%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU013+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 : n006.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 4.41s 1.28s
% Output : CNFRefutation 4.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 104 ( 32 unt; 1 def)
% Number of atoms : 524 ( 58 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 535 ( 225 ~; 232 |; 57 &)
% ( 6 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 117 ( 0 sgn 109 !; 8 ?; 31 :)
% 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/sandbox/benchmark/theBenchmark.p',d8_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(f26,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(f27,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] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ( one_to_one(X1)
& one_to_one(X0) )
=> one_to_one(relation_composition(X0,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_funct_1) ).
fof(f31,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ( one_to_one(X1)
& one_to_one(X0) )
=> one_to_one(relation_composition(X0,X1)) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f44,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(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(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f47,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(flattening,[],[f46]) ).
fof(f50,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(f51,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
inference(flattening,[],[f50]) ).
fof(f59,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,[],[f26]) ).
fof(f60,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,[],[f59]) ).
fof(f61,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,[],[f27]) ).
fof(f62,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,[],[f61]) ).
fof(f66,plain,
? [X0] :
( function(X0)
& relation(X0)
& ? [X1] :
( function(X1)
& relation(X1)
& one_to_one(X1)
& one_to_one(X0)
& ~ one_to_one(relation_composition(X0,X1)) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f67,plain,
? [X0] :
( function(X0)
& relation(X0)
& ? [X1] :
( function(X1)
& relation(X1)
& one_to_one(X1)
& one_to_one(X0)
& ~ one_to_one(relation_composition(X0,X1)) ) ),
inference(flattening,[],[f66]) ).
fof(f74,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,[],[f45]) ).
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 ) )
& ( ? [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,[],[f74]) ).
fof(f76,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))],[f75]) ).
fof(f86,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,[],[f60]) ).
fof(f87,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,[],[f86]) ).
fof(f88,plain,
( function(sK11)
& relation(sK11)
& function(sK12)
& relation(sK12)
& one_to_one(sK12)
& one_to_one(sK11)
& ~ one_to_one(relation_composition(sK11,sK12)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X0,sK11),skolemize(X1,sK12)],[f67]) ).
fof(f92,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,[],[f76]) ).
fof(f93,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| apply(X0,sK0(X0)) = apply(X0,sK1(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f94,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK1(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f95,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK0(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f96,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| sK0(X0) != sK1(X0)
| one_to_one(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f97,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f103,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| function(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f129,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,[],[f87]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f87]) ).
fof(f132,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,[],[f62]) ).
fof(f135,plain,
function(sK11),
inference(cnf_transformation,[],[f88]) ).
fof(f136,plain,
relation(sK11),
inference(cnf_transformation,[],[f88]) ).
fof(f137,plain,
function(sK12),
inference(cnf_transformation,[],[f88]) ).
fof(f138,plain,
relation(sK12),
inference(cnf_transformation,[],[f88]) ).
fof(f139,plain,
one_to_one(sK12),
inference(cnf_transformation,[],[f88]) ).
fof(f140,plain,
one_to_one(sK11),
inference(cnf_transformation,[],[f88]) ).
fof(f141,plain,
~ one_to_one(relation_composition(sK11,sK12)),
inference(cnf_transformation,[],[f88]) ).
tcf(c_52,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| ( sK0(X0) != sK1(X0) ) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_53,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK0(X0),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_54,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK1(X0),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f94]) ).
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,[],[f93]) ).
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,[],[f92]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( function(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X2)
| ~ function(X1)
| ~ in(X0,relation_dom(relation_composition(X1,X2))) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_91,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,[],[f129]) ).
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(relation_composition(X1,X2))) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_95,negated_conjecture,
~ one_to_one(relation_composition(sK11,sK12)),
inference(cnf_transformation,[],[f141]) ).
tcf(c_96,negated_conjecture,
one_to_one(sK11),
inference(cnf_transformation,[],[f140]) ).
tcf(c_97,negated_conjecture,
one_to_one(sK12),
inference(cnf_transformation,[],[f139]) ).
tcf(c_98,negated_conjecture,
relation(sK12),
inference(cnf_transformation,[],[f138]) ).
tcf(c_99,negated_conjecture,
function(sK12),
inference(cnf_transformation,[],[f137]) ).
tcf(c_100,negated_conjecture,
relation(sK11),
inference(cnf_transformation,[],[f136]) ).
tcf(c_101,negated_conjecture,
function(sK11),
inference(cnf_transformation,[],[f135]) ).
tcf(c_1547,definition,
iPr_def_10 = relation_composition(sK11,sK12),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1548,negated_conjecture,
function(sK11),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_1549,negated_conjecture,
relation(sK11),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_1550,negated_conjecture,
function(sK12),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_1551,negated_conjecture,
relation(sK12),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_1552,negated_conjecture,
one_to_one(sK12),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_1553,negated_conjecture,
one_to_one(sK11),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_1554,negated_conjecture,
~ one_to_one(iPr_def_10),
inference(demodulation,[status(thm)],[c_95,c_1547]) ).
tcf(c_2373,plain,
( relation(iPr_def_10)
| ~ relation(sK12)
| ~ relation(sK11) ),
inference(superposition,[status(thm)],[c_1547,c_57]) ).
tcf(c_2374,plain,
relation(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2373,c_1551,c_1549]) ).
tcf(c_2749,plain,
( one_to_one(iPr_def_10)
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10)
| ( sK0(iPr_def_10) != sK1(iPr_def_10) ) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_2750,plain,
( one_to_one(iPr_def_10)
| in(sK0(iPr_def_10),relation_dom(iPr_def_10))
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_2751,plain,
( one_to_one(iPr_def_10)
| in(sK1(iPr_def_10),relation_dom(iPr_def_10))
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_2863,plain,
( function(iPr_def_10)
| ~ relation(sK12)
| ~ relation(sK11)
| ~ function(sK12)
| ~ function(sK11) ),
inference(superposition,[status(thm)],[c_1547,c_64]) ).
tcf(c_2865,plain,
function(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2863,c_1551,c_1549,c_1550,c_1548]) ).
tcf(c_2889,plain,
! [X0: $i] :
( in(X0,relation_dom(sK11))
| ~ relation(sK12)
| ~ relation(sK11)
| ~ function(sK12)
| ~ function(sK11)
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_1547,c_90]) ).
tcf(c_2890,plain,
! [X0: $i] :
( in(X0,relation_dom(sK11))
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2889,c_1551,c_1549,c_1550,c_1548]) ).
tcf(c_2938,plain,
! [X0: $i] :
( in(apply(sK11,X0),relation_dom(sK12))
| ~ relation(sK12)
| ~ relation(sK11)
| ~ function(sK12)
| ~ function(sK11)
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_1547,c_91]) ).
tcf(c_2939,plain,
! [X0: $i] :
( in(apply(sK11,X0),relation_dom(sK12))
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2938,c_1551,c_1549,c_1550,c_1548]) ).
tcf(c_2989,plain,
( one_to_one(iPr_def_10)
| ( apply(iPr_def_10,sK0(iPr_def_10)) = apply(iPr_def_10,sK1(iPr_def_10)) )
| ~ relation(iPr_def_10) ),
inference(superposition,[status(thm)],[c_2865,c_55]) ).
tcf(c_2990,plain,
apply(iPr_def_10,sK0(iPr_def_10)) = apply(iPr_def_10,sK1(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_2989,c_1554,c_2374]) ).
tcf(c_2995,plain,
( one_to_one(iPr_def_10)
| in(sK0(iPr_def_10),relation_dom(sK11))
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53,c_2890]) ).
tcf(c_2996,plain,
( one_to_one(iPr_def_10)
| in(sK1(iPr_def_10),relation_dom(sK11))
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_54,c_2890]) ).
tcf(c_3000,plain,
in(sK1(iPr_def_10),relation_dom(sK11)),
inference(forward_subsumption_resolution,[status(thm)],[c_2996,c_1554,c_2374,c_2865]) ).
tcf(c_3001,plain,
in(sK0(iPr_def_10),relation_dom(sK11)),
inference(forward_subsumption_resolution,[status(thm)],[c_2995,c_1554,c_2374,c_2865]) ).
tcf(c_3093,plain,
! [X0: $i] :
( ( apply(relation_composition(sK11,sK12),X0) = apply(sK12,apply(sK11,X0)) )
| ~ relation(sK12)
| ~ relation(sK11)
| ~ function(sK12)
| ~ function(sK11)
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_1547,c_92]) ).
tcf(c_3094,plain,
! [X0: $i] :
( ( apply(sK12,apply(sK11,X0)) = apply(iPr_def_10,X0) )
| ~ relation(sK12)
| ~ relation(sK11)
| ~ function(sK12)
| ~ function(sK11)
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(light_normalisation,[status(thm)],[c_3093,c_1547]) ).
tcf(c_3095,plain,
! [X0: $i] :
( ( apply(sK12,apply(sK11,X0)) = apply(iPr_def_10,X0) )
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3094,c_1551,c_1549,c_1550,c_1548]) ).
tcf(c_3146,plain,
( one_to_one(iPr_def_10)
| ( apply(sK12,apply(sK11,sK0(iPr_def_10))) = apply(iPr_def_10,sK0(iPr_def_10)) )
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53,c_3095]) ).
tcf(c_3147,plain,
( one_to_one(iPr_def_10)
| ( apply(sK12,apply(sK11,sK1(iPr_def_10))) = apply(iPr_def_10,sK1(iPr_def_10)) )
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_54,c_3095]) ).
tcf(c_3151,plain,
( one_to_one(iPr_def_10)
| ( apply(sK12,apply(sK11,sK1(iPr_def_10))) = apply(iPr_def_10,sK0(iPr_def_10)) )
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_3147,c_2990]) ).
tcf(c_3152,plain,
apply(sK12,apply(sK11,sK1(iPr_def_10))) = apply(iPr_def_10,sK0(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_3151,c_1554,c_2374,c_2865]) ).
tcf(c_3153,plain,
apply(sK12,apply(sK11,sK0(iPr_def_10))) = apply(iPr_def_10,sK0(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_3146,c_1554,c_2374,c_2865]) ).
tcf(c_3155,plain,
! [X0: $i] :
( ( apply(sK11,sK1(iPr_def_10)) = X0 )
| ~ one_to_one(sK12)
| ~ relation(sK12)
| ~ function(sK12)
| ~ in(X0,relation_dom(sK12))
| ~ in(apply(sK11,sK1(iPr_def_10)),relation_dom(sK12))
| ( apply(iPr_def_10,sK0(iPr_def_10)) != apply(sK12,X0) ) ),
inference(superposition,[status(thm)],[c_3152,c_56]) ).
tcf(c_3163,plain,
! [X0: $i] :
( ( apply(sK11,sK1(iPr_def_10)) = X0 )
| ~ in(X0,relation_dom(sK12))
| ~ in(apply(sK11,sK1(iPr_def_10)),relation_dom(sK12))
| ( apply(iPr_def_10,sK0(iPr_def_10)) != apply(sK12,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3155,c_1552,c_1551,c_1550]) ).
tcf(c_3194,plain,
( ( apply(sK11,sK0(iPr_def_10)) = apply(sK11,sK1(iPr_def_10)) )
| ~ in(apply(sK11,sK1(iPr_def_10)),relation_dom(sK12))
| ~ in(apply(sK11,sK0(iPr_def_10)),relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_3153,c_3163]) ).
tcf(c_4136,plain,
( ( apply(sK11,sK0(iPr_def_10)) = apply(sK11,sK1(iPr_def_10)) )
| ~ in(sK1(iPr_def_10),relation_dom(iPr_def_10))
| ~ in(apply(sK11,sK0(iPr_def_10)),relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_2939,c_3194]) ).
tcf(c_5116,plain,
( ( apply(sK11,sK0(iPr_def_10)) = apply(sK11,sK1(iPr_def_10)) )
| ~ in(apply(sK11,sK0(iPr_def_10)),relation_dom(sK12)) ),
inference(global_subsumption_just,[status(thm)],[c_4136,c_1554,c_2374,c_2751,c_2865,c_4136]) ).
tcf(c_5122,plain,
( ( apply(sK11,sK0(iPr_def_10)) = apply(sK11,sK1(iPr_def_10)) )
| ~ in(sK0(iPr_def_10),relation_dom(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_2939,c_5116]) ).
tcf(c_5142,plain,
apply(sK11,sK0(iPr_def_10)) = apply(sK11,sK1(iPr_def_10)),
inference(global_subsumption_just,[status(thm)],[c_5122,c_1554,c_2374,c_2750,c_2865,c_5122]) ).
tcf(c_5168,plain,
! [X0: $i] :
( ( sK1(iPr_def_10) = X0 )
| ~ one_to_one(sK11)
| ~ relation(sK11)
| ~ function(sK11)
| ~ in(X0,relation_dom(sK11))
| ~ in(sK1(iPr_def_10),relation_dom(sK11))
| ( apply(sK11,sK0(iPr_def_10)) != apply(sK11,X0) ) ),
inference(superposition,[status(thm)],[c_5142,c_56]) ).
tcf(c_5184,plain,
! [X0: $i] :
( ( sK1(iPr_def_10) = X0 )
| ~ in(X0,relation_dom(sK11))
| ( apply(sK11,sK0(iPr_def_10)) != apply(sK11,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5168,c_1553,c_1549,c_1548,c_3000]) ).
tcf(c_5197,plain,
( ( sK0(iPr_def_10) = sK1(iPr_def_10) )
| ~ in(sK0(iPr_def_10),relation_dom(sK11)) ),
inference(equality_resolution,[status(thm)],[c_5184]) ).
tcf(c_5198,plain,
sK0(iPr_def_10) = sK1(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_5197,c_3001]) ).
tcf(c_5208,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5198,c_2865,c_2749,c_2374,c_1554]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU013+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n006.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 12:34:27 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.41 % Detected problem language: tptp
% 0.08/0.42 % Proving...
% 4.41/1.28 % SZS status Started for theBenchmark.p
% 4.41/1.28 % SZS status Theorem for theBenchmark.p
% 4.41/1.28
% 4.41/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.41/1.28
% 4.41/1.28 % ------ iProver source info
% 4.41/1.28
% 4.41/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.41/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.41/1.28 % git: non_committed_changes: false
% 4.41/1.28
% 4.41/1.28 % ------ Parsing...
% 4.41/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.41/1.28
% 4.41/1.28 % ------ 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 %
% 4.41/1.28
% 4.41/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.41/1.28
% 4.41/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.41/1.28 % ------ Proving...
% 4.41/1.28 % ------ Problem Properties
% 4.41/1.28
% 4.41/1.28 %
% 4.41/1.28 % clauses 54
% 4.41/1.28 % conjectures 7
% 4.41/1.28 % EPR 26
% 4.41/1.28 % Horn 49
% 4.41/1.28 % unary 24
% 4.41/1.28 % binary 10
% 4.41/1.28 % lits 127
% 4.41/1.28 % lits eq 8
% 4.41/1.28 % fd_pure 0
% 4.41/1.28 % fd_pseudo 0
% 4.41/1.28 % fd_cond 1
% 4.41/1.28 % fd_pseudo_cond 2
% 4.41/1.28 % AC symbols 0
% 4.41/1.28
% 4.41/1.28 % ------ Schedule dynamic 5 is on
% 4.41/1.28
% 4.41/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.41/1.28
% 4.41/1.28
% 4.41/1.28 % ------
% 4.41/1.28 % Current options:
% 4.41/1.28 % ------
% 4.41/1.28
% 4.41/1.28
% 4.41/1.28 %
% 4.41/1.28
% 4.41/1.28 % ------ Proving...
% 4.41/1.28 %
% 4.41/1.28
% 4.41/1.28 % SZS status Theorem for theBenchmark.p
% 4.41/1.28
% 4.41/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.41/1.28
% 4.41/1.28
%------------------------------------------------------------------------------