%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU340+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 : Tue Sep 29 12:52:56 PM UTC 2026
% Result : Theorem 0.22s 0.56s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 113 ( 28 unt; 3 def)
% Number of atoms : 340 ( 4 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 405 ( 178 ~; 169 |; 26 &)
% ( 11 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 4 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 184 ( 0 sgn 176 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0] :
( rel_str(X0)
=> ( transitive_relstr(X0)
<=> is_transitive_in(the_InternalRel(X0),the_carrier(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_orders_2) ).
fof(f5,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( ( in(X2,X1)
& in(X3,X1)
& in(X4,X1)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X3,X4),X0) )
=> in(ordered_pair(X2,X4),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_2) ).
fof(f7,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(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(f37,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f39,conjecture,
! [X0] :
( ( transitive_relstr(X0)
& rel_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( ( related(X0,X1,X2)
& related(X0,X2,X3) )
=> related(X0,X1,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_orders_2) ).
fof(f40,negated_conjecture,
~ ! [X0] :
( ( transitive_relstr(X0)
& rel_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( ( related(X0,X1,X2)
& related(X0,X2,X3) )
=> related(X0,X1,X3) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f41,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f43,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f44,axiom,
! [X0,X1,X2] :
~ ( in(X0,X1)
& element(X1,powerset(X2))
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f53,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f54,plain,
! [X0] :
( ( transitive_relstr(X0)
<=> is_transitive_in(the_InternalRel(X0),the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(X2,X1)
| ~ in(X3,X1)
| ~ in(X4,X1)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X3,X4),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(X2,X1)
| ~ in(X3,X1)
| ~ in(X4,X1)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X3,X4),X0) ) )
| ~ relation(X0) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( related(X0,X1,X2)
<=> in(ordered_pair(X1,X2),the_InternalRel(X0)) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f58,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f59,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f64,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ related(X0,X1,X3)
& related(X0,X1,X2)
& related(X0,X2,X3)
& element(X3,the_carrier(X0)) )
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& transitive_relstr(X0)
& rel_str(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f65,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ related(X0,X1,X3)
& related(X0,X1,X2)
& related(X0,X2,X3)
& element(X3,the_carrier(X0)) )
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& transitive_relstr(X0)
& rel_str(X0) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f67,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f66]) ).
fof(f69,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f43]) ).
fof(f70,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| ~ empty(X2) ),
inference(ennf_transformation,[],[f44]) ).
fof(f76,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f53]) ).
fof(f77,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f79,plain,
! [X0] :
( ~ transitive_relstr(X0)
| is_transitive_in(the_InternalRel(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f80,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f81,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1)
| in(ordered_pair(X2,X4),X0)
| ~ is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f88,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,[],[f57]) ).
fof(f89,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,[],[f57]) ).
fof(f90,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f58]) ).
fof(f91,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f110,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f111,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f114,plain,
element(sK14,the_carrier(sK11)),
inference(cnf_transformation,[],[f65]) ).
fof(f115,plain,
related(sK11,sK13,sK14),
inference(cnf_transformation,[],[f65]) ).
fof(f116,plain,
related(sK11,sK12,sK13),
inference(cnf_transformation,[],[f65]) ).
fof(f117,plain,
~ related(sK11,sK12,sK14),
inference(cnf_transformation,[],[f65]) ).
fof(f118,plain,
element(sK13,the_carrier(sK11)),
inference(cnf_transformation,[],[f65]) ).
fof(f119,plain,
element(sK12,the_carrier(sK11)),
inference(cnf_transformation,[],[f65]) ).
fof(f120,plain,
rel_str(sK11),
inference(cnf_transformation,[],[f65]) ).
fof(f121,plain,
transitive_relstr(sK11),
inference(cnf_transformation,[],[f65]) ).
fof(f122,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f132,plain,
! [X2,X3,X0,X1,X4] :
( ~ is_transitive_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1)
| in(unordered_pair(unordered_pair(X2,X4),singleton(X2)),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f81,f80,f80,f80]) ).
fof(f133,plain,
! [X2,X0,X1] :
( ~ related(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X0))
| ~ rel_str(X0) ),
inference(definition_unfolding,[],[f89,f80]) ).
fof(f134,plain,
! [X2,X0,X1] :
( related(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X0))
| ~ rel_str(X0) ),
inference(definition_unfolding,[],[f88,f80]) ).
fof(f136,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f111,f80]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f110,f80]) ).
fof(f187,definition,
( spl15_4
<=> in(sK14,the_carrier(sK11)) ),
introduced(definition,[new_symbols(definition,[spl15_4])],[avatar_definition]) ).
fof(f188,plain,
( ~ in(sK14,the_carrier(sK11))
| spl15_4 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f189,plain,
( in(sK14,the_carrier(sK11))
| ~ spl15_4 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f196,plain,
( is_transitive_in(the_InternalRel(sK11),the_carrier(sK11))
| ~ rel_str(sK11) ),
inference(resolution,[],[f79,f121]) ).
fof(f197,plain,
is_transitive_in(the_InternalRel(sK11),the_carrier(sK11)),
inference(forward_subsumption_resolution,[],[f196,f120]) ).
fof(f217,plain,
! [X0] :
( ~ rel_str(X0)
| element(the_InternalRel(X0),powerset(cartesian_product2(the_carrier(X0),the_carrier(X0)))) ),
inference(resolution,[],[f90,f91]) ).
fof(f227,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X1))
| ~ in(X0,X2)
| in(X0,X1)
| empty(X1) ),
inference(resolution,[],[f124,f122]) ).
fof(f230,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X1))
| ~ in(X0,X2)
| in(X0,X1) ),
inference(forward_subsumption_resolution,[],[f227,f125]) ).
fof(f235,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(superposition,[],[f136,f77]) ).
fof(f243,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(superposition,[],[f137,f77]) ).
fof(f272,plain,
( ~ element(sK13,the_carrier(sK11))
| ~ element(sK14,the_carrier(sK11))
| in(unordered_pair(unordered_pair(sK13,sK14),singleton(sK13)),the_InternalRel(sK11))
| ~ rel_str(sK11) ),
inference(resolution,[],[f133,f115]) ).
fof(f273,plain,
( ~ element(sK12,the_carrier(sK11))
| ~ element(sK13,the_carrier(sK11))
| in(unordered_pair(unordered_pair(sK12,sK13),singleton(sK12)),the_InternalRel(sK11))
| ~ rel_str(sK11) ),
inference(resolution,[],[f133,f116]) ).
fof(f274,plain,
( ~ element(sK13,the_carrier(sK11))
| in(unordered_pair(unordered_pair(sK12,sK13),singleton(sK12)),the_InternalRel(sK11))
| ~ rel_str(sK11) ),
inference(forward_subsumption_resolution,[],[f273,f119]) ).
fof(f275,plain,
( ~ element(sK14,the_carrier(sK11))
| in(unordered_pair(unordered_pair(sK13,sK14),singleton(sK13)),the_InternalRel(sK11))
| ~ rel_str(sK11) ),
inference(forward_subsumption_resolution,[],[f272,f118]) ).
fof(f276,plain,
( in(unordered_pair(unordered_pair(sK12,sK13),singleton(sK12)),the_InternalRel(sK11))
| ~ rel_str(sK11) ),
inference(forward_subsumption_resolution,[],[f274,f118]) ).
fof(f277,plain,
( in(unordered_pair(unordered_pair(sK13,sK14),singleton(sK13)),the_InternalRel(sK11))
| ~ rel_str(sK11) ),
inference(forward_subsumption_resolution,[],[f275,f114]) ).
fof(f278,plain,
in(unordered_pair(unordered_pair(sK12,sK13),singleton(sK12)),the_InternalRel(sK11)),
inference(forward_subsumption_resolution,[],[f276,f120]) ).
fof(f279,plain,
in(unordered_pair(unordered_pair(sK13,sK14),singleton(sK13)),the_InternalRel(sK11)),
inference(forward_subsumption_resolution,[],[f277,f120]) ).
fof(f280,plain,
in(unordered_pair(singleton(sK12),unordered_pair(sK12,sK13)),the_InternalRel(sK11)),
inference(forward_demodulation,[],[f278,f77]) ).
fof(f281,plain,
in(unordered_pair(singleton(sK13),unordered_pair(sK13,sK14)),the_InternalRel(sK11)),
inference(forward_demodulation,[],[f279,f77]) ).
fof(f284,plain,
( ~ element(sK12,the_carrier(sK11))
| ~ element(sK14,the_carrier(sK11))
| ~ in(unordered_pair(unordered_pair(sK12,sK14),singleton(sK12)),the_InternalRel(sK11))
| ~ rel_str(sK11) ),
inference(resolution,[],[f134,f117]) ).
fof(f287,plain,
( ~ element(sK14,the_carrier(sK11))
| ~ in(unordered_pair(unordered_pair(sK12,sK14),singleton(sK12)),the_InternalRel(sK11))
| ~ rel_str(sK11) ),
inference(forward_subsumption_resolution,[],[f284,f119]) ).
fof(f288,plain,
( ~ in(unordered_pair(unordered_pair(sK12,sK14),singleton(sK12)),the_InternalRel(sK11))
| ~ rel_str(sK11) ),
inference(forward_subsumption_resolution,[],[f287,f114]) ).
fof(f289,plain,
~ in(unordered_pair(unordered_pair(sK12,sK14),singleton(sK12)),the_InternalRel(sK11)),
inference(forward_subsumption_resolution,[],[f288,f120]) ).
fof(f290,plain,
~ in(unordered_pair(singleton(sK12),unordered_pair(sK12,sK14)),the_InternalRel(sK11)),
inference(forward_demodulation,[],[f289,f77]) ).
fof(f293,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),the_InternalRel(sK11))
| ~ in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),the_InternalRel(sK11))
| ~ in(X1,the_carrier(sK11))
| ~ in(X0,the_carrier(sK11))
| ~ in(X2,the_carrier(sK11))
| in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),the_InternalRel(sK11))
| ~ relation(the_InternalRel(sK11)) ),
inference(resolution,[],[f132,f197]) ).
fof(f312,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(sK11))
| ~ in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),the_InternalRel(sK11))
| ~ in(X1,the_carrier(sK11))
| ~ in(X0,the_carrier(sK11))
| ~ in(X2,the_carrier(sK11))
| in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),the_InternalRel(sK11))
| ~ relation(the_InternalRel(sK11)) ),
inference(forward_demodulation,[],[f293,f77]) ).
fof(f319,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),the_InternalRel(sK11))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(sK11))
| ~ in(X1,the_carrier(sK11))
| ~ in(X0,the_carrier(sK11))
| ~ in(X2,the_carrier(sK11))
| in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),the_InternalRel(sK11))
| ~ relation(the_InternalRel(sK11)) ),
inference(forward_demodulation,[],[f312,f77]) ).
fof(f326,plain,
! [X2,X0,X1] :
( in(unordered_pair(singleton(X2),unordered_pair(X2,X1)),the_InternalRel(sK11))
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),the_InternalRel(sK11))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(sK11))
| ~ in(X1,the_carrier(sK11))
| ~ in(X0,the_carrier(sK11))
| ~ in(X2,the_carrier(sK11))
| ~ relation(the_InternalRel(sK11)) ),
inference(forward_demodulation,[],[f319,f77]) ).
fof(f331,definition,
( spl15_5
<=> relation(the_InternalRel(sK11)) ),
introduced(definition,[new_symbols(definition,[spl15_5])],[avatar_definition]) ).
fof(f333,plain,
( ~ relation(the_InternalRel(sK11))
| spl15_5 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f335,definition,
( spl15_6
<=> ! [X2,X0,X1] :
( in(unordered_pair(singleton(X2),unordered_pair(X2,X1)),the_InternalRel(sK11))
| ~ in(X2,the_carrier(sK11))
| ~ in(X0,the_carrier(sK11))
| ~ in(X1,the_carrier(sK11))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(sK11))
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),the_InternalRel(sK11)) ) ),
introduced(definition,[new_symbols(definition,[spl15_6])],[avatar_definition]) ).
fof(f336,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(X2),unordered_pair(X2,X1)),the_InternalRel(sK11))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(sK11))
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),the_InternalRel(sK11))
| ~ in(X1,the_carrier(sK11))
| ~ in(X2,the_carrier(sK11))
| ~ in(X0,the_carrier(sK11)) )
| ~ spl15_6 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f337,plain,
( ~ spl15_5
| spl15_6 ),
inference(avatar_split_clause,[],[f326,f335,f331]) ).
fof(f338,plain,
( ! [X0,X1] : ~ element(the_InternalRel(sK11),powerset(cartesian_product2(X0,X1)))
| spl15_5 ),
inference(resolution,[],[f333,f76]) ).
fof(f405,plain,
element(the_InternalRel(sK11),powerset(cartesian_product2(the_carrier(sK11),the_carrier(sK11)))),
inference(resolution,[],[f217,f120]) ).
fof(f407,plain,
( $false
| spl15_5 ),
inference(forward_subsumption_resolution,[],[f405,f338]) ).
fof(f408,plain,
spl15_5,
inference(avatar_contradiction_clause,[],[f407]) ).
fof(f421,plain,
! [X0] :
( in(X0,cartesian_product2(the_carrier(sK11),the_carrier(sK11)))
| ~ in(X0,the_InternalRel(sK11)) ),
inference(resolution,[],[f405,f230]) ).
fof(f446,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(sK11))
| in(X1,the_carrier(sK11)) ),
inference(resolution,[],[f421,f243]) ).
fof(f447,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(sK11))
| in(X0,the_carrier(sK11)) ),
inference(resolution,[],[f421,f235]) ).
fof(f507,plain,
in(sK14,the_carrier(sK11)),
inference(resolution,[],[f446,f281]) ).
fof(f534,plain,
( ! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK14)),the_InternalRel(sK11))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK13)),the_InternalRel(sK11))
| ~ in(sK14,the_carrier(sK11))
| ~ in(X0,the_carrier(sK11))
| ~ in(sK13,the_carrier(sK11)) )
| ~ spl15_6 ),
inference(resolution,[],[f336,f281]) ).
fof(f557,plain,
( ! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK14)),the_InternalRel(sK11))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK13)),the_InternalRel(sK11))
| ~ in(sK14,the_carrier(sK11))
| ~ in(sK13,the_carrier(sK11)) )
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f534,f447]) ).
fof(f572,plain,
( ! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK14)),the_InternalRel(sK11))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK13)),the_InternalRel(sK11))
| ~ in(sK14,the_carrier(sK11)) )
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f557,f446]) ).
fof(f587,plain,
( ! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK14)),the_InternalRel(sK11))
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK13)),the_InternalRel(sK11)) )
| ~ spl15_4
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f572,f189]) ).
fof(f598,plain,
( ~ in(unordered_pair(singleton(sK12),unordered_pair(sK12,sK13)),the_InternalRel(sK11))
| ~ spl15_4
| ~ spl15_6 ),
inference(resolution,[],[f587,f290]) ).
fof(f611,plain,
( $false
| ~ spl15_4
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f598,f280]) ).
fof(f612,plain,
( ~ spl15_4
| ~ spl15_6 ),
inference(avatar_contradiction_clause,[],[f611]) ).
fof(f617,plain,
( $false
| spl15_4 ),
inference(forward_subsumption_resolution,[],[f507,f188]) ).
fof(f618,plain,
spl15_4,
inference(avatar_contradiction_clause,[],[f617]) ).
cnf(s4,plain,
( ~ spl15_5
| spl15_6 ),
inference(sat_conversion,[],[f337]) ).
cnf(s5,plain,
spl15_5,
inference(sat_conversion,[],[f408]) ).
cnf(s7,plain,
( ~ spl15_4
| ~ spl15_6 ),
inference(sat_conversion,[],[f612]) ).
cnf(s8,plain,
spl15_4,
inference(sat_conversion,[],[f618]) ).
cnf(s9,plain,
~ spl15_6,
inference(rat,[],[s7,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s4,s9,s5]) ).
fof(f619,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU340+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.18/0.43 % Computer : n001.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 28 04:54:02 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.22/0.48 Running first-order model finding
% 0.22/0.48 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.56 % (29058)Will run a generic schedule for satisfiability detection.
% 0.22/0.56 % (29068)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2108510718:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.56 % (29064)% WARNING: option uhcvi not known.
% 0.22/0.56 % (29063)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3831527417_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.56 % (29064)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3047820730:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.56 % (29065)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2643712762:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.56 % (29066)dis+10_1_sil=32000:sp=arity:random_seed=3509930423:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.56 % (29067)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=603579995:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.56 % (29069)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2484165130:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.56 % TRYING [1]
% 0.22/0.56 % TRYING [2]
% 0.22/0.56 % TRYING [3]
% 0.22/0.56 % TRYING [4]
% 0.22/0.56 % (29067) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-29058-29067"...
% 0.22/0.56 % (29067)...printing done.
% 0.22/0.56 % (29067)Refutation found. Thanks to Tanya!
% 0.22/0.56 % SZS status Theorem for theBenchmark
% 0.22/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.57 % (29067)------------------------------
% 0.22/0.57 % (29067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.57 % (29067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.57 % (29067)CaDiCaL version: 2.1.3
% 0.22/0.57 % (29067)Termination reason: Refutation
% 0.22/0.57 % (29067)Time elapsed: 0.031 s
% 0.22/0.57 % (29067)Peak memory usage: 12 MB
% 0.22/0.57 % (29067)Instructions burned: 29 (million)
% 0.22/0.57 % (29058)Success in time 0.074 s
% 0.22/0.57 % Vampire exiting
%------------------------------------------------------------------------------