%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU238+2 : 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 : n020.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 12:47:57 PM UTC 2026
% Result : Theorem 12.10s 2.33s
% Output : Refutation 12.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 43
% Syntax : Number of formulae : 305 ( 35 unt; 19 def)
% Number of atoms : 1086 ( 203 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1296 ( 515 ~; 586 |; 141 &)
% ( 36 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 18 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 4 con; 0-3 aty)
% Number of variables : 314 ( 0 sgn 287 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f10,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f14,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f22,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f25,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f28,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f31,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X0
| X3 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f32,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f39,axiom,
! [X0] :
( ordinal(X0)
<=> ( epsilon_transitive(X0)
& epsilon_connected(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_ordinal1) ).
fof(f42,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X2,X3)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f43,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& ~ in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f48,axiom,
! [X0] :
( being_limit_ordinal(X0)
<=> X0 = union(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_ordinal1) ).
fof(f106,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(f160,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f169,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f196,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(f197,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X0,X1)
& X0 != X1
& ~ in(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f225,axiom,
! [X0,X1] : set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(f226,axiom,
! [X0] :
( ordinal(X0)
=> ( being_limit_ordinal(X0)
<=> ! [X1] :
( ordinal(X1)
=> ( in(X1,X0)
=> in(succ(X1),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_ordinal1) ).
fof(f227,conjecture,
! [X0] :
( ordinal(X0)
=> ( ~ ( ~ being_limit_ordinal(X0)
& ! [X1] :
( ordinal(X1)
=> X0 != succ(X1) ) )
& ~ ( ? [X1] :
( ordinal(X1)
& X0 = succ(X1) )
& being_limit_ordinal(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_ordinal1) ).
fof(f228,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ( ~ ( ~ being_limit_ordinal(X0)
& ! [X1] :
( ordinal(X1)
=> X0 != succ(X1) ) )
& ~ ( ? [X1] :
( ordinal(X1)
& X0 = succ(X1) )
& being_limit_ordinal(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f227]) ).
fof(f235,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
fof(f256,axiom,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f258,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f267,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f288,plain,
~ ! [X0] :
( ordinal(X0)
=> ( ~ ( ~ being_limit_ordinal(X0)
& ! [X1] :
( ordinal(X1)
=> X0 != succ(X1) ) )
& ~ ( ? [X2] :
( ordinal(X2)
& succ(X2) = X0 )
& being_limit_ordinal(X0) ) ) ),
inference(rectify,[],[f228]) ).
fof(f294,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f318,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f368,plain,
! [X0] :
( ( ~ empty(succ(X0))
& epsilon_transitive(succ(X0))
& epsilon_connected(succ(X0))
& ordinal(succ(X0)) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f106]) ).
fof(f417,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f169]) ).
fof(f454,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f196]) ).
fof(f455,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(flattening,[],[f454]) ).
fof(f456,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| X0 = X1
| in(X1,X0)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f197]) ).
fof(f457,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| X0 = X1
| in(X1,X0)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(flattening,[],[f456]) ).
fof(f480,plain,
! [X0] :
( ( being_limit_ordinal(X0)
<=> ! [X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1) ) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f226]) ).
fof(f481,plain,
! [X0] :
( ( being_limit_ordinal(X0)
<=> ! [X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1) ) )
| ~ ordinal(X0) ),
inference(flattening,[],[f480]) ).
fof(f482,plain,
? [X0] :
( ( ( ~ being_limit_ordinal(X0)
& ! [X1] :
( X0 != succ(X1)
| ~ ordinal(X1) ) )
| ( ? [X2] :
( ordinal(X2)
& succ(X2) = X0 )
& being_limit_ordinal(X0) ) )
& ordinal(X0) ),
inference(ennf_transformation,[],[f288]) ).
fof(f491,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f235]) ).
fof(f554,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f555,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f554]) ).
fof(f587,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f588,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f587]) ).
fof(f589,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK24(X0,X1) != X0
| ~ in(sK24(X0,X1),X1) )
& ( sK24(X0,X1) = X0
| in(sK24(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(X2,sK24(X0,X1))],[f588]) ).
fof(f596,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,[],[f318]) ).
fof(f597,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f596]) ).
fof(f598,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK27(X0),X0)
& in(sK27(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(X1,sK27(X0))],[f597]) ).
fof(f603,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f604,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(flattening,[],[f603]) ).
fof(f605,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f604]) ).
fof(f606,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ( ( ( sK30(X0,X1,X2) != X0
& sK30(X0,X1,X2) != X1 )
| ~ in(sK30(X0,X1,X2),X2) )
& ( sK30(X0,X1,X2) = X0
| sK30(X0,X1,X2) = X1
| in(sK30(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(X3,sK30(X0,X1,X2))],[f605]) ).
fof(f607,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f608,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f607]) ).
fof(f609,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f608]) ).
fof(f610,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ( ( ( ~ in(sK31(X0,X1,X2),X0)
& ~ in(sK31(X0,X1,X2),X1) )
| ~ in(sK31(X0,X1,X2),X2) )
& ( in(sK31(X0,X1,X2),X0)
| in(sK31(X0,X1,X2),X1)
| in(sK31(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(X3,sK31(X0,X1,X2))],[f609]) ).
fof(f628,plain,
! [X0] :
( ( ordinal(X0)
| ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0) )
& ( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
| ~ ordinal(X0) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f629,plain,
! [X0] :
( ( ordinal(X0)
| ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0) )
& ( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
| ~ ordinal(X0) ) ),
inference(flattening,[],[f628]) ).
fof(f633,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X2,X3)
& in(X3,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) ) )
& ( ? [X3] :
( in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) ) )
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f634,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X2,X4)
& in(X4,X0) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X5,X6)
| ~ in(X6,X0) ) )
& ( ? [X7] :
( in(X5,X7)
& in(X7,X0) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(rectify,[],[f633]) ).
fof(f635,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ( ( ! [X3] :
( ~ in(sK46(X0,X1),X3)
| ~ in(X3,X0) )
| ~ in(sK46(X0,X1),X1) )
& ( ( in(sK46(X0,X1),sK47(X0,X1))
& in(sK47(X0,X1),X0) )
| in(sK46(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X5,X6)
| ~ in(X6,X0) ) )
& ( ( in(X5,sK48(X0,X5))
& in(sK48(X0,X5),X0) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46,sK47,sK48]),skolemize(X2,sK46(X0,X1)),skolemize(X4,sK47(X0,X1)),skolemize(X7,sK48(X0,X5))],[f634]) ).
fof(f636,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f637,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f636]) ).
fof(f638,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f637]) ).
fof(f639,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ( ( ~ in(sK49(X0,X1,X2),X0)
| in(sK49(X0,X1,X2),X1)
| ~ in(sK49(X0,X1,X2),X2) )
& ( ( in(sK49(X0,X1,X2),X0)
& ~ in(sK49(X0,X1,X2),X1) )
| in(sK49(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(X3,sK49(X0,X1,X2))],[f638]) ).
fof(f646,plain,
! [X0] :
( ( being_limit_ordinal(X0)
| union(X0) != X0 )
& ( X0 = union(X0)
| ~ being_limit_ordinal(X0) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f716,plain,
! [X0] :
( ( ( being_limit_ordinal(X0)
| ? [X1] :
( ~ in(succ(X1),X0)
& in(X1,X0)
& ordinal(X1) ) )
& ( ! [X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1) )
| ~ being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(nnf_transformation,[],[f481]) ).
fof(f717,plain,
! [X0] :
( ( ( being_limit_ordinal(X0)
| ? [X1] :
( ~ in(succ(X1),X0)
& in(X1,X0)
& ordinal(X1) ) )
& ( ! [X2] :
( in(succ(X2),X0)
| ~ in(X2,X0)
| ~ ordinal(X2) )
| ~ being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(rectify,[],[f716]) ).
fof(f718,plain,
! [X0] :
( ( ( being_limit_ordinal(X0)
| ( ~ in(succ(sK89(X0)),X0)
& in(sK89(X0),X0)
& ordinal(sK89(X0)) ) )
& ( ! [X2] :
( in(succ(X2),X0)
| ~ in(X2,X0)
| ~ ordinal(X2) )
| ~ being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(X1,sK89(X0))],[f717]) ).
fof(f719,plain,
( ( ( ~ being_limit_ordinal(sK90)
& ! [X1] :
( succ(X1) != sK90
| ~ ordinal(X1) ) )
| ( ordinal(sK91)
& sK90 = succ(sK91)
& being_limit_ordinal(sK90) ) )
& ordinal(sK90) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90,sK91]),skolemize(X0,sK90),skolemize(X2,sK91)],[f482]) ).
fof(f731,plain,
! [X0,X1] :
( ( set_difference(X0,singleton(X1)) = X0
| in(X1,X0) )
& ( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 ) ),
inference(nnf_transformation,[],[f256]) ).
fof(f745,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f294]) ).
fof(f759,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f770,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f555]) ).
fof(f817,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f829,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f589]) ).
fof(f839,plain,
! [X2,X0] :
( ~ in(X2,X0)
| subset(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f598]) ).
fof(f852,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f606]) ).
fof(f856,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f610]) ).
fof(f893,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f629]) ).
fof(f902,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X5,X6)
| ~ in(X6,X0)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f635]) ).
fof(f906,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f639]) ).
fof(f924,plain,
! [X0] :
( ~ being_limit_ordinal(X0)
| union(X0) = X0 ),
inference(cnf_transformation,[],[f646]) ).
fof(f996,plain,
! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f368]) ).
fof(f1095,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f160]) ).
fof(f1107,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f417]) ).
fof(f1145,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ordinal(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f455]) ).
fof(f1146,plain,
! [X0,X1] :
( in(X1,X0)
| in(X0,X1)
| X0 = X1
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f457]) ).
fof(f1195,plain,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
inference(cnf_transformation,[],[f225]) ).
fof(f1196,plain,
! [X2,X0] :
( in(succ(X2),X0)
| ~ in(X2,X0)
| ~ ordinal(X2)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f718]) ).
fof(f1197,plain,
! [X0] :
( ordinal(sK89(X0))
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f718]) ).
fof(f1198,plain,
! [X0] :
( in(sK89(X0),X0)
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f718]) ).
fof(f1199,plain,
! [X0] :
( being_limit_ordinal(X0)
| ~ in(succ(sK89(X0)),X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f718]) ).
fof(f1200,plain,
ordinal(sK90),
inference(cnf_transformation,[],[f719]) ).
fof(f1201,plain,
! [X1] :
( succ(X1) != sK90
| ~ ordinal(X1)
| being_limit_ordinal(sK90) ),
inference(cnf_transformation,[],[f719]) ).
fof(f1205,plain,
( ~ being_limit_ordinal(sK90)
| sK90 = succ(sK91) ),
inference(cnf_transformation,[],[f719]) ).
fof(f1206,plain,
( ~ being_limit_ordinal(sK90)
| ordinal(sK91) ),
inference(cnf_transformation,[],[f719]) ).
fof(f1214,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f491]) ).
fof(f1252,plain,
! [X0,X1] :
( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 ),
inference(cnf_transformation,[],[f731]) ).
fof(f1253,plain,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
| in(X1,X0) ),
inference(cnf_transformation,[],[f731]) ).
fof(f1258,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f258]) ).
fof(f1271,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f267]) ).
fof(f1295,plain,
! [X0] : succ(X0) = set_union2(X0,unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f817,f1258]) ).
fof(f1328,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f829,f1258]) ).
fof(f1375,plain,
! [X0] :
( ordinal(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f996,f1295]) ).
fof(f1393,plain,
! [X0] : in(X0,set_union2(X0,unordered_pair(X0,X0))),
inference(definition_unfolding,[],[f1095,f1295]) ).
fof(f1419,plain,
! [X0] :
( ~ in(set_union2(sK89(X0),unordered_pair(sK89(X0),sK89(X0))),X0)
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1199,f1295]) ).
fof(f1420,plain,
! [X2,X0] :
( in(set_union2(X2,unordered_pair(X2,X2)),X0)
| ~ in(X2,X0)
| ~ ordinal(X2)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1196,f1295]) ).
fof(f1421,plain,
( ~ being_limit_ordinal(sK90)
| sK90 = set_union2(sK91,unordered_pair(sK91,sK91)) ),
inference(definition_unfolding,[],[f1205,f1295]) ).
fof(f1424,plain,
! [X1] :
( sK90 != set_union2(X1,unordered_pair(X1,X1))
| ~ ordinal(X1)
| being_limit_ordinal(sK90) ),
inference(definition_unfolding,[],[f1201,f1295]) ).
fof(f1425,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(unordered_pair(X0,X0),X1) = X1 ),
inference(definition_unfolding,[],[f1214,f1258]) ).
fof(f1429,plain,
! [X0,X1] :
( in(X1,X0)
| set_difference(X0,unordered_pair(X1,X1)) = X0 ),
inference(definition_unfolding,[],[f1253,f1258]) ).
fof(f1430,plain,
! [X0,X1] :
( set_difference(X0,unordered_pair(X1,X1)) != X0
| ~ in(X1,X0) ),
inference(definition_unfolding,[],[f1252,f1258]) ).
fof(f1486,plain,
! [X3,X0] :
( ~ in(X3,unordered_pair(X0,X0))
| X0 = X3 ),
inference(equality_resolution,[],[f1328]) ).
fof(f1492,plain,
! [X2,X1,X4] :
( in(X4,X2)
| unordered_pair(X4,X1) != X2 ),
inference(equality_resolution,[],[f852]) ).
fof(f1493,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f1492]) ).
fof(f1499,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f856]) ).
fof(f1513,plain,
! [X0,X6,X5] :
( ~ in(X6,X0)
| ~ in(X5,X6)
| in(X5,union(X0)) ),
inference(equality_resolution,[],[f902]) ).
fof(f1518,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f906]) ).
fof(f1552,definition,
sF101 = unordered_pair(sK91,sK91),
introduced(definition,[new_symbols(definition,[sF101])],[function_definition]) ).
fof(f1553,plain,
unordered_pair(sK91,sK91) = sF101,
inference(reorient_equations,[],[f1552]) ).
fof(f1554,definition,
sF102 = set_union2(sK91,sF101),
introduced(definition,[new_symbols(definition,[sF102])],[function_definition]) ).
fof(f1555,plain,
set_union2(sK91,sF101) = sF102,
inference(reorient_equations,[],[f1554]) ).
fof(f1556,plain,
( ~ being_limit_ordinal(sK90)
| sK90 = sF102 ),
inference(definition_folding,[],[f1421,f1555,f1553]) ).
fof(f1561,definition,
( spl103_1
<=> being_limit_ordinal(sK90) ),
introduced(definition,[new_symbols(definition,[spl103_1])],[avatar_definition]) ).
fof(f1562,plain,
( ~ being_limit_ordinal(sK90)
| spl103_1 ),
inference(avatar_component_clause,[],[f1561]) ).
fof(f1563,plain,
( being_limit_ordinal(sK90)
| ~ spl103_1 ),
inference(avatar_component_clause,[],[f1561]) ).
fof(f1565,definition,
( spl103_2
<=> ! [X1] :
( sK90 != set_union2(X1,unordered_pair(X1,X1))
| ~ ordinal(X1) ) ),
introduced(definition,[new_symbols(definition,[spl103_2])],[avatar_definition]) ).
fof(f1566,plain,
( ! [X1] :
( sK90 != set_union2(X1,unordered_pair(X1,X1))
| ~ ordinal(X1) )
| ~ spl103_2 ),
inference(avatar_component_clause,[],[f1565]) ).
fof(f1567,plain,
( spl103_1
| spl103_2 ),
inference(avatar_split_clause,[],[f1424,f1565,f1561]) ).
fof(f1569,definition,
( spl103_3
<=> sK90 = sF102 ),
introduced(definition,[new_symbols(definition,[spl103_3])],[avatar_definition]) ).
fof(f1571,plain,
( sK90 = sF102
| ~ spl103_3 ),
inference(avatar_component_clause,[],[f1569]) ).
fof(f1574,definition,
( spl103_4
<=> ordinal(sK91) ),
introduced(definition,[new_symbols(definition,[spl103_4])],[avatar_definition]) ).
fof(f1576,plain,
( ordinal(sK91)
| ~ spl103_4 ),
inference(avatar_component_clause,[],[f1574]) ).
fof(f1578,plain,
( spl103_3
| ~ spl103_1 ),
inference(avatar_split_clause,[],[f1556,f1561,f1569]) ).
fof(f1579,plain,
( spl103_4
| ~ spl103_1 ),
inference(avatar_split_clause,[],[f1206,f1561,f1574]) ).
fof(f1614,plain,
! [X0] :
( in(set_union2(sK91,sF101),X0)
| ~ in(sK91,X0)
| ~ ordinal(sK91)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(superposition,[],[f1420,f1553]) ).
fof(f1620,plain,
! [X0] :
( ~ in(X0,sF102)
| in(X0,sF101)
| in(X0,sK91) ),
inference(superposition,[],[f1499,f1555]) ).
fof(f1633,plain,
! [X2,X0,X1] :
( in(set_union2(X1,X2),X0)
| set_union2(X1,X2) = X0
| ~ ordinal(set_union2(X1,X2))
| ~ ordinal(X0)
| in(X0,X2)
| in(X0,X1) ),
inference(resolution,[],[f1146,f1499]) ).
fof(f1698,plain,
! [X0] :
( ~ in(X0,sF101)
| sK91 = X0 ),
inference(superposition,[],[f1486,f1553]) ).
fof(f1710,plain,
subset(sK91,sF102),
inference(superposition,[],[f1271,f1555]) ).
fof(f1712,plain,
! [X0,X1] : subset(X1,set_union2(X0,X1)),
inference(superposition,[],[f1271,f759]) ).
fof(f1714,plain,
( ~ subset(sF102,sK91)
| sK91 = sF102 ),
inference(resolution,[],[f1710,f770]) ).
fof(f1716,definition,
( spl103_7
<=> sK91 = sF102 ),
introduced(definition,[new_symbols(definition,[spl103_7])],[avatar_definition]) ).
fof(f1717,plain,
( sK91 != sF102
| spl103_7 ),
inference(avatar_component_clause,[],[f1716]) ).
fof(f1718,plain,
( sK91 = sF102
| ~ spl103_7 ),
inference(avatar_component_clause,[],[f1716]) ).
fof(f1720,definition,
( spl103_8
<=> subset(sF102,sK91) ),
introduced(definition,[new_symbols(definition,[spl103_8])],[avatar_definition]) ).
fof(f1722,plain,
( ~ subset(sF102,sK91)
| spl103_8 ),
inference(avatar_component_clause,[],[f1720]) ).
fof(f1723,plain,
( spl103_7
| ~ spl103_8 ),
inference(avatar_split_clause,[],[f1714,f1720,f1716]) ).
fof(f1751,plain,
! [X0] :
( subset(sK89(X0),X0)
| ~ epsilon_transitive(X0)
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(resolution,[],[f839,f1198]) ).
fof(f1758,plain,
! [X0] :
( in(set_union2(sK91,sF101),X0)
| ~ in(sK91,X0)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[],[f1614,f1145]) ).
fof(f1829,plain,
! [X0] :
( subset(sK89(X0),X0)
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[],[f1751,f893]) ).
fof(f1834,plain,
! [X0] :
( ~ in(sK91,X0)
| in(sF102,X0)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(forward_demodulation,[],[f1758,f1555]) ).
fof(f1865,plain,
set_difference(sK91,sF101) = set_difference(sF102,sF101),
inference(superposition,[],[f1195,f1555]) ).
fof(f1877,plain,
! [X0] :
( set_union2(sK89(X0),X0) = X0
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(resolution,[],[f1107,f1829]) ).
fof(f1881,plain,
! [X0] :
( ~ ordinal(X0)
| being_limit_ordinal(X0)
| set_union2(X0,sK89(X0)) = X0 ),
inference(forward_demodulation,[],[f1877,f759]) ).
fof(f1882,plain,
( being_limit_ordinal(sK90)
| sK90 = set_union2(sK90,sK89(sK90)) ),
inference(resolution,[],[f1881,f1200]) ).
fof(f1885,plain,
( sK90 = set_union2(sK90,sK89(sK90))
| spl103_1 ),
inference(forward_subsumption_resolution,[],[f1882,f1562]) ).
fof(f1890,plain,
( subset(sK89(sK90),sK90)
| spl103_1 ),
inference(superposition,[],[f1712,f1885]) ).
fof(f1982,plain,
in(sK91,set_union2(sK91,sF101)),
inference(superposition,[],[f1393,f1553]) ).
fof(f1984,plain,
in(sK91,sF102),
inference(forward_demodulation,[],[f1982,f1555]) ).
fof(f2001,definition,
( spl103_31
<=> in(sK91,sK91) ),
introduced(definition,[new_symbols(definition,[spl103_31])],[avatar_definition]) ).
fof(f2002,plain,
( ~ in(sK91,sK91)
| spl103_31 ),
inference(avatar_component_clause,[],[f2001]) ).
fof(f2003,plain,
( in(sK91,sK91)
| ~ spl103_31 ),
inference(avatar_component_clause,[],[f2001]) ).
fof(f2015,plain,
( sK91 = set_union2(unordered_pair(sK91,sK91),sK91)
| ~ spl103_31 ),
inference(resolution,[],[f2003,f1425]) ).
fof(f2017,plain,
( sK91 = set_union2(sK91,unordered_pair(sK91,sK91))
| ~ spl103_31 ),
inference(forward_demodulation,[],[f2015,f759]) ).
fof(f2018,plain,
( sK91 = set_union2(sK91,sF101)
| ~ spl103_31 ),
inference(forward_demodulation,[],[f2017,f1553]) ).
fof(f2020,plain,
( sK91 = sF102
| ~ spl103_31 ),
inference(superposition,[],[f1555,f2018]) ).
fof(f2026,plain,
( spl103_7
| ~ spl103_31 ),
inference(avatar_split_clause,[],[f2020,f2001,f1716]) ).
fof(f2073,plain,
! [X0] :
( ~ ordinal(X0)
| being_limit_ordinal(X0)
| set_difference(X0,unordered_pair(set_union2(sK89(X0),unordered_pair(sK89(X0),sK89(X0))),set_union2(sK89(X0),unordered_pair(sK89(X0),sK89(X0))))) = X0 ),
inference(resolution,[],[f1429,f1419]) ).
fof(f2078,plain,
! [X0] :
( set_difference(X0,unordered_pair(sK91,sK91)) = X0
| in(sF102,X0)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(resolution,[],[f1429,f1834]) ).
fof(f2079,plain,
! [X0] :
( in(sF102,X0)
| set_difference(X0,sF101) = X0
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(forward_demodulation,[],[f2078,f1553]) ).
fof(f2245,plain,
( being_limit_ordinal(sK90)
| sK90 = set_difference(sK90,unordered_pair(set_union2(sK89(sK90),unordered_pair(sK89(sK90),sK89(sK90))),set_union2(sK89(sK90),unordered_pair(sK89(sK90),sK89(sK90))))) ),
inference(resolution,[],[f2073,f1200]) ).
fof(f2246,plain,
( sK90 = set_difference(sK90,unordered_pair(set_union2(sK89(sK90),unordered_pair(sK89(sK90),sK89(sK90))),set_union2(sK89(sK90),unordered_pair(sK89(sK90),sK89(sK90)))))
| spl103_1 ),
inference(forward_subsumption_resolution,[],[f2245,f1562]) ).
fof(f2449,plain,
! [X0] :
( in(X0,union(sF102))
| ~ in(X0,sK91) ),
inference(resolution,[],[f1513,f1984]) ).
fof(f2502,definition,
( spl103_40
<=> epsilon_transitive(sK91) ),
introduced(definition,[new_symbols(definition,[spl103_40])],[avatar_definition]) ).
fof(f2503,plain,
( epsilon_transitive(sK91)
| ~ spl103_40 ),
inference(avatar_component_clause,[],[f2502]) ).
fof(f2504,plain,
( ~ epsilon_transitive(sK91)
| spl103_40 ),
inference(avatar_component_clause,[],[f2502]) ).
fof(f2567,plain,
( sF102 = set_difference(sF102,sF101)
| ~ being_limit_ordinal(sF102)
| ~ ordinal(sF102)
| in(sF102,sF101)
| in(sF102,sK91) ),
inference(resolution,[],[f2079,f1620]) ).
fof(f2635,plain,
( ~ subset(sK90,sK89(sK90))
| sK90 = sK89(sK90)
| spl103_1 ),
inference(resolution,[],[f1890,f770]) ).
fof(f2647,definition,
( spl103_49
<=> sK90 = sK89(sK90) ),
introduced(definition,[new_symbols(definition,[spl103_49])],[avatar_definition]) ).
fof(f2648,plain,
( sK90 != sK89(sK90)
| spl103_49 ),
inference(avatar_component_clause,[],[f2647]) ).
fof(f2649,plain,
( sK90 = sK89(sK90)
| ~ spl103_49 ),
inference(avatar_component_clause,[],[f2647]) ).
fof(f2651,definition,
( spl103_50
<=> subset(sK90,sK89(sK90)) ),
introduced(definition,[new_symbols(definition,[spl103_50])],[avatar_definition]) ).
fof(f2653,plain,
( ~ subset(sK90,sK89(sK90))
| spl103_50 ),
inference(avatar_component_clause,[],[f2651]) ).
fof(f2654,plain,
( spl103_49
| ~ spl103_50
| spl103_1 ),
inference(avatar_split_clause,[],[f2635,f1561,f2651,f2647]) ).
fof(f2660,definition,
( spl103_52
<=> ordinal(sK89(sK90)) ),
introduced(definition,[new_symbols(definition,[spl103_52])],[avatar_definition]) ).
fof(f2661,plain,
( ordinal(sK89(sK90))
| ~ spl103_52 ),
inference(avatar_component_clause,[],[f2660]) ).
fof(f2662,plain,
( ~ ordinal(sK89(sK90))
| spl103_52 ),
inference(avatar_component_clause,[],[f2660]) ).
fof(f2670,plain,
( being_limit_ordinal(sK90)
| ~ ordinal(sK90)
| spl103_52 ),
inference(resolution,[],[f2662,f1197]) ).
fof(f2671,plain,
( ~ ordinal(sK90)
| spl103_1
| spl103_52 ),
inference(forward_subsumption_resolution,[],[f2670,f1562]) ).
fof(f2672,plain,
( $false
| spl103_1
| spl103_52 ),
inference(forward_subsumption_resolution,[],[f2671,f1200]) ).
fof(f2673,plain,
( spl103_1
| spl103_52 ),
inference(avatar_contradiction_clause,[],[f2672]) ).
fof(f2683,plain,
( in(sK90,sK90)
| being_limit_ordinal(sK90)
| ~ ordinal(sK90)
| ~ spl103_49 ),
inference(superposition,[],[f1198,f2649]) ).
fof(f2684,plain,
( in(sK90,sK90)
| ~ ordinal(sK90)
| spl103_1
| ~ spl103_49 ),
inference(forward_subsumption_resolution,[],[f2683,f1562]) ).
fof(f2686,plain,
( in(sK90,sK90)
| spl103_1
| ~ spl103_49 ),
inference(forward_subsumption_resolution,[],[f2684,f1200]) ).
fof(f2691,plain,
( sK90 = set_union2(unordered_pair(sK90,sK90),sK90)
| spl103_1
| ~ spl103_49 ),
inference(resolution,[],[f2686,f1425]) ).
fof(f2693,plain,
( sK90 = set_union2(sK90,unordered_pair(sK90,sK90))
| spl103_1
| ~ spl103_49 ),
inference(forward_demodulation,[],[f2691,f759]) ).
fof(f3501,plain,
( ! [X0] :
( ~ in(X0,unordered_pair(set_union2(sK89(sK90),unordered_pair(sK89(sK90),sK89(sK90))),set_union2(sK89(sK90),unordered_pair(sK89(sK90),sK89(sK90)))))
| ~ in(X0,sK90) )
| spl103_1 ),
inference(superposition,[],[f1518,f2246]) ).
fof(f3504,plain,
( ! [X0] :
( ~ in(X0,unordered_pair(set_union2(sK90,unordered_pair(sK90,sK90)),set_union2(sK90,unordered_pair(sK90,sK90))))
| ~ in(X0,sK90) )
| spl103_1
| ~ spl103_49 ),
inference(forward_demodulation,[],[f3501,f2649]) ).
fof(f3508,plain,
( ! [X0] :
( ~ in(X0,unordered_pair(sK90,sK90))
| ~ in(X0,sK90) )
| spl103_1
| ~ spl103_49 ),
inference(forward_demodulation,[],[f3504,f2693]) ).
fof(f3509,plain,
( ~ in(sK90,sK90)
| spl103_1
| ~ spl103_49 ),
inference(resolution,[],[f3508,f1493]) ).
fof(f3564,plain,
( $false
| spl103_1
| ~ spl103_49 ),
inference(forward_subsumption_resolution,[],[f3509,f2686]) ).
fof(f3565,plain,
( spl103_1
| ~ spl103_49 ),
inference(avatar_contradiction_clause,[],[f3564]) ).
fof(f3586,definition,
( spl103_80
<=> epsilon_transitive(sK89(sK90)) ),
introduced(definition,[new_symbols(definition,[spl103_80])],[avatar_definition]) ).
fof(f3587,plain,
( ~ epsilon_transitive(sK89(sK90))
| spl103_80 ),
inference(avatar_component_clause,[],[f3586]) ).
fof(f3588,plain,
( epsilon_transitive(sK89(sK90))
| ~ spl103_80 ),
inference(avatar_component_clause,[],[f3586]) ).
fof(f3651,plain,
( epsilon_transitive(sK89(sK90))
| ~ spl103_52 ),
inference(resolution,[],[f2661,f893]) ).
fof(f3924,plain,
( sK90 != sK90
| ~ in(set_union2(sK89(sK90),unordered_pair(sK89(sK90),sK89(sK90))),sK90)
| spl103_1 ),
inference(superposition,[],[f1430,f2246]) ).
fof(f3925,plain,
( ~ in(set_union2(sK89(sK90),unordered_pair(sK89(sK90),sK89(sK90))),sK90)
| spl103_1 ),
inference(trivial_inequality_removal,[],[f3924]) ).
fof(f3935,definition,
( spl103_92
<=> ordinal(set_union2(sK89(sK90),unordered_pair(sK89(sK90),sK89(sK90)))) ),
introduced(definition,[new_symbols(definition,[spl103_92])],[avatar_definition]) ).
fof(f3936,plain,
( ordinal(set_union2(sK89(sK90),unordered_pair(sK89(sK90),sK89(sK90))))
| ~ spl103_92 ),
inference(avatar_component_clause,[],[f3935]) ).
fof(f3937,plain,
( ~ ordinal(set_union2(sK89(sK90),unordered_pair(sK89(sK90),sK89(sK90))))
| spl103_92 ),
inference(avatar_component_clause,[],[f3935]) ).
fof(f3939,definition,
( spl103_93
<=> sK90 = set_union2(sK89(sK90),unordered_pair(sK89(sK90),sK89(sK90))) ),
introduced(definition,[new_symbols(definition,[spl103_93])],[avatar_definition]) ).
fof(f3941,plain,
( sK90 = set_union2(sK89(sK90),unordered_pair(sK89(sK90),sK89(sK90)))
| ~ spl103_93 ),
inference(avatar_component_clause,[],[f3939]) ).
fof(f3948,plain,
( ~ ordinal(sK89(sK90))
| spl103_92 ),
inference(resolution,[],[f3937,f1375]) ).
fof(f3949,plain,
( $false
| ~ spl103_52
| spl103_92 ),
inference(forward_subsumption_resolution,[],[f3948,f2661]) ).
fof(f3950,plain,
( ~ spl103_52
| spl103_92 ),
inference(avatar_contradiction_clause,[],[f3949]) ).
fof(f4594,plain,
( sK90 = set_union2(sK89(sK90),unordered_pair(sK89(sK90),sK89(sK90)))
| ~ ordinal(set_union2(sK89(sK90),unordered_pair(sK89(sK90),sK89(sK90))))
| ~ ordinal(sK90)
| in(sK90,unordered_pair(sK89(sK90),sK89(sK90)))
| in(sK90,sK89(sK90))
| spl103_1 ),
inference(resolution,[],[f1633,f3925]) ).
fof(f4640,plain,
( sK90 = set_union2(sK89(sK90),unordered_pair(sK89(sK90),sK89(sK90)))
| ~ ordinal(sK90)
| in(sK90,unordered_pair(sK89(sK90),sK89(sK90)))
| in(sK90,sK89(sK90))
| spl103_1
| ~ spl103_92 ),
inference(forward_subsumption_resolution,[],[f4594,f3936]) ).
fof(f4642,plain,
( sK90 = set_union2(sK89(sK90),unordered_pair(sK89(sK90),sK89(sK90)))
| in(sK90,unordered_pair(sK89(sK90),sK89(sK90)))
| in(sK90,sK89(sK90))
| spl103_1
| ~ spl103_92 ),
inference(forward_subsumption_resolution,[],[f4640,f1200]) ).
fof(f4644,definition,
( spl103_121
<=> in(sK90,sK89(sK90)) ),
introduced(definition,[new_symbols(definition,[spl103_121])],[avatar_definition]) ).
fof(f4646,plain,
( in(sK90,sK89(sK90))
| ~ spl103_121 ),
inference(avatar_component_clause,[],[f4644]) ).
fof(f4648,definition,
( spl103_122
<=> in(sK90,unordered_pair(sK89(sK90),sK89(sK90))) ),
introduced(definition,[new_symbols(definition,[spl103_122])],[avatar_definition]) ).
fof(f4650,plain,
( in(sK90,unordered_pair(sK89(sK90),sK89(sK90)))
| ~ spl103_122 ),
inference(avatar_component_clause,[],[f4648]) ).
fof(f4651,plain,
( spl103_121
| spl103_122
| spl103_93
| spl103_1
| ~ spl103_92 ),
inference(avatar_split_clause,[],[f4642,f3935,f1561,f3939,f4648,f4644]) ).
fof(f4661,plain,
( sK90 != sK90
| ~ ordinal(sK89(sK90))
| ~ spl103_2
| ~ spl103_93 ),
inference(superposition,[],[f1566,f3941]) ).
fof(f4678,plain,
( ~ ordinal(sK89(sK90))
| ~ spl103_2
| ~ spl103_93 ),
inference(trivial_inequality_removal,[],[f4661]) ).
fof(f4690,plain,
( $false
| ~ spl103_2
| ~ spl103_52
| ~ spl103_93 ),
inference(forward_subsumption_resolution,[],[f4678,f2661]) ).
fof(f4691,plain,
( ~ spl103_2
| ~ spl103_52
| ~ spl103_93 ),
inference(avatar_contradiction_clause,[],[f4690]) ).
fof(f4701,plain,
( subset(sK90,sK89(sK90))
| ~ epsilon_transitive(sK89(sK90))
| ~ spl103_121 ),
inference(resolution,[],[f4646,f839]) ).
fof(f4711,plain,
( ~ epsilon_transitive(sK89(sK90))
| spl103_50
| ~ spl103_121 ),
inference(forward_subsumption_resolution,[],[f4701,f2653]) ).
fof(f4712,plain,
( $false
| spl103_50
| ~ spl103_80
| ~ spl103_121 ),
inference(forward_subsumption_resolution,[],[f4711,f3588]) ).
fof(f4713,plain,
( spl103_50
| ~ spl103_80
| ~ spl103_121 ),
inference(avatar_contradiction_clause,[],[f4712]) ).
fof(f4714,plain,
( $false
| ~ spl103_52
| spl103_80 ),
inference(forward_subsumption_resolution,[],[f3651,f3587]) ).
fof(f4715,plain,
( ~ spl103_52
| spl103_80 ),
inference(avatar_contradiction_clause,[],[f4714]) ).
fof(f4738,plain,
( sK90 = sK89(sK90)
| ~ spl103_122 ),
inference(resolution,[],[f4650,f1486]) ).
fof(f4757,plain,
( $false
| spl103_49
| ~ spl103_122 ),
inference(forward_subsumption_resolution,[],[f4738,f2648]) ).
fof(f4758,plain,
( spl103_49
| ~ spl103_122 ),
inference(avatar_contradiction_clause,[],[f4757]) ).
fof(f4769,plain,
( sF102 = set_difference(sK91,sF101)
| ~ being_limit_ordinal(sF102)
| ~ ordinal(sF102)
| in(sF102,sF101)
| in(sF102,sK91) ),
inference(forward_demodulation,[],[f2567,f1865]) ).
fof(f4907,plain,
( sK90 = sK91
| ~ spl103_3
| ~ spl103_7 ),
inference(superposition,[],[f1718,f1571]) ).
fof(f4912,plain,
( in(sK91,sK90)
| ~ spl103_3 ),
inference(superposition,[],[f1984,f1571]) ).
fof(f4916,plain,
( ! [X0] :
( in(X0,union(sK90))
| ~ in(X0,sK91) )
| ~ spl103_3 ),
inference(superposition,[],[f2449,f1571]) ).
fof(f4954,plain,
( epsilon_transitive(sK91)
| ~ spl103_4 ),
inference(resolution,[],[f1576,f893]) ).
fof(f4969,plain,
( sK90 = union(sK90)
| ~ spl103_1 ),
inference(resolution,[],[f1563,f924]) ).
fof(f4971,plain,
( in(sF102,sK90)
| ~ being_limit_ordinal(sK90)
| ~ ordinal(sK90)
| ~ spl103_3 ),
inference(resolution,[],[f4912,f1834]) ).
fof(f4983,plain,
( in(sF102,sK90)
| ~ ordinal(sK90)
| ~ spl103_1
| ~ spl103_3 ),
inference(forward_subsumption_resolution,[],[f4971,f1563]) ).
fof(f4987,plain,
( in(sF102,sK90)
| ~ spl103_1
| ~ spl103_3 ),
inference(forward_subsumption_resolution,[],[f4983,f1200]) ).
fof(f5001,plain,
( ! [X0,X1] :
( ~ in(X0,sK91)
| ~ in(X1,X0)
| in(X1,union(union(sK90))) )
| ~ spl103_3 ),
inference(resolution,[],[f4916,f1513]) ).
fof(f6596,plain,
( sK90 != sK91
| ~ spl103_3
| spl103_7 ),
inference(forward_demodulation,[],[f1717,f1571]) ).
fof(f6597,plain,
( ~ subset(sK90,sK91)
| ~ spl103_3
| spl103_8 ),
inference(forward_demodulation,[],[f1722,f1571]) ).
fof(f6679,plain,
( in(sK90,sK90)
| ~ spl103_1
| ~ spl103_3 ),
inference(forward_demodulation,[],[f4987,f1571]) ).
fof(f7597,plain,
( sK91 = set_difference(sK91,unordered_pair(sK91,sK91))
| spl103_31 ),
inference(resolution,[],[f2002,f1429]) ).
fof(f7599,plain,
( sK91 = set_difference(sK91,sF101)
| spl103_31 ),
inference(forward_demodulation,[],[f7597,f1553]) ).
fof(f7705,plain,
( ! [X0,X1] :
( in(X1,union(sK90))
| ~ in(X0,sK91)
| ~ in(X1,X0) )
| ~ spl103_1
| ~ spl103_3 ),
inference(forward_demodulation,[],[f5001,f4969]) ).
fof(f7821,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,sK91)
| in(X1,sK90) )
| ~ spl103_1
| ~ spl103_3 ),
inference(forward_demodulation,[],[f7705,f4969]) ).
fof(f7979,plain,
( sK91 = sF102
| ~ being_limit_ordinal(sF102)
| ~ ordinal(sF102)
| in(sF102,sF101)
| in(sF102,sK91)
| spl103_31 ),
inference(forward_demodulation,[],[f4769,f7599]) ).
fof(f7996,plain,
( sK91 = sF102
| ~ being_limit_ordinal(sF102)
| ~ ordinal(sF102)
| in(sF102,sK91)
| spl103_31 ),
inference(forward_subsumption_resolution,[],[f7979,f1698]) ).
fof(f8005,definition,
( spl103_171
<=> in(sK90,sK91) ),
introduced(definition,[new_symbols(definition,[spl103_171])],[avatar_definition]) ).
fof(f8007,plain,
( in(sK90,sK91)
| ~ spl103_171 ),
inference(avatar_component_clause,[],[f8005]) ).
fof(f8013,plain,
( sK90 = sK91
| ~ being_limit_ordinal(sF102)
| ~ ordinal(sF102)
| in(sF102,sK91)
| ~ spl103_3
| spl103_31 ),
inference(forward_demodulation,[],[f7996,f1571]) ).
fof(f8017,plain,
( ~ being_limit_ordinal(sF102)
| ~ ordinal(sF102)
| in(sF102,sK91)
| ~ spl103_3
| spl103_7
| spl103_31 ),
inference(forward_subsumption_resolution,[],[f8013,f6596]) ).
fof(f8019,plain,
( ~ being_limit_ordinal(sK90)
| ~ ordinal(sF102)
| in(sF102,sK91)
| ~ spl103_3
| spl103_7
| spl103_31 ),
inference(forward_demodulation,[],[f8017,f1571]) ).
fof(f8021,plain,
( ~ ordinal(sF102)
| in(sF102,sK91)
| ~ spl103_1
| ~ spl103_3
| spl103_7
| spl103_31 ),
inference(forward_subsumption_resolution,[],[f8019,f1563]) ).
fof(f8023,plain,
( ~ ordinal(sK90)
| in(sF102,sK91)
| ~ spl103_1
| ~ spl103_3
| spl103_7
| spl103_31 ),
inference(forward_demodulation,[],[f8021,f1571]) ).
fof(f8025,plain,
( in(sF102,sK91)
| ~ spl103_1
| ~ spl103_3
| spl103_7
| spl103_31 ),
inference(forward_subsumption_resolution,[],[f8023,f1200]) ).
fof(f8026,plain,
( in(sK90,sK91)
| ~ spl103_1
| ~ spl103_3
| spl103_7
| spl103_31 ),
inference(forward_demodulation,[],[f8025,f1571]) ).
fof(f8027,plain,
( spl103_171
| ~ spl103_1
| ~ spl103_3
| spl103_7
| spl103_31 ),
inference(avatar_split_clause,[],[f8026,f2001,f1716,f1569,f1561,f8005]) ).
fof(f8379,plain,
( subset(sK90,sK91)
| ~ epsilon_transitive(sK91)
| ~ spl103_171 ),
inference(resolution,[],[f8007,f839]) ).
fof(f8390,plain,
( ~ epsilon_transitive(sK91)
| ~ spl103_3
| spl103_8
| ~ spl103_171 ),
inference(forward_subsumption_resolution,[],[f8379,f6597]) ).
fof(f8392,plain,
( $false
| ~ spl103_3
| spl103_8
| ~ spl103_40
| ~ spl103_171 ),
inference(forward_subsumption_resolution,[],[f8390,f2503]) ).
fof(f8393,plain,
( ~ spl103_3
| spl103_8
| ~ spl103_40
| ~ spl103_171 ),
inference(avatar_contradiction_clause,[],[f8392]) ).
fof(f8395,plain,
( $false
| ~ spl103_4
| spl103_40 ),
inference(forward_subsumption_resolution,[],[f4954,f2504]) ).
fof(f8396,plain,
( ~ spl103_4
| spl103_40 ),
inference(avatar_contradiction_clause,[],[f8395]) ).
fof(f9654,plain,
( ~ in(sK90,sK91)
| in(sK91,sK90)
| ~ spl103_1
| ~ spl103_3 ),
inference(resolution,[],[f7821,f4912]) ).
fof(f9667,plain,
( ~ in(sK90,sK91)
| ~ spl103_1
| ~ spl103_3 ),
inference(forward_subsumption_resolution,[],[f9654,f745]) ).
fof(f9709,plain,
( ~ in(sK90,sK90)
| ~ spl103_1
| ~ spl103_3
| ~ spl103_7 ),
inference(forward_demodulation,[],[f9667,f4907]) ).
fof(f9790,plain,
( $false
| ~ spl103_1
| ~ spl103_3
| ~ spl103_7 ),
inference(forward_subsumption_resolution,[],[f9709,f6679]) ).
fof(f9791,plain,
( ~ spl103_1
| ~ spl103_3
| ~ spl103_7 ),
inference(avatar_contradiction_clause,[],[f9790]) ).
cnf(s1,plain,
( spl103_1
| spl103_2 ),
inference(sat_conversion,[],[f1567]) ).
cnf(s4,plain,
( ~ spl103_1
| spl103_3 ),
inference(sat_conversion,[],[f1578]) ).
cnf(s5,plain,
( ~ spl103_1
| spl103_4 ),
inference(sat_conversion,[],[f1579]) ).
cnf(s7,plain,
( spl103_7
| ~ spl103_8 ),
inference(sat_conversion,[],[f1723]) ).
cnf(s30,plain,
( spl103_7
| ~ spl103_31 ),
inference(sat_conversion,[],[f2026]) ).
cnf(s43,plain,
( spl103_1
| spl103_49
| ~ spl103_50 ),
inference(sat_conversion,[],[f2654]) ).
cnf(s46,plain,
( spl103_1
| spl103_52 ),
inference(sat_conversion,[],[f2673]) ).
cnf(s71,plain,
( spl103_1
| ~ spl103_49 ),
inference(sat_conversion,[],[f3565]) ).
cnf(s87,plain,
( ~ spl103_52
| spl103_92 ),
inference(sat_conversion,[],[f3950]) ).
cnf(s107,plain,
( spl103_1
| ~ spl103_92
| spl103_93
| spl103_121
| spl103_122 ),
inference(sat_conversion,[],[f4651]) ).
cnf(s109,plain,
( ~ spl103_2
| ~ spl103_52
| ~ spl103_93 ),
inference(sat_conversion,[],[f4691]) ).
cnf(s112,plain,
( spl103_50
| ~ spl103_80
| ~ spl103_121 ),
inference(sat_conversion,[],[f4713]) ).
cnf(s113,plain,
( ~ spl103_52
| spl103_80 ),
inference(sat_conversion,[],[f4715]) ).
cnf(s118,plain,
( spl103_49
| ~ spl103_122 ),
inference(sat_conversion,[],[f4758]) ).
cnf(s209,plain,
( ~ spl103_1
| ~ spl103_3
| spl103_7
| spl103_31
| spl103_171 ),
inference(sat_conversion,[],[f8027]) ).
cnf(s221,plain,
( ~ spl103_3
| spl103_8
| ~ spl103_40
| ~ spl103_171 ),
inference(sat_conversion,[],[f8393]) ).
cnf(s222,plain,
( ~ spl103_4
| spl103_40 ),
inference(sat_conversion,[],[f8396]) ).
cnf(s252,plain,
( ~ spl103_1
| ~ spl103_3
| ~ spl103_7 ),
inference(sat_conversion,[],[f9791]) ).
cnf(s255,plain,
spl103_1,
inference(rat,[],[s107,s112,s109,s87,s113,s43,s118,s1,s46,s71]) ).
cnf(s256,plain,
spl103_4,
inference(rat,[],[s5,s255]) ).
cnf(s257,plain,
spl103_3,
inference(rat,[],[s4,s255]) ).
cnf(s258,plain,
spl103_40,
inference(rat,[],[s222,s256]) ).
cnf(s262,plain,
~ spl103_7,
inference(rat,[],[s252,s255,s257]) ).
cnf(s266,plain,
~ spl103_31,
inference(rat,[],[s30,s262]) ).
cnf(s267,plain,
~ spl103_8,
inference(rat,[],[s7,s262]) ).
cnf(s269,plain,
spl103_171,
inference(rat,[],[s209,s262,s257,s255,s266]) ).
cnf(s271,plain,
$false,
inference(rat,[],[s221,s257,s258,s267,s269]) ).
fof(f9810,plain,
$false,
inference(avatar_sat_refutation,[],[s271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU238+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 04:16:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 12.10/2.33 % (4017730)Detected formulas, will run a generic FOF schedule.
% 12.10/2.33 % (4017740)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=569305831:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 12.10/2.33 % (4017735)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=2590605283:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 12.10/2.33 % (4017738)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3842270079:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 12.10/2.33 % (4017739)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=43169680:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 12.10/2.33 % (4017737)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=4168125638:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 12.10/2.33 % (4017736)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=1092787893:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 12.10/2.33 % (4017741)dis-21_1_sil=8000:lcm=predicate:random_seed=1821336340: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)
% 12.10/2.33 % (4017740)Instruction limit reached!
% 12.10/2.33 % (4017740)------------------------------
% 12.10/2.33 % (4017740)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.10/2.33 % (4017740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.10/2.33 % (4017740)CaDiCaL version: 2.1.3
% 12.10/2.33 % (4017740)Termination reason: Instruction limit
% 12.10/2.33 % (4017740)Termination phase: Saturation
% 12.10/2.33 % (4017740)Time elapsed: 0.052 s
% 12.10/2.33 % (4017740)Peak memory usage: 90 MB
% 12.10/2.33 % (4017740)Instructions burned: 139 (million)
% 12.10/2.33 % (4017738)Instruction limit reached!
% 12.10/2.33 % (4017738)------------------------------
% 12.10/2.33 % (4017738)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.10/2.33 % (4017738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.10/2.33 % (4017738)CaDiCaL version: 2.1.3
% 12.10/2.33 % (4017738)Termination reason: Instruction limit
% 12.10/2.33 % (4017738)Termination phase: Saturation
% 12.10/2.33 % (4017738)Time elapsed: 0.069 s
% 12.10/2.33 % (4017738)Peak memory usage: 90 MB
% 12.10/2.33 % (4017738)Instructions burned: 110 (million)
% 12.10/2.33 % (4017741)Instruction limit reached!
% 12.10/2.33 % (4017741)------------------------------
% 12.10/2.33 % (4017741)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.10/2.33 % (4017741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.10/2.33 % (4017741)CaDiCaL version: 2.1.3
% 12.10/2.33 % (4017741)Termination reason: Instruction limit
% 12.10/2.33 % (4017741)Termination phase: Saturation
% 12.10/2.33 % (4017741)Time elapsed: 0.073 s
% 12.10/2.33 % (4017741)Peak memory usage: 90 MB
% 12.10/2.33 % (4017741)Instructions burned: 130 (million)
% 12.10/2.33 % (4017739)Instruction limit reached!
% 12.10/2.33 % (4017739)------------------------------
% 12.10/2.33 % (4017739)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.10/2.33 % (4017739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.10/2.33 % (4017739)CaDiCaL version: 2.1.3
% 12.10/2.33 % (4017739)Termination reason: Instruction limit
% 12.10/2.33 % (4017739)Termination phase: Saturation
% 12.10/2.33 % (4017739)Time elapsed: 0.079 s
% 12.10/2.33 % (4017739)Peak memory usage: 89 MB
% 12.10/2.33 % (4017739)Instructions burned: 119 (million)
% 12.10/2.33 % (4017749)lrs+10_1_sil=8000:sp=occurrence:random_seed=899915887:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 12.10/2.33 % (4017750)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3744900199:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 12.10/2.33 % (4017751)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3601270256:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 12.10/2.33 % (4017752)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=1482413630:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 12.10/2.33 % (4017749)Instruction limit reached!
% 12.10/2.33 % (4017749)------------------------------
% 12.10/2.33 % (4017749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.10/2.33 % (4017749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.10/2.33 % (4017749)CaDiCaL version: 2.1.3
% 12.10/2.33 % (4017749)Termination reason: Instruction limit
% 12.10/2.33 % (4017749)Termination phase: Saturation
% 12.10/2.33 % (4017749)Time elapsed: 0.102 s
% 12.10/2.33 % (4017749)Peak memory usage: 93 MB
% 12.10/2.33 % (4017749)Instructions burned: 287 (million)
% 12.10/2.33 % (4017750)Instruction limit reached!
% 12.10/2.33 % (4017750)------------------------------
% 12.10/2.33 % (4017750)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.10/2.33 % (4017750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.10/2.33 % (4017750)CaDiCaL version: 2.1.3
% 12.10/2.33 % (4017750)Termination reason: Instruction limit
% 12.10/2.33 % (4017750)Termination phase: Saturation
% 12.10/2.33 % (4017750)Time elapsed: 0.077 s
% 12.10/2.33 % (4017750)Peak memory usage: 93 MB
% 12.10/2.33 % (4017750)Instructions burned: 157 (million)
% 12.10/2.33 % (4017757)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=345257352:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 12.10/2.33 % (4017752)Instruction limit reached!
% 12.10/2.33 % (4017752)------------------------------
% 12.10/2.33 % (4017752)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.10/2.33 % (4017752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.10/2.33 % (4017752)CaDiCaL version: 2.1.3
% 12.10/2.33 % (4017752)Termination reason: Instruction limit
% 12.10/2.33 % (4017752)Termination phase: Saturation
% 12.10/2.33 % (4017752)Time elapsed: 0.146 s
% 12.10/2.33 % (4017752)Peak memory usage: 93 MB
% 12.10/2.33 % (4017752)Instructions burned: 250 (million)
% 12.10/2.33 % (4017758)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1315030759:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 12.10/2.33 % (4017751)Instruction limit reached!
% 12.10/2.33 % (4017751)------------------------------
% 12.10/2.33 % (4017751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.10/2.33 % (4017751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.10/2.33 % (4017751)CaDiCaL version: 2.1.3
% 12.10/2.33 % (4017751)Termination reason: Instruction limit
% 12.10/2.33 % (4017751)Termination phase: Saturation
% 12.10/2.33 % (4017751)Time elapsed: 0.222 s
% 12.10/2.33 % (4017751)Peak memory usage: 92 MB
% 12.10/2.33 % (4017751)Instructions burned: 327 (million)
% 12.10/2.33 % (4017757)Instruction limit reached!
% 12.10/2.33 % (4017757)------------------------------
% 12.10/2.33 % (4017757)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.10/2.33 % (4017757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.10/2.33 % (4017757)CaDiCaL version: 2.1.3
% 12.10/2.33 % (4017757)Termination reason: Instruction limit
% 12.10/2.33 % (4017757)Termination phase: Saturation
% 12.10/2.33 % (4017757)Time elapsed: 0.101 s
% 12.10/2.33 % (4017757)Peak memory usage: 91 MB
% 12.10/2.33 % (4017757)Instructions burned: 294 (million)
% 12.10/2.33 % (4017760)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2894981148:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 12.10/2.33 % (4017762)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3360044060:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 12.10/2.33 % (4017762)Instruction limit reached!
% 12.10/2.33 % (4017762)------------------------------
% 12.10/2.33 % (4017762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.10/2.33 % (4017762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.10/2.33 % (4017762)CaDiCaL version: 2.1.3
% 12.10/2.33 % (4017762)Termination reason: Instruction limit
% 12.10/2.33 % (4017762)Termination phase: Saturation
% 12.10/2.33 % (4017762)Time elapsed: 0.037 s
% 12.10/2.33 % (4017762)Peak memory usage: 90 MB
% 12.10/2.33 % (4017762)Instructions burned: 127 (million)
% 12.10/2.33 % (4017763)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=786487689:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 12.10/2.33 % (4017760)Instruction limit reached!
% 12.10/2.33 % (4017760)------------------------------
% 12.10/2.33 % (4017760)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.10/2.33 % (4017760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.10/2.33 % (4017760)CaDiCaL version: 2.1.3
% 12.10/2.33 % (4017760)Termination reason: Instruction limit
% 12.10/2.33 % (4017760)Termination phase: Saturation
% 12.10/2.33 % (4017760)Time elapsed: 0.070 s
% 12.10/2.33 % (4017760)Peak memory usage: 90 MB
% 12.10/2.33 % (4017760)Instructions burned: 114 (million)
% 12.10/2.33 % (4017763)Instruction limit reached!
% 12.10/2.33 % (4017763)------------------------------
% 12.10/2.33 % (4017763)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.10/2.33 % (4017763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.10/2.33 % (4017763)CaDiCaL version: 2.1.3
% 12.10/2.33 % (4017763)Termination reason: Instruction limit
% 12.10/2.33 % (4017763)Termination phase: Saturation
% 12.10/2.33 % (4017763)Time elapsed: 0.068 s
% 12.10/2.33 % (4017763)Peak memory usage: 89 MB
% 12.10/2.33 % (4017763)Instructions burned: 115 (million)
% 12.10/2.33 % (4017766)lrs+10_1_sil=8000:sp=occurrence:random_seed=2482344830:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2993 on theBenchmark for (2993ds/907Mi)
% 12.10/2.33 % (4017768)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=420219138:i=437:sd=1:aac=none:ss=included_2993 on theBenchmark for (2993ds/437Mi)
% 12.10/2.33 % (4017770)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2682702231:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 12.10/2.33 % (4017766)Instruction limit reached!
% 12.10/2.33 % (4017766)------------------------------
% 12.10/2.33 % (4017766)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.10/2.33 % (4017766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.10/2.33 % (4017766)CaDiCaL version: 2.1.3
% 12.10/2.33 % (4017766)Termination reason: Instruction limit
% 12.10/2.33 % (4017766)Termination phase: Saturation
% 12.10/2.33 % (4017766)Time elapsed: 0.302 s
% 12.10/2.33 % (4017766)Peak memory usage: 100 MB
% 12.10/2.33 % (4017766)Instructions burned: 908 (million)
% 12.10/2.33 % (4017768)Instruction limit reached!
% 12.10/2.33 % (4017768)------------------------------
% 12.10/2.33 % (4017768)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.10/2.33 % (4017768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.10/2.33 % (4017768)CaDiCaL version: 2.1.3
% 12.10/2.33 % (4017768)Termination reason: Instruction limit
% 12.10/2.33 % (4017768)Termination phase: Saturation
% 12.10/2.33 % (4017768)Time elapsed: 0.269 s
% 12.10/2.33 % (4017768)Peak memory usage: 93 MB
% 12.10/2.33 % (4017768)Instructions burned: 437 (million)
% 12.10/2.33 % (4017773)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3838878889:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2989 on theBenchmark for (2989ds/134Mi)
% 12.10/2.33 % (4017773)Instruction limit reached!
% 12.10/2.33 % (4017773)------------------------------
% 12.10/2.33 % (4017773)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.10/2.33 % (4017773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.10/2.33 % (4017773)CaDiCaL version: 2.1.3
% 12.10/2.33 % (4017773)Termination reason: Instruction limit
% 12.10/2.33 % (4017773)Termination phase: Saturation
% 12.10/2.33 % (4017773)Time elapsed: 0.044 s
% 12.10/2.33 % (4017773)Peak memory usage: 92 MB
% 12.10/2.33 % (4017773)Instructions burned: 135 (million)
% 12.10/2.33 % (4017774)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3214252099:st=8:i=592:sd=3:ep=RST:ss=axioms_2989 on theBenchmark for (2989ds/592Mi)
% 12.10/2.33 % (4017776)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=1308821207:st=3:i=13193:sd=3:ss=axioms_2988 on theBenchmark for (2988ds/13193Mi)
% 12.10/2.33 % (4017758)First to succeed.
% 12.10/2.33 % (4017758)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4017730"
% 12.10/2.33 % (4017774)Instruction limit reached!
% 12.10/2.33 % (4017774)------------------------------
% 12.10/2.33 % (4017774)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.10/2.33 % (4017774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.10/2.33 % (4017774)CaDiCaL version: 2.1.3
% 12.10/2.33 % (4017774)Termination reason: Instruction limit
% 12.10/2.33 % (4017774)Termination phase: Saturation
% 12.10/2.33 % (4017774)Time elapsed: 0.377 s
% 12.10/2.33 % (4017774)Peak memory usage: 97 MB
% 12.10/2.33 % (4017774)Instructions burned: 593 (million)
% 12.10/2.33 % (4017758)Refutation found. Thanks to Tanya!
% 12.10/2.33 % SZS status Theorem for theBenchmark
% 12.10/2.33 % SZS output start Proof for theBenchmark
% See solution above
% 12.53/2.52 % (4017758)------------------------------
% 12.53/2.52 % (4017758)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.53/2.52 % (4017758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.53/2.52 % (4017758)CaDiCaL version: 2.1.3
% 12.53/2.52 % (4017758)Termination reason: Refutation
% 12.53/2.52 % (4017758)Time elapsed: 1.028 s
% 12.53/2.52 % (4017758)Peak memory usage: 140 MB
% 12.53/2.52 % (4017758)Instructions burned: 2043 (million)
% 12.53/2.52 % (4017758)------------------------------
% 12.53/2.52 % (4017758)------------------------------
% 12.53/2.52 % (4017730)Success in time 1.728 s
% 12.53/2.52 % Vampire exiting
%------------------------------------------------------------------------------