%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU099+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 12:47:14 PM UTC 2026
% Result : Theorem 5.93s 1.79s
% Output : Refutation 7.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 33
% Syntax : Number of formulae : 221 ( 22 unt; 19 def)
% Number of atoms : 856 ( 110 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 1081 ( 446 ~; 470 |; 125 &)
% ( 27 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 19 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 2 con; 0-3 aty)
% Number of variables : 283 ( 1 sgn 244 !; 39 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f14,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f15,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f16,axiom,
! [X0] :
( inclusion_linear(X0)
<=> ! [X1,X2] :
( ( in(X1,X0)
& in(X2,X0) )
=> inclusion_comparable(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_ordinal1) ).
fof(f17,axiom,
! [X0,X1] :
( inclusion_comparable(X0,X1)
<=> ( subset(X0,X1)
| subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_xboole_0) ).
fof(f58,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f60,axiom,
! [X0] :
( ( finite(X0)
& ~ ( empty_set != empty_set
& ! [X1] :
~ ( in(X1,empty_set)
& ! [X2] :
( in(X2,empty_set)
=> subset(X1,X2) ) ) )
& ! [X3,X4] :
( ( in(X3,X0)
& subset(X4,X0)
& ~ ( X4 != empty_set
& ! [X5] :
~ ( in(X5,X4)
& ! [X6] :
( in(X6,X4)
=> subset(X5,X6) ) ) ) )
=> ~ ( set_union2(X4,singleton(X3)) != empty_set
& ! [X7] :
~ ( in(X7,set_union2(X4,singleton(X3)))
& ! [X8] :
( in(X8,set_union2(X4,singleton(X3)))
=> subset(X7,X8) ) ) ) ) )
=> ~ ( X0 != empty_set
& ! [X9] :
~ ( in(X9,X0)
& ! [X10] :
( in(X10,X0)
=> subset(X9,X10) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_finset_1__e6_46__finset_1) ).
fof(f62,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
fof(f64,axiom,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X1,X2) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f65,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f66,conjecture,
! [X0] :
~ ( finite(X0)
& X0 != empty_set
& inclusion_linear(X0)
& ! [X1] :
~ ( in(X1,X0)
& ! [X2] :
( in(X2,X0)
=> subset(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_finset_1) ).
fof(f67,negated_conjecture,
~ ! [X0] :
~ ( finite(X0)
& X0 != empty_set
& inclusion_linear(X0)
& ! [X1] :
~ ( in(X1,X0)
& ! [X2] :
( in(X2,X0)
=> subset(X1,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f66]) ).
fof(f68,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f69,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f71,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f75,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f58]) ).
fof(f93,plain,
! [X0] :
( inclusion_linear(X0)
<=> ! [X1,X2] :
( inclusion_comparable(X1,X2)
| ~ in(X1,X0)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f94,plain,
! [X0] :
( inclusion_linear(X0)
<=> ! [X1,X2] :
( inclusion_comparable(X1,X2)
| ~ in(X1,X0)
| ~ in(X2,X0) ) ),
inference(flattening,[],[f93]) ).
fof(f104,plain,
! [X0] :
( empty_set = X0
| ? [X9] :
( in(X9,X0)
& ! [X10] :
( subset(X9,X10)
| ~ in(X10,X0) ) )
| ~ finite(X0)
| ( empty_set != empty_set
& ! [X1] :
( ~ in(X1,empty_set)
| ? [X2] :
( ~ subset(X1,X2)
& in(X2,empty_set) ) ) )
| ? [X3,X4] :
( set_union2(X4,singleton(X3)) != empty_set
& ! [X7] :
( ~ in(X7,set_union2(X4,singleton(X3)))
| ? [X8] :
( ~ subset(X7,X8)
& in(X8,set_union2(X4,singleton(X3))) ) )
& in(X3,X0)
& subset(X4,X0)
& ( empty_set = X4
| ? [X5] :
( in(X5,X4)
& ! [X6] :
( subset(X5,X6)
| ~ in(X6,X4) ) ) ) ) ),
inference(ennf_transformation,[],[f60]) ).
fof(f105,plain,
! [X0] :
( empty_set = X0
| ? [X9] :
( in(X9,X0)
& ! [X10] :
( subset(X9,X10)
| ~ in(X10,X0) ) )
| ~ finite(X0)
| ( empty_set != empty_set
& ! [X1] :
( ~ in(X1,empty_set)
| ? [X2] :
( ~ subset(X1,X2)
& in(X2,empty_set) ) ) )
| ? [X3,X4] :
( set_union2(X4,singleton(X3)) != empty_set
& ! [X7] :
( ~ in(X7,set_union2(X4,singleton(X3)))
| ? [X8] :
( ~ subset(X7,X8)
& in(X8,set_union2(X4,singleton(X3))) ) )
& in(X3,X0)
& subset(X4,X0)
& ( empty_set = X4
| ? [X5] :
( in(X5,X4)
& ! [X6] :
( subset(X5,X6)
| ~ in(X6,X4) ) ) ) ) ),
inference(flattening,[],[f104]) ).
fof(f108,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(ennf_transformation,[],[f64]) ).
fof(f109,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(flattening,[],[f108]) ).
fof(f110,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f65]) ).
fof(f111,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f110]) ).
fof(f112,plain,
? [X0] :
( finite(X0)
& X0 != empty_set
& inclusion_linear(X0)
& ! [X1] :
( ~ in(X1,X0)
| ? [X2] :
( ~ subset(X1,X2)
& in(X2,X0) ) ) ),
inference(ennf_transformation,[],[f67]) ).
fof(f113,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f69]) ).
fof(f114,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f113]) ).
fof(f116,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f119,definition,
! [X0] :
( ? [X3,X4] :
( set_union2(X4,singleton(X3)) != empty_set
& ! [X7] :
( ~ in(X7,set_union2(X4,singleton(X3)))
| ? [X8] :
( ~ subset(X7,X8)
& in(X8,set_union2(X4,singleton(X3))) ) )
& in(X3,X0)
& subset(X4,X0)
& ( empty_set = X4
| ? [X5] :
( in(X5,X4)
& ! [X6] :
( subset(X5,X6)
| ~ in(X6,X4) ) ) ) )
| ~ sP0(X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f120,plain,
! [X0] :
( empty_set = X0
| ? [X9] :
( in(X9,X0)
& ! [X10] :
( subset(X9,X10)
| ~ in(X10,X0) ) )
| ~ finite(X0)
| ( empty_set != empty_set
& ! [X1] :
( ~ in(X1,empty_set)
| ? [X2] :
( ~ subset(X1,X2)
& in(X2,empty_set) ) ) )
| sP0(X0) ),
inference(definition_folding,[],[f105,f119]) ).
fof(f121,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,[],[f14]) ).
fof(f122,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,[],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK1(X0,X1) != X0
| ~ in(sK1(X0,X1),X1) )
& ( sK1(X0,X1) = X0
| in(sK1(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f122]) ).
fof(f124,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,[],[f15]) ).
fof(f125,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,[],[f124]) ).
fof(f126,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,[],[f125]) ).
fof(f127,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ( ( ( ~ in(sK2(X0,X1,X2),X0)
& ~ in(sK2(X0,X1,X2),X1) )
| ~ in(sK2(X0,X1,X2),X2) )
& ( in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),X1)
| in(sK2(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,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f126]) ).
fof(f128,plain,
! [X0] :
( ( inclusion_linear(X0)
| ? [X1,X2] :
( ~ inclusion_comparable(X1,X2)
& in(X1,X0)
& in(X2,X0) ) )
& ( ! [X1,X2] :
( inclusion_comparable(X1,X2)
| ~ in(X1,X0)
| ~ in(X2,X0) )
| ~ inclusion_linear(X0) ) ),
inference(nnf_transformation,[],[f94]) ).
fof(f129,plain,
! [X0] :
( ( inclusion_linear(X0)
| ? [X1,X2] :
( ~ inclusion_comparable(X1,X2)
& in(X1,X0)
& in(X2,X0) ) )
& ( ! [X3,X4] :
( inclusion_comparable(X3,X4)
| ~ in(X3,X0)
| ~ in(X4,X0) )
| ~ inclusion_linear(X0) ) ),
inference(rectify,[],[f128]) ).
fof(f130,plain,
! [X0] :
( ( inclusion_linear(X0)
| ( ~ inclusion_comparable(sK3(X0),sK4(X0))
& in(sK3(X0),X0)
& in(sK4(X0),X0) ) )
& ( ! [X3,X4] :
( inclusion_comparable(X3,X4)
| ~ in(X3,X0)
| ~ in(X4,X0) )
| ~ inclusion_linear(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X1,sK3(X0)),skolemize(X2,sK4(X0))],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( ( inclusion_comparable(X0,X1)
| ( ~ subset(X0,X1)
& ~ subset(X1,X0) ) )
& ( subset(X0,X1)
| subset(X1,X0)
| ~ inclusion_comparable(X0,X1) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f132,plain,
! [X0,X1] :
( ( inclusion_comparable(X0,X1)
| ( ~ subset(X0,X1)
& ~ subset(X1,X0) ) )
& ( subset(X0,X1)
| subset(X1,X0)
| ~ inclusion_comparable(X0,X1) ) ),
inference(flattening,[],[f131]) ).
fof(f160,plain,
! [X0] :
( ? [X3,X4] :
( set_union2(X4,singleton(X3)) != empty_set
& ! [X7] :
( ~ in(X7,set_union2(X4,singleton(X3)))
| ? [X8] :
( ~ subset(X7,X8)
& in(X8,set_union2(X4,singleton(X3))) ) )
& in(X3,X0)
& subset(X4,X0)
& ( empty_set = X4
| ? [X5] :
( in(X5,X4)
& ! [X6] :
( subset(X5,X6)
| ~ in(X6,X4) ) ) ) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f119]) ).
fof(f161,plain,
! [X0] :
( ? [X1,X2] :
( empty_set != set_union2(X2,singleton(X1))
& ! [X3] :
( ~ in(X3,set_union2(X2,singleton(X1)))
| ? [X4] :
( ~ subset(X3,X4)
& in(X4,set_union2(X2,singleton(X1))) ) )
& in(X1,X0)
& subset(X2,X0)
& ( empty_set = X2
| ? [X5] :
( in(X5,X2)
& ! [X6] :
( subset(X5,X6)
| ~ in(X6,X2) ) ) ) )
| ~ sP0(X0) ),
inference(rectify,[],[f160]) ).
fof(f162,plain,
! [X0] :
( ( empty_set != set_union2(sK33(X0),singleton(sK32(X0)))
& ! [X3] :
( ~ in(X3,set_union2(sK33(X0),singleton(sK32(X0))))
| ( ~ subset(X3,sK34(X0,X3))
& in(sK34(X0,X3),set_union2(sK33(X0),singleton(sK32(X0)))) ) )
& in(sK32(X0),X0)
& subset(sK33(X0),X0)
& ( empty_set = sK33(X0)
| ( in(sK35(X0),sK33(X0))
& ! [X6] :
( subset(sK35(X0),X6)
| ~ in(X6,sK33(X0)) ) ) ) )
| ~ sP0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32,sK33,sK34,sK35]),skolemize(X1,sK32(X0)),skolemize(X2,sK33(X0)),skolemize(X4,sK34(X0,X3)),skolemize(X5,sK35(X0))],[f161]) ).
fof(f163,plain,
! [X0] :
( empty_set = X0
| ? [X1] :
( in(X1,X0)
& ! [X2] :
( subset(X1,X2)
| ~ in(X2,X0) ) )
| ~ finite(X0)
| ( empty_set != empty_set
& ! [X3] :
( ~ in(X3,empty_set)
| ? [X4] :
( ~ subset(X3,X4)
& in(X4,empty_set) ) ) )
| sP0(X0) ),
inference(rectify,[],[f120]) ).
fof(f164,plain,
! [X0] :
( empty_set = X0
| ( in(sK36(X0),X0)
& ! [X2] :
( subset(sK36(X0),X2)
| ~ in(X2,X0) ) )
| ~ finite(X0)
| ( empty_set != empty_set
& ! [X3] :
( ~ in(X3,empty_set)
| ( ~ subset(X3,sK37(X3))
& in(sK37(X3),empty_set) ) ) )
| sP0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36,sK37]),skolemize(X1,sK36(X0)),skolemize(X4,sK37(X3))],[f163]) ).
fof(f165,plain,
( finite(sK38)
& empty_set != sK38
& inclusion_linear(sK38)
& ! [X1] :
( ~ in(X1,sK38)
| ( ~ subset(X1,sK39(X1))
& in(sK39(X1),sK38) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38,sK39]),skolemize(X0,sK38),skolemize(X2,sK39(X1))],[f112]) ).
fof(f166,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f192,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f13]) ).
fof(f193,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f123]) ).
fof(f194,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f123]) ).
fof(f197,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f127]) ).
fof(f199,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f127]) ).
fof(f203,plain,
! [X3,X0,X4] :
( ~ inclusion_linear(X0)
| ~ in(X3,X0)
| ~ in(X4,X0)
| inclusion_comparable(X3,X4) ),
inference(cnf_transformation,[],[f130]) ).
fof(f207,plain,
! [X0,X1] :
( ~ inclusion_comparable(X0,X1)
| subset(X1,X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f132]) ).
fof(f323,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f75]) ).
fof(f325,plain,
! [X0,X6] :
( ~ sP0(X0)
| subset(sK35(X0),X6)
| ~ in(X6,sK33(X0))
| empty_set = sK33(X0) ),
inference(cnf_transformation,[],[f162]) ).
fof(f326,plain,
! [X0] :
( in(sK35(X0),sK33(X0))
| empty_set = sK33(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f162]) ).
fof(f327,plain,
! [X0] :
( ~ sP0(X0)
| subset(sK33(X0),X0) ),
inference(cnf_transformation,[],[f162]) ).
fof(f328,plain,
! [X0] :
( ~ sP0(X0)
| in(sK32(X0),X0) ),
inference(cnf_transformation,[],[f162]) ).
fof(f329,plain,
! [X3,X0] :
( in(sK34(X0,X3),set_union2(sK33(X0),singleton(sK32(X0))))
| ~ in(X3,set_union2(sK33(X0),singleton(sK32(X0))))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f162]) ).
fof(f330,plain,
! [X3,X0] :
( ~ sP0(X0)
| ~ subset(X3,sK34(X0,X3))
| ~ in(X3,set_union2(sK33(X0),singleton(sK32(X0)))) ),
inference(cnf_transformation,[],[f162]) ).
fof(f334,plain,
! [X2,X0] :
( empty_set = X0
| subset(sK36(X0),X2)
| ~ in(X2,X0)
| ~ finite(X0)
| empty_set != empty_set
| sP0(X0) ),
inference(cnf_transformation,[],[f164]) ).
fof(f337,plain,
! [X0] :
( empty_set = X0
| in(sK36(X0),X0)
| ~ finite(X0)
| empty_set != empty_set
| sP0(X0) ),
inference(cnf_transformation,[],[f164]) ).
fof(f339,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f62]) ).
fof(f341,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f342,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f343,plain,
! [X1] :
( in(sK39(X1),sK38)
| ~ in(X1,sK38) ),
inference(cnf_transformation,[],[f165]) ).
fof(f344,plain,
! [X1] :
( ~ subset(X1,sK39(X1))
| ~ in(X1,sK38) ),
inference(cnf_transformation,[],[f165]) ).
fof(f345,plain,
inclusion_linear(sK38),
inference(cnf_transformation,[],[f165]) ).
fof(f346,plain,
empty_set != sK38,
inference(cnf_transformation,[],[f165]) ).
fof(f347,plain,
finite(sK38),
inference(cnf_transformation,[],[f165]) ).
fof(f349,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f166]) ).
fof(f350,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f114]) ).
fof(f352,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f116]) ).
fof(f355,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f194]) ).
fof(f356,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f355]) ).
fof(f357,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f193]) ).
fof(f358,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f199]) ).
fof(f360,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f197]) ).
fof(f361,plain,
! [X2,X0] :
( empty_set = X0
| subset(sK36(X0),X2)
| ~ in(X2,X0)
| ~ finite(X0)
| sP0(X0) ),
inference(trivial_inequality_removal,[],[f334]) ).
fof(f362,plain,
! [X0] :
( empty_set = X0
| in(sK36(X0),X0)
| ~ finite(X0)
| sP0(X0) ),
inference(trivial_inequality_removal,[],[f337]) ).
fof(f367,definition,
( spl40_2
<=> ! [X2,X0] :
( empty_set = X0
| sP0(X0)
| ~ finite(X0)
| ~ in(X2,X0)
| subset(sK36(X0),X2) ) ),
introduced(definition,[new_symbols(definition,[spl40_2])],[avatar_definition]) ).
fof(f368,plain,
( ! [X2,X0] :
( ~ finite(X0)
| sP0(X0)
| empty_set = X0
| ~ in(X2,X0)
| subset(sK36(X0),X2) )
| ~ spl40_2 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f374,plain,
spl40_2,
inference(avatar_split_clause,[],[f361,f367]) ).
fof(f376,definition,
( spl40_4
<=> ! [X0] :
( empty_set = X0
| sP0(X0)
| ~ finite(X0)
| in(sK36(X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl40_4])],[avatar_definition]) ).
fof(f377,plain,
( ! [X0] :
( ~ finite(X0)
| sP0(X0)
| empty_set = X0
| in(sK36(X0),X0) )
| ~ spl40_4 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f380,plain,
spl40_4,
inference(avatar_split_clause,[],[f362,f376]) ).
fof(f381,plain,
( ! [X0] :
( sP0(sK38)
| empty_set = sK38
| ~ in(X0,sK38)
| subset(sK36(sK38),X0) )
| ~ spl40_2 ),
inference(resolution,[],[f368,f347]) ).
fof(f382,plain,
( ! [X0] :
( sP0(sK38)
| ~ in(X0,sK38)
| subset(sK36(sK38),X0) )
| ~ spl40_2 ),
inference(forward_subsumption_resolution,[],[f381,f346]) ).
fof(f384,definition,
( spl40_5
<=> ! [X0] :
( ~ in(X0,sK38)
| subset(sK36(sK38),X0) ) ),
introduced(definition,[new_symbols(definition,[spl40_5])],[avatar_definition]) ).
fof(f385,plain,
( ! [X0] :
( subset(sK36(sK38),X0)
| ~ in(X0,sK38) )
| ~ spl40_5 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f387,definition,
( spl40_6
<=> sP0(sK38) ),
introduced(definition,[new_symbols(definition,[spl40_6])],[avatar_definition]) ).
fof(f388,plain,
( sP0(sK38)
| ~ spl40_6 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f389,plain,
( spl40_5
| spl40_6
| ~ spl40_2 ),
inference(avatar_split_clause,[],[f382,f367,f387,f384]) ).
fof(f390,plain,
( ~ in(sK39(sK36(sK38)),sK38)
| ~ in(sK36(sK38),sK38)
| ~ spl40_5 ),
inference(resolution,[],[f385,f344]) ).
fof(f391,plain,
( ~ in(sK36(sK38),sK38)
| ~ spl40_5 ),
inference(forward_subsumption_resolution,[],[f390,f343]) ).
fof(f392,plain,
( sP0(sK38)
| empty_set = sK38
| in(sK36(sK38),sK38)
| ~ spl40_4 ),
inference(resolution,[],[f377,f347]) ).
fof(f393,plain,
( sP0(sK38)
| in(sK36(sK38),sK38)
| ~ spl40_4 ),
inference(forward_subsumption_resolution,[],[f392,f346]) ).
fof(f394,plain,
( sP0(sK38)
| ~ spl40_4
| ~ spl40_5 ),
inference(forward_subsumption_resolution,[],[f393,f391]) ).
fof(f395,plain,
( spl40_6
| ~ spl40_4
| ~ spl40_5 ),
inference(avatar_split_clause,[],[f394,f384,f376,f387]) ).
fof(f396,plain,
( in(sK32(sK38),sK38)
| ~ spl40_6 ),
inference(resolution,[],[f388,f328]) ).
fof(f397,plain,
( ! [X0] :
( subset(sK35(sK38),X0)
| ~ in(X0,sK33(sK38))
| empty_set = sK33(sK38) )
| ~ spl40_6 ),
inference(resolution,[],[f388,f325]) ).
fof(f398,plain,
( subset(sK33(sK38),sK38)
| ~ spl40_6 ),
inference(resolution,[],[f388,f327]) ).
fof(f400,definition,
( spl40_7
<=> empty_set = sK33(sK38) ),
introduced(definition,[new_symbols(definition,[spl40_7])],[avatar_definition]) ).
fof(f401,plain,
( empty_set = sK33(sK38)
| ~ spl40_7 ),
inference(avatar_component_clause,[],[f400]) ).
fof(f403,definition,
( spl40_8
<=> ! [X0] :
( subset(sK35(sK38),X0)
| ~ in(X0,sK33(sK38)) ) ),
introduced(definition,[new_symbols(definition,[spl40_8])],[avatar_definition]) ).
fof(f404,plain,
( ! [X0] :
( ~ in(X0,sK33(sK38))
| subset(sK35(sK38),X0) )
| ~ spl40_8 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f405,plain,
( spl40_7
| spl40_8
| ~ spl40_6 ),
inference(avatar_split_clause,[],[f397,f387,f403,f400]) ).
fof(f411,plain,
( ! [X0] :
( ~ subset(X0,sK34(sK38,X0))
| ~ in(X0,set_union2(sK33(sK38),singleton(sK32(sK38)))) )
| ~ spl40_6 ),
inference(resolution,[],[f330,f388]) ).
fof(f423,plain,
! [X0,X1] :
( ~ sP0(X0)
| in(sK34(X0,X1),sK33(X0))
| ~ in(X1,set_union2(sK33(X0),singleton(sK32(X0))))
| in(sK34(X0,X1),singleton(sK32(X0))) ),
inference(resolution,[],[f360,f329]) ).
fof(f432,plain,
! [X0,X1] :
( inclusion_comparable(X0,X1)
| ~ in(X1,sK38)
| ~ in(X0,sK38) ),
inference(resolution,[],[f203,f345]) ).
fof(f433,plain,
! [X0,X1] :
( ~ in(X1,sK38)
| ~ in(X0,sK38)
| subset(X0,X1)
| subset(X1,X0) ),
inference(resolution,[],[f432,f207]) ).
fof(f434,plain,
( ! [X0] :
( ~ in(X0,sK38)
| subset(X0,sK32(sK38))
| subset(sK32(sK38),X0) )
| ~ spl40_6 ),
inference(resolution,[],[f433,f396]) ).
fof(f458,plain,
( ! [X0] :
( ~ in(X0,set_union2(sK33(sK38),singleton(sK32(sK38))))
| in(sK34(sK38,X0),sK33(sK38))
| in(sK34(sK38,X0),singleton(sK32(sK38))) )
| ~ spl40_6 ),
inference(resolution,[],[f423,f388]) ).
fof(f517,plain,
! [X0] : set_union2(empty_set,X0) = X0,
inference(superposition,[],[f192,f339]) ).
fof(f658,plain,
( ! [X0] :
( in(sK34(sK38,X0),set_union2(empty_set,singleton(sK32(sK38))))
| ~ in(X0,set_union2(empty_set,singleton(sK32(sK38))))
| ~ sP0(sK38) )
| ~ spl40_7 ),
inference(superposition,[],[f329,f401]) ).
fof(f661,plain,
( ! [X0] :
( in(sK34(sK38,X0),set_union2(empty_set,singleton(sK32(sK38))))
| ~ in(X0,set_union2(empty_set,singleton(sK32(sK38)))) )
| ~ spl40_6
| ~ spl40_7 ),
inference(forward_subsumption_resolution,[],[f658,f388]) ).
fof(f663,plain,
( ! [X0] :
( in(sK34(sK38,X0),singleton(sK32(sK38)))
| ~ in(X0,set_union2(empty_set,singleton(sK32(sK38)))) )
| ~ spl40_6
| ~ spl40_7 ),
inference(forward_demodulation,[],[f661,f517]) ).
fof(f664,plain,
( ! [X0] :
( in(sK34(sK38,X0),singleton(sK32(sK38)))
| ~ in(X0,singleton(sK32(sK38))) )
| ~ spl40_6
| ~ spl40_7 ),
inference(forward_demodulation,[],[f663,f517]) ).
fof(f666,plain,
( ! [X0] :
( in(sK34(sK38,X0),singleton(sK32(sK38)))
| in(sK34(sK38,X0),sK33(sK38))
| ~ in(X0,sK33(sK38)) )
| ~ spl40_6 ),
inference(resolution,[],[f458,f358]) ).
fof(f671,plain,
( ! [X0] :
( in(sK34(sK38,sK34(sK38,X0)),sK33(sK38))
| in(sK34(sK38,sK34(sK38,X0)),singleton(sK32(sK38)))
| ~ in(X0,set_union2(sK33(sK38),singleton(sK32(sK38))))
| ~ sP0(sK38) )
| ~ spl40_6 ),
inference(resolution,[],[f458,f329]) ).
fof(f674,plain,
( ! [X0] :
( in(sK34(sK38,sK34(sK38,X0)),singleton(sK32(sK38)))
| in(sK34(sK38,sK34(sK38,X0)),sK33(sK38))
| ~ in(X0,set_union2(sK33(sK38),singleton(sK32(sK38)))) )
| ~ spl40_6 ),
inference(forward_subsumption_resolution,[],[f671,f388]) ).
fof(f708,plain,
( ! [X0] :
( ~ in(X0,singleton(sK32(sK38)))
| sK32(sK38) = sK34(sK38,X0) )
| ~ spl40_6
| ~ spl40_7 ),
inference(resolution,[],[f664,f357]) ).
fof(f709,plain,
( sK32(sK38) = sK34(sK38,sK32(sK38))
| ~ spl40_6
| ~ spl40_7 ),
inference(resolution,[],[f708,f356]) ).
fof(f715,plain,
( ~ subset(sK32(sK38),sK32(sK38))
| ~ in(sK32(sK38),set_union2(sK33(sK38),singleton(sK32(sK38))))
| ~ spl40_6
| ~ spl40_7 ),
inference(superposition,[],[f411,f709]) ).
fof(f717,plain,
( ~ in(sK32(sK38),set_union2(sK33(sK38),singleton(sK32(sK38))))
| ~ spl40_6
| ~ spl40_7 ),
inference(forward_subsumption_resolution,[],[f715,f323]) ).
fof(f718,plain,
( ~ in(sK32(sK38),set_union2(empty_set,singleton(sK32(sK38))))
| ~ spl40_6
| ~ spl40_7 ),
inference(forward_demodulation,[],[f717,f401]) ).
fof(f719,plain,
( ~ in(sK32(sK38),singleton(sK32(sK38)))
| ~ spl40_6
| ~ spl40_7 ),
inference(forward_demodulation,[],[f718,f517]) ).
fof(f720,plain,
( $false
| ~ spl40_6
| ~ spl40_7 ),
inference(forward_subsumption_resolution,[],[f719,f356]) ).
fof(f721,plain,
( ~ spl40_6
| ~ spl40_7 ),
inference(avatar_contradiction_clause,[],[f720]) ).
fof(f750,plain,
( ! [X0] :
( in(sK34(sK38,sK34(sK38,X0)),sK33(sK38))
| ~ in(X0,set_union2(sK33(sK38),singleton(sK32(sK38))))
| sK32(sK38) = sK34(sK38,sK34(sK38,X0)) )
| ~ spl40_6 ),
inference(resolution,[],[f674,f357]) ).
fof(f751,plain,
( ! [X0] :
( in(sK34(sK38,X0),sK33(sK38))
| ~ in(X0,sK33(sK38))
| sK32(sK38) = sK34(sK38,X0) )
| ~ spl40_6 ),
inference(resolution,[],[f666,f357]) ).
fof(f752,plain,
( ! [X0] :
( subset(sK35(sK38),sK34(sK38,X0))
| sK32(sK38) = sK34(sK38,X0)
| ~ in(X0,sK33(sK38)) )
| ~ spl40_6
| ~ spl40_8 ),
inference(resolution,[],[f751,f404]) ).
fof(f753,plain,
( sK32(sK38) = sK34(sK38,sK35(sK38))
| ~ in(sK35(sK38),sK33(sK38))
| ~ in(sK35(sK38),set_union2(sK33(sK38),singleton(sK32(sK38))))
| ~ spl40_6
| ~ spl40_8 ),
inference(resolution,[],[f752,f411]) ).
fof(f755,plain,
( sK32(sK38) = sK34(sK38,sK35(sK38))
| ~ in(sK35(sK38),sK33(sK38))
| ~ spl40_6
| ~ spl40_8 ),
inference(forward_subsumption_resolution,[],[f753,f358]) ).
fof(f757,definition,
( spl40_38
<=> in(sK35(sK38),sK33(sK38)) ),
introduced(definition,[new_symbols(definition,[spl40_38])],[avatar_definition]) ).
fof(f758,plain,
( ~ in(sK35(sK38),sK33(sK38))
| spl40_38 ),
inference(avatar_component_clause,[],[f757]) ).
fof(f760,definition,
( spl40_39
<=> sK32(sK38) = sK34(sK38,sK35(sK38)) ),
introduced(definition,[new_symbols(definition,[spl40_39])],[avatar_definition]) ).
fof(f761,plain,
( sK32(sK38) = sK34(sK38,sK35(sK38))
| ~ spl40_39 ),
inference(avatar_component_clause,[],[f760]) ).
fof(f762,plain,
( ~ spl40_38
| spl40_39
| ~ spl40_6
| ~ spl40_8 ),
inference(avatar_split_clause,[],[f755,f403,f387,f760,f757]) ).
fof(f763,plain,
( empty_set = sK33(sK38)
| ~ sP0(sK38)
| spl40_38 ),
inference(resolution,[],[f758,f326]) ).
fof(f764,plain,
( empty_set = sK33(sK38)
| ~ spl40_6
| spl40_38 ),
inference(forward_subsumption_resolution,[],[f763,f388]) ).
fof(f765,plain,
( spl40_7
| ~ spl40_6
| spl40_38 ),
inference(avatar_split_clause,[],[f764,f757,f387,f400]) ).
fof(f768,plain,
( ~ subset(sK35(sK38),sK32(sK38))
| ~ in(sK35(sK38),set_union2(sK33(sK38),singleton(sK32(sK38))))
| ~ spl40_6
| ~ spl40_39 ),
inference(superposition,[],[f411,f761]) ).
fof(f769,plain,
( in(sK32(sK38),set_union2(sK33(sK38),singleton(sK32(sK38))))
| ~ in(sK35(sK38),set_union2(sK33(sK38),singleton(sK32(sK38))))
| ~ sP0(sK38)
| ~ spl40_39 ),
inference(superposition,[],[f329,f761]) ).
fof(f770,plain,
( in(sK32(sK38),set_union2(sK33(sK38),singleton(sK32(sK38))))
| ~ in(sK35(sK38),set_union2(sK33(sK38),singleton(sK32(sK38))))
| ~ spl40_6
| ~ spl40_39 ),
inference(forward_subsumption_resolution,[],[f769,f388]) ).
fof(f772,definition,
( spl40_40
<=> in(sK35(sK38),set_union2(sK33(sK38),singleton(sK32(sK38)))) ),
introduced(definition,[new_symbols(definition,[spl40_40])],[avatar_definition]) ).
fof(f773,plain,
( ~ in(sK35(sK38),set_union2(sK33(sK38),singleton(sK32(sK38))))
| spl40_40 ),
inference(avatar_component_clause,[],[f772]) ).
fof(f775,definition,
( spl40_41
<=> subset(sK35(sK38),sK32(sK38)) ),
introduced(definition,[new_symbols(definition,[spl40_41])],[avatar_definition]) ).
fof(f776,plain,
( ~ subset(sK35(sK38),sK32(sK38))
| spl40_41 ),
inference(avatar_component_clause,[],[f775]) ).
fof(f777,plain,
( ~ spl40_40
| ~ spl40_41
| ~ spl40_6
| ~ spl40_39 ),
inference(avatar_split_clause,[],[f768,f760,f387,f775,f772]) ).
fof(f779,definition,
( spl40_42
<=> in(sK34(sK38,sK32(sK38)),sK33(sK38)) ),
introduced(definition,[new_symbols(definition,[spl40_42])],[avatar_definition]) ).
fof(f780,plain,
( in(sK34(sK38,sK32(sK38)),sK33(sK38))
| ~ spl40_42 ),
inference(avatar_component_clause,[],[f779]) ).
fof(f786,definition,
( spl40_44
<=> in(sK32(sK38),set_union2(sK33(sK38),singleton(sK32(sK38)))) ),
introduced(definition,[new_symbols(definition,[spl40_44])],[avatar_definition]) ).
fof(f787,plain,
( in(sK32(sK38),set_union2(sK33(sK38),singleton(sK32(sK38))))
| ~ spl40_44 ),
inference(avatar_component_clause,[],[f786]) ).
fof(f788,plain,
( ~ spl40_40
| spl40_44
| ~ spl40_6
| ~ spl40_39 ),
inference(avatar_split_clause,[],[f770,f760,f387,f786,f772]) ).
fof(f789,plain,
( ~ in(sK35(sK38),sK33(sK38))
| spl40_40 ),
inference(resolution,[],[f773,f358]) ).
fof(f791,plain,
( ~ spl40_38
| spl40_40 ),
inference(avatar_split_clause,[],[f789,f772,f757]) ).
fof(f814,plain,
( ! [X0] :
( subset(sK35(sK38),sK34(sK38,sK34(sK38,X0)))
| sK32(sK38) = sK34(sK38,sK34(sK38,X0))
| ~ in(X0,set_union2(sK33(sK38),singleton(sK32(sK38)))) )
| ~ spl40_6
| ~ spl40_8 ),
inference(resolution,[],[f750,f404]) ).
fof(f815,plain,
( in(sK34(sK38,sK32(sK38)),sK33(sK38))
| ~ in(sK35(sK38),set_union2(sK33(sK38),singleton(sK32(sK38))))
| sK32(sK38) = sK34(sK38,sK32(sK38))
| ~ spl40_6
| ~ spl40_39 ),
inference(superposition,[],[f750,f761]) ).
fof(f820,plain,
( subset(sK35(sK38),sK34(sK38,sK32(sK38)))
| sK32(sK38) = sK34(sK38,sK32(sK38))
| ~ in(sK35(sK38),set_union2(sK33(sK38),singleton(sK32(sK38))))
| ~ spl40_6
| ~ spl40_8
| ~ spl40_39 ),
inference(superposition,[],[f814,f761]) ).
fof(f2453,definition,
( spl40_226
<=> sK32(sK38) = sK34(sK38,sK32(sK38)) ),
introduced(definition,[new_symbols(definition,[spl40_226])],[avatar_definition]) ).
fof(f2454,plain,
( sK32(sK38) = sK34(sK38,sK32(sK38))
| ~ spl40_226 ),
inference(avatar_component_clause,[],[f2453]) ).
fof(f2465,plain,
( ~ subset(sK32(sK38),sK32(sK38))
| ~ in(sK32(sK38),set_union2(sK33(sK38),singleton(sK32(sK38))))
| ~ spl40_6
| ~ spl40_226 ),
inference(superposition,[],[f411,f2454]) ).
fof(f2473,plain,
( ~ in(sK32(sK38),set_union2(sK33(sK38),singleton(sK32(sK38))))
| ~ spl40_6
| ~ spl40_226 ),
inference(forward_subsumption_resolution,[],[f2465,f323]) ).
fof(f2476,plain,
( $false
| ~ spl40_6
| ~ spl40_44
| ~ spl40_226 ),
inference(forward_subsumption_resolution,[],[f2473,f787]) ).
fof(f2477,plain,
( ~ spl40_6
| ~ spl40_44
| ~ spl40_226 ),
inference(avatar_contradiction_clause,[],[f2476]) ).
fof(f2575,plain,
! [X2,X0,X1] :
( ~ in(X2,X0)
| ~ subset(X0,X1)
| element(X2,X1) ),
inference(resolution,[],[f349,f350]) ).
fof(f2625,plain,
( ! [X0] :
( element(sK34(sK38,sK32(sK38)),X0)
| ~ subset(sK33(sK38),X0) )
| ~ spl40_42 ),
inference(resolution,[],[f2575,f780]) ).
fof(f2639,plain,
( ! [X0] :
( ~ subset(sK33(sK38),X0)
| in(sK34(sK38,sK32(sK38)),X0)
| empty(X0) )
| ~ spl40_42 ),
inference(resolution,[],[f2625,f342]) ).
fof(f2708,plain,
( in(sK34(sK38,sK32(sK38)),sK38)
| empty(sK38)
| ~ spl40_6
| ~ spl40_42 ),
inference(resolution,[],[f2639,f398]) ).
fof(f2798,definition,
( spl40_262
<=> empty(sK38) ),
introduced(definition,[new_symbols(definition,[spl40_262])],[avatar_definition]) ).
fof(f2799,plain,
( empty(sK38)
| ~ spl40_262 ),
inference(avatar_component_clause,[],[f2798]) ).
fof(f2801,definition,
( spl40_263
<=> in(sK34(sK38,sK32(sK38)),sK38) ),
introduced(definition,[new_symbols(definition,[spl40_263])],[avatar_definition]) ).
fof(f2802,plain,
( in(sK34(sK38,sK32(sK38)),sK38)
| ~ spl40_263 ),
inference(avatar_component_clause,[],[f2801]) ).
fof(f2803,plain,
( spl40_262
| spl40_263
| ~ spl40_6
| ~ spl40_42 ),
inference(avatar_split_clause,[],[f2708,f779,f387,f2801,f2798]) ).
fof(f2807,plain,
( empty_set = sK38
| ~ spl40_262 ),
inference(resolution,[],[f2799,f352]) ).
fof(f2810,plain,
( $false
| ~ spl40_262 ),
inference(forward_subsumption_resolution,[],[f2807,f346]) ).
fof(f2811,plain,
~ spl40_262,
inference(avatar_contradiction_clause,[],[f2810]) ).
fof(f2813,plain,
( subset(sK34(sK38,sK32(sK38)),sK32(sK38))
| subset(sK32(sK38),sK34(sK38,sK32(sK38)))
| ~ spl40_6
| ~ spl40_263 ),
inference(resolution,[],[f2802,f434]) ).
fof(f2843,definition,
( spl40_268
<=> subset(sK32(sK38),sK34(sK38,sK32(sK38))) ),
introduced(definition,[new_symbols(definition,[spl40_268])],[avatar_definition]) ).
fof(f2844,plain,
( subset(sK32(sK38),sK34(sK38,sK32(sK38)))
| ~ spl40_268 ),
inference(avatar_component_clause,[],[f2843]) ).
fof(f2846,definition,
( spl40_269
<=> subset(sK34(sK38,sK32(sK38)),sK32(sK38)) ),
introduced(definition,[new_symbols(definition,[spl40_269])],[avatar_definition]) ).
fof(f2847,plain,
( subset(sK34(sK38,sK32(sK38)),sK32(sK38))
| ~ spl40_269 ),
inference(avatar_component_clause,[],[f2846]) ).
fof(f2848,plain,
( spl40_268
| spl40_269
| ~ spl40_6
| ~ spl40_263 ),
inference(avatar_split_clause,[],[f2813,f2801,f387,f2846,f2843]) ).
fof(f2849,plain,
( spl40_226
| ~ spl40_40
| spl40_42
| ~ spl40_6
| ~ spl40_39 ),
inference(avatar_split_clause,[],[f815,f760,f387,f779,f772,f2453]) ).
fof(f2851,definition,
( spl40_270
<=> subset(sK35(sK38),sK34(sK38,sK32(sK38))) ),
introduced(definition,[new_symbols(definition,[spl40_270])],[avatar_definition]) ).
fof(f2852,plain,
( subset(sK35(sK38),sK34(sK38,sK32(sK38)))
| ~ spl40_270 ),
inference(avatar_component_clause,[],[f2851]) ).
fof(f2853,plain,
( ~ spl40_40
| spl40_226
| spl40_270
| ~ spl40_6
| ~ spl40_8
| ~ spl40_39 ),
inference(avatar_split_clause,[],[f820,f760,f403,f387,f2851,f2453,f772]) ).
fof(f2885,plain,
( ~ in(sK32(sK38),set_union2(sK33(sK38),singleton(sK32(sK38))))
| ~ spl40_6
| ~ spl40_268 ),
inference(resolution,[],[f2844,f411]) ).
fof(f2889,plain,
( $false
| ~ spl40_6
| ~ spl40_44
| ~ spl40_268 ),
inference(forward_subsumption_resolution,[],[f2885,f787]) ).
fof(f2890,plain,
( ~ spl40_6
| ~ spl40_44
| ~ spl40_268 ),
inference(avatar_contradiction_clause,[],[f2889]) ).
fof(f2891,plain,
( $false
| spl40_41
| ~ spl40_269
| ~ spl40_270 ),
inference(unit_resulting_resolution,[],[f341,f776,f2852,f2847]) ).
fof(f2893,plain,
( spl40_41
| ~ spl40_269
| ~ spl40_270 ),
inference(avatar_contradiction_clause,[],[f2891]) ).
cnf(s3,plain,
spl40_2,
inference(sat_conversion,[],[f374]) ).
cnf(s6,plain,
spl40_4,
inference(sat_conversion,[],[f380]) ).
cnf(s7,plain,
( ~ spl40_2
| spl40_5
| spl40_6 ),
inference(sat_conversion,[],[f389]) ).
cnf(s8,plain,
( ~ spl40_4
| ~ spl40_5
| spl40_6 ),
inference(sat_conversion,[],[f395]) ).
cnf(s9,plain,
( ~ spl40_6
| spl40_7
| spl40_8 ),
inference(sat_conversion,[],[f405]) ).
cnf(s26,plain,
( ~ spl40_6
| ~ spl40_7 ),
inference(sat_conversion,[],[f721]) ).
cnf(s30,plain,
( ~ spl40_6
| ~ spl40_8
| ~ spl40_38
| spl40_39 ),
inference(sat_conversion,[],[f762]) ).
cnf(s31,plain,
( ~ spl40_6
| spl40_7
| spl40_38 ),
inference(sat_conversion,[],[f765]) ).
cnf(s32,plain,
( ~ spl40_6
| ~ spl40_39
| ~ spl40_40
| ~ spl40_41 ),
inference(sat_conversion,[],[f777]) ).
cnf(s34,plain,
( ~ spl40_6
| ~ spl40_39
| ~ spl40_40
| spl40_44 ),
inference(sat_conversion,[],[f788]) ).
cnf(s35,plain,
( ~ spl40_38
| spl40_40 ),
inference(sat_conversion,[],[f791]) ).
cnf(s190,plain,
( ~ spl40_6
| ~ spl40_44
| ~ spl40_226 ),
inference(sat_conversion,[],[f2477]) ).
cnf(s215,plain,
( ~ spl40_6
| ~ spl40_42
| spl40_262
| spl40_263 ),
inference(sat_conversion,[],[f2803]) ).
cnf(s218,plain,
~ spl40_262,
inference(sat_conversion,[],[f2811]) ).
cnf(s221,plain,
( ~ spl40_6
| ~ spl40_263
| spl40_268
| spl40_269 ),
inference(sat_conversion,[],[f2848]) ).
cnf(s222,plain,
( ~ spl40_6
| ~ spl40_39
| ~ spl40_40
| spl40_42
| spl40_226 ),
inference(sat_conversion,[],[f2849]) ).
cnf(s223,plain,
( ~ spl40_6
| ~ spl40_8
| ~ spl40_39
| ~ spl40_40
| spl40_226
| spl40_270 ),
inference(sat_conversion,[],[f2853]) ).
cnf(s234,plain,
( ~ spl40_6
| ~ spl40_44
| ~ spl40_268 ),
inference(sat_conversion,[],[f2890]) ).
cnf(s235,plain,
( spl40_41
| ~ spl40_269
| ~ spl40_270 ),
inference(sat_conversion,[],[f2893]) ).
cnf(s236,plain,
( ~ spl40_6
| ~ spl40_42
| spl40_263 ),
inference(rat,[],[s215,s218]) ).
cnf(s237,plain,
( spl40_7
| ~ spl40_6 ),
inference(rat,[],[s221,s236,s235,s222,s223,s190,s234,s32,s34,s30,s35,s9,s31]) ).
cnf(s238,plain,
~ spl40_6,
inference(rat,[],[s237,s26]) ).
cnf(s239,plain,
~ spl40_5,
inference(rat,[],[s8,s6,s238]) ).
cnf(s240,plain,
$false,
inference(rat,[],[s7,s3,s238,s239]) ).
fof(f2894,plain,
$false,
inference(avatar_sat_refutation,[],[s240]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU099+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n014.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 03:33:46 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.93/1.79 % (1411247)Detected formulas, will run a generic FOF schedule.
% 5.93/1.79 % (1411253)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=2449680547:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.93/1.79 % (1411256)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=229083329:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.93/1.79 % (1411258)dis-21_1_sil=8000:lcm=predicate:random_seed=1590658242: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)
% 5.93/1.79 % (1411254)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=4158324569:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.93/1.79 % (1411252)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=3860811744:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.93/1.79 % (1411255)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3503075702:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.93/1.79 % (1411257)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3384770010:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.93/1.79 % (1411255)Refutation not found, incomplete strategy
% 5.93/1.79 % (1411255)------------------------------
% 5.93/1.79 % (1411255)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.79 % (1411255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.79 % (1411255)CaDiCaL version: 2.1.3
% 5.93/1.79 % (1411255)Termination reason: Refutation not found, incomplete strategy
% 5.93/1.79 % (1411255)Time elapsed: 0.002 s
% 5.93/1.79 % (1411255)Peak memory usage: 88 MB
% 5.93/1.79 % (1411255)Instructions burned: 2 (million)
% 5.93/1.79 % (1411258)Instruction limit reached!
% 5.93/1.79 % (1411258)------------------------------
% 5.93/1.79 % (1411258)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.79 % (1411258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.79 % (1411258)CaDiCaL version: 2.1.3
% 5.93/1.79 % (1411258)Termination reason: Instruction limit
% 5.93/1.79 % (1411258)Termination phase: Saturation
% 5.93/1.79 % (1411258)Time elapsed: 0.069 s
% 5.93/1.79 % (1411258)Peak memory usage: 89 MB
% 5.93/1.79 % (1411258)Instructions burned: 131 (million)
% 5.93/1.79 % (1411256)Instruction limit reached!
% 5.93/1.79 % (1411256)------------------------------
% 5.93/1.79 % (1411256)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.79 % (1411256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.79 % (1411256)CaDiCaL version: 2.1.3
% 5.93/1.79 % (1411256)Termination reason: Instruction limit
% 5.93/1.79 % (1411256)Termination phase: Saturation
% 5.93/1.79 % (1411256)Time elapsed: 0.072 s
% 5.93/1.79 % (1411256)Peak memory usage: 88 MB
% 5.93/1.79 % (1411256)Instructions burned: 119 (million)
% 5.93/1.79 % (1411257)Instruction limit reached!
% 5.93/1.79 % (1411257)------------------------------
% 5.93/1.79 % (1411257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.79 % (1411257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.79 % (1411257)CaDiCaL version: 2.1.3
% 5.93/1.79 % (1411257)Termination reason: Instruction limit
% 5.93/1.79 % (1411257)Termination phase: Saturation
% 5.93/1.79 % (1411257)Time elapsed: 0.087 s
% 5.93/1.79 % (1411257)Peak memory usage: 89 MB
% 5.93/1.79 % (1411257)Instructions burned: 139 (million)
% 5.93/1.79 % (1411266)lrs+10_1_sil=8000:sp=occurrence:random_seed=443736228:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.93/1.79 % (1411267)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3200652126:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.93/1.79 % (1411268)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3482064130:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.93/1.79 % (1411255)------------------------------
% 5.93/1.79 % (1411255)------------------------------
% 5.93/1.79 % (1411267)Instruction limit reached!
% 5.93/1.79 % (1411267)------------------------------
% 5.93/1.79 % (1411267)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.79 % (1411267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.79 % (1411267)CaDiCaL version: 2.1.3
% 5.93/1.79 % (1411267)Termination reason: Instruction limit
% 5.93/1.79 % (1411267)Termination phase: Saturation
% 5.93/1.79 % (1411267)Time elapsed: 0.094 s
% 5.93/1.79 % (1411267)Peak memory usage: 90 MB
% 5.93/1.79 % (1411267)Instructions burned: 159 (million)
% 5.93/1.79 % (1411266)Instruction limit reached!
% 5.93/1.79 % (1411266)------------------------------
% 5.93/1.79 % (1411266)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.79 % (1411266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.79 % (1411266)CaDiCaL version: 2.1.3
% 5.93/1.79 % (1411266)Termination reason: Instruction limit
% 5.93/1.79 % (1411266)Termination phase: Saturation
% 5.93/1.79 % (1411266)Time elapsed: 0.166 s
% 5.93/1.79 % (1411266)Peak memory usage: 91 MB
% 5.93/1.79 % (1411266)Instructions burned: 286 (million)
% 5.93/1.79 % (1411272)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=2846158369:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 5.93/1.79 % (1411268)Instruction limit reached!
% 5.93/1.79 % (1411268)------------------------------
% 5.93/1.79 % (1411268)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.79 % (1411268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.79 % (1411268)CaDiCaL version: 2.1.3
% 5.93/1.79 % (1411268)Termination reason: Instruction limit
% 5.93/1.79 % (1411268)Termination phase: Saturation
% 5.93/1.79 % (1411268)Time elapsed: 0.191 s
% 5.93/1.79 % (1411268)Peak memory usage: 91 MB
% 5.93/1.79 % (1411268)Instructions burned: 327 (million)
% 5.93/1.79 % (1411273)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=280469844:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.93/1.79 % (1411272)Instruction limit reached!
% 5.93/1.79 % (1411272)------------------------------
% 5.93/1.79 % (1411272)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.79 % (1411272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.79 % (1411272)CaDiCaL version: 2.1.3
% 5.93/1.79 % (1411272)Termination reason: Instruction limit
% 5.93/1.79 % (1411272)Termination phase: Saturation
% 5.93/1.79 % (1411272)Time elapsed: 0.142 s
% 5.93/1.79 % (1411272)Peak memory usage: 95 MB
% 5.93/1.79 % (1411272)Instructions burned: 249 (million)
% 5.93/1.79 % (1411275)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3601982371:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.93/1.79 % (1411276)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4246894735:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 5.93/1.79 % (1411253)First to succeed.
% 5.93/1.79 % (1411253)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1411247"
% 5.93/1.79 % (1411273)Instruction limit reached!
% 5.93/1.79 % (1411273)------------------------------
% 5.93/1.79 % (1411273)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.79 % (1411273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.79 % (1411273)CaDiCaL version: 2.1.3
% 5.93/1.79 % (1411273)Termination reason: Instruction limit
% 5.93/1.79 % (1411273)Termination phase: Saturation
% 5.93/1.79 % (1411273)Time elapsed: 0.157 s
% 5.93/1.79 % (1411273)Peak memory usage: 88 MB
% 5.93/1.79 % (1411273)Instructions burned: 296 (million)
% 5.93/1.79 % (1411276)Instruction limit reached!
% 5.93/1.79 % (1411276)------------------------------
% 5.93/1.79 % (1411276)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.79 % (1411276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.79 % (1411276)CaDiCaL version: 2.1.3
% 5.93/1.79 % (1411276)Termination reason: Instruction limit
% 5.93/1.79 % (1411276)Termination phase: Saturation
% 5.93/1.79 % (1411276)Time elapsed: 0.079 s
% 5.93/1.79 % (1411276)Peak memory usage: 90 MB
% 5.93/1.79 % (1411276)Instructions burned: 114 (million)
% 5.93/1.79 % (1411278)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=952441050:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 5.93/1.79 % (1411253)Refutation found. Thanks to Tanya!
% 5.93/1.79 % SZS status Theorem for theBenchmark
% 5.93/1.79 % SZS output start Proof for theBenchmark
% See solution above
% 7.06/1.90 % (1411253)------------------------------
% 7.06/1.90 % (1411253)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.06/1.90 % (1411253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.06/1.90 % (1411253)CaDiCaL version: 2.1.3
% 7.06/1.90 % (1411253)Termination reason: Refutation
% 7.06/1.90 % (1411253)Time elapsed: 0.638 s
% 7.06/1.90 % (1411253)Peak memory usage: 134 MB
% 7.06/1.90 % (1411253)Instructions burned: 1384 (million)
% 7.06/1.90 % (1411253)------------------------------
% 7.06/1.90 % (1411253)------------------------------
% 7.06/1.90 % (1411247)Success in time 0.937 s
% 7.06/1.90 % Vampire exiting
%------------------------------------------------------------------------------