%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU017+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 : n002.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 7.84s 1.84s
% Output : CNFRefutation 7.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 122 ( 29 unt; 0 def)
% Number of atoms : 505 ( 148 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 641 ( 258 ~; 255 |; 96 &)
% ( 13 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-2 aty)
% Number of variables : 200 ( 0 sgn 178 !; 22 ?; 38 :)
% 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/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
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/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f16,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f18,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f31,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(f32,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f33,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f34,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f35,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f36,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( ( relation_composition(X2,X1) = X1
& one_to_one(X1)
& subset(relation_rng(X2),X0)
& relation_dom(X2) = X0
& relation_dom(X1) = X0 )
=> X2 = identity_relation(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_funct_1) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( ( relation_composition(X2,X1) = X1
& one_to_one(X1)
& subset(relation_rng(X2),X0)
& relation_dom(X2) = X0
& relation_dom(X1) = X0 )
=> X2 = identity_relation(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f40,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f43,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f44,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& ? [X2] :
( function(X2)
& relation(X2)
& relation_composition(X2,X1) = X1
& one_to_one(X1)
& subset(relation_rng(X2),X0)
& relation_dom(X2) = X0
& relation_dom(X1) = X0
& identity_relation(X0) != X2 ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f45,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& ? [X2] :
( function(X2)
& relation(X2)
& relation_composition(X2,X1) = X1
& one_to_one(X1)
& subset(relation_rng(X2),X0)
& relation_dom(X2) = X0
& relation_dom(X1) = X0
& identity_relation(X0) != X2 ) ),
inference(flattening,[],[f44]) ).
fof(f50,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(f51,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,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f53,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f54,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(flattening,[],[f53]) ).
fof(f58,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,[],[f31]) ).
fof(f59,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,[],[f58]) ).
fof(f67,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f68,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(flattening,[],[f67]) ).
fof(f69,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(f70,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,[],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(ennf_transformation,[],[f43]) ).
fof(f72,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f73,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f74,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f73]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f35]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f78]) ).
fof(f81,plain,
( function(sK1)
& relation(sK1)
& function(sK2)
& relation(sK2)
& sK1 = relation_composition(sK2,sK1)
& one_to_one(sK1)
& subset(relation_rng(sK2),sK0)
& sK0 = relation_dom(sK2)
& sK0 = relation_dom(sK1)
& sK2 != identity_relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f45]) ).
fof(f82,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,[],[f51]) ).
fof(f83,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,[],[f82]) ).
fof(f84,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( apply(X0,sK5(X0,X5)) = X5
& in(sK5(X0,X5),relation_dom(X0)) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) )
| in(X5,X1) ) ) )
& ( ( ( in(sK3(X0,X1),X1)
| ( sK3(X0,X1) = apply(X0,sK4(X0,X1))
& in(sK4(X0,X1),relation_dom(X0)) ) )
& ( ~ in(sK3(X0,X1),X1)
| ! [X3] :
( apply(X0,X3) != sK3(X0,X1)
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X2,sK3(X0,X1)),skolemize(X4,sK4(X0,X1)),skolemize(X7,sK5(X0,X5))],[f83]) ).
fof(f88,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f89,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(flattening,[],[f88]) ).
fof(f90,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(rectify,[],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( ( in(sK9(X0,X1),X0)
& sK9(X0,X1) != apply(X1,sK9(X0,X1)) )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X0,X1))],[f90]) ).
fof(f92,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,[],[f70]) ).
fof(f93,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,[],[f92]) ).
fof(f94,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,sK10(X0)) = apply(X0,sK11(X0))
& in(sK11(X0),relation_dom(X0))
& in(sK10(X0),relation_dom(X0))
& sK10(X0) != sK11(X0) )
| one_to_one(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X1,sK10(X0)),skolemize(X2,sK11(X0))],[f93]) ).
fof(f100,plain,
function(sK1),
inference(cnf_transformation,[],[f81]) ).
fof(f101,plain,
relation(sK1),
inference(cnf_transformation,[],[f81]) ).
fof(f102,plain,
function(sK2),
inference(cnf_transformation,[],[f81]) ).
fof(f103,plain,
relation(sK2),
inference(cnf_transformation,[],[f81]) ).
fof(f104,plain,
sK1 = relation_composition(sK2,sK1),
inference(cnf_transformation,[],[f81]) ).
fof(f105,plain,
one_to_one(sK1),
inference(cnf_transformation,[],[f81]) ).
fof(f106,plain,
subset(relation_rng(sK2),sK0),
inference(cnf_transformation,[],[f81]) ).
fof(f107,plain,
sK0 = relation_dom(sK2),
inference(cnf_transformation,[],[f81]) ).
fof(f108,plain,
sK0 = relation_dom(sK1),
inference(cnf_transformation,[],[f81]) ).
fof(f109,plain,
sK2 != identity_relation(sK0),
inference(cnf_transformation,[],[f81]) ).
fof(f116,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,[],[f84]) ).
fof(f121,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f122,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f128,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,[],[f59]) ).
fof(f141,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| in(sK9(X0,X1),X0)
| relation_dom(X1) != X0
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f91]) ).
fof(f142,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| sK9(X0,X1) != apply(X1,sK9(X0,X1))
| relation_dom(X1) != X0
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f91]) ).
fof(f146,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,[],[f94]) ).
fof(f151,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f155,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f156,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f160,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f79]) ).
fof(f167,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,[],[f116]) ).
fof(f168,plain,
! [X0,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),relation_rng(X0)) ),
inference(equality_resolution,[],[f167]) ).
fof(f171,plain,
! [X1] :
( ~ function(X1)
| ~ relation(X1)
| sK9(relation_dom(X1),X1) != apply(X1,sK9(relation_dom(X1),X1))
| identity_relation(relation_dom(X1)) = X1 ),
inference(equality_resolution,[],[f142]) ).
fof(f172,plain,
! [X1] :
( ~ function(X1)
| ~ relation(X1)
| in(sK9(relation_dom(X1),X1),relation_dom(X1))
| identity_relation(relation_dom(X1)) = X1 ),
inference(equality_resolution,[],[f141]) ).
tcf(c_49,negated_conjecture,
identity_relation(sK0) != sK2,
inference(cnf_transformation,[],[f109]) ).
tcf(c_50,negated_conjecture,
relation_dom(sK1) = sK0,
inference(cnf_transformation,[],[f108]) ).
tcf(c_51,negated_conjecture,
relation_dom(sK2) = sK0,
inference(cnf_transformation,[],[f107]) ).
tcf(c_52,negated_conjecture,
subset(relation_rng(sK2),sK0),
inference(cnf_transformation,[],[f106]) ).
tcf(c_53,negated_conjecture,
one_to_one(sK1),
inference(cnf_transformation,[],[f105]) ).
tcf(c_54,negated_conjecture,
relation_composition(sK2,sK1) = sK1,
inference(cnf_transformation,[],[f104]) ).
tcf(c_55,negated_conjecture,
relation(sK2),
inference(cnf_transformation,[],[f103]) ).
tcf(c_56,negated_conjecture,
function(sK2),
inference(cnf_transformation,[],[f102]) ).
tcf(c_57,negated_conjecture,
relation(sK1),
inference(cnf_transformation,[],[f101]) ).
tcf(c_58,negated_conjecture,
function(sK1),
inference(cnf_transformation,[],[f100]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( in(apply(X1,X0),relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_69,plain,
! [X0: $i] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_71,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_88,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(X0)) = X0 )
| ~ function(X0)
| ~ relation(X0)
| ( apply(X0,sK9(relation_dom(X0),X0)) != sK9(relation_dom(X0),X0) ) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_89,plain,
! [X0: $i] :
( in(sK9(relation_dom(X0),X0),relation_dom(X0))
| ( identity_relation(relation_dom(X0)) = X0 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| ( apply(X0,X1) != apply(X0,X2) ) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_742,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ( X1 != sK0 )
| ( relation_rng(sK2) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_100]) ).
tcf(c_743,plain,
element(relation_rng(sK2),powerset(sK0)),
inference(unflattening,[status(thm)],[c_742]) ).
tcf(c_2453,plain,
( empty(sK0)
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_50,c_69]) ).
tcf(c_2826,plain,
( empty(sK1)
| ~ empty(sK0)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_50,c_71]) ).
tcf(c_2832,plain,
( empty(sK1)
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2826,c_57]) ).
tcf(c_3591,plain,
! [X0: $i] :
( element(X0,sK0)
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_743,c_109]) ).
tcf(c_3811,plain,
! [X0: $i] :
( element(apply(sK2,X0),sK0)
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_66,c_3591]) ).
tcf(c_3823,plain,
! [X0: $i] :
( element(apply(sK2,X0),sK0)
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(X0,sK0) ),
inference(light_normalisation,[status(thm)],[c_3811,c_51]) ).
tcf(c_3824,plain,
! [X0: $i] :
( element(apply(sK2,X0),sK0)
| ~ in(X0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3823,c_56,c_55]) ).
tcf(c_3853,plain,
! [X0: $i] :
( empty(sK0)
| in(apply(sK2,X0),sK0)
| ~ in(X0,sK0) ),
inference(superposition,[status(thm)],[c_3824,c_105]) ).
tcf(c_4153,plain,
( in(sK9(sK0,sK2),sK0)
| ( identity_relation(relation_dom(sK2)) = sK2 )
| ~ function(sK2)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_51,c_89]) ).
tcf(c_4163,plain,
( in(sK9(sK0,sK2),sK0)
| ( identity_relation(sK0) = sK2 )
| ~ function(sK2)
| ~ relation(sK2) ),
inference(light_normalisation,[status(thm)],[c_4153,c_51]) ).
tcf(c_4164,plain,
in(sK9(sK0,sK2),sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_4163,c_49,c_56,c_55]) ).
tcf(c_4196,plain,
~ empty(sK0),
inference(superposition,[status(thm)],[c_4164,c_104]) ).
tcf(c_4198,plain,
~ empty(sK1),
inference(backward_subsumption_resolution,[status(thm)],[c_2453,c_4196]) ).
tcf(c_4283,plain,
( ( identity_relation(relation_dom(sK2)) = sK2 )
| ~ function(sK2)
| ~ relation(sK2)
| ( apply(sK2,sK9(sK0,sK2)) != sK9(sK0,sK2) ) ),
inference(superposition,[status(thm)],[c_51,c_88]) ).
tcf(c_4285,plain,
( ( identity_relation(sK0) = sK2 )
| ~ function(sK2)
| ~ relation(sK2)
| ( apply(sK2,sK9(sK0,sK2)) != sK9(sK0,sK2) ) ),
inference(light_normalisation,[status(thm)],[c_4283,c_51]) ).
tcf(c_4286,plain,
apply(sK2,sK9(sK0,sK2)) != sK9(sK0,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_4285,c_49,c_56,c_55]) ).
tcf(c_4319,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(sK2,X1),X0) = apply(X1,apply(sK2,X0)) )
| ~ function(sK2)
| ~ relation(sK2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK0) ),
inference(superposition,[status(thm)],[c_51,c_77]) ).
tcf(c_4321,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(sK2,X1),X0) = apply(X1,apply(sK2,X0)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4319,c_56,c_55]) ).
tcf(c_4629,plain,
! [X0: $i] :
( ( apply(relation_composition(sK2,X0),sK9(sK0,sK2)) = apply(X0,apply(sK2,sK9(sK0,sK2))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_4164,c_4321]) ).
tcf(c_5049,plain,
! [X0: $i] :
( ~ in(X0,sK0)
| in(apply(sK2,X0),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_3853,c_2832,c_3853,c_4198]) ).
tcf(c_5050,plain,
! [X0: $i] :
( in(apply(sK2,X0),sK0)
| ~ in(X0,sK0) ),
inference(renaming,[status(thm)],[c_5049]) ).
tcf(c_6785,plain,
( ( apply(relation_composition(sK2,sK1),sK9(sK0,sK2)) = apply(sK1,apply(sK2,sK9(sK0,sK2))) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_58,c_4629]) ).
tcf(c_6794,plain,
( ( apply(sK1,apply(sK2,sK9(sK0,sK2))) = apply(sK1,sK9(sK0,sK2)) )
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_6785,c_54]) ).
tcf(c_6795,plain,
apply(sK1,apply(sK2,sK9(sK0,sK2))) = apply(sK1,sK9(sK0,sK2)),
inference(forward_subsumption_resolution,[status(thm)],[c_6794,c_57]) ).
tcf(c_6836,plain,
! [X0: $i] :
( ( apply(sK2,sK9(sK0,sK2)) = X0 )
| ~ function(sK1)
| ~ relation(sK1)
| ~ one_to_one(sK1)
| ~ in(X0,relation_dom(sK1))
| ~ in(apply(sK2,sK9(sK0,sK2)),relation_dom(sK1))
| ( apply(sK1,sK9(sK0,sK2)) != apply(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_6795,c_99]) ).
tcf(c_6850,plain,
! [X0: $i] :
( ( apply(sK2,sK9(sK0,sK2)) = X0 )
| ~ function(sK1)
| ~ relation(sK1)
| ~ one_to_one(sK1)
| ~ in(X0,sK0)
| ~ in(apply(sK2,sK9(sK0,sK2)),sK0)
| ( apply(sK1,sK9(sK0,sK2)) != apply(sK1,X0) ) ),
inference(light_normalisation,[status(thm)],[c_6836,c_50]) ).
tcf(c_6851,plain,
! [X0: $i] :
( ( apply(sK2,sK9(sK0,sK2)) = X0 )
| ~ in(X0,sK0)
| ~ in(apply(sK2,sK9(sK0,sK2)),sK0)
| ( apply(sK1,sK9(sK0,sK2)) != apply(sK1,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6850,c_58,c_57,c_53]) ).
tcf(c_7354,plain,
( ( apply(sK2,sK9(sK0,sK2)) = sK9(sK0,sK2) )
| ~ in(sK9(sK0,sK2),sK0)
| ~ in(apply(sK2,sK9(sK0,sK2)),sK0) ),
inference(equality_resolution,[status(thm)],[c_6851]) ).
tcf(c_7355,plain,
~ in(apply(sK2,sK9(sK0,sK2)),sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_7354,c_4286,c_4164]) ).
tcf(c_7356,plain,
~ in(sK9(sK0,sK2),sK0),
inference(superposition,[status(thm)],[c_5050,c_7355]) ).
tcf(c_7357,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7356,c_4164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU017+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.56 % Computer : n002.cluster.edu
% 0.10/0.56 % Model : x86_64 x86_64
% 0.10/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.56 % Memory : 8046.5625MB
% 0.10/0.56 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Thu Sep 24 12:37:22 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.57 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.61 Running first-order theorem proving
% 0.10/0.61 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
% 0.10/0.62
% 0.10/0.62 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.62
% 0.10/0.62 % Detected problem language: tptp
% 0.13/0.63 % Proving...
% 7.84/1.84 % SZS status Started for theBenchmark.p
% 7.84/1.84 % SZS status Theorem for theBenchmark.p
% 7.84/1.84
% 7.84/1.84 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.84/1.84
% 7.84/1.84 % ------ iProver source info
% 7.84/1.84
% 7.84/1.84 % git: date: 2026-07-19 20:42:38 +0200
% 7.84/1.84 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.84/1.84 % git: non_committed_changes: false
% 7.84/1.84
% 7.84/1.84 % ------ Parsing...
% 7.84/1.84 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.84/1.84
% 7.84/1.84 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 7.84/1.84
% 7.84/1.84 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.84/1.84
% 7.84/1.84 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.84/1.84 % ------ Proving...
% 7.84/1.84 % ------ Problem Properties
% 7.84/1.84
% 7.84/1.84 %
% 7.84/1.84 % clauses 64
% 7.84/1.84 % conjectures 9
% 7.84/1.84 % EPR 20
% 7.84/1.84 % Horn 56
% 7.84/1.84 % unary 26
% 7.84/1.84 % binary 12
% 7.84/1.84 % lits 153
% 7.84/1.84 % lits eq 21
% 7.84/1.84 % fd_pure 0
% 7.84/1.84 % fd_pseudo 0
% 7.84/1.84 % fd_cond 0
% 7.84/1.84 % fd_pseudo_cond 5
% 7.84/1.84 % AC symbols 0
% 7.84/1.84
% 7.84/1.84 % ------ Schedule dynamic 5 is on
% 7.84/1.84
% 7.84/1.84 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.84/1.84
% 7.84/1.84
% 7.84/1.84 % ------
% 7.84/1.84 % Current options:
% 7.84/1.84 % ------
% 7.84/1.84
% 7.84/1.84
% 7.84/1.84 %
% 7.84/1.84
% 7.84/1.84 % ------ Proving...
% 7.84/1.84 %
% 7.84/1.84
% 7.84/1.84 % SZS status Theorem for theBenchmark.p
% 7.84/1.84
% 7.84/1.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.84/1.84
% 7.84/1.84
%------------------------------------------------------------------------------