%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU291+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 : n019.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 3.18s 16.24s
% Output : CNFRefutation 3.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of formulae : 134 ( 28 unt; 2 def)
% Number of atoms : 410 ( 129 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 419 ( 176 ~; 180 |; 41 &)
% ( 8 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 197 ( 0 sgn 188 !; 9 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,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(f11,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> element(relation_dom_as_subset(X0,X1,X2),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).
fof(f16,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f21,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f39,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(f40,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(f42,axiom,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
=> ( subset(X0,X1)
=> relation_of2_as_subset(X3,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
fof(f44,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f45,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f48,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f49,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f51,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f52,conjecture,
! [X0,X1,X2,X3] :
( ( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ( subset(X1,X2)
=> ( ( relation_of2_as_subset(X3,X0,X2)
& quasi_total(X3,X0,X2)
& function(X3) )
| ( X0 != empty_set
& X1 = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_2) ).
fof(f53,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ( subset(X1,X2)
=> ( ( relation_of2_as_subset(X3,X0,X2)
& quasi_total(X3,X0,X2)
& function(X3) )
| ( X0 != empty_set
& X1 = empty_set ) ) ) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f67,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,[],[f6]) ).
fof(f68,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,[],[f67]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ~ relation_of2(X2,X0,X1)
| element(relation_dom_as_subset(X0,X1,X2),powerset(X0)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ~ relation_of2(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
inference(ennf_transformation,[],[f39]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X2,X0)
| ~ subset(X0,X1)
| relation_of2_as_subset(X3,X2,X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X2,X0)
| ~ subset(X0,X1)
| relation_of2_as_subset(X3,X2,X1) ),
inference(flattening,[],[f78]) ).
fof(f81,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f82,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f81]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f48]) ).
fof(f87,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f49]) ).
fof(f89,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f90,plain,
? [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3)
& subset(X1,X2)
& ( ~ relation_of2_as_subset(X3,X0,X2)
| ~ quasi_total(X3,X0,X2)
| ~ function(X3) )
& ( empty_set = X0
| empty_set != X1 ) ),
inference(ennf_transformation,[],[f53]) ).
fof(f91,plain,
? [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3)
& subset(X1,X2)
& ( ~ relation_of2_as_subset(X3,X0,X2)
| ~ quasi_total(X3,X0,X2)
| ~ function(X3) )
& ( empty_set = X0
| empty_set != X1 ) ),
inference(flattening,[],[f90]) ).
fof(f92,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,[],[f68]) ).
fof(f94,plain,
! [X0] : element(sK1(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f16]) ).
fof(f110,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,[],[f40]) ).
fof(f111,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f112,plain,
( relation_of2_as_subset(sK20,sK17,sK18)
& quasi_total(sK20,sK17,sK18)
& function(sK20)
& subset(sK18,sK19)
& ( ~ relation_of2_as_subset(sK20,sK17,sK19)
| ~ quasi_total(sK20,sK17,sK19)
| ~ function(sK20) )
& ( empty_set = sK17
| empty_set != sK18 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18,sK19,sK20]),skolemize(X0,sK17),skolemize(X1,sK18),skolemize(X2,sK19),skolemize(X3,sK20)],[f91]) ).
fof(f121,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,[],[f92]) ).
fof(f123,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| empty_set = X1
| relation_dom_as_subset(X0,X1,X2) != X0
| quasi_total(X2,X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| empty_set != X0
| relation_dom_as_subset(X0,X1,X2) != X0
| quasi_total(X2,X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| element(relation_dom_as_subset(X0,X1,X2),powerset(X0)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f128,plain,
! [X0] : element(sK1(X0),X0),
inference(cnf_transformation,[],[f94]) ).
fof(f135,plain,
empty(empty_set),
inference(cnf_transformation,[],[f21]) ).
fof(f170,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
inference(cnf_transformation,[],[f77]) ).
fof(f171,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f172,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f174,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X3,X2,X0)
| ~ subset(X0,X1)
| relation_of2_as_subset(X3,X2,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f176,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f178,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f111]) ).
fof(f181,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f182,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f87]) ).
fof(f184,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f185,plain,
relation_of2_as_subset(sK20,sK17,sK18),
inference(cnf_transformation,[],[f112]) ).
fof(f186,plain,
quasi_total(sK20,sK17,sK18),
inference(cnf_transformation,[],[f112]) ).
fof(f187,plain,
function(sK20),
inference(cnf_transformation,[],[f112]) ).
fof(f188,plain,
subset(sK18,sK19),
inference(cnf_transformation,[],[f112]) ).
fof(f189,plain,
( ~ relation_of2_as_subset(sK20,sK17,sK19)
| ~ quasi_total(sK20,sK17,sK19)
| ~ function(sK20) ),
inference(cnf_transformation,[],[f112]) ).
fof(f190,plain,
( empty_set = sK17
| empty_set != sK18 ),
inference(cnf_transformation,[],[f112]) ).
fof(f191,plain,
! [X2,X1] :
( ~ relation_of2_as_subset(X2,empty_set,X1)
| empty_set != relation_dom_as_subset(empty_set,X1,X2)
| quasi_total(X2,empty_set,X1) ),
inference(equality_resolution,[],[f124]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( quasi_total(X1,empty_set,X0)
| ~ relation_of2_as_subset(X1,empty_set,X0)
| ( relation_dom_as_subset(empty_set,X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( quasi_total(X2,X0,X1)
| ( X1 = empty_set )
| ~ relation_of2_as_subset(X2,X0,X1)
| ( relation_dom_as_subset(X0,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_56,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,[],[f121]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(relation_dom_as_subset(X1,X2,X0),powerset(X1))
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_62,plain,
! [X0: $i] : element(sK1(X0),X0),
inference(cnf_transformation,[],[f128]) ).
tcf(c_68,plain,
empty(empty_set),
inference(cnf_transformation,[],[f135]) ).
tcf(c_104,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,[],[f170]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2_as_subset(X0,X1,X2)
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( relation_of2_as_subset(X0,X1,X3)
| ~ subset(X2,X3)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_116,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_119,negated_conjecture,
( ( empty_set = sK17 )
| ( empty_set != sK18 ) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_120,negated_conjecture,
( ~ function(sK20)
| ~ relation_of2_as_subset(sK20,sK17,sK19)
| ~ quasi_total(sK20,sK17,sK19) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_121,negated_conjecture,
subset(sK18,sK19),
inference(cnf_transformation,[],[f188]) ).
tcf(c_122,negated_conjecture,
function(sK20),
inference(cnf_transformation,[],[f187]) ).
tcf(c_123,negated_conjecture,
quasi_total(sK20,sK17,sK18),
inference(cnf_transformation,[],[f186]) ).
tcf(c_124,negated_conjecture,
relation_of2_as_subset(sK20,sK17,sK18),
inference(cnf_transformation,[],[f185]) ).
tcf(c_161,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_105]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_111]) ).
tcf(c_215,plain,
( ~ relation_of2_as_subset(sK20,sK17,sK19)
| ~ quasi_total(sK20,sK17,sK19) ),
inference(prop_impl_just,[status(thm)],[c_122,c_120]) ).
tcf(c_336,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_56,c_161]) ).
tcf(c_337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( relation_of2_as_subset(X0,X1,X3)
| ~ subset(X2,X3)
| ~ relation_of2(X0,X1,X2) ),
inference(bin_hyper_res,[status(thm)],[c_108,c_161]) ).
tcf(c_339,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_115,c_165]) ).
tcf(c_794,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( relation_of2_as_subset(X2,X3,X1)
| ~ relation_of2(X2,X3,X0)
| ( X1 != sK19 )
| ( X0 != sK18 ) ),
inference(resolution_lifted,[status(thm)],[c_337,c_121]) ).
tcf(c_795,plain,
! [X0: $i,X1: $i] :
( relation_of2_as_subset(X0,X1,sK19)
| ~ relation_of2(X0,X1,sK18) ),
inference(unflattening,[status(thm)],[c_794]) ).
tcf(c_847,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ( X1 != sK19 )
| ( X0 != sK18 ) ),
inference(resolution_lifted,[status(thm)],[c_121,c_339]) ).
tcf(c_848,plain,
! [X0: $i] :
( ~ empty(sK19)
| ~ in(X0,sK18) ),
inference(unflattening,[status(thm)],[c_847]) ).
tcf(c_1247,plain,
! [X0: $i,X1: $i] :
( ~ relation_of2_as_subset(sK20,sK17,sK19)
| ~ relation_of2_as_subset(X1,empty_set,X0)
| ( empty_set != sK17 )
| ( X1 != sK20 )
| ( X0 != sK19 )
| ( relation_dom_as_subset(empty_set,X0,X1) != empty_set ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_215]) ).
tcf(c_1248,plain,
( ~ relation_of2_as_subset(sK20,sK17,sK19)
| ~ relation_of2_as_subset(sK20,empty_set,sK19)
| ( empty_set != sK17 )
| ( relation_dom_as_subset(empty_set,sK19,sK20) != empty_set ) ),
inference(unflattening,[status(thm)],[c_1247]) ).
tcf(c_1267,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = empty_set )
| ~ relation_of2_as_subset(sK20,sK17,sK19)
| ~ relation_of2_as_subset(X2,X0,X1)
| ( X2 != sK20 )
| ( X1 != sK19 )
| ( X0 != sK17 )
| ( relation_dom_as_subset(X0,X1,X2) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_215]) ).
tcf(c_1268,plain,
( ( sK19 = empty_set )
| ~ relation_of2_as_subset(sK20,sK17,sK19)
| ( relation_dom_as_subset(sK17,sK19,sK20) != sK17 ) ),
inference(unflattening,[status(thm)],[c_1267]) ).
tcf(c_1312,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = empty_set )
| ( relation_dom_as_subset(X1,X2,X0) = X1 )
| ~ relation_of2(X0,X1,X2)
| ( X2 != sK18 )
| ( X1 != sK17 )
| ( X0 != sK20 ) ),
inference(resolution_lifted,[status(thm)],[c_336,c_123]) ).
tcf(c_1313,plain,
( ( sK18 = empty_set )
| ( relation_dom_as_subset(sK17,sK18,sK20) = sK17 )
| ~ relation_of2(sK20,sK17,sK18) ),
inference(unflattening,[status(thm)],[c_1312]) ).
tcf(c_1376,plain,
( ~ relation_of2_as_subset(sK20,sK17,sK19)
| ( sK20 != sK20 )
| ( sK17 != sK17 )
| ( sK18 != sK19 ) ),
inference(resolution_lifted,[status(thm)],[c_215,c_123]) ).
tcf(c_1622,plain,
( ~ relation_of2_as_subset(sK20,sK17,sK19)
| ( sK18 != sK19 ) ),
inference(equality_resolution_simp,[status(thm)],[c_1376]) ).
tcf(c_1693,plain,
! [X0: $i,X1: $i] :
( relation_of2_as_subset(X0,X1,sK19)
| ~ relation_of2(X0,X1,sK18) ),
inference(prop_impl_just,[status(thm)],[c_795]) ).
tcf(c_1703,plain,
! [X0: $i] :
( ~ in(X0,sK18)
| ~ empty(sK19) ),
inference(prop_impl_just,[status(thm)],[c_848]) ).
tcf(c_1704,plain,
! [X0: $i] :
( ~ empty(sK19)
| ~ in(X0,sK18) ),
inference(renaming,[status(thm)],[c_1703]) ).
tcf(c_2543,definition,
iPr_def_10 = relation_dom_as_subset(sK17,sK18,sK20),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2544,definition,
iPr_def_11 = relation_dom_as_subset(empty_set,sK18,sK20),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2547,plain,
( ( iPr_def_10 = sK17 )
| ( sK18 = empty_set )
| ~ relation_of2(sK20,sK17,sK18) ),
inference(demodulation,[status(thm)],[c_1313,c_2543]) ).
tcf(c_2550,negated_conjecture,
relation_of2_as_subset(sK20,sK17,sK18),
inference(demodulation,[status(thm)],[c_124]) ).
tcf(c_2551,negated_conjecture,
( ( empty_set = sK17 )
| ( empty_set != sK18 ) ),
inference(demodulation,[status(thm)],[c_119]) ).
tcf(c_3842,plain,
relation_of2(sK20,sK17,sK18),
inference(superposition,[status(thm)],[c_2550,c_106]) ).
tcf(c_3846,plain,
( ( sK17 = iPr_def_10 )
| ( empty_set = sK18 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2547,c_3842]) ).
tcf(c_3856,plain,
! [X0: $i] :
( empty(X0)
| in(sK1(X0),X0) ),
inference(superposition,[status(thm)],[c_62,c_110]) ).
tcf(c_3906,plain,
relation_of2_as_subset(sK20,sK17,sK19),
inference(superposition,[status(thm)],[c_3842,c_1693]) ).
tcf(c_3907,plain,
( ~ relation_of2_as_subset(sK20,empty_set,sK19)
| ( empty_set != sK17 )
| ( relation_dom_as_subset(empty_set,sK19,sK20) != empty_set ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1248,c_3906]) ).
tcf(c_3911,plain,
relation_of2(sK20,sK17,sK19),
inference(superposition,[status(thm)],[c_3906,c_106]) ).
tcf(c_3925,plain,
( ( sK17 = iPr_def_10 )
| ( empty_set = sK17 ) ),
inference(superposition,[status(thm)],[c_3846,c_2551]) ).
tcf(c_3955,plain,
( relation_of2_as_subset(sK20,empty_set,sK19)
| ( sK17 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_3925,c_3906]) ).
tcf(c_3956,plain,
( relation_of2(sK20,empty_set,sK18)
| ( sK17 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_3925,c_3842]) ).
tcf(c_3998,plain,
( relation_of2(sK20,empty_set,sK19)
| ( sK17 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_3955,c_106]) ).
tcf(c_4018,plain,
( element(iPr_def_11,powerset(empty_set))
| ~ relation_of2(sK20,empty_set,sK18) ),
inference(superposition,[status(thm)],[c_2544,c_59]) ).
tcf(c_4019,plain,
( element(iPr_def_10,powerset(sK17))
| ~ relation_of2(sK20,sK17,sK18) ),
inference(superposition,[status(thm)],[c_2543,c_59]) ).
tcf(c_4024,plain,
element(iPr_def_10,powerset(sK17)),
inference(forward_subsumption_resolution,[status(thm)],[c_4019,c_3842]) ).
tcf(c_4099,plain,
relation_dom_as_subset(sK17,sK18,sK20) = relation_dom(sK20),
inference(superposition,[status(thm)],[c_3842,c_104]) ).
tcf(c_4102,plain,
relation_dom(sK20) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_4099,c_2543]) ).
tcf(c_4119,plain,
( ( sK18 = sK19 )
| ~ empty(sK19)
| ~ empty(sK18) ),
inference(instantiation,[status(thm)],[c_118]) ).
tcf(c_4131,plain,
! [X0: $i] :
( ~ empty(sK17)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_4024,c_115]) ).
tcf(c_4227,plain,
relation_dom_as_subset(sK17,sK19,sK20) = relation_dom(sK20),
inference(superposition,[status(thm)],[c_3911,c_104]) ).
tcf(c_4229,plain,
relation_dom_as_subset(sK17,sK19,sK20) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_4227,c_4102]) ).
tcf(c_4346,plain,
( ( sK17 = iPr_def_10 )
| ( relation_dom_as_subset(empty_set,sK19,sK20) = relation_dom(sK20) ) ),
inference(superposition,[status(thm)],[c_3998,c_104]) ).
tcf(c_4348,plain,
( ( sK17 = iPr_def_10 )
| ( relation_dom_as_subset(empty_set,sK19,sK20) = iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_4346,c_4102]) ).
tcf(c_4370,plain,
( empty(sK18)
| ~ empty(sK19) ),
inference(superposition,[status(thm)],[c_3856,c_1704]) ).
tcf(c_4372,plain,
( empty(iPr_def_10)
| ~ empty(sK17) ),
inference(superposition,[status(thm)],[c_3856,c_4131]) ).
tcf(c_4397,plain,
~ empty(sK19),
inference(global_subsumption_just,[status(thm)],[c_4370,c_1622,c_3906,c_4119,c_4370]) ).
tcf(c_4405,plain,
( empty(iPr_def_10)
| ( sK17 = iPr_def_10 )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_3925,c_4372]) ).
tcf(c_4406,plain,
( empty(iPr_def_10)
| ( sK17 = iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4405,c_68]) ).
tcf(c_4421,plain,
( ( sK17 = iPr_def_10 )
| ( empty_set = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_4406,c_116]) ).
tcf(c_5003,plain,
( element(iPr_def_11,powerset(empty_set))
| ( sK17 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_3956,c_4018]) ).
tcf(c_5014,plain,
! [X0: $i] :
( ( sK17 = iPr_def_10 )
| ~ empty(empty_set)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_5003,c_115]) ).
tcf(c_5020,plain,
! [X0: $i] :
( ( sK17 = iPr_def_10 )
| ~ in(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5014,c_68]) ).
tcf(c_5055,plain,
( ( sK17 = iPr_def_10 )
| ~ relation_of2_as_subset(sK20,empty_set,sK19)
| ( empty_set != iPr_def_10 )
| ( empty_set != sK17 ) ),
inference(superposition,[status(thm)],[c_4348,c_3907]) ).
tcf(c_5060,plain,
sK17 = iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_5020,c_3925,c_3955,c_4421,c_5055]) ).
tcf(c_5860,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_5060,c_4397,c_4229,c_3906,c_1268,c_68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU291+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/15.43 % Computer : n019.cluster.edu
% 0.15/15.43 % Model : x86_64 x86_64
% 0.15/15.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/15.43 % Memory : 8046.5625MB
% 0.15/15.43 % OS : Linux 6.8.0-71-generic
% 0.15/15.43 % CPULimit : 300
% 0.15/15.43 % WCLimit : 300
% 0.15/15.43 % DateTime : Thu Sep 24 13:34:21 UTC 2026
% 0.15/15.43 % CPUTime :
% 0.15/15.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/15.46 Running first-order theorem proving
% 0.15/15.46 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
% 0.15/15.47
% 0.15/15.47 % ======== iProver multi-core TPTP/SMT =========
% 0.15/15.47
% 0.15/15.47 % Detected problem language: tptp
% 0.15/15.48 % Proving...
% 3.18/16.24 % SZS status Started for theBenchmark.p
% 3.18/16.24 % SZS status Theorem for theBenchmark.p
% 3.18/16.24
% 3.18/16.24 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.18/16.24
% 3.18/16.24 % ------ iProver source info
% 3.18/16.24
% 3.18/16.24 % git: date: 2026-07-19 20:42:38 +0200
% 3.18/16.24 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.18/16.24 % git: non_committed_changes: false
% 3.18/16.24
% 3.18/16.24 % ------ Parsing...
% 3.18/16.24 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.18/16.24
% 3.18/16.24 % ------ Preprocessing... sup_sim: 0 sf_s rm: 11 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 3.18/16.24
% 3.18/16.24 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.18/16.24
% 3.18/16.24 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.18/16.24 % ------ Proving...
% 3.18/16.24 % ------ Problem Properties
% 3.18/16.24
% 3.18/16.24 %
% 3.18/16.24 % clauses 71
% 3.18/16.24 % conjectures 2
% 3.18/16.24 % EPR 37
% 3.18/16.24 % Horn 64
% 3.18/16.24 % unary 33
% 3.18/16.24 % binary 25
% 3.18/16.24 % lits 126
% 3.18/16.24 % lits eq 32
% 3.18/16.24 % fd_pure 0
% 3.18/16.24 % fd_pseudo 0
% 3.18/16.24 % fd_cond 3
% 3.18/16.24 % fd_pseudo_cond 1
% 3.18/16.24 % AC symbols 0
% 3.18/16.24
% 3.18/16.24 % ------ Schedule dynamic 5 is on
% 3.18/16.24
% 3.18/16.24 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.18/16.24
% 3.18/16.24
% 3.18/16.24 % ------
% 3.18/16.24 % Current options:
% 3.18/16.24 % ------
% 3.18/16.24
% 3.18/16.24
% 3.18/16.24 %
% 3.18/16.24
% 3.18/16.24 % ------ Proving...
% 3.18/16.24 %
% 3.18/16.24
% 3.18/16.24 % SZS status Theorem for theBenchmark.p
% 3.18/16.24
% 3.18/16.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.18/16.24
% 3.18/16.24
%------------------------------------------------------------------------------