ( sK0(X0) != sK1(X0) ) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_53,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK0(X0),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_54,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK1(X0),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_55,plain,
! [X0: $i] :
( one_to_one(X0)
| ( apply(X0,sK0(X0)) = apply(X0,sK1(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_56,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,[],[f94]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( function(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) )
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X2)
| ~ function(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(X0,X1)) = relation_dom(X0) )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_rng(X0),relation_dom(X1)) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_97,negated_conjecture,
~ one_to_one(sK12),
inference(cnf_transformation,[],[f145]) ).
tcf(c_98,negated_conjecture,
one_to_one(relation_composition(sK12,sK11)),
inference(cnf_transformation,[],[f144]) ).
tcf(c_99,negated_conjecture,
subset(relation_rng(sK12),relation_dom(sK11)),
inference(cnf_transformation,[],[f143]) ).
tcf(c_100,negated_conjecture,
relation(sK12),
inference(cnf_transformation,[],[f142]) ).
tcf(c_101,negated_conjecture,
function(sK12),
inference(cnf_transformation,[],[f141]) ).
tcf(c_102,negated_conjecture,
relation(sK11),
inference(cnf_transformation,[],[f140]) ).
tcf(c_103,negated_conjecture,
function(sK11),
inference(cnf_transformation,[],[f139]) ).
tcf(c_1104,plain,
! [X0: $i] :
( ~ relation(X0)
| ~ function(X0)
| ( X0 != sK12 )
| ( sK0(X0) != sK1(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_97]) ).
tcf(c_1105,plain,
( ~ relation(sK12)
| ~ function(sK12)
| ( sK0(sK12) != sK1(sK12) ) ),
inference(unflattening,[status(thm)],[c_1104]) ).
tcf(c_2193,definition,
iPr_def_10 = relation_rng(sK12),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2194,definition,
iPr_def_11 = relation_dom(sK11),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2195,definition,
iPr_def_12 = relation_composition(sK12,sK11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2196,negated_conjecture,
function(sK11),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_2197,negated_conjecture,
relation(sK11),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_2198,negated_conjecture,
function(sK12),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_2199,negated_conjecture,
relation(sK12),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_2200,negated_conjecture,
subset(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_99,c_2194,c_2193]) ).
tcf(c_2201,negated_conjecture,
one_to_one(iPr_def_12),
inference(demodulation,[status(thm)],[c_98,c_2195]) ).
tcf(c_2202,negated_conjecture,
~ one_to_one(sK12),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_3391,plain,
( relation(iPr_def_12)
| ~ relation(sK11)
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_2195,c_57]) ).
tcf(c_3392,plain,
relation(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_3391,c_2197,c_2199]) ).
tcf(c_3792,plain,
( function(iPr_def_12)
| ~ relation(sK11)
| ~ relation(sK12)
| ~ function(sK11)
| ~ function(sK12) ),
inference(superposition,[status(thm)],[c_2195,c_64]) ).
tcf(c_3793,plain,
function(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_3792,c_2197,c_2199,c_2196,c_2198]) ).
tcf(c_3888,plain,
( one_to_one(sK12)
| ( apply(sK12,sK0(sK12)) = apply(sK12,sK1(sK12)) )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_2198,c_55]) ).
tcf(c_3897,plain,
apply(sK12,sK0(sK12)) = apply(sK12,sK1(sK12)),
inference(forward_subsumption_resolution,[status(thm)],[c_3888,c_2202,c_2199]) ).
tcf(c_3939,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(X0,sK11)) = relation_dom(X0) )
| ~ relation(sK11)
| ~ relation(X0)
| ~ subset(relation_rng(X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_2194,c_96]) ).
tcf(c_3945,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(X0,sK11)) = relation_dom(X0) )
| ~ relation(X0)
| ~ subset(relation_rng(X0),iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3939,c_2197]) ).
tcf(c_4130,plain,
( ( relation_dom(relation_composition(sK12,sK11)) = relation_dom(sK12) )
| ~ relation(sK12)
| ~ subset(iPr_def_10,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2193,c_3945]) ).
tcf(c_4134,plain,
( ( relation_dom(sK12) = relation_dom(iPr_def_12) )
| ~ relation(sK12)
| ~ subset(iPr_def_10,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_4130,c_2195]) ).
tcf(c_4135,plain,
relation_dom(sK12) = relation_dom(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_4134,c_2199,c_2200]) ).
tcf(c_4136,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(sK12,X1),X0) = apply(X1,apply(sK12,X0)) )
| ~ relation(sK12)
| ~ function(sK12)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(iPr_def_12)) ),
inference(superposition,[status(thm)],[c_4135,c_92]) ).
tcf(c_4138,plain,
( one_to_one(sK12)
| in(sK1(sK12),relation_dom(iPr_def_12))
| ~ relation(sK12)
| ~ function(sK12) ),
inference(superposition,[status(thm)],[c_4135,c_54]) ).
tcf(c_4139,plain,
( one_to_one(sK12)
| in(sK0(sK12),relation_dom(iPr_def_12))
| ~ relation(sK12)
| ~ function(sK12) ),
inference(superposition,[status(thm)],[c_4135,c_53]) ).
tcf(c_4153,plain,
in(sK0(sK12),relation_dom(iPr_def_12)),
inference(forward_subsumption_resolution,[status(thm)],[c_4139,c_2202,c_2199,c_2198]) ).
tcf(c_4154,plain,
in(sK1(sK12),relation_dom(iPr_def_12)),
inference(forward_subsumption_resolution,[status(thm)],[c_4138,c_2202,c_2199,c_2198]) ).
tcf(c_4159,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(sK12,X1),X0) = apply(X1,apply(sK12,X0)) )
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(iPr_def_12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4136,c_2199,c_2198]) ).
tcf(c_4327,plain,
! [X0: $i] :
( ( apply(relation_composition(sK12,X0),sK1(sK12)) = apply(X0,apply(sK12,sK1(sK12))) )
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_4154,c_4159]) ).
tcf(c_4328,plain,
! [X0: $i] :
( ( apply(relation_composition(sK12,X0),sK0(sK12)) = apply(X0,apply(sK12,sK0(sK12))) )
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_4153,c_4159]) ).
tcf(c_4332,plain,
! [X0: $i] :
( ( apply(relation_composition(sK12,X0),sK1(sK12)) = apply(X0,apply(sK12,sK0(sK12))) )
| ~ relation(X0)
| ~ function(X0) ),
inference(light_normalisation,[status(thm)],[c_4327,c_3897]) ).
tcf(c_4669,plain,
( ( apply(relation_composition(sK12,sK11),sK0(sK12)) = apply(sK11,apply(sK12,sK0(sK12))) )
| ~ relation(sK11) ),
inference(superposition,[status(thm)],[c_2196,c_4328]) ).
tcf(c_4677,plain,
( ( apply(sK11,apply(sK12,sK0(sK12))) = apply(iPr_def_12,sK0(sK12)) )
| ~ relation(sK11) ),
inference(light_normalisation,[status(thm)],[c_4669,c_2195]) ).
tcf(c_4678,plain,
apply(sK11,apply(sK12,sK0(sK12))) = apply(iPr_def_12,sK0(sK12)),
inference(forward_subsumption_resolution,[status(thm)],[c_4677,c_2197]) ).
tcf(c_5241,plain,
( ( apply(relation_composition(sK12,sK11),sK1(sK12)) = apply(sK11,apply(sK12,sK0(sK12))) )
| ~ relation(sK11) ),
inference(superposition,[status(thm)],[c_2196,c_4332]) ).
tcf(c_5249,plain,
( ( apply(iPr_def_12,sK0(sK12)) = apply(iPr_def_12,sK1(sK12)) )
| ~ relation(sK11) ),
inference(light_normalisation,[status(thm)],[c_5241,c_2195,c_4678]) ).
tcf(c_5250,plain,
apply(iPr_def_12,sK0(sK12)) = apply(iPr_def_12,sK1(sK12)),
inference(forward_subsumption_resolution,[status(thm)],[c_5249,c_2197]) ).
tcf(c_5333,plain,
! [X0: $i] :
( ( sK1(sK12) = X0 )
| ~ one_to_one(iPr_def_12)
| ~ relation(iPr_def_12)
| ~ function(iPr_def_12)
| ~ in(X0,relation_dom(iPr_def_12))
| ~ in(sK1(sK12),relation_dom(iPr_def_12))
| ( apply(iPr_def_12,sK0(sK12)) != apply(iPr_def_12,X0) ) ),
inference(superposition,[status(thm)],[c_5250,c_56]) ).
tcf(c_5335,plain,
! [X0: $i] :
( ( sK1(sK12) = X0 )
| ~ in(X0,relation_dom(iPr_def_12))
| ( apply(iPr_def_12,sK0(sK12)) != apply(iPr_def_12,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5333,c_2201,c_3392,c_3793,c_4154]) ).
tcf(c_5357,plain,
( ( sK0(sK12) = sK1(sK12) )
| ~ in(sK0(sK12),relation_dom(iPr_def_12)) ),
inference(equality_resolution,[status(thm)],[c_5335]) ).
tcf(c_5358,plain,
sK0(sK12) = sK1(sK12),
inference(forward_subsumption_resolution,[status(thm)],[c_5357,c_4153]) ).
tcf(c_5370,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5358,c_1105,c_100,c_101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU014+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/5.66 % Computer : n026.cluster.edu
% 0.17/5.66 % Model : x86_64 x86_64
% 0.17/5.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.66 % Memory : 8046.5625MB
% 0.17/5.66 % OS : Linux 6.8.0-71-generic
% 0.17/5.66 % CPULimit : 300
% 0.17/5.66 % WCLimit : 300
% 0.17/5.66 % DateTime : Thu Sep 24 12:37:15 UTC 2026
% 0.17/5.66 % CPUTime :
% 0.17/5.66 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/5.70 Running first-order theorem proving
% 0.19/5.70 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
% 0.19/5.71
% 0.19/5.71 % ======== iProver multi-core TPTP/SMT =========
% 0.19/5.71
% 0.19/5.71 % Detected problem language: tptp
% 0.19/5.73 % Proving...
% 0.79/6.49 % SZS status Started for theBenchmark.p
% 0.79/6.49 % SZS status Theorem for theBenchmark.p
% 0.79/6.49
% 0.79/6.49 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.79/6.49
% 0.79/6.49 % ------ iProver source info
% 0.79/6.49
% 0.79/6.49 % git: date: 2026-07-19 20:42:38 +0200
% 0.79/6.49 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.79/6.49 % git: non_committed_changes: false
% 0.79/6.49
% 0.79/6.49 % ------ Parsing...
% 0.79/6.49 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.79/6.49
% 0.79/6.49 % ------ 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 %
% 0.79/6.49
% 0.79/6.49 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.79/6.49
% 0.79/6.49 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.79/6.49 % ------ Proving...
% 0.79/6.49 % ------ Problem Properties
% 0.79/6.49
% 0.79/6.49 %
% 0.79/6.49 % clauses 59
% 0.79/6.49 % conjectures 7
% 0.79/6.49 % EPR 29
% 0.79/6.49 % Horn 54
% 0.79/6.49 % unary 26
% 0.79/6.49 % binary 14
% 0.79/6.49 % lits 125
% 0.79/6.49 % lits eq 11
% 0.79/6.49 % fd_pure 0
% 0.79/6.49 % fd_pseudo 0
% 0.79/6.49 % fd_cond 1
% 0.79/6.49 % fd_pseudo_cond 2
% 0.79/6.49 % AC symbols 0
% 0.79/6.49
% 0.79/6.49 % ------ Schedule dynamic 5 is on
% 0.79/6.49
% 0.79/6.49 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.79/6.49
% 0.79/6.49
% 0.79/6.49 % ------
% 0.79/6.49 % Current options:
% 0.79/6.49 % ------
% 0.79/6.49
% 0.79/6.49
% 0.79/6.49 %
% 0.79/6.49
% 0.79/6.49 % ------ Proving...
% 0.79/6.49 %
% 0.79/6.49
% 0.79/6.49 % SZS status Theorem for theBenchmark.p
% 0.79/6.49
% 0.79/6.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.79/6.49
% 0.79/6.49
%------------------------------------------------------------------------------