%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU293+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n014.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 02:56:30 PM UTC 2026
% Result : Theorem 4.52s 1.30s
% Output : CNFRefutation 4.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 101 ( 18 unt; 0 def)
% Number of atoms : 387 ( 95 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 465 ( 179 ~; 187 |; 69 &)
% ( 15 <=>; 13 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 208 ( 0 sgn 185 !; 23 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f6,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f7,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( ( X1 = empty_set
=> ( ( quasi_total(X2,X0,X1)
<=> X2 = empty_set )
| X0 = empty_set ) )
& ( ( X1 = empty_set
=> X0 = empty_set )
=> ( quasi_total(X2,X0,X1)
<=> X0 = relation_dom_as_subset(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
fof(f17,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f24,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f42,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(f43,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f48,conjecture,
! [X0,X1,X2,X3] :
( ( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ( X1 != empty_set
=> ! [X4] :
( in(X4,relation_inverse_image(X3,X2))
<=> ( in(apply(X3,X4),X2)
& in(X4,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_2) ).
fof(f49,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ( X1 != empty_set
=> ! [X4] :
( in(X4,relation_inverse_image(X3,X2))
<=> ( in(apply(X3,X4),X2)
& in(X4,X0) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f52,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(ennf_transformation,[],[f4]) ).
fof(f69,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f70,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ( ( empty_set != X1
| ( quasi_total(X2,X0,X1)
<=> X2 = empty_set )
| X0 = empty_set )
& ( ( X1 = empty_set
& empty_set != X0 )
| ( quasi_total(X2,X0,X1)
<=> X0 = relation_dom_as_subset(X0,X1,X2) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ( ( empty_set != X1
| ( quasi_total(X2,X0,X1)
<=> X2 = empty_set )
| X0 = empty_set )
& ( ( X1 = empty_set
& empty_set != X0 )
| ( quasi_total(X2,X0,X1)
<=> X0 = relation_dom_as_subset(X0,X1,X2) ) ) ) ),
inference(flattening,[],[f71]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f17]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ~ relation_of2(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
inference(ennf_transformation,[],[f42]) ).
fof(f86,plain,
? [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3)
& X1 != empty_set
& ? [X4] :
( in(X4,relation_inverse_image(X3,X2))
<~> ( in(apply(X3,X4),X2)
& in(X4,X0) ) ) ),
inference(ennf_transformation,[],[f49]) ).
fof(f87,plain,
? [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3)
& X1 != empty_set
& ? [X4] :
( in(X4,relation_inverse_image(X3,X2))
<~> ( in(apply(X3,X4),X2)
& in(X4,X0) ) ) ),
inference(flattening,[],[f86]) ).
fof(f91,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f52]) ).
fof(f94,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f70]) ).
fof(f95,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(apply(X0,X4),X1)
& in(X4,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(rectify,[],[f95]) ).
fof(f97,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(apply(X0,X4),X1)
& in(X4,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| ( in(apply(X0,sK0(X0,X1,X2)),X1)
& in(sK0(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ~ in(apply(X0,sK0(X0,X1,X2)),X1)
| ~ in(sK0(X0,X1,X2),relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f96]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ( ( empty_set != X1
| ( ( ~ quasi_total(X2,X0,X1)
| X2 = empty_set )
& ( empty_set != X2
| quasi_total(X2,X0,X1) ) )
| X0 = empty_set )
& ( ( X1 = empty_set
& empty_set != X0 )
| ( ( ~ quasi_total(X2,X0,X1)
| X0 = relation_dom_as_subset(X0,X1,X2) )
& ( relation_dom_as_subset(X0,X1,X2) != X0
| quasi_total(X2,X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f72]) ).
fof(f116,plain,
! [X0,X1,X2] :
( ( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) )
& ( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f117,plain,
? [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3)
& X1 != empty_set
& ? [X4] :
( ( in(X4,relation_inverse_image(X3,X2))
| ( in(apply(X3,X4),X2)
& in(X4,X0) ) )
& ( ~ in(X4,relation_inverse_image(X3,X2))
| ~ in(apply(X3,X4),X2)
| ~ in(X4,X0) ) ) ),
inference(nnf_transformation,[],[f87]) ).
fof(f118,plain,
? [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3)
& X1 != empty_set
& ? [X4] :
( ( in(X4,relation_inverse_image(X3,X2))
| ( in(apply(X3,X4),X2)
& in(X4,X0) ) )
& ( ~ in(X4,relation_inverse_image(X3,X2))
| ~ in(apply(X3,X4),X2)
| ~ in(X4,X0) ) ) ),
inference(flattening,[],[f117]) ).
fof(f119,plain,
( relation_of2_as_subset(sK21,sK18,sK19)
& quasi_total(sK21,sK18,sK19)
& function(sK21)
& empty_set != sK19
& ( in(sK22,relation_inverse_image(sK21,sK20))
| ( in(apply(sK21,sK22),sK20)
& in(sK22,sK18) ) )
& ( ~ in(sK22,relation_inverse_image(sK21,sK20))
| ~ in(apply(sK21,sK22),sK20)
| ~ in(sK22,sK18) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21,sK22]),skolemize(X0,sK18),skolemize(X1,sK19),skolemize(X2,sK20),skolemize(X3,sK21),skolemize(X4,sK22)],[f118]) ).
fof(f123,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f126,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X4,X2)
| in(apply(X0,X4),X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f127,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,relation_dom(X0)) ),
inference(cnf_transformation,[],[f97]) ).
fof(f128,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ),
inference(cnf_transformation,[],[f97]) ).
fof(f134,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| empty_set = X1
| ~ quasi_total(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = X0 ),
inference(cnf_transformation,[],[f98]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f74]) ).
fof(f148,plain,
empty(empty_set),
inference(cnf_transformation,[],[f24]) ).
fof(f183,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
inference(cnf_transformation,[],[f81]) ).
fof(f184,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f185,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f190,plain,
relation_of2_as_subset(sK21,sK18,sK19),
inference(cnf_transformation,[],[f119]) ).
fof(f191,plain,
quasi_total(sK21,sK18,sK19),
inference(cnf_transformation,[],[f119]) ).
fof(f192,plain,
function(sK21),
inference(cnf_transformation,[],[f119]) ).
fof(f193,plain,
empty_set != sK19,
inference(cnf_transformation,[],[f119]) ).
fof(f194,plain,
( in(sK22,relation_inverse_image(sK21,sK20))
| in(apply(sK21,sK22),sK20) ),
inference(cnf_transformation,[],[f119]) ).
fof(f195,plain,
( in(sK22,relation_inverse_image(sK21,sK20))
| in(sK22,sK18) ),
inference(cnf_transformation,[],[f119]) ).
fof(f196,plain,
( ~ in(sK22,relation_inverse_image(sK21,sK20))
| ~ in(apply(sK21,sK22),sK20)
| ~ in(sK22,sK18) ),
inference(cnf_transformation,[],[f119]) ).
fof(f199,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f91]) ).
fof(f202,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,relation_inverse_image(X0,X1)) ),
inference(equality_resolution,[],[f128]) ).
fof(f203,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(X4,relation_dom(X0)) ),
inference(equality_resolution,[],[f127]) ).
fof(f204,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(apply(X0,X4),X1) ),
inference(equality_resolution,[],[f126]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X0)
| ~ element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0)
| ~ function(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),X2) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f203]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f204]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = empty_set )
| ( relation_dom_as_subset(X1,X2,X0) = X1 )
| ~ relation_of2_as_subset(X0,X1,X2)
| ~ quasi_total(X0,X1,X2) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_74,plain,
empty(empty_set),
inference(cnf_transformation,[],[f148]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom_as_subset(X1,X2,X0) = relation_dom(X0) )
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2_as_subset(X0,X1,X2)
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_117,negated_conjecture,
( ~ in(sK22,sK18)
| ~ in(sK22,relation_inverse_image(sK21,sK20))
| ~ in(apply(sK21,sK22),sK20) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_118,negated_conjecture,
( in(sK22,sK18)
| in(sK22,relation_inverse_image(sK21,sK20)) ),
inference(cnf_transformation,[],[f195]) ).
tcf(c_119,negated_conjecture,
( in(sK22,relation_inverse_image(sK21,sK20))
| in(apply(sK21,sK22),sK20) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_120,negated_conjecture,
empty_set != sK19,
inference(cnf_transformation,[],[f193]) ).
tcf(c_121,negated_conjecture,
function(sK21),
inference(cnf_transformation,[],[f192]) ).
tcf(c_122,negated_conjecture,
quasi_total(sK21,sK18,sK19),
inference(cnf_transformation,[],[f191]) ).
tcf(c_123,negated_conjecture,
relation_of2_as_subset(sK21,sK18,sK19),
inference(cnf_transformation,[],[f190]) ).
tcf(c_126,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_147,plain,
( ( empty_set = empty_set )
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_126]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_of2(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_112]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_166]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2_as_subset(X0,X1,X2)
| ~ relation_of2(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_111]) ).
tcf(c_208,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation_of2(X0,X1,X2)
| relation(X0) ),
inference(prop_impl_just,[status(thm)],[c_111,c_52,c_66]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X0)
| ~ relation_of2(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_208]) ).
tcf(c_246,plain,
( in(sK22,relation_inverse_image(sK21,sK20))
| in(apply(sK21,sK22),sK20) ),
inference(prop_impl_just,[status(thm)],[c_119]) ).
tcf(c_284,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = empty_set )
| ( relation_dom_as_subset(X1,X2,X0) = X1 )
| ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2) ),
inference(bin_hyper_res,[status(thm)],[c_62,c_168]) ).
tcf(c_629,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2(X0,X1,X2)
| ( X2 != sK19 )
| ( X1 != sK18 )
| ( X0 != sK21 ) ),
inference(resolution_lifted,[status(thm)],[c_167,c_123]) ).
tcf(c_630,plain,
relation_of2(sK21,sK18,sK19),
inference(unflattening,[status(thm)],[c_629]) ).
tcf(c_746,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = empty_set )
| ( relation_dom_as_subset(X1,X2,X0) = X1 )
| ~ relation_of2(X0,X1,X2)
| ( X2 != sK19 )
| ( X1 != sK18 )
| ( X0 != sK21 ) ),
inference(resolution_lifted,[status(thm)],[c_284,c_122]) ).
tcf(c_747,plain,
( ( sK19 = empty_set )
| ( relation_dom_as_subset(sK18,sK19,sK21) = sK18 )
| ~ relation_of2(sK21,sK18,sK19) ),
inference(unflattening,[status(thm)],[c_746]) ).
tcf(c_748,plain,
( ( sK19 = empty_set )
| ( relation_dom_as_subset(sK18,sK19,sK21) = sK18 ) ),
inference(global_subsumption_just,[status(thm)],[c_747,c_630,c_747]) ).
tcf(c_791,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2(X0,X1,X2)
| ( X2 != sK19 )
| ( X1 != sK18 )
| ( X0 != sK21 ) ),
inference(resolution_lifted,[status(thm)],[c_167,c_123]) ).
tcf(c_792,plain,
relation_of2(sK21,sK18,sK19),
inference(unflattening,[status(thm)],[c_791]) ).
tcf(c_955,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X0)
| ( X2 != sK19 )
| ( X1 != sK18 )
| ( X0 != sK21 ) ),
inference(resolution_lifted,[status(thm)],[c_209,c_792]) ).
tcf(c_956,plain,
relation(sK21),
inference(unflattening,[status(thm)],[c_955]) ).
tcf(c_1531,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,X1),X2)
| ~ relation(X0)
| ~ in(X1,relation_inverse_image(X0,X2))
| ( X0 != sK21 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_121]) ).
tcf(c_1532,plain,
! [X0: $i,X1: $i] :
( in(apply(sK21,X0),X1)
| ~ relation(sK21)
| ~ in(X0,relation_inverse_image(sK21,X1)) ),
inference(unflattening,[status(thm)],[c_1531]) ).
tcf(c_1534,plain,
! [X0: $i,X1: $i] :
( in(apply(sK21,X0),X1)
| ~ in(X0,relation_inverse_image(sK21,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_1532,c_956,c_1532]) ).
tcf(c_2157,plain,
in(apply(sK21,sK22),sK20),
inference(backward_subsumption_resolution,[status(thm)],[c_246,c_1534]) ).
tcf(c_4575,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_4765,plain,
! [X0: $i] :
( ( empty_set = sK19 )
| ( sK19 != X0 )
| ( empty_set != X0 ) ),
inference(instantiation,[status(thm)],[c_4575]) ).
tcf(c_4766,plain,
( ( empty_set = sK19 )
| ( sK19 != empty_set )
| ( empty_set != empty_set ) ),
inference(instantiation,[status(thm)],[c_4765]) ).
tcf(c_5138,plain,
relation_dom_as_subset(sK18,sK19,sK21) = sK18,
inference(global_subsumption_just,[status(thm)],[c_748,c_74,c_120,c_147,c_748,c_4766]) ).
tcf(c_5308,plain,
relation_dom_as_subset(sK18,sK19,sK21) = relation_dom(sK21),
inference(superposition,[status(thm)],[c_792,c_110]) ).
tcf(c_5309,plain,
relation_dom(sK21) = sK18,
inference(demodulation,[status(thm)],[c_5308,c_5138]) ).
tcf(c_5314,plain,
( in(sK22,sK18)
| in(sK22,relation_dom(sK21))
| ~ relation(sK21)
| ~ function(sK21) ),
inference(superposition,[status(thm)],[c_118,c_57]) ).
tcf(c_5319,plain,
( in(sK22,sK18)
| ~ relation(sK21)
| ~ function(sK21) ),
inference(demodulation,[status(thm)],[c_5314,c_5309]) ).
tcf(c_5341,plain,
( in(sK22,relation_inverse_image(sK21,sK20))
| ~ relation(sK21)
| ~ function(sK21)
| ~ in(sK22,relation_dom(sK21)) ),
inference(superposition,[status(thm)],[c_2157,c_56]) ).
tcf(c_5346,plain,
( in(sK22,relation_inverse_image(sK21,sK20))
| ~ relation(sK21)
| ~ function(sK21)
| ~ in(sK22,sK18) ),
inference(demodulation,[status(thm)],[c_5341,c_5309]) ).
tcf(c_5351,plain,
( in(sK22,relation_inverse_image(sK21,sK20))
| ~ relation(sK21)
| ~ function(sK21) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5346,c_5319]) ).
tcf(c_5358,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5351,c_5319,c_2157,c_956,c_117,c_121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU293+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.37 % Computer : n014.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Thu Sep 24 13:34:02 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 0.08/0.42
% 0.08/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.42
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.44 % Proving...
% 4.52/1.30 % SZS status Started for theBenchmark.p
% 4.52/1.30 % SZS status Theorem for theBenchmark.p
% 4.52/1.30
% 4.52/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.52/1.30
% 4.52/1.30 % ------ iProver source info
% 4.52/1.30
% 4.52/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 4.52/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.52/1.30 % git: non_committed_changes: false
% 4.52/1.30
% 4.52/1.30 % ------ Parsing...
% 4.52/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.52/1.30
% 4.52/1.30 % ------ Preprocessing... sup_sim: 0 pe_s pe:1:0s pe:2:0s pe_e %
% 4.52/1.30
% 4.52/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 1 0s scvd_e snvd_s sp: 0 0s snvd_e %
% 4.52/1.30
% 4.52/1.30 % ------ Preprocessing...
% 4.52/1.30 % ------ Proving...
% 4.52/1.30 % ------ Problem Properties
% 4.52/1.30
% 4.52/1.30 %
% 4.52/1.30 % clauses 85
% 4.52/1.30 % conjectures 3
% 4.52/1.30 % EPR 34
% 4.52/1.30 % Horn 71
% 4.52/1.30 % unary 39
% 4.52/1.30 % binary 31
% 4.52/1.30 % lits 158
% 4.52/1.30 % lits eq 25
% 4.52/1.30 % fd_pure 0
% 4.52/1.30 % fd_pseudo 0
% 4.52/1.30 % fd_cond 4
% 4.52/1.30 % fd_pseudo_cond 4
% 4.52/1.30 % AC symbols 0
% 4.52/1.30
% 4.52/1.30 % ------ Input Options Time Limit: Unbounded
% 4.52/1.30
% 4.52/1.30
% 4.52/1.30 % ------
% 4.52/1.30 % Current options:
% 4.52/1.30 % ------
% 4.52/1.30
% 4.52/1.30
% 4.52/1.30 %
% 4.52/1.30
% 4.52/1.30 % ------ Proving...
% 4.52/1.30 %
% 4.52/1.30
% 4.52/1.30 % SZS status Theorem for theBenchmark.p
% 4.52/1.30
% 4.52/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.52/1.30
% 4.52/1.30
%------------------------------------------------------------------------------