%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU002+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 : n015.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 02:55:00 PM UTC 2026
% Result : Theorem 3.78s 1.29s
% Output : CNFRefutation 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 89 ( 29 unt; 3 def)
% Number of atoms : 416 ( 51 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 463 ( 196 ~; 188 |; 56 &)
% ( 9 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 138 ( 0 sgn 123 !; 15 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f5,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f28,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
fof(f29,axiom,
! [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(f30,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_rng(relation_composition(X2,X1)))
=> in(X0,relation_rng(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_funct_1) ).
fof(f31,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_rng(relation_composition(X2,X1)))
=> in(X0,relation_rng(X1)) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f46,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f47,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(flattening,[],[f48]) ).
fof(f52,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(f53,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
inference(flattening,[],[f52]) ).
fof(f64,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f65,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ) ) ),
inference(flattening,[],[f64]) ).
fof(f66,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,[],[f29]) ).
fof(f67,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,[],[f66]) ).
fof(f68,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& ? [X2] :
( function(X2)
& relation(X2)
& in(X0,relation_rng(relation_composition(X2,X1)))
& ~ in(X0,relation_rng(X1)) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f69,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& ? [X2] :
( function(X2)
& relation(X2)
& in(X0,relation_rng(relation_composition(X2,X1)))
& ~ in(X0,relation_rng(X1)) ) ),
inference(flattening,[],[f68]) ).
fof(f79,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) )
& ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f80,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) )
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( apply(X0,sK2(X0,X5)) = X5
& in(sK2(X0,X5),relation_dom(X0)) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) )
| in(X5,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| ( sK0(X0,X1) = apply(X0,sK1(X0,X1))
& in(sK1(X0,X1),relation_dom(X0)) ) )
& ( ~ in(sK0(X0,X1),X1)
| ! [X3] :
( apply(X0,X3) != sK0(X0,X1)
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X4,sK1(X0,X1)),skolemize(X7,sK2(X0,X5))],[f80]) ).
fof(f91,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
& ( ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2))
| in(X0,relation_dom(relation_composition(X2,X1))) ) ) ) ),
inference(nnf_transformation,[],[f65]) ).
fof(f92,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
& ( ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2))
| in(X0,relation_dom(relation_composition(X2,X1))) ) ) ) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
( function(sK13)
& relation(sK13)
& function(sK14)
& relation(sK14)
& in(sK12,relation_rng(relation_composition(sK14,sK13)))
& ~ in(sK12,relation_rng(sK13)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14)],[f69]) ).
fof(f97,plain,
! [X0,X1,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| apply(X0,sK2(X0,X5)) = X5 ),
inference(cnf_transformation,[],[f81]) ).
fof(f98,plain,
! [X0,X1,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(sK2(X0,X5),relation_dom(X0)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f99,plain,
! [X0,X1,X6,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0))
| in(X5,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f103,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f109,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| function(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f138,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| in(apply(X2,X0),relation_dom(X1)) ),
inference(cnf_transformation,[],[f92]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f142,plain,
function(sK13),
inference(cnf_transformation,[],[f93]) ).
fof(f143,plain,
relation(sK13),
inference(cnf_transformation,[],[f93]) ).
fof(f144,plain,
function(sK14),
inference(cnf_transformation,[],[f93]) ).
fof(f145,plain,
relation(sK14),
inference(cnf_transformation,[],[f93]) ).
fof(f146,plain,
in(sK12,relation_rng(relation_composition(sK14,sK13))),
inference(cnf_transformation,[],[f93]) ).
fof(f147,plain,
~ in(sK12,relation_rng(sK13)),
inference(cnf_transformation,[],[f93]) ).
fof(f155,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),X1) ),
inference(equality_resolution,[],[f99]) ).
fof(f156,plain,
! [X0,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),relation_rng(X0)) ),
inference(equality_resolution,[],[f155]) ).
fof(f157,plain,
! [X0,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(sK2(X0,X5),relation_dom(X0)) ),
inference(equality_resolution,[],[f98]) ).
fof(f158,plain,
! [X0,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| apply(X0,sK2(X0,X5)) = X5 ),
inference(equality_resolution,[],[f97]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( in(apply(X1,X0),relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,X0),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,sK2(X1,X0)) = X0 )
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( function(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),relation_dom(X2))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X2)
| ~ function(X1)
| ~ in(X0,relation_dom(relation_composition(X1,X2))) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_96,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(relation_composition(X1,X2))) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_97,negated_conjecture,
~ in(sK12,relation_rng(sK13)),
inference(cnf_transformation,[],[f147]) ).
tcf(c_98,negated_conjecture,
in(sK12,relation_rng(relation_composition(sK14,sK13))),
inference(cnf_transformation,[],[f146]) ).
tcf(c_99,negated_conjecture,
relation(sK14),
inference(cnf_transformation,[],[f145]) ).
tcf(c_100,negated_conjecture,
function(sK14),
inference(cnf_transformation,[],[f144]) ).
tcf(c_101,negated_conjecture,
relation(sK13),
inference(cnf_transformation,[],[f143]) ).
tcf(c_102,negated_conjecture,
function(sK13),
inference(cnf_transformation,[],[f142]) ).
tcf(c_1185,definition,
iPr_def_10 = relation_composition(sK14,sK13),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1186,definition,
iPr_def_11 = relation_rng(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1187,definition,
iPr_def_12 = relation_rng(sK13),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1188,negated_conjecture,
function(sK13),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_1189,negated_conjecture,
relation(sK13),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_1190,negated_conjecture,
function(sK14),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_1191,negated_conjecture,
relation(sK14),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_1192,negated_conjecture,
in(sK12,iPr_def_11),
inference(demodulation,[status(thm)],[c_98,c_1185,c_1186]) ).
tcf(c_1193,negated_conjecture,
~ in(sK12,iPr_def_12),
inference(demodulation,[status(thm)],[c_97,c_1187]) ).
tcf(c_2096,plain,
( relation(iPr_def_10)
| ~ relation(sK14)
| ~ relation(sK13) ),
inference(superposition,[status(thm)],[c_1185,c_58]) ).
tcf(c_2097,plain,
relation(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2096,c_1191,c_1189]) ).
tcf(c_2518,plain,
( function(iPr_def_10)
| ~ relation(sK14)
| ~ relation(sK13)
| ~ function(sK14)
| ~ function(sK13) ),
inference(superposition,[status(thm)],[c_1185,c_65]) ).
tcf(c_2519,plain,
function(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2518,c_1191,c_1189,c_1190,c_1188]) ).
tcf(c_2528,plain,
! [X0: $i] :
( in(apply(sK13,X0),iPr_def_12)
| ~ relation(sK13)
| ~ function(sK13)
| ~ in(X0,relation_dom(sK13)) ),
inference(superposition,[status(thm)],[c_1187,c_55]) ).
tcf(c_2546,plain,
! [X0: $i] :
( in(apply(sK13,X0),iPr_def_12)
| ~ in(X0,relation_dom(sK13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2528,c_1189,c_1188]) ).
tcf(c_2802,plain,
! [X0: $i] :
( ( apply(iPr_def_10,sK2(iPr_def_10,X0)) = X0 )
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_1186,c_57]) ).
tcf(c_2803,plain,
! [X0: $i] :
( ( apply(iPr_def_10,sK2(iPr_def_10,X0)) = X0 )
| ~ in(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2802,c_2097,c_2519]) ).
tcf(c_2918,plain,
! [X0: $i] :
( in(apply(sK14,X0),relation_dom(sK13))
| ~ relation(sK14)
| ~ relation(sK13)
| ~ function(sK14)
| ~ function(sK13)
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_1185,c_95]) ).
tcf(c_2919,plain,
! [X0: $i] :
( in(apply(sK14,X0),relation_dom(sK13))
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2918,c_1191,c_1189,c_1190,c_1188]) ).
tcf(c_3291,plain,
! [X0: $i] :
( ( apply(relation_composition(sK14,sK13),X0) = apply(sK13,apply(sK14,X0)) )
| ~ relation(sK14)
| ~ relation(sK13)
| ~ function(sK14)
| ~ function(sK13)
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_1185,c_96]) ).
tcf(c_3292,plain,
! [X0: $i] :
( ( apply(sK13,apply(sK14,X0)) = apply(iPr_def_10,X0) )
| ~ relation(sK14)
| ~ relation(sK13)
| ~ function(sK14)
| ~ function(sK13)
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(light_normalisation,[status(thm)],[c_3291,c_1185]) ).
tcf(c_3293,plain,
! [X0: $i] :
( ( apply(sK13,apply(sK14,X0)) = apply(iPr_def_10,X0) )
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3292,c_1191,c_1189,c_1190,c_1188]) ).
tcf(c_3377,plain,
! [X0: $i] :
( ( apply(sK13,apply(sK14,sK2(iPr_def_10,X0))) = apply(iPr_def_10,sK2(iPr_def_10,X0)) )
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10)
| ~ in(X0,relation_rng(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_56,c_3293]) ).
tcf(c_3381,plain,
! [X0: $i] :
( ( apply(sK13,apply(sK14,sK2(iPr_def_10,X0))) = apply(iPr_def_10,sK2(iPr_def_10,X0)) )
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10)
| ~ in(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_3377,c_1186]) ).
tcf(c_3382,plain,
! [X0: $i] :
( ( apply(sK13,apply(sK14,sK2(iPr_def_10,X0))) = apply(iPr_def_10,sK2(iPr_def_10,X0)) )
| ~ in(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3381,c_2097,c_2519]) ).
tcf(c_3417,plain,
apply(iPr_def_10,sK2(iPr_def_10,sK12)) = sK12,
inference(superposition,[status(thm)],[c_1192,c_2803]) ).
tcf(c_5268,plain,
apply(sK13,apply(sK14,sK2(iPr_def_10,sK12))) = apply(iPr_def_10,sK2(iPr_def_10,sK12)),
inference(superposition,[status(thm)],[c_1192,c_3382]) ).
tcf(c_5274,plain,
apply(sK13,apply(sK14,sK2(iPr_def_10,sK12))) = sK12,
inference(light_normalisation,[status(thm)],[c_5268,c_3417]) ).
tcf(c_5747,plain,
( in(sK12,iPr_def_12)
| ~ in(apply(sK14,sK2(iPr_def_10,sK12)),relation_dom(sK13)) ),
inference(superposition,[status(thm)],[c_5274,c_2546]) ).
tcf(c_5748,plain,
~ in(apply(sK14,sK2(iPr_def_10,sK12)),relation_dom(sK13)),
inference(forward_subsumption_resolution,[status(thm)],[c_5747,c_1193]) ).
tcf(c_5749,plain,
~ in(sK2(iPr_def_10,sK12),relation_dom(iPr_def_10)),
inference(superposition,[status(thm)],[c_2919,c_5748]) ).
tcf(c_5750,plain,
( ~ relation(iPr_def_10)
| ~ function(iPr_def_10)
| ~ in(sK12,relation_rng(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_56,c_5749]) ).
tcf(c_5751,plain,
( ~ relation(iPr_def_10)
| ~ function(iPr_def_10)
| ~ in(sK12,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_5750,c_1186]) ).
tcf(c_5752,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5751,c_2097,c_2519,c_1192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU002+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:36:10 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 3.78/1.29 % SZS status Started for theBenchmark.p
% 3.78/1.29 % SZS status Theorem for theBenchmark.p
% 3.78/1.29
% 3.78/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.78/1.29
% 3.78/1.29 % ------ iProver source info
% 3.78/1.29
% 3.78/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 3.78/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.78/1.29 % git: non_committed_changes: false
% 3.78/1.29
% 3.78/1.29 % ------ Parsing...
% 3.78/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.78/1.29
% 3.78/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.78/1.29
% 3.78/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.78/1.29
% 3.78/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.78/1.29 % ------ Proving...
% 3.78/1.29 % ------ Problem Properties
% 3.78/1.29
% 3.78/1.29 %
% 3.78/1.29 % clauses 59
% 3.78/1.29 % conjectures 6
% 3.78/1.29 % EPR 25
% 3.78/1.29 % Horn 55
% 3.78/1.29 % unary 25
% 3.78/1.29 % binary 12
% 3.78/1.29 % lits 140
% 3.78/1.29 % lits eq 12
% 3.78/1.29 % fd_pure 0
% 3.78/1.29 % fd_pseudo 0
% 3.78/1.29 % fd_cond 1
% 3.78/1.29 % fd_pseudo_cond 4
% 3.78/1.29 % AC symbols 0
% 3.78/1.29
% 3.78/1.29 % ------ Schedule dynamic 5 is on
% 3.78/1.29
% 3.78/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.78/1.29
% 3.78/1.29
% 3.78/1.29 % ------
% 3.78/1.29 % Current options:
% 3.78/1.29 % ------
% 3.78/1.29
% 3.78/1.29
% 3.78/1.29 %
% 3.78/1.29
% 3.78/1.29 % ------ Proving...
% 3.78/1.29 %
% 3.78/1.29
% 3.78/1.29 % SZS status Theorem for theBenchmark.p
% 3.78/1.29
% 3.78/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.78/1.29
% 3.78/1.29
%------------------------------------------------------------------------------