%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU363+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 : n017.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 02:57:13 PM UTC 2026
% Result : Theorem 3.62s 6.10s
% Output : CNFRefutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 110 ( 34 unt; 0 def)
% Number of atoms : 345 ( 44 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 386 ( 151 ~; 141 |; 60 &)
% ( 8 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 202 ( 0 sgn 190 !; 12 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f5,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( subrelstr(X1,X0)
=> ( full_subrelstr(X1,X0)
<=> the_InternalRel(X1) = relation_restriction_as_relation_of(the_InternalRel(X0),the_carrier(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_yellow_0) ).
fof(f6,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( related(X0,X1,X2)
<=> in(ordered_pair(X1,X2),the_InternalRel(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_orders_2) ).
fof(f17,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( subrelstr(X1,X0)
=> rel_str(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_yellow_0) ).
fof(f18,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(f19,axiom,
! [X0] :
( rel_str(X0)
=> relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
fof(f34,axiom,
! [X0,X1] :
( relation(X0)
=> relation_restriction_as_relation_of(X0,X1) = relation_restriction(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_toler_1) ).
fof(f35,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(f37,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f38,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f44,conjecture,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( ( subrelstr(X1,X0)
& full_subrelstr(X1,X0) )
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ! [X3] :
( element(X3,the_carrier(X0))
=> ! [X4] :
( element(X4,the_carrier(X1))
=> ! [X5] :
( element(X5,the_carrier(X1))
=> ( ( in(X5,the_carrier(X1))
& in(X4,the_carrier(X1))
& related(X0,X2,X3)
& X5 = X3
& X4 = X2 )
=> related(X1,X4,X5) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_yellow_0) ).
fof(f45,negated_conjecture,
~ ! [X0] :
( rel_str(X0)
=> ! [X1] :
( ( subrelstr(X1,X0)
& full_subrelstr(X1,X0) )
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ! [X3] :
( element(X3,the_carrier(X0))
=> ! [X4] :
( element(X4,the_carrier(X1))
=> ! [X5] :
( element(X5,the_carrier(X1))
=> ( ( in(X5,the_carrier(X1))
& in(X4,the_carrier(X1))
& related(X0,X2,X3)
& X5 = X3
& X4 = X2 )
=> related(X1,X4,X5) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(ennf_transformation,[],[f3]) ).
fof(f57,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1] :
( ~ subrelstr(X1,X0)
| ( full_subrelstr(X1,X0)
<=> the_InternalRel(X1) = relation_restriction_as_relation_of(the_InternalRel(X0),the_carrier(X1)) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f58,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( related(X0,X1,X2)
<=> in(ordered_pair(X1,X2),the_InternalRel(X0)) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f61,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1] :
( ~ subrelstr(X1,X0)
| rel_str(X1) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f18]) ).
fof(f63,plain,
! [X0] :
( ~ rel_str(X0)
| relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
inference(ennf_transformation,[],[f19]) ).
fof(f69,plain,
! [X0,X1] :
( ~ relation(X0)
| relation_restriction_as_relation_of(X0,X1) = relation_restriction(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f78,plain,
? [X0] :
( rel_str(X0)
& ? [X1] :
( subrelstr(X1,X0)
& full_subrelstr(X1,X0)
& ? [X2] :
( element(X2,the_carrier(X0))
& ? [X3] :
( element(X3,the_carrier(X0))
& ? [X4] :
( element(X4,the_carrier(X1))
& ? [X5] :
( element(X5,the_carrier(X1))
& in(X5,the_carrier(X1))
& in(X4,the_carrier(X1))
& related(X0,X2,X3)
& X5 = X3
& X4 = X2
& ~ related(X1,X4,X5) ) ) ) ) ) ),
inference(ennf_transformation,[],[f45]) ).
fof(f79,plain,
? [X0] :
( rel_str(X0)
& ? [X1] :
( subrelstr(X1,X0)
& full_subrelstr(X1,X0)
& ? [X2] :
( element(X2,the_carrier(X0))
& ? [X3] :
( element(X3,the_carrier(X0))
& ? [X4] :
( element(X4,the_carrier(X1))
& ? [X5] :
( element(X5,the_carrier(X1))
& in(X5,the_carrier(X1))
& in(X4,the_carrier(X1))
& related(X0,X2,X3)
& X5 = X3
& X4 = X2
& ~ related(X1,X4,X5) ) ) ) ) ) ),
inference(flattening,[],[f78]) ).
fof(f83,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1] :
( ~ subrelstr(X1,X0)
| ( ( ~ full_subrelstr(X1,X0)
| the_InternalRel(X1) = relation_restriction_as_relation_of(the_InternalRel(X0),the_carrier(X1)) )
& ( the_InternalRel(X1) != relation_restriction_as_relation_of(the_InternalRel(X0),the_carrier(X1))
| full_subrelstr(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f84,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( ( ~ related(X0,X1,X2)
| in(ordered_pair(X1,X2),the_InternalRel(X0)) )
& ( ~ in(ordered_pair(X1,X2),the_InternalRel(X0))
| related(X0,X1,X2) ) ) ) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f95,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,[],[f35]) ).
fof(f96,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f97,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_restriction(X2,X1))
| ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
& ( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1)) ) ) ),
inference(nnf_transformation,[],[f70]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_restriction(X2,X1))
| ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
& ( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1)) ) ) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
( rel_str(sK10)
& subrelstr(sK11,sK10)
& full_subrelstr(sK11,sK10)
& element(sK12,the_carrier(sK10))
& element(sK13,the_carrier(sK10))
& element(sK14,the_carrier(sK11))
& element(sK15,the_carrier(sK11))
& in(sK15,the_carrier(sK11))
& in(sK14,the_carrier(sK11))
& related(sK10,sK12,sK13)
& sK13 = sK15
& sK12 = sK14
& ~ related(sK11,sK14,sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13,sK14,sK15]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12),skolemize(X3,sK13),skolemize(X4,sK14),skolemize(X5,sK15)],[f79]) ).
fof(f103,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f55]) ).
fof(f105,plain,
! [X0,X1] :
( ~ rel_str(X0)
| ~ subrelstr(X1,X0)
| ~ full_subrelstr(X1,X0)
| the_InternalRel(X1) = relation_restriction_as_relation_of(the_InternalRel(X0),the_carrier(X1)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ related(X0,X1,X2)
| in(ordered_pair(X1,X2),the_InternalRel(X0)) ),
inference(cnf_transformation,[],[f84]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ in(ordered_pair(X1,X2),the_InternalRel(X0))
| related(X0,X1,X2) ),
inference(cnf_transformation,[],[f84]) ).
fof(f111,plain,
! [X0,X1] :
( ~ rel_str(X0)
| ~ subrelstr(X1,X0)
| rel_str(X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f62]) ).
fof(f113,plain,
! [X0] :
( ~ rel_str(X0)
| relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f131,plain,
! [X0,X1] :
( ~ relation(X0)
| relation_restriction_as_relation_of(X0,X1) = relation_restriction(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f132,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f133,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f97]) ).
fof(f140,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1)) ),
inference(cnf_transformation,[],[f99]) ).
fof(f146,plain,
rel_str(sK10),
inference(cnf_transformation,[],[f100]) ).
fof(f147,plain,
subrelstr(sK11,sK10),
inference(cnf_transformation,[],[f100]) ).
fof(f148,plain,
full_subrelstr(sK11,sK10),
inference(cnf_transformation,[],[f100]) ).
fof(f149,plain,
element(sK12,the_carrier(sK10)),
inference(cnf_transformation,[],[f100]) ).
fof(f150,plain,
element(sK13,the_carrier(sK10)),
inference(cnf_transformation,[],[f100]) ).
fof(f151,plain,
element(sK14,the_carrier(sK11)),
inference(cnf_transformation,[],[f100]) ).
fof(f152,plain,
element(sK15,the_carrier(sK11)),
inference(cnf_transformation,[],[f100]) ).
fof(f153,plain,
in(sK15,the_carrier(sK11)),
inference(cnf_transformation,[],[f100]) ).
fof(f154,plain,
in(sK14,the_carrier(sK11)),
inference(cnf_transformation,[],[f100]) ).
fof(f155,plain,
related(sK10,sK12,sK13),
inference(cnf_transformation,[],[f100]) ).
fof(f156,plain,
sK13 = sK15,
inference(cnf_transformation,[],[f100]) ).
fof(f157,plain,
sK12 = sK14,
inference(cnf_transformation,[],[f100]) ).
fof(f158,plain,
~ related(sK11,sK14,sK15),
inference(cnf_transformation,[],[f100]) ).
fof(f162,plain,
related(sK10,sK14,sK15),
inference(definition_unfolding,[],[f155,f157,f156]) ).
fof(f163,plain,
element(sK15,the_carrier(sK10)),
inference(definition_unfolding,[],[f150,f156]) ).
fof(f164,plain,
element(sK14,the_carrier(sK10)),
inference(definition_unfolding,[],[f149,f157]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X0)
| ~ element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( relation_restriction_as_relation_of(the_InternalRel(X1),the_carrier(X0)) = the_InternalRel(X0) )
| ~ rel_str(X1)
| ~ subrelstr(X0,X1)
| ~ full_subrelstr(X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( related(X2,X0,X1)
| ~ rel_str(X2)
| ~ element(X1,the_carrier(X2))
| ~ element(X0,the_carrier(X2))
| ~ in(ordered_pair(X0,X1),the_InternalRel(X2)) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ related(X0,X1,X2) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( rel_str(X0)
| ~ rel_str(X1)
| ~ subrelstr(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_61,plain,
! [X0: $i] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( ( relation_restriction_as_relation_of(X0,X1) = relation_restriction(X0,X1) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2_as_subset(X0,X1,X2)
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(X2,X0),cartesian_product2(X3,X1))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_restriction(X2,X1))
| ~ relation(X2)
| ~ in(X0,X2)
| ~ in(X0,cartesian_product2(X1,X1)) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_94,negated_conjecture,
~ related(sK11,sK14,sK15),
inference(cnf_transformation,[],[f158]) ).
tcf(c_95,negated_conjecture,
related(sK10,sK14,sK15),
inference(cnf_transformation,[],[f162]) ).
tcf(c_96,negated_conjecture,
in(sK14,the_carrier(sK11)),
inference(cnf_transformation,[],[f154]) ).
tcf(c_97,negated_conjecture,
in(sK15,the_carrier(sK11)),
inference(cnf_transformation,[],[f153]) ).
tcf(c_98,negated_conjecture,
element(sK15,the_carrier(sK11)),
inference(cnf_transformation,[],[f152]) ).
tcf(c_99,negated_conjecture,
element(sK14,the_carrier(sK11)),
inference(cnf_transformation,[],[f151]) ).
tcf(c_100,negated_conjecture,
element(sK15,the_carrier(sK10)),
inference(cnf_transformation,[],[f163]) ).
tcf(c_101,negated_conjecture,
element(sK14,the_carrier(sK10)),
inference(cnf_transformation,[],[f164]) ).
tcf(c_102,negated_conjecture,
full_subrelstr(sK11,sK10),
inference(cnf_transformation,[],[f148]) ).
tcf(c_103,negated_conjecture,
subrelstr(sK11,sK10),
inference(cnf_transformation,[],[f147]) ).
tcf(c_104,negated_conjecture,
rel_str(sK10),
inference(cnf_transformation,[],[f146]) ).
tcf(c_143,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_81]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_143]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation_of2(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(prop_impl_just,[status(thm)],[c_80,c_60]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_175]) ).
tcf(c_185,plain,
! [X0: $i] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_61]) ).
tcf(c_586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(X1,powerset(cartesian_product2(X3,X5)))
| ~ relation_of2_as_subset(X0,X2,X4)
| ( X4 != X5 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_144,c_176]) ).
tcf(c_587,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(unflattening,[status(thm)],[c_586]) ).
tcf(c_621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ rel_str(X0)
| ( the_carrier(X0) != X3 )
| ( the_carrier(X0) != X2 )
| ( the_InternalRel(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_587,c_185]) ).
tcf(c_622,plain,
! [X0: $i] :
( element(the_InternalRel(X0),powerset(cartesian_product2(the_carrier(X0),the_carrier(X0))))
| ~ rel_str(X0) ),
inference(unflattening,[status(thm)],[c_621]) ).
tcf(c_645,plain,
! [X0: $i,X1: $i] :
( ( relation_restriction_as_relation_of(the_InternalRel(X1),the_carrier(X0)) = the_InternalRel(X0) )
| ~ rel_str(X1)
| ~ subrelstr(X0,X1)
| ( X1 != sK10 )
| ( X0 != sK11 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_102]) ).
tcf(c_646,plain,
( ( relation_restriction_as_relation_of(the_InternalRel(sK10),the_carrier(sK11)) = the_InternalRel(sK11) )
| ~ rel_str(sK10)
| ~ subrelstr(sK11,sK10) ),
inference(unflattening,[status(thm)],[c_645]) ).
tcf(c_647,plain,
relation_restriction_as_relation_of(the_InternalRel(sK10),the_carrier(sK11)) = the_InternalRel(sK11),
inference(global_subsumption_just,[status(thm)],[c_646,c_104,c_103,c_646]) ).
tcf(c_662,plain,
! [X0: $i,X1: $i] :
( rel_str(X0)
| ~ rel_str(X1)
| ( X1 != sK10 )
| ( X0 != sK11 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_103]) ).
tcf(c_663,plain,
( rel_str(sK11)
| ~ rel_str(sK10) ),
inference(unflattening,[status(thm)],[c_662]) ).
tcf(c_674,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ rel_str(X2)
| ~ element(X1,the_carrier(X2))
| ~ element(X0,the_carrier(X2))
| ~ in(ordered_pair(X0,X1),the_InternalRel(X2))
| ( X2 != sK11 )
| ( X1 != sK15 )
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_94]) ).
tcf(c_675,plain,
( ~ rel_str(sK11)
| ~ element(sK15,the_carrier(sK11))
| ~ element(sK14,the_carrier(sK11))
| ~ in(ordered_pair(sK14,sK15),the_InternalRel(sK11)) ),
inference(unflattening,[status(thm)],[c_674]) ).
tcf(c_681,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ( X2 != sK15 )
| ( X1 != sK14 )
| ( X0 != sK10 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_95]) ).
tcf(c_682,plain,
( in(ordered_pair(sK14,sK15),the_InternalRel(sK10))
| ~ rel_str(sK10)
| ~ element(sK15,the_carrier(sK10))
| ~ element(sK14,the_carrier(sK10)) ),
inference(unflattening,[status(thm)],[c_681]) ).
tcf(c_683,plain,
in(ordered_pair(sK14,sK15),the_InternalRel(sK10)),
inference(global_subsumption_just,[status(thm)],[c_682,c_104,c_101,c_100,c_682]) ).
tcf(c_1410,plain,
! [X0: $i] :
( relation(the_InternalRel(X0))
| ~ rel_str(X0) ),
inference(superposition,[status(thm)],[c_622,c_51]) ).
tcf(c_1521,plain,
! [X0: $i,X1: $i] :
( ( relation_restriction_as_relation_of(the_InternalRel(X0),X1) = relation_restriction(the_InternalRel(X0),X1) )
| ~ rel_str(X0) ),
inference(superposition,[status(thm)],[c_1410,c_79]) ).
tcf(c_1536,plain,
! [X0: $i] : relation_restriction_as_relation_of(the_InternalRel(sK10),X0) = relation_restriction(the_InternalRel(sK10),X0),
inference(superposition,[status(thm)],[c_104,c_1521]) ).
tcf(c_1542,plain,
relation_restriction(the_InternalRel(sK10),the_carrier(sK11)) = the_InternalRel(sK11),
inference(superposition,[status(thm)],[c_647,c_1536]) ).
tcf(c_1640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(X0,X1),relation_restriction(X2,X3))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(X0,X3)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_83,c_86]) ).
tcf(c_1662,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X0,X1),the_InternalRel(sK11))
| ~ relation(the_InternalRel(sK10))
| ~ in(X1,the_carrier(sK11))
| ~ in(X0,the_carrier(sK11))
| ~ in(ordered_pair(X0,X1),the_InternalRel(sK10)) ),
inference(superposition,[status(thm)],[c_1542,c_1640]) ).
tcf(c_1715,plain,
( in(ordered_pair(sK14,sK15),the_InternalRel(sK11))
| ~ relation(the_InternalRel(sK10))
| ~ in(sK15,the_carrier(sK11))
| ~ in(sK14,the_carrier(sK11)) ),
inference(superposition,[status(thm)],[c_683,c_1662]) ).
tcf(c_1716,plain,
~ relation(the_InternalRel(sK10)),
inference(global_subsumption_just,[status(thm)],[c_1715,c_104,c_99,c_98,c_97,c_96,c_663,c_675,c_1715]) ).
tcf(c_1718,plain,
~ rel_str(sK10),
inference(superposition,[status(thm)],[c_1410,c_1716]) ).
tcf(c_1719,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1718,c_104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU363+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n017.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 13:46:06 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.42 Running first-order theorem proving
% 0.16/5.42 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
% 0.16/5.44
% 0.16/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.44
% 0.16/5.44 % Detected problem language: tptp
% 0.16/5.45 % Proving...
% 3.62/6.10 % SZS status Started for theBenchmark.p
% 3.62/6.10 % SZS status Theorem for theBenchmark.p
% 3.62/6.10
% 3.62/6.10 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.62/6.10
% 3.62/6.10 % ------ iProver source info
% 3.62/6.10
% 3.62/6.10 % git: date: 2026-07-19 20:42:38 +0200
% 3.62/6.10 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.62/6.10 % git: non_committed_changes: false
% 3.62/6.10
% 3.62/6.10 % ------ Parsing...
% 3.62/6.10 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.62/6.10
% 3.62/6.10 % ------ Preprocessing... sup_sim: 0 sf_s rm: 8 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 7 0s sf_e pe_s pe_e %
% 3.62/6.10
% 3.62/6.10 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.62/6.10
% 3.62/6.10 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.62/6.10 % ------ Proving...
% 3.62/6.10 % ------ Problem Properties
% 3.62/6.10
% 3.62/6.10 %
% 3.62/6.10 % clauses 45
% 3.62/6.10 % conjectures 7
% 3.62/6.10 % EPR 14
% 3.62/6.10 % Horn 42
% 3.62/6.10 % unary 21
% 3.62/6.10 % binary 16
% 3.62/6.10 % lits 78
% 3.62/6.10 % lits eq 5
% 3.62/6.10 % fd_pure 0
% 3.62/6.10 % fd_pseudo 0
% 3.62/6.10 % fd_cond 1
% 3.62/6.10 % fd_pseudo_cond 1
% 3.62/6.10 % AC symbols 0
% 3.62/6.10
% 3.62/6.10 % ------ Input Options Time Limit: Unbounded
% 3.62/6.10
% 3.62/6.10
% 3.62/6.10 % ------
% 3.62/6.10 % Current options:
% 3.62/6.10 % ------
% 3.62/6.10
% 3.62/6.10
% 3.62/6.10 %
% 3.62/6.10
% 3.62/6.10 % ------ Proving...
% 3.62/6.10 %
% 3.62/6.10
% 3.62/6.10 % SZS status Theorem for theBenchmark.p
% 3.62/6.10
% 3.62/6.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.62/6.11
% 3.62/6.11
%------------------------------------------------------------------------------