%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU273+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 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 : Tue Sep 29 12:48:07 PM UTC 2026
% Result : Theorem 17.82s 3.48s
% Output : Refutation 18.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 20
% Syntax : Number of formulae : 206 ( 16 unt; 5 def)
% Number of atoms : 851 ( 121 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 1053 ( 408 ~; 523 |; 83 &)
% ( 15 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 6 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 348 ( 0 sgn 317 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ? [X1] :
( ordinal(X1)
& in(X1,X0) )
=> ? [X1] :
( ordinal(X1)
& in(X1,X0)
& ! [X2] :
( ordinal(X2)
=> ( in(X2,X0)
=> ordinal_subset(X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_ordinal1__e8_6__wellord2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ? [X1] :
( ordinal(X1)
& in(X1,X0) )
=> ? [X1] :
( ordinal(X1)
& in(X1,X0)
& ! [X2] :
( ordinal(X2)
=> ( in(X2,X0)
=> ordinal_subset(X1,X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f7,axiom,
! [X0,X1] :
( ( ordinal(X0)
& ordinal(X1) )
=> ( ordinal_subset(X0,X1)
| ordinal_subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(f9,axiom,
! [X0,X1] :
( ( ordinal(X0)
& ordinal(X1) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f10,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_transitive(X0)
& epsilon_connected(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f11,axiom,
! [X0,X1] :
( ordinal(X1)
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,succ(X1))
& ? [X4] :
( ordinal(X4)
& X3 = X4
& in(X4,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e8_6__wellord2__1) ).
fof(f18,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f19,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f20,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f21,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( subset(X0,X1)
& X0 != X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f35,axiom,
! [X0] :
( ordinal(X0)
=> ( ~ empty(succ(X0))
& epsilon_transitive(succ(X0))
& epsilon_connected(succ(X0))
& ordinal(succ(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_ordinal1) ).
fof(f37,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f51,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f54,axiom,
! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ( proper_subset(X0,X1)
=> in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_ordinal1) ).
fof(f56,axiom,
! [X0,X1] :
( ordinal(X1)
=> ~ ( subset(X0,X1)
& X0 != empty_set
& ! [X2] :
( ordinal(X2)
=> ~ ( in(X2,X0)
& ! [X3] :
( ordinal(X3)
=> ( in(X3,X0)
=> ordinal_subset(X2,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_ordinal1) ).
fof(f61,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f63,plain,
~ ! [X0] :
( ? [X1] :
( ordinal(X1)
& in(X1,X0) )
=> ? [X2] :
( ordinal(X2)
& in(X2,X0)
& ! [X3] :
( ordinal(X3)
=> ( in(X3,X0)
=> ordinal_subset(X2,X3) ) ) ) ),
inference(rectify,[],[f2]) ).
fof(f67,plain,
! [X0,X1] :
( ( subset(X0,X1)
& X0 != X1 )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f21]) ).
fof(f76,plain,
? [X0] :
( ! [X2] :
( ~ ordinal(X2)
| ~ in(X2,X0)
| ? [X3] :
( ~ ordinal_subset(X2,X3)
& in(X3,X0)
& ordinal(X3) ) )
& ? [X1] :
( ordinal(X1)
& in(X1,X0) ) ),
inference(ennf_transformation,[],[f63]) ).
fof(f77,plain,
? [X0] :
( ! [X2] :
( ~ ordinal(X2)
| ~ in(X2,X0)
| ? [X3] :
( ~ ordinal_subset(X2,X3)
& in(X3,X0)
& ordinal(X3) ) )
& ? [X1] :
( ordinal(X1)
& in(X1,X0) ) ),
inference(flattening,[],[f76]) ).
fof(f82,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f83,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(flattening,[],[f82]) ).
fof(f85,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f86,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0] :
( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f88,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,succ(X1))
& ? [X4] :
( ordinal(X4)
& X3 = X4
& in(X4,X0) ) ) )
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f95,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f96,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f97,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f67]) ).
fof(f98,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f97]) ).
fof(f102,plain,
! [X0] :
( ( ~ empty(succ(X0))
& epsilon_transitive(succ(X0))
& epsilon_connected(succ(X0))
& ordinal(succ(X0)) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1) )
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1) )
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f105]) ).
fof(f109,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = X0
| ? [X2] :
( in(X2,X0)
& ! [X3] :
( ordinal_subset(X2,X3)
| ~ in(X3,X0)
| ~ ordinal(X3) )
& ordinal(X2) )
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f56]) ).
fof(f110,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = X0
| ? [X2] :
( in(X2,X0)
& ! [X3] :
( ordinal_subset(X2,X3)
| ~ in(X3,X0)
| ~ ordinal(X3) )
& ordinal(X2) )
| ~ ordinal(X1) ),
inference(flattening,[],[f109]) ).
fof(f115,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f61]) ).
fof(f117,plain,
? [X0] :
( ! [X1] :
( ~ ordinal(X1)
| ~ in(X1,X0)
| ? [X2] :
( ~ ordinal_subset(X1,X2)
& in(X2,X0)
& ordinal(X2) ) )
& ? [X3] :
( ordinal(X3)
& in(X3,X0) ) ),
inference(rectify,[],[f77]) ).
fof(f118,plain,
( ! [X1] :
( ~ ordinal(X1)
| ~ in(X1,sK0)
| ( ~ ordinal_subset(X1,sK1(X1))
& in(sK1(X1),sK0)
& ordinal(sK1(X1)) ) )
& ordinal(sK2)
& in(sK2,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X2,sK1(X1)),skolemize(X3,sK2)],[f117]) ).
fof(f120,plain,
! [X0,X1] :
( ( ( ordinal_subset(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ ordinal_subset(X0,X1) ) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(nnf_transformation,[],[f86]) ).
fof(f121,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ~ in(X3,succ(X1))
| ! [X4] :
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X0) ) )
& ( ( in(X3,succ(X1))
& ? [X4] :
( ordinal(X4)
& X3 = X4
& in(X4,X0) ) )
| ~ in(X3,X2) ) )
| ~ ordinal(X1) ),
inference(nnf_transformation,[],[f88]) ).
fof(f122,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ~ in(X3,succ(X1))
| ! [X4] :
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X0) ) )
& ( ( in(X3,succ(X1))
& ? [X4] :
( ordinal(X4)
& X3 = X4
& in(X4,X0) ) )
| ~ in(X3,X2) ) )
| ~ ordinal(X1) ),
inference(flattening,[],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ~ in(X3,succ(X1))
| ! [X4] :
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X0) ) )
& ( ( in(X3,succ(X1))
& ? [X5] :
( ordinal(X5)
& X3 = X5
& in(X5,X0) ) )
| ~ in(X3,X2) ) )
| ~ ordinal(X1) ),
inference(rectify,[],[f122]) ).
fof(f124,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK4(X0,X1))
| ~ in(X3,succ(X1))
| ! [X4] :
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X0) ) )
& ( ( in(X3,succ(X1))
& ordinal(sK5(X0,X3))
& sK5(X0,X3) = X3
& in(sK5(X0,X3),X0) )
| ~ in(X3,sK4(X0,X1)) ) )
| ~ ordinal(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X2,sK4(X0,X1)),skolemize(X5,sK5(X0,X3))],[f123]) ).
fof(f125,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f95]) ).
fof(f126,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f125]) ).
fof(f127,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK6(X0),X0)
& in(sK6(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X1,sK6(X0))],[f126]) ).
fof(f128,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f96]) ).
fof(f129,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f128]) ).
fof(f130,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK7(X0,X1),X1)
& in(sK7(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f129]) ).
fof(f143,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = X0
| ( in(sK20(X0),X0)
& ! [X3] :
( ordinal_subset(sK20(X0),X3)
| ~ in(X3,X0)
| ~ ordinal(X3) )
& ordinal(sK20(X0)) )
| ~ ordinal(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X2,sK20(X0))],[f110]) ).
fof(f145,plain,
in(sK2,sK0),
inference(cnf_transformation,[],[f118]) ).
fof(f146,plain,
ordinal(sK2),
inference(cnf_transformation,[],[f118]) ).
fof(f147,plain,
! [X1] :
( ~ in(X1,sK0)
| ~ ordinal(X1)
| ordinal(sK1(X1)) ),
inference(cnf_transformation,[],[f118]) ).
fof(f148,plain,
! [X1] :
( in(sK1(X1),sK0)
| ~ in(X1,sK0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f149,plain,
! [X1] :
( ~ ordinal_subset(X1,sK1(X1))
| ~ in(X1,sK0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f156,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f158,plain,
! [X0,X1] :
( ~ ordinal_subset(X0,X1)
| subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f120]) ).
fof(f159,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ordinal_subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f120]) ).
fof(f161,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f162,plain,
! [X3,X0,X1] :
( ~ in(X3,sK4(X0,X1))
| in(sK5(X0,X3),X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f124]) ).
fof(f163,plain,
! [X3,X0,X1] :
( ~ in(X3,sK4(X0,X1))
| sK5(X0,X3) = X3
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f124]) ).
fof(f164,plain,
! [X3,X0,X1] :
( ~ in(X3,sK4(X0,X1))
| ordinal(sK5(X0,X3))
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f124]) ).
fof(f165,plain,
! [X3,X0,X1] :
( in(X3,succ(X1))
| ~ in(X3,sK4(X0,X1))
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f124]) ).
fof(f166,plain,
! [X3,X0,X1,X4] :
( in(X3,sK4(X0,X1))
| ~ in(X3,succ(X1))
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f124]) ).
fof(f176,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f18]) ).
fof(f177,plain,
! [X2,X0] :
( ~ in(X2,X0)
| subset(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f180,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f181,plain,
! [X0,X1] :
( in(sK7(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f182,plain,
! [X0,X1] :
( ~ in(sK7(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f183,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| proper_subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f98]) ).
fof(f197,plain,
! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f199,plain,
! [X0] :
( epsilon_transitive(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f203,plain,
empty(empty_set),
inference(cnf_transformation,[],[f37]) ).
fof(f232,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f51]) ).
fof(f235,plain,
! [X0,X1] :
( ~ proper_subset(X0,X1)
| in(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f237,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = X0
| ordinal(sK20(X0))
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f143]) ).
fof(f238,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| empty_set = X0
| ordinal_subset(sK20(X0),X3)
| ~ in(X3,X0)
| ~ ordinal(X3)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f143]) ).
fof(f239,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = X0
| in(sK20(X0),X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f143]) ).
fof(f245,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f115]) ).
fof(f247,plain,
! [X3,X0,X1,X4] :
( in(X3,sK4(X0,X1))
| ~ in(X3,set_union2(X1,singleton(X1)))
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X0)
| ~ ordinal(X1) ),
inference(definition_unfolding,[],[f166,f176]) ).
fof(f248,plain,
! [X3,X0,X1] :
( ~ in(X3,sK4(X0,X1))
| in(X3,set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
inference(definition_unfolding,[],[f165,f176]) ).
fof(f251,plain,
! [X0] :
( epsilon_transitive(set_union2(X0,singleton(X0)))
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f199,f176]) ).
fof(f253,plain,
! [X0] :
( ordinal(set_union2(X0,singleton(X0)))
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f197,f176]) ).
fof(f254,plain,
! [X0] : in(X0,set_union2(X0,singleton(X0))),
inference(definition_unfolding,[],[f232,f176]) ).
fof(f255,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X1,singleton(X1)))
| in(X4,sK4(X0,X1))
| ~ ordinal(X4)
| ~ in(X4,X0)
| ~ ordinal(X1) ),
inference(equality_resolution,[],[f247]) ).
fof(f286,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(X1,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[],[f158,f156]) ).
fof(f287,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1) ),
inference(duplicate_literal_removal,[],[f286]) ).
fof(f295,plain,
! [X0,X1] :
( in(X0,sK4(X1,X0))
| ~ ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X0) ),
inference(resolution,[],[f255,f254]) ).
fof(f297,plain,
! [X0,X1] :
( in(X0,sK4(X1,X0))
| ~ ordinal(X0)
| ~ in(X0,X1) ),
inference(duplicate_literal_removal,[],[f295]) ).
fof(f303,plain,
! [X2,X0,X1] :
( in(sK7(sK4(X0,X1),X2),set_union2(X1,singleton(X1)))
| ~ ordinal(X1)
| subset(sK4(X0,X1),X2) ),
inference(resolution,[],[f248,f181]) ).
fof(f306,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1)
| subset(X1,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[],[f287,f158]) ).
fof(f307,plain,
! [X0,X1] :
( subset(X1,X0)
| subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(duplicate_literal_removal,[],[f306]) ).
fof(f412,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(resolution,[],[f183,f307]) ).
fof(f416,plain,
! [X0,X1] :
( in(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0)
| X0 = X1
| subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(resolution,[],[f235,f412]) ).
fof(f417,plain,
! [X0,X1] :
( in(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0)
| X0 = X1
| subset(X1,X0)
| ~ ordinal(X0) ),
inference(duplicate_literal_removal,[],[f416]) ).
fof(f419,plain,
! [X0,X1] :
( in(X0,X1)
| ~ ordinal(X1)
| X0 = X1
| subset(X1,X0)
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[],[f417,f161]) ).
fof(f424,plain,
! [X2,X0,X1] :
( ~ ordinal(set_union2(X0,singleton(X0)))
| set_union2(X0,singleton(X0)) = X1
| subset(set_union2(X0,singleton(X0)),X1)
| ~ ordinal(X1)
| in(X1,sK4(X2,X0))
| ~ ordinal(X1)
| ~ in(X1,X2)
| ~ ordinal(X0) ),
inference(resolution,[],[f419,f255]) ).
fof(f434,plain,
! [X2,X0,X1] :
( ~ ordinal(set_union2(X0,singleton(X0)))
| set_union2(X0,singleton(X0)) = X1
| subset(set_union2(X0,singleton(X0)),X1)
| ~ ordinal(X1)
| in(X1,sK4(X2,X0))
| ~ in(X1,X2)
| ~ ordinal(X0) ),
inference(duplicate_literal_removal,[],[f424]) ).
fof(f437,plain,
! [X2,X0,X1] :
( subset(set_union2(X0,singleton(X0)),X1)
| in(X1,sK4(X2,X0))
| ~ ordinal(X1)
| set_union2(X0,singleton(X0)) = X1
| ~ in(X1,X2)
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[],[f434,f253]) ).
fof(f500,plain,
! [X0,X1] :
( ~ ordinal(X0)
| subset(sK4(X1,X0),set_union2(X0,singleton(X0)))
| subset(sK4(X1,X0),set_union2(X0,singleton(X0))) ),
inference(resolution,[],[f303,f182]) ).
fof(f509,plain,
! [X0,X1] :
( subset(sK4(X1,X0),set_union2(X0,singleton(X0)))
| ~ ordinal(X0) ),
inference(duplicate_literal_removal,[],[f500]) ).
fof(f545,plain,
! [X2,X0,X1] :
( ~ ordinal(X0)
| empty_set = sK4(X1,X0)
| ordinal_subset(sK20(sK4(X1,X0)),X2)
| ~ in(X2,sK4(X1,X0))
| ~ ordinal(X2)
| ~ ordinal(set_union2(X0,singleton(X0))) ),
inference(resolution,[],[f509,f238]) ).
fof(f549,plain,
! [X2,X0,X1] :
( ordinal_subset(sK20(sK4(X1,X0)),X2)
| empty_set = sK4(X1,X0)
| ~ ordinal(X0)
| ~ in(X2,sK4(X1,X0))
| ~ ordinal(X2) ),
inference(forward_subsumption_resolution,[],[f545,f253]) ).
fof(f552,plain,
! [X0,X1] :
( empty_set = sK4(X0,X1)
| ~ ordinal(X1)
| ~ in(sK1(sK20(sK4(X0,X1))),sK4(X0,X1))
| ~ ordinal(sK1(sK20(sK4(X0,X1))))
| ~ in(sK20(sK4(X0,X1)),sK0)
| ~ ordinal(sK20(sK4(X0,X1))) ),
inference(resolution,[],[f549,f149]) ).
fof(f555,plain,
! [X0,X1] :
( ~ in(sK1(sK20(sK4(X0,X1))),sK4(X0,X1))
| ~ ordinal(X1)
| empty_set = sK4(X0,X1)
| ~ in(sK20(sK4(X0,X1)),sK0)
| ~ ordinal(sK20(sK4(X0,X1))) ),
inference(forward_subsumption_resolution,[],[f552,f147]) ).
fof(f610,plain,
! [X2,X3,X0,X1] :
( ~ in(X3,set_union2(X0,singleton(X0)))
| ~ ordinal(X1)
| set_union2(X0,singleton(X0)) = X1
| ~ in(X1,X2)
| ~ ordinal(X0)
| in(X1,sK4(X2,X0))
| in(X3,X1) ),
inference(resolution,[],[f437,f180]) ).
fof(f678,plain,
! [X0,X1] :
( empty_set = sK4(X0,X1)
| ordinal(sK20(sK4(X0,X1)))
| ~ ordinal(set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
inference(resolution,[],[f237,f509]) ).
fof(f686,plain,
! [X0,X1] :
( ordinal(sK20(sK4(X0,X1)))
| empty_set = sK4(X0,X1)
| ~ ordinal(X1) ),
inference(forward_subsumption_resolution,[],[f678,f253]) ).
fof(f733,plain,
! [X0,X1] :
( empty_set = sK4(X0,X1)
| in(sK20(sK4(X0,X1)),sK4(X0,X1))
| ~ ordinal(set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
inference(resolution,[],[f239,f509]) ).
fof(f743,plain,
! [X0,X1] :
( in(sK20(sK4(X0,X1)),sK4(X0,X1))
| empty_set = sK4(X0,X1)
| ~ ordinal(X1) ),
inference(forward_subsumption_resolution,[],[f733,f253]) ).
fof(f745,plain,
! [X0,X1] :
( empty_set = sK4(X0,X1)
| ~ ordinal(X1)
| in(sK5(X0,sK20(sK4(X0,X1))),X0)
| ~ ordinal(X1) ),
inference(resolution,[],[f743,f162]) ).
fof(f746,plain,
! [X0,X1] :
( empty_set = sK4(X0,X1)
| ~ ordinal(X1)
| sK20(sK4(X0,X1)) = sK5(X0,sK20(sK4(X0,X1)))
| ~ ordinal(X1) ),
inference(resolution,[],[f743,f163]) ).
fof(f747,plain,
! [X0,X1] :
( empty_set = sK4(X0,X1)
| ~ ordinal(X1)
| in(sK20(sK4(X0,X1)),set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
inference(resolution,[],[f743,f248]) ).
fof(f748,plain,
! [X0,X1] :
( empty_set = sK4(X0,X1)
| ~ ordinal(X1)
| ordinal(sK5(X0,sK20(sK4(X0,X1))))
| ~ ordinal(X1) ),
inference(resolution,[],[f743,f164]) ).
fof(f758,plain,
! [X0,X1] :
( ordinal(sK5(X0,sK20(sK4(X0,X1))))
| ~ ordinal(X1)
| empty_set = sK4(X0,X1) ),
inference(duplicate_literal_removal,[],[f748]) ).
fof(f759,plain,
! [X0,X1] :
( in(sK20(sK4(X0,X1)),set_union2(X1,singleton(X1)))
| ~ ordinal(X1)
| empty_set = sK4(X0,X1) ),
inference(duplicate_literal_removal,[],[f747]) ).
fof(f760,plain,
! [X0,X1] :
( ~ ordinal(X1)
| empty_set = sK4(X0,X1)
| sK20(sK4(X0,X1)) = sK5(X0,sK20(sK4(X0,X1))) ),
inference(duplicate_literal_removal,[],[f746]) ).
fof(f761,plain,
! [X0,X1] :
( in(sK5(X0,sK20(sK4(X0,X1))),X0)
| ~ ordinal(X1)
| empty_set = sK4(X0,X1) ),
inference(duplicate_literal_removal,[],[f745]) ).
fof(f767,plain,
! [X0,X1] :
( ~ ordinal(X0)
| empty_set = sK4(X1,X0)
| subset(sK20(sK4(X1,X0)),set_union2(X0,singleton(X0)))
| ~ epsilon_transitive(set_union2(X0,singleton(X0))) ),
inference(resolution,[],[f759,f177]) ).
fof(f779,plain,
! [X0,X1] :
( subset(sK20(sK4(X1,X0)),set_union2(X0,singleton(X0)))
| empty_set = sK4(X1,X0)
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[],[f767,f251]) ).
fof(f786,plain,
! [X0] :
( sK20(sK4(X0,sK2)) = sK5(X0,sK20(sK4(X0,sK2)))
| empty_set = sK4(X0,sK2) ),
inference(resolution,[],[f760,f146]) ).
fof(f826,plain,
! [X0] :
( ~ ordinal(X0)
| empty_set = sK4(sK0,X0)
| ~ ordinal(sK5(sK0,sK20(sK4(sK0,X0))))
| ordinal(sK1(sK5(sK0,sK20(sK4(sK0,X0))))) ),
inference(resolution,[],[f761,f147]) ).
fof(f832,plain,
! [X0] :
( in(sK20(sK4(X0,sK2)),X0)
| ~ ordinal(sK2)
| empty_set = sK4(X0,sK2)
| empty_set = sK4(X0,sK2) ),
inference(superposition,[],[f761,f786]) ).
fof(f833,plain,
! [X0] :
( in(sK20(sK4(X0,sK2)),X0)
| ~ ordinal(sK2)
| empty_set = sK4(X0,sK2) ),
inference(duplicate_literal_removal,[],[f832]) ).
fof(f834,plain,
! [X0] :
( in(sK20(sK4(X0,sK2)),X0)
| empty_set = sK4(X0,sK2) ),
inference(forward_subsumption_resolution,[],[f833,f146]) ).
fof(f835,plain,
! [X0] :
( ordinal(sK1(sK5(sK0,sK20(sK4(sK0,X0)))))
| empty_set = sK4(sK0,X0)
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[],[f826,f758]) ).
fof(f863,plain,
! [X0,X1] :
( empty_set = sK4(X0,X1)
| ~ ordinal(X1)
| ordinal_subset(sK20(sK4(X0,X1)),set_union2(X1,singleton(X1)))
| ~ ordinal(sK20(sK4(X0,X1)))
| ~ ordinal(set_union2(X1,singleton(X1))) ),
inference(resolution,[],[f779,f159]) ).
fof(f864,plain,
! [X0,X1] :
( empty_set = sK4(X0,X1)
| ~ ordinal(X1)
| ordinal_subset(sK20(sK4(X0,X1)),set_union2(X1,singleton(X1)))
| ~ ordinal(set_union2(X1,singleton(X1))) ),
inference(forward_subsumption_resolution,[],[f863,f686]) ).
fof(f868,plain,
! [X0,X1] :
( ordinal_subset(sK20(sK4(X0,X1)),set_union2(X1,singleton(X1)))
| ~ ordinal(X1)
| empty_set = sK4(X0,X1) ),
inference(forward_subsumption_resolution,[],[f864,f253]) ).
fof(f874,plain,
( ordinal(sK1(sK20(sK4(sK0,sK2))))
| empty_set = sK4(sK0,sK2)
| ~ ordinal(sK2)
| empty_set = sK4(sK0,sK2) ),
inference(superposition,[],[f835,f786]) ).
fof(f875,plain,
( ordinal(sK1(sK20(sK4(sK0,sK2))))
| empty_set = sK4(sK0,sK2)
| ~ ordinal(sK2) ),
inference(duplicate_literal_removal,[],[f874]) ).
fof(f876,plain,
( ordinal(sK1(sK20(sK4(sK0,sK2))))
| empty_set = sK4(sK0,sK2) ),
inference(forward_subsumption_resolution,[],[f875,f146]) ).
fof(f878,definition,
( spl21_11
<=> empty_set = sK4(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl21_11])],[avatar_definition]) ).
fof(f879,plain,
( empty_set != sK4(sK0,sK2)
| spl21_11 ),
inference(avatar_component_clause,[],[f878]) ).
fof(f880,plain,
( empty_set = sK4(sK0,sK2)
| ~ spl21_11 ),
inference(avatar_component_clause,[],[f878]) ).
fof(f882,definition,
( spl21_12
<=> ordinal(sK1(sK20(sK4(sK0,sK2)))) ),
introduced(definition,[new_symbols(definition,[spl21_12])],[avatar_definition]) ).
fof(f884,plain,
( ordinal(sK1(sK20(sK4(sK0,sK2))))
| ~ spl21_12 ),
inference(avatar_component_clause,[],[f882]) ).
fof(f885,plain,
( spl21_11
| spl21_12 ),
inference(avatar_split_clause,[],[f876,f882,f878]) ).
fof(f892,plain,
( in(sK2,empty_set)
| ~ ordinal(sK2)
| ~ in(sK2,sK0)
| ~ spl21_11 ),
inference(superposition,[],[f297,f880]) ).
fof(f905,plain,
( in(sK2,empty_set)
| ~ in(sK2,sK0)
| ~ spl21_11 ),
inference(forward_subsumption_resolution,[],[f892,f146]) ).
fof(f912,plain,
( in(sK2,empty_set)
| ~ spl21_11 ),
inference(forward_subsumption_resolution,[],[f905,f145]) ).
fof(f916,plain,
( ~ empty(empty_set)
| ~ spl21_11 ),
inference(resolution,[],[f912,f245]) ).
fof(f923,plain,
( $false
| ~ spl21_11 ),
inference(forward_subsumption_resolution,[],[f916,f203]) ).
fof(f924,plain,
~ spl21_11,
inference(avatar_contradiction_clause,[],[f923]) ).
fof(f950,definition,
( spl21_13
<=> ordinal(sK20(sK4(sK0,sK2))) ),
introduced(definition,[new_symbols(definition,[spl21_13])],[avatar_definition]) ).
fof(f951,plain,
( ordinal(sK20(sK4(sK0,sK2)))
| ~ spl21_13 ),
inference(avatar_component_clause,[],[f950]) ).
fof(f952,plain,
( ~ ordinal(sK20(sK4(sK0,sK2)))
| spl21_13 ),
inference(avatar_component_clause,[],[f950]) ).
fof(f968,plain,
( empty_set = sK4(sK0,sK2)
| ~ ordinal(sK2)
| spl21_13 ),
inference(resolution,[],[f952,f686]) ).
fof(f969,plain,
( ~ ordinal(sK2)
| spl21_11
| spl21_13 ),
inference(forward_subsumption_resolution,[],[f968,f879]) ).
fof(f970,plain,
( $false
| spl21_11
| spl21_13 ),
inference(forward_subsumption_resolution,[],[f969,f146]) ).
fof(f971,plain,
( spl21_11
| spl21_13 ),
inference(avatar_contradiction_clause,[],[f970]) ).
fof(f1422,plain,
! [X2,X3,X0,X1] :
( ~ ordinal(X0)
| set_union2(X1,singleton(X1)) = X0
| ~ in(X0,X2)
| ~ ordinal(X1)
| in(X0,sK4(X2,X1))
| in(sK20(sK4(X3,X1)),X0)
| ~ ordinal(X1)
| empty_set = sK4(X3,X1) ),
inference(resolution,[],[f610,f759]) ).
fof(f1434,plain,
! [X2,X3,X0,X1] :
( in(sK20(sK4(X3,X1)),X0)
| in(X0,sK4(X2,X1))
| ~ in(X0,X2)
| ~ ordinal(X1)
| set_union2(X1,singleton(X1)) = X0
| ~ ordinal(X0)
| empty_set = sK4(X3,X1) ),
inference(duplicate_literal_removal,[],[f1422]) ).
fof(f2715,definition,
( spl21_78
<=> in(sK1(sK20(sK4(sK0,sK2))),sK0) ),
introduced(definition,[new_symbols(definition,[spl21_78])],[avatar_definition]) ).
fof(f2716,plain,
( in(sK1(sK20(sK4(sK0,sK2))),sK0)
| ~ spl21_78 ),
inference(avatar_component_clause,[],[f2715]) ).
fof(f2717,plain,
( ~ in(sK1(sK20(sK4(sK0,sK2))),sK0)
| spl21_78 ),
inference(avatar_component_clause,[],[f2715]) ).
fof(f3409,plain,
( ~ in(sK20(sK4(sK0,sK2)),sK0)
| ~ ordinal(sK20(sK4(sK0,sK2)))
| spl21_78 ),
inference(resolution,[],[f2717,f148]) ).
fof(f3412,plain,
( ~ in(sK20(sK4(sK0,sK2)),sK0)
| ~ spl21_13
| spl21_78 ),
inference(forward_subsumption_resolution,[],[f3409,f951]) ).
fof(f3413,plain,
( empty_set = sK4(sK0,sK2)
| ~ spl21_13
| spl21_78 ),
inference(resolution,[],[f3412,f834]) ).
fof(f3417,plain,
( $false
| spl21_11
| ~ spl21_13
| spl21_78 ),
inference(forward_subsumption_resolution,[],[f3413,f879]) ).
fof(f3418,plain,
( spl21_11
| ~ spl21_13
| spl21_78 ),
inference(avatar_contradiction_clause,[],[f3417]) ).
fof(f5539,definition,
( spl21_259
<=> in(sK20(sK4(sK0,sK2)),sK0) ),
introduced(definition,[new_symbols(definition,[spl21_259])],[avatar_definition]) ).
fof(f5540,plain,
( in(sK20(sK4(sK0,sK2)),sK0)
| ~ spl21_259 ),
inference(avatar_component_clause,[],[f5539]) ).
fof(f5541,plain,
( ~ in(sK20(sK4(sK0,sK2)),sK0)
| spl21_259 ),
inference(avatar_component_clause,[],[f5539]) ).
fof(f6927,plain,
( empty_set = sK4(sK0,sK2)
| spl21_259 ),
inference(resolution,[],[f5541,f834]) ).
fof(f6931,plain,
( $false
| spl21_11
| spl21_259 ),
inference(forward_subsumption_resolution,[],[f6927,f879]) ).
fof(f6932,plain,
( spl21_11
| spl21_259 ),
inference(avatar_contradiction_clause,[],[f6931]) ).
fof(f12024,plain,
! [X2,X3,X0,X1] :
( in(sK20(sK4(X3,X2)),X0)
| ~ in(X0,X1)
| ~ ordinal(X2)
| set_union2(X2,singleton(X2)) = X0
| ~ ordinal(X0)
| empty_set = sK4(X3,X2)
| in(X0,set_union2(X2,singleton(X2)))
| ~ ordinal(X2) ),
inference(resolution,[],[f1434,f248]) ).
fof(f12075,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,X1)
| in(sK20(sK4(X3,X2)),X0)
| ~ ordinal(X2)
| set_union2(X2,singleton(X2)) = X0
| ~ ordinal(X0)
| empty_set = sK4(X3,X2)
| in(X0,set_union2(X2,singleton(X2))) ),
inference(duplicate_literal_removal,[],[f12024]) ).
fof(f15004,plain,
! [X2,X0,X1] :
( in(sK20(sK4(X0,X1)),X2)
| in(X2,set_union2(X1,singleton(X1)))
| set_union2(X1,singleton(X1)) = X2
| ~ ordinal(X2)
| empty_set = sK4(X0,X1)
| ~ ordinal(X1) ),
inference(resolution,[],[f12075,f254]) ).
fof(f15129,plain,
! [X2,X0,X1] :
( in(X2,set_union2(X1,singleton(X1)))
| set_union2(X1,singleton(X1)) = X2
| ~ ordinal(X2)
| empty_set = sK4(X0,X1)
| ~ ordinal(X1)
| subset(sK20(sK4(X0,X1)),X2)
| ~ epsilon_transitive(X2) ),
inference(resolution,[],[f15004,f177]) ).
fof(f15227,plain,
! [X2,X0,X1] :
( subset(sK20(sK4(X0,X1)),X2)
| in(X2,set_union2(X1,singleton(X1)))
| ~ ordinal(X2)
| empty_set = sK4(X0,X1)
| ~ ordinal(X1)
| set_union2(X1,singleton(X1)) = X2 ),
inference(forward_subsumption_resolution,[],[f15129,f161]) ).
fof(f15234,plain,
! [X2,X0,X1] :
( in(X2,set_union2(X1,singleton(X1)))
| ~ ordinal(X2)
| empty_set = sK4(X0,X1)
| ~ ordinal(X1)
| set_union2(X1,singleton(X1)) = X2
| ordinal_subset(sK20(sK4(X0,X1)),X2)
| ~ ordinal(sK20(sK4(X0,X1)))
| ~ ordinal(X2) ),
inference(resolution,[],[f15227,f159]) ).
fof(f15269,plain,
! [X2,X0,X1] :
( in(X2,set_union2(X1,singleton(X1)))
| ~ ordinal(X2)
| empty_set = sK4(X0,X1)
| ~ ordinal(X1)
| set_union2(X1,singleton(X1)) = X2
| ordinal_subset(sK20(sK4(X0,X1)),X2)
| ~ ordinal(sK20(sK4(X0,X1))) ),
inference(duplicate_literal_removal,[],[f15234]) ).
fof(f15278,plain,
! [X2,X0,X1] :
( ordinal_subset(sK20(sK4(X0,X1)),X2)
| in(X2,set_union2(X1,singleton(X1)))
| empty_set = sK4(X0,X1)
| ~ ordinal(X1)
| set_union2(X1,singleton(X1)) = X2
| ~ ordinal(X2) ),
inference(forward_subsumption_resolution,[],[f15269,f686]) ).
fof(f15282,plain,
! [X2,X3,X0,X1] :
( ordinal_subset(sK20(sK4(X2,X1)),X0)
| empty_set = sK4(X2,X1)
| ~ ordinal(X1)
| set_union2(X1,singleton(X1)) = X0
| ~ ordinal(X0)
| in(X0,sK4(X3,X1))
| ~ ordinal(X0)
| ~ in(X0,X3)
| ~ ordinal(X1) ),
inference(resolution,[],[f15278,f255]) ).
fof(f15313,plain,
! [X2,X3,X0,X1] :
( ordinal_subset(sK20(sK4(X2,X1)),X0)
| in(X0,sK4(X3,X1))
| ~ ordinal(X1)
| set_union2(X1,singleton(X1)) = X0
| ~ ordinal(X0)
| empty_set = sK4(X2,X1)
| ~ in(X0,X3) ),
inference(duplicate_literal_removal,[],[f15282]) ).
fof(f15322,plain,
! [X2,X0,X1] :
( in(sK1(sK20(sK4(X0,X1))),sK4(X2,X1))
| ~ ordinal(X1)
| set_union2(X1,singleton(X1)) = sK1(sK20(sK4(X0,X1)))
| ~ ordinal(sK1(sK20(sK4(X0,X1))))
| empty_set = sK4(X0,X1)
| ~ in(sK1(sK20(sK4(X0,X1))),X2)
| ~ in(sK20(sK4(X0,X1)),sK0)
| ~ ordinal(sK20(sK4(X0,X1))) ),
inference(resolution,[],[f15313,f149]) ).
fof(f15392,plain,
! [X2,X0,X1] :
( in(sK1(sK20(sK4(X0,X1))),sK4(X2,X1))
| ~ ordinal(X1)
| set_union2(X1,singleton(X1)) = sK1(sK20(sK4(X0,X1)))
| ~ ordinal(sK1(sK20(sK4(X0,X1))))
| empty_set = sK4(X0,X1)
| ~ in(sK1(sK20(sK4(X0,X1))),X2)
| ~ in(sK20(sK4(X0,X1)),sK0) ),
inference(forward_subsumption_resolution,[],[f15322,f686]) ).
fof(f15898,plain,
! [X0,X1] :
( ~ ordinal(X0)
| set_union2(X0,singleton(X0)) = sK1(sK20(sK4(X1,X0)))
| ~ ordinal(sK1(sK20(sK4(X1,X0))))
| empty_set = sK4(X1,X0)
| ~ in(sK1(sK20(sK4(X1,X0))),X1)
| ~ in(sK20(sK4(X1,X0)),sK0)
| ~ ordinal(X0)
| empty_set = sK4(X1,X0)
| ~ in(sK20(sK4(X1,X0)),sK0)
| ~ ordinal(sK20(sK4(X1,X0))) ),
inference(resolution,[],[f15392,f555]) ).
fof(f15963,plain,
! [X0,X1] :
( ~ ordinal(X0)
| set_union2(X0,singleton(X0)) = sK1(sK20(sK4(X1,X0)))
| ~ ordinal(sK1(sK20(sK4(X1,X0))))
| empty_set = sK4(X1,X0)
| ~ in(sK1(sK20(sK4(X1,X0))),X1)
| ~ in(sK20(sK4(X1,X0)),sK0)
| ~ ordinal(sK20(sK4(X1,X0))) ),
inference(duplicate_literal_removal,[],[f15898]) ).
fof(f15977,plain,
! [X0,X1] :
( ~ in(sK1(sK20(sK4(X1,X0))),X1)
| set_union2(X0,singleton(X0)) = sK1(sK20(sK4(X1,X0)))
| ~ ordinal(sK1(sK20(sK4(X1,X0))))
| empty_set = sK4(X1,X0)
| ~ ordinal(X0)
| ~ in(sK20(sK4(X1,X0)),sK0) ),
inference(forward_subsumption_resolution,[],[f15963,f686]) ).
fof(f16008,plain,
( sK1(sK20(sK4(sK0,sK2))) = set_union2(sK2,singleton(sK2))
| ~ ordinal(sK1(sK20(sK4(sK0,sK2))))
| empty_set = sK4(sK0,sK2)
| ~ ordinal(sK2)
| ~ in(sK20(sK4(sK0,sK2)),sK0)
| ~ spl21_78 ),
inference(resolution,[],[f15977,f2716]) ).
fof(f16045,plain,
( sK1(sK20(sK4(sK0,sK2))) = set_union2(sK2,singleton(sK2))
| ~ ordinal(sK1(sK20(sK4(sK0,sK2))))
| empty_set = sK4(sK0,sK2)
| ~ ordinal(sK2)
| ~ spl21_78 ),
inference(forward_subsumption_resolution,[],[f16008,f834]) ).
fof(f16048,plain,
( sK1(sK20(sK4(sK0,sK2))) = set_union2(sK2,singleton(sK2))
| empty_set = sK4(sK0,sK2)
| ~ ordinal(sK2)
| ~ spl21_12
| ~ spl21_78 ),
inference(forward_subsumption_resolution,[],[f16045,f884]) ).
fof(f16049,plain,
( sK1(sK20(sK4(sK0,sK2))) = set_union2(sK2,singleton(sK2))
| ~ ordinal(sK2)
| spl21_11
| ~ spl21_12
| ~ spl21_78 ),
inference(forward_subsumption_resolution,[],[f16048,f879]) ).
fof(f16050,plain,
( sK1(sK20(sK4(sK0,sK2))) = set_union2(sK2,singleton(sK2))
| spl21_11
| ~ spl21_12
| ~ spl21_78 ),
inference(forward_subsumption_resolution,[],[f16049,f146]) ).
fof(f16102,plain,
( ~ ordinal_subset(sK20(sK4(sK0,sK2)),set_union2(sK2,singleton(sK2)))
| ~ in(sK20(sK4(sK0,sK2)),sK0)
| ~ ordinal(sK20(sK4(sK0,sK2)))
| spl21_11
| ~ spl21_12
| ~ spl21_78 ),
inference(superposition,[],[f149,f16050]) ).
fof(f16152,plain,
( ~ ordinal_subset(sK20(sK4(sK0,sK2)),set_union2(sK2,singleton(sK2)))
| ~ ordinal(sK20(sK4(sK0,sK2)))
| spl21_11
| ~ spl21_12
| ~ spl21_78
| ~ spl21_259 ),
inference(forward_subsumption_resolution,[],[f16102,f5540]) ).
fof(f16183,plain,
( ~ ordinal_subset(sK20(sK4(sK0,sK2)),set_union2(sK2,singleton(sK2)))
| spl21_11
| ~ spl21_12
| ~ spl21_13
| ~ spl21_78
| ~ spl21_259 ),
inference(forward_subsumption_resolution,[],[f16152,f951]) ).
fof(f16286,plain,
( ~ ordinal(sK2)
| empty_set = sK4(sK0,sK2)
| spl21_11
| ~ spl21_12
| ~ spl21_13
| ~ spl21_78
| ~ spl21_259 ),
inference(resolution,[],[f16183,f868]) ).
fof(f16309,plain,
( empty_set = sK4(sK0,sK2)
| spl21_11
| ~ spl21_12
| ~ spl21_13
| ~ spl21_78
| ~ spl21_259 ),
inference(forward_subsumption_resolution,[],[f16286,f146]) ).
fof(f16311,plain,
( $false
| spl21_11
| ~ spl21_12
| ~ spl21_13
| ~ spl21_78
| ~ spl21_259 ),
inference(forward_subsumption_resolution,[],[f16309,f879]) ).
fof(f16312,plain,
( spl21_11
| ~ spl21_12
| ~ spl21_13
| ~ spl21_78
| ~ spl21_259 ),
inference(avatar_contradiction_clause,[],[f16311]) ).
cnf(s7,plain,
( spl21_11
| spl21_12 ),
inference(sat_conversion,[],[f885]) ).
cnf(s8,plain,
~ spl21_11,
inference(sat_conversion,[],[f924]) ).
cnf(s12,plain,
( spl21_11
| spl21_13 ),
inference(sat_conversion,[],[f971]) ).
cnf(s89,plain,
( spl21_11
| ~ spl21_13
| spl21_78 ),
inference(sat_conversion,[],[f3418]) ).
cnf(s274,plain,
( spl21_11
| spl21_259 ),
inference(sat_conversion,[],[f6932]) ).
cnf(s621,plain,
( spl21_11
| ~ spl21_12
| ~ spl21_13
| ~ spl21_78
| ~ spl21_259 ),
inference(sat_conversion,[],[f16312]) ).
cnf(s680,plain,
spl21_259,
inference(rat,[],[s274,s8]) ).
cnf(s682,plain,
spl21_13,
inference(rat,[],[s12,s8]) ).
cnf(s686,plain,
spl21_78,
inference(rat,[],[s89,s8,s682]) ).
cnf(s691,plain,
~ spl21_12,
inference(rat,[],[s621,s680,s686,s8,s682]) ).
cnf(s696,plain,
$false,
inference(rat,[],[s7,s691,s8]) ).
fof(f16314,plain,
$false,
inference(avatar_sat_refutation,[],[s696]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU273+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n019.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 04:26:04 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.07/2.68 % (3656889)Detected formulas, will run a generic FOF schedule.
% 12.07/2.68 % (3656896)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2819616410:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 12.07/2.68 % (3656897)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2760289936:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 12.07/2.68 % (3656898)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1120952936:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 12.07/2.68 % (3656894)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2973861541:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 12.07/2.68 % (3656900)dis-21_1_sil=8000:lcm=predicate:random_seed=955921808:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 12.07/2.68 % (3656895)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3727203132:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 12.07/2.68 % (3656899)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2453747170:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 12.07/2.68 % (3656897)Refutation not found, incomplete strategy
% 12.07/2.68 % (3656897)------------------------------
% 12.07/2.68 % (3656897)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.07/2.68 % (3656897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.07/2.68 % (3656897)CaDiCaL version: 2.1.3
% 12.07/2.68 % (3656897)Termination reason: Refutation not found, incomplete strategy
% 12.07/2.68 % (3656897)Time elapsed: 0.004 s
% 12.07/2.68 % (3656897)Peak memory usage: 88 MB
% 12.07/2.68 % (3656897)Instructions burned: 4 (million)
% 12.07/2.68 % (3656898)Instruction limit reached!
% 12.07/2.68 % (3656898)------------------------------
% 12.07/2.68 % (3656898)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.07/2.68 % (3656898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.07/2.68 % (3656898)CaDiCaL version: 2.1.3
% 12.07/2.68 % (3656898)Termination reason: Instruction limit
% 12.07/2.68 % (3656898)Termination phase: Saturation
% 12.07/2.68 % (3656898)Time elapsed: 0.069 s
% 12.07/2.68 % (3656898)Peak memory usage: 88 MB
% 12.07/2.68 % (3656898)Instructions burned: 121 (million)
% 12.07/2.68 % (3656900)Instruction limit reached!
% 12.07/2.68 % (3656900)------------------------------
% 12.07/2.68 % (3656900)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.07/2.68 % (3656900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.07/2.68 % (3656900)CaDiCaL version: 2.1.3
% 12.07/2.68 % (3656900)Termination reason: Instruction limit
% 12.07/2.68 % (3656900)Termination phase: Saturation
% 12.07/2.68 % (3656900)Time elapsed: 0.080 s
% 12.07/2.68 % (3656900)Peak memory usage: 90 MB
% 12.07/2.68 % (3656900)Instructions burned: 130 (million)
% 12.07/2.68 % (3656899)Instruction limit reached!
% 12.07/2.68 % (3656899)------------------------------
% 12.07/2.68 % (3656899)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.07/2.68 % (3656899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.07/2.68 % (3656899)CaDiCaL version: 2.1.3
% 12.07/2.68 % (3656899)Termination reason: Instruction limit
% 12.07/2.68 % (3656899)Termination phase: Saturation
% 12.07/2.68 % (3656899)Time elapsed: 0.099 s
% 12.07/2.68 % (3656899)Peak memory usage: 90 MB
% 12.07/2.68 % (3656899)Instructions burned: 140 (million)
% 12.07/2.68 % (3656908)lrs+10_1_sil=8000:sp=occurrence:random_seed=2177978236:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 12.07/2.68 % (3656909)lrs+10_1_sil=32000:urr=on:br=off:random_seed=259709189:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 12.07/2.68 % (3656910)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3167186343:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 12.07/2.68 % (3656897)------------------------------
% 12.07/2.68 % (3656897)------------------------------
% 12.07/2.68 % (3656909)Instruction limit reached!
% 12.07/2.68 % (3656909)------------------------------
% 12.07/2.68 % (3656909)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.82/3.48 % (3656909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.82/3.48 % (3656909)CaDiCaL version: 2.1.3
% 17.82/3.48 % (3656909)Termination reason: Instruction limit
% 17.82/3.48 % (3656909)Termination phase: Saturation
% 17.82/3.48 % (3656909)Time elapsed: 0.078 s
% 17.82/3.48 % (3656909)Peak memory usage: 89 MB
% 17.82/3.48 % (3656909)Instructions burned: 158 (million)
% 17.82/3.48 % (3656914)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3101109895:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 17.82/3.48 % (3656908)Instruction limit reached!
% 17.82/3.48 % (3656908)------------------------------
% 17.82/3.48 % (3656908)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.82/3.48 % (3656908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.82/3.48 % (3656908)CaDiCaL version: 2.1.3
% 17.82/3.48 % (3656908)Termination reason: Instruction limit
% 17.82/3.48 % (3656908)Termination phase: Saturation
% 17.82/3.48 % (3656908)Time elapsed: 0.168 s
% 17.82/3.48 % (3656908)Peak memory usage: 91 MB
% 17.82/3.48 % (3656908)Instructions burned: 286 (million)
% 17.82/3.48 % (3656915)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1945732111:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 17.82/3.48 % (3656915)Refutation not found, incomplete strategy
% 17.82/3.48 % (3656915)------------------------------
% 17.82/3.48 % (3656915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.82/3.48 % (3656915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.82/3.48 % (3656915)CaDiCaL version: 2.1.3
% 17.82/3.48 % (3656915)Termination reason: Refutation not found, incomplete strategy
% 17.82/3.48 % (3656915)Time elapsed: 0.004 s
% 17.82/3.48 % (3656915)Peak memory usage: 88 MB
% 17.82/3.48 % (3656915)Instructions burned: 5 (million)
% 17.82/3.48 % (3656910)Instruction limit reached!
% 17.82/3.48 % (3656910)------------------------------
% 17.82/3.48 % (3656910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.82/3.48 % (3656910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.82/3.48 % (3656910)CaDiCaL version: 2.1.3
% 17.82/3.48 % (3656910)Termination reason: Instruction limit
% 17.82/3.48 % (3656910)Termination phase: Saturation
% 17.82/3.48 % (3656910)Time elapsed: 0.217 s
% 17.82/3.48 % (3656910)Peak memory usage: 92 MB
% 17.82/3.48 % (3656910)Instructions burned: 325 (million)
% 17.82/3.48 % (3656917)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3566911209:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 17.82/3.48 % (3656914)Instruction limit reached!
% 17.82/3.48 % (3656914)------------------------------
% 17.82/3.48 % (3656914)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.82/3.48 % (3656914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.82/3.48 % (3656914)CaDiCaL version: 2.1.3
% 17.82/3.48 % (3656914)Termination reason: Instruction limit
% 17.82/3.48 % (3656914)Termination phase: Saturation
% 17.82/3.48 % (3656914)Time elapsed: 0.140 s
% 17.82/3.48 % (3656914)Peak memory usage: 95 MB
% 17.82/3.48 % (3656914)Instructions burned: 249 (million)
% 17.82/3.48 % (3656919)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1964480029:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 17.82/3.48 % (3656921)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=579847385:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 17.82/3.48 % (3656919)Instruction limit reached!
% 17.82/3.48 % (3656919)------------------------------
% 17.82/3.48 % (3656919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.82/3.48 % (3656919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.82/3.48 % (3656919)CaDiCaL version: 2.1.3
% 17.82/3.48 % (3656919)Termination reason: Instruction limit
% 17.82/3.48 % (3656919)Termination phase: Saturation
% 17.82/3.48 % (3656919)Time elapsed: 0.082 s
% 17.82/3.48 % (3656919)Peak memory usage: 90 MB
% 17.82/3.48 % (3656919)Instructions burned: 114 (million)
% 17.82/3.48 % (3656915)------------------------------
% 17.82/3.48 % (3656915)------------------------------
% 17.82/3.48 % (3656921)Instruction limit reached!
% 17.82/3.48 % (3656921)------------------------------
% 17.82/3.48 % (3656921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.82/3.48 % (3656921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.82/3.48 % (3656921)CaDiCaL version: 2.1.3
% 17.82/3.48 % (3656921)Termination reason: Instruction limit
% 17.82/3.48 % (3656921)Termination phase: Saturation
% 17.82/3.48 % (3656921)Time elapsed: 0.070 s
% 17.82/3.48 % (3656921)Peak memory usage: 89 MB
% 17.82/3.48 % (3656921)Instructions burned: 128 (million)
% 17.82/3.48 % (3656924)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1334920131:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 17.82/3.48 % (3656925)lrs+10_1_sil=8000:sp=occurrence:random_seed=4276231395:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 17.82/3.48 % (3656926)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1010583324:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 17.82/3.48 % (3656924)Instruction limit reached!
% 17.82/3.48 % (3656924)------------------------------
% 17.82/3.48 % (3656924)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.82/3.48 % (3656924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.82/3.48 % (3656924)CaDiCaL version: 2.1.3
% 17.82/3.48 % (3656924)Termination reason: Instruction limit
% 17.82/3.48 % (3656924)Termination phase: Saturation
% 17.82/3.48 % (3656924)Time elapsed: 0.073 s
% 17.82/3.48 % (3656924)Peak memory usage: 89 MB
% 17.82/3.48 % (3656924)Instructions burned: 115 (million)
% 17.82/3.48 % (3656930)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=630181689:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 17.82/3.48 % (3656926)Instruction limit reached!
% 17.82/3.48 % (3656926)------------------------------
% 17.82/3.48 % (3656926)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.82/3.48 % (3656926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.82/3.48 % (3656926)CaDiCaL version: 2.1.3
% 17.82/3.48 % (3656926)Termination reason: Instruction limit
% 17.82/3.48 % (3656926)Termination phase: Saturation
% 17.82/3.48 % (3656926)Time elapsed: 0.241 s
% 17.82/3.48 % (3656926)Peak memory usage: 90 MB
% 17.82/3.48 % (3656926)Instructions burned: 438 (million)
% 17.82/3.48 % (3656932)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=678167131:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2987 on theBenchmark for (2987ds/134Mi)
% 17.82/3.48 % (3656932)Instruction limit reached!
% 17.82/3.48 % (3656932)------------------------------
% 17.82/3.48 % (3656932)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.82/3.48 % (3656932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.82/3.48 % (3656932)CaDiCaL version: 2.1.3
% 17.82/3.48 % (3656932)Termination reason: Instruction limit
% 17.82/3.48 % (3656932)Termination phase: Saturation
% 17.82/3.48 % (3656932)Time elapsed: 0.071 s
% 17.82/3.48 % (3656932)Peak memory usage: 93 MB
% 17.82/3.48 % (3656932)Instructions burned: 134 (million)
% 17.82/3.48 % (3656925)Instruction limit reached!
% 17.82/3.48 % (3656925)------------------------------
% 17.82/3.48 % (3656925)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.82/3.48 % (3656925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.82/3.48 % (3656925)CaDiCaL version: 2.1.3
% 17.82/3.48 % (3656925)Termination reason: Instruction limit
% 17.82/3.48 % (3656925)Termination phase: Saturation
% 17.82/3.48 % (3656925)Time elapsed: 0.546 s
% 17.82/3.48 % (3656925)Peak memory usage: 98 MB
% 17.82/3.48 % (3656925)Instructions burned: 907 (million)
% 17.82/3.48 % (3656934)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=2695436666:st=8:i=592:sd=3:ep=RST:ss=axioms_2985 on theBenchmark for (2985ds/592Mi)
% 17.82/3.48 % (3656934)Refutation not found, incomplete strategy
% 17.82/3.48 % (3656934)------------------------------
% 17.82/3.48 % (3656934)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.82/3.48 % (3656934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.82/3.48 % (3656934)CaDiCaL version: 2.1.3
% 17.82/3.48 % (3656934)Termination reason: Refutation not found, incomplete strategy
% 17.82/3.48 % (3656934)Time elapsed: 0.004 s
% 17.82/3.48 % (3656934)Peak memory usage: 88 MB
% 17.82/3.48 % (3656934)Instructions burned: 4 (million)
% 17.82/3.48 % (3656935)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2547103186:st=3:i=13193:sd=3:ss=axioms_2985 on theBenchmark for (2985ds/13193Mi)
% 17.82/3.48 % (3656934)------------------------------
% 17.82/3.48 % (3656934)------------------------------
% 17.82/3.48 % (3656938)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=4040831151:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2981 on theBenchmark for (2981ds/125Mi)
% 17.82/3.48 % (3656938)Instruction limit reached!
% 17.82/3.48 % (3656938)------------------------------
% 17.82/3.48 % (3656938)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.82/3.48 % (3656938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.82/3.48 % (3656938)CaDiCaL version: 2.1.3
% 17.82/3.48 % (3656938)Termination reason: Instruction limit
% 17.82/3.48 % (3656938)Termination phase: Saturation
% 17.82/3.48 % (3656938)Time elapsed: 0.093 s
% 17.82/3.48 % (3656938)Peak memory usage: 91 MB
% 17.82/3.48 % (3656938)Instructions burned: 125 (million)
% 17.82/3.48 % (3656941)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=1659030793:i=134:gtgl=5:slsql=off:gtg=exists_sym_2979 on theBenchmark for (2979ds/134Mi)
% 17.82/3.48 % (3656917)Instruction limit reached!
% 17.82/3.48 % (3656917)------------------------------
% 17.82/3.48 % (3656917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.82/3.48 % (3656917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.82/3.48 % (3656917)CaDiCaL version: 2.1.3
% 17.82/3.48 % (3656917)Termination reason: Instruction limit
% 17.82/3.48 % (3656917)Termination phase: Saturation
% 17.82/3.48 % (3656917)Time elapsed: 1.515 s
% 17.82/3.48 % (3656917)Peak memory usage: 140 MB
% 17.82/3.48 % (3656917)Instructions burned: 2351 (million)
% 17.82/3.48 % (3656941)Instruction limit reached!
% 17.82/3.48 % (3656941)------------------------------
% 17.82/3.48 % (3656941)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.82/3.48 % (3656941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.82/3.48 % (3656941)CaDiCaL version: 2.1.3
% 17.82/3.48 % (3656941)Termination reason: Instruction limit
% 17.82/3.48 % (3656941)Termination phase: Saturation
% 17.82/3.48 % (3656941)Time elapsed: 0.091 s
% 17.82/3.48 % (3656941)Peak memory usage: 90 MB
% 17.82/3.48 % (3656941)Instructions burned: 135 (million)
% 17.82/3.48 % (3656943)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=2819394233:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2978 on theBenchmark for (2978ds/141Mi)
% 17.82/3.48 % (3656894)First to succeed.
% 17.82/3.48 % (3656894)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3656889"
% 17.82/3.48 % (3656944)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=1924778883:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2977 on theBenchmark for (2977ds/431Mi)
% 17.82/3.48 % (3656943)Instruction limit reached!
% 17.82/3.48 % (3656943)------------------------------
% 17.82/3.48 % (3656943)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.82/3.48 % (3656943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.82/3.48 % (3656943)CaDiCaL version: 2.1.3
% 17.82/3.48 % (3656943)Termination reason: Instruction limit
% 17.82/3.48 % (3656943)Termination phase: Saturation
% 17.82/3.48 % (3656943)Time elapsed: 0.073 s
% 17.82/3.48 % (3656943)Peak memory usage: 90 MB
% 17.82/3.48 % (3656943)Instructions burned: 143 (million)
% 17.82/3.48 % (3656947)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=1710042945:i=6060:aac=none:ins=25_2976 on theBenchmark for (2976ds/6060Mi)
% 17.82/3.48 % (3656894)Refutation found. Thanks to Tanya!
% 17.82/3.48 % SZS status Theorem for theBenchmark
% 17.82/3.48 % SZS output start Proof for theBenchmark
% See solution above
% 18.94/3.67 % (3656894)------------------------------
% 18.94/3.67 % (3656894)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.94/3.67 % (3656894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.94/3.67 % (3656894)CaDiCaL version: 2.1.3
% 18.94/3.67 % (3656894)Termination reason: Refutation
% 18.94/3.67 % (3656894)Time elapsed: 2.185 s
% 18.94/3.67 % (3656894)Peak memory usage: 150 MB
% 18.94/3.67 % (3656894)Instructions burned: 3376 (million)
% 18.94/3.67 % (3656894)------------------------------
% 18.94/3.67 % (3656894)------------------------------
% 18.94/3.67 % (3656889)Success in time 2.6 s
% 18.94/3.67 % Vampire exiting
%------------------------------------------------------------------------------