%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU334+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:48:23 PM UTC 2026
% Result : Theorem 9.45s 2.19s
% Output : Refutation 9.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 26
% Syntax : Number of formulae : 279 ( 30 unt; 20 def)
% Number of atoms : 1320 ( 356 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 1725 ( 684 ~; 787 |; 169 &)
% ( 27 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 13 prp; 0-3 aty)
% Number of functors : 31 ( 31 usr; 6 con; 0-3 aty)
% Number of variables : 509 ( 0 sgn 448 !; 61 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( ( one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ( ( ! [X2,X3,X4] :
( ( in(X2,X1)
& ! [X5] :
( element(X5,powerset(the_carrier(X0)))
=> ( X5 = X2
=> X3 = subset_complement(the_carrier(X0),X5) ) )
& ! [X6] :
( element(X6,powerset(the_carrier(X0)))
=> ( X6 = X2
=> X4 = subset_complement(the_carrier(X0),X6) ) ) )
=> X3 = X4 )
& ! [X2] :
~ ( in(X2,X1)
& ! [X3] :
~ ! [X7] :
( element(X7,powerset(the_carrier(X0)))
=> ( X7 = X2
=> X3 = subset_complement(the_carrier(X0),X7) ) ) ) )
=> ? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> ! [X8] :
( element(X8,powerset(the_carrier(X0)))
=> ( X8 = X3
=> apply(X2,X3) = subset_complement(the_carrier(X0),X8) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_funct_1__e4_7_2__tops_2) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ( one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ( ( ! [X2,X3,X4] :
( ( in(X2,X1)
& ! [X5] :
( element(X5,powerset(the_carrier(X0)))
=> ( X5 = X2
=> X3 = subset_complement(the_carrier(X0),X5) ) )
& ! [X6] :
( element(X6,powerset(the_carrier(X0)))
=> ( X6 = X2
=> X4 = subset_complement(the_carrier(X0),X6) ) ) )
=> X3 = X4 )
& ! [X2] :
~ ( in(X2,X1)
& ! [X3] :
~ ! [X7] :
( element(X7,powerset(the_carrier(X0)))
=> ( X7 = X2
=> X3 = subset_complement(the_carrier(X0),X7) ) ) ) )
=> ? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> ! [X8] :
( element(X8,powerset(the_carrier(X0)))
=> ( X8 = X3
=> apply(X2,X3) = subset_complement(the_carrier(X0),X8) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f31,axiom,
! [X0,X1] :
( ( one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ( ! [X2,X3,X4] :
( ( in(X2,X1)
& ! [X5] :
( element(X5,powerset(the_carrier(X0)))
=> ( X5 = X2
=> X3 = subset_complement(the_carrier(X0),X5) ) )
& in(X2,X1)
& ! [X6] :
( element(X6,powerset(the_carrier(X0)))
=> ( X6 = X2
=> X4 = subset_complement(the_carrier(X0),X6) ) ) )
=> X3 = X4 )
=> ? [X2] :
( relation(X2)
& function(X2)
& ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& in(X3,X1)
& ! [X7] :
( element(X7,powerset(the_carrier(X0)))
=> ( X7 = X3
=> X4 = subset_complement(the_carrier(X0),X7) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_funct_1__e4_7_2__tops_2__1) ).
fof(f35,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( ( in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) )
& ( ~ in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> X2 = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f36,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f37,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f42,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f63,plain,
~ ! [X0,X1] :
( ( one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ( ( ! [X2,X3,X4] :
( ( in(X2,X1)
& ! [X5] :
( element(X5,powerset(the_carrier(X0)))
=> ( X5 = X2
=> X3 = subset_complement(the_carrier(X0),X5) ) )
& ! [X6] :
( element(X6,powerset(the_carrier(X0)))
=> ( X6 = X2
=> X4 = subset_complement(the_carrier(X0),X6) ) ) )
=> X3 = X4 )
& ! [X7] :
~ ( in(X7,X1)
& ! [X8] :
~ ! [X9] :
( element(X9,powerset(the_carrier(X0)))
=> ( X7 = X9
=> subset_complement(the_carrier(X0),X9) = X8 ) ) ) )
=> ? [X10] :
( relation(X10)
& function(X10)
& relation_dom(X10) = X1
& ! [X11] :
( in(X11,X1)
=> ! [X12] :
( element(X12,powerset(the_carrier(X0)))
=> ( X11 = X12
=> apply(X10,X11) = subset_complement(the_carrier(X0),X12) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
fof(f64,plain,
! [X0,X1] :
( ( one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ( ! [X2,X3,X4] :
( ( in(X2,X1)
& ! [X5] :
( element(X5,powerset(the_carrier(X0)))
=> ( X5 = X2
=> X3 = subset_complement(the_carrier(X0),X5) ) )
& in(X2,X1)
& ! [X6] :
( element(X6,powerset(the_carrier(X0)))
=> ( X6 = X2
=> X4 = subset_complement(the_carrier(X0),X6) ) ) )
=> X3 = X4 )
=> ? [X7] :
( relation(X7)
& function(X7)
& ! [X8,X9] :
( in(ordered_pair(X8,X9),X7)
<=> ( in(X8,X1)
& in(X8,X1)
& ! [X10] :
( element(X10,powerset(the_carrier(X0)))
=> ( X8 = X10
=> subset_complement(the_carrier(X0),X10) = X9 ) ) ) ) ) ) ),
inference(rectify,[],[f31]) ).
fof(f82,plain,
? [X0,X1] :
( ! [X10] :
( ~ relation(X10)
| ~ function(X10)
| relation_dom(X10) != X1
| ? [X11] :
( ? [X12] :
( apply(X10,X11) != subset_complement(the_carrier(X0),X12)
& X11 = X12
& element(X12,powerset(the_carrier(X0))) )
& in(X11,X1) ) )
& ! [X2,X3,X4] :
( X3 = X4
| ~ in(X2,X1)
| ? [X5] :
( subset_complement(the_carrier(X0),X5) != X3
& X5 = X2
& element(X5,powerset(the_carrier(X0))) )
| ? [X6] :
( subset_complement(the_carrier(X0),X6) != X4
& X6 = X2
& element(X6,powerset(the_carrier(X0))) ) )
& ! [X7] :
( ~ in(X7,X1)
| ? [X8] :
! [X9] :
( subset_complement(the_carrier(X0),X9) = X8
| X7 != X9
| ~ element(X9,powerset(the_carrier(X0))) ) )
& one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(ennf_transformation,[],[f63]) ).
fof(f83,plain,
? [X0,X1] :
( ! [X10] :
( ~ relation(X10)
| ~ function(X10)
| relation_dom(X10) != X1
| ? [X11] :
( ? [X12] :
( apply(X10,X11) != subset_complement(the_carrier(X0),X12)
& X11 = X12
& element(X12,powerset(the_carrier(X0))) )
& in(X11,X1) ) )
& ! [X2,X3,X4] :
( X3 = X4
| ~ in(X2,X1)
| ? [X5] :
( subset_complement(the_carrier(X0),X5) != X3
& X5 = X2
& element(X5,powerset(the_carrier(X0))) )
| ? [X6] :
( subset_complement(the_carrier(X0),X6) != X4
& X6 = X2
& element(X6,powerset(the_carrier(X0))) ) )
& ! [X7] :
( ~ in(X7,X1)
| ? [X8] :
! [X9] :
( subset_complement(the_carrier(X0),X9) = X8
| X7 != X9
| ~ element(X9,powerset(the_carrier(X0))) ) )
& one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(flattening,[],[f82]) ).
fof(f98,plain,
! [X0,X1] :
( ? [X7] :
( relation(X7)
& function(X7)
& ! [X8,X9] :
( in(ordered_pair(X8,X9),X7)
<=> ( in(X8,X1)
& in(X8,X1)
& ! [X10] :
( subset_complement(the_carrier(X0),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(X0))) ) ) ) )
| ? [X2,X3,X4] :
( X3 != X4
& in(X2,X1)
& ! [X5] :
( X3 = subset_complement(the_carrier(X0),X5)
| X2 != X5
| ~ element(X5,powerset(the_carrier(X0))) )
& in(X2,X1)
& ! [X6] :
( X4 = subset_complement(the_carrier(X0),X6)
| X2 != X6
| ~ element(X6,powerset(the_carrier(X0))) ) )
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(ennf_transformation,[],[f64]) ).
fof(f99,plain,
! [X0,X1] :
( ? [X7] :
( relation(X7)
& function(X7)
& ! [X8,X9] :
( in(ordered_pair(X8,X9),X7)
<=> ( in(X8,X1)
& in(X8,X1)
& ! [X10] :
( subset_complement(the_carrier(X0),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(X0))) ) ) ) )
| ? [X2,X3,X4] :
( X3 != X4
& in(X2,X1)
& ! [X5] :
( X3 = subset_complement(the_carrier(X0),X5)
| X2 != X5
| ~ element(X5,powerset(the_carrier(X0))) )
& in(X2,X1)
& ! [X6] :
( X4 = subset_complement(the_carrier(X0),X6)
| X2 != X6
| ~ element(X6,powerset(the_carrier(X0))) ) )
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(flattening,[],[f98]) ).
fof(f102,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f103,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f102]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f115,definition,
! [X4,X0,X2] :
( ? [X6] :
( subset_complement(the_carrier(X0),X6) != X4
& X6 = X2
& element(X6,powerset(the_carrier(X0))) )
| ~ sP0(X4,X0,X2) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f116,plain,
? [X0,X1] :
( ! [X10] :
( ~ relation(X10)
| ~ function(X10)
| relation_dom(X10) != X1
| ? [X11] :
( ? [X12] :
( apply(X10,X11) != subset_complement(the_carrier(X0),X12)
& X11 = X12
& element(X12,powerset(the_carrier(X0))) )
& in(X11,X1) ) )
& ! [X2,X3,X4] :
( X3 = X4
| ~ in(X2,X1)
| ? [X5] :
( subset_complement(the_carrier(X0),X5) != X3
& X5 = X2
& element(X5,powerset(the_carrier(X0))) )
| sP0(X4,X0,X2) )
& ! [X7] :
( ~ in(X7,X1)
| ? [X8] :
! [X9] :
( subset_complement(the_carrier(X0),X9) = X8
| X7 != X9
| ~ element(X9,powerset(the_carrier(X0))) ) )
& one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(definition_folding,[],[f83,f115]) ).
fof(f117,definition,
! [X1,X0] :
( ? [X7] :
( relation(X7)
& function(X7)
& ! [X8,X9] :
( in(ordered_pair(X8,X9),X7)
<=> ( in(X8,X1)
& in(X8,X1)
& ! [X10] :
( subset_complement(the_carrier(X0),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(X0))) ) ) ) )
| ~ sP1(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f118,plain,
! [X0,X1] :
( sP1(X1,X0)
| ? [X2,X3,X4] :
( X3 != X4
& in(X2,X1)
& ! [X5] :
( X3 = subset_complement(the_carrier(X0),X5)
| X2 != X5
| ~ element(X5,powerset(the_carrier(X0))) )
& in(X2,X1)
& ! [X6] :
( X4 = subset_complement(the_carrier(X0),X6)
| X2 != X6
| ~ element(X6,powerset(the_carrier(X0))) ) )
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(definition_folding,[],[f99,f117]) ).
fof(f119,plain,
! [X4,X0,X2] :
( ? [X6] :
( subset_complement(the_carrier(X0),X6) != X4
& X6 = X2
& element(X6,powerset(the_carrier(X0))) )
| ~ sP0(X4,X0,X2) ),
inference(nnf_transformation,[],[f115]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ? [X3] :
( subset_complement(the_carrier(X1),X3) != X0
& X2 = X3
& element(X3,powerset(the_carrier(X1))) )
| ~ sP0(X0,X1,X2) ),
inference(rectify,[],[f119]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ( subset_complement(the_carrier(X1),sK2(X0,X1,X2)) != X0
& sK2(X0,X1,X2) = X2
& element(sK2(X0,X1,X2),powerset(the_carrier(X1))) )
| ~ sP0(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f120]) ).
fof(f122,plain,
? [X0,X1] :
( ! [X2] :
( ~ relation(X2)
| ~ function(X2)
| relation_dom(X2) != X1
| ? [X3] :
( ? [X4] :
( apply(X2,X3) != subset_complement(the_carrier(X0),X4)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) )
& in(X3,X1) ) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ in(X5,X1)
| ? [X8] :
( subset_complement(the_carrier(X0),X8) != X6
& X5 = X8
& element(X8,powerset(the_carrier(X0))) )
| sP0(X7,X0,X5) )
& ! [X9] :
( ~ in(X9,X1)
| ? [X10] :
! [X11] :
( subset_complement(the_carrier(X0),X11) = X10
| X9 != X11
| ~ element(X11,powerset(the_carrier(X0))) ) )
& one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(rectify,[],[f116]) ).
fof(f123,plain,
( ! [X2] :
( ~ relation(X2)
| ~ function(X2)
| relation_dom(X2) != sK4
| ( apply(X2,sK5(X2)) != subset_complement(the_carrier(sK3),sK6(X2))
& sK5(X2) = sK6(X2)
& element(sK6(X2),powerset(the_carrier(sK3)))
& in(sK5(X2),sK4) ) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ in(X5,sK4)
| ( subset_complement(the_carrier(sK3),sK7(X5,X6)) != X6
& sK7(X5,X6) = X5
& element(sK7(X5,X6),powerset(the_carrier(sK3))) )
| sP0(X7,sK3,X5) )
& ! [X9] :
( ~ in(X9,sK4)
| ! [X11] :
( sK8(X9) = subset_complement(the_carrier(sK3),X11)
| X9 != X11
| ~ element(X11,powerset(the_carrier(sK3))) ) )
& one_sorted_str(sK3)
& element(sK4,powerset(powerset(the_carrier(sK3)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X3,sK5(X2)),skolemize(X4,sK6(X2)),skolemize(X8,sK7(X5,X6)),skolemize(X10,sK8(X9))],[f122]) ).
fof(f127,plain,
! [X1,X0] :
( ? [X7] :
( relation(X7)
& function(X7)
& ! [X8,X9] :
( ( in(ordered_pair(X8,X9),X7)
| ~ in(X8,X1)
| ~ in(X8,X1)
| ? [X10] :
( subset_complement(the_carrier(X0),X10) != X9
& X8 = X10
& element(X10,powerset(the_carrier(X0))) ) )
& ( ( in(X8,X1)
& in(X8,X1)
& ! [X10] :
( subset_complement(the_carrier(X0),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(X0))) ) )
| ~ in(ordered_pair(X8,X9),X7) ) ) )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f117]) ).
fof(f128,plain,
! [X1,X0] :
( ? [X7] :
( relation(X7)
& function(X7)
& ! [X8,X9] :
( ( in(ordered_pair(X8,X9),X7)
| ~ in(X8,X1)
| ~ in(X8,X1)
| ? [X10] :
( subset_complement(the_carrier(X0),X10) != X9
& X8 = X10
& element(X10,powerset(the_carrier(X0))) ) )
& ( ( in(X8,X1)
& in(X8,X1)
& ! [X10] :
( subset_complement(the_carrier(X0),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(X0))) ) )
| ~ in(ordered_pair(X8,X9),X7) ) ) )
| ~ sP1(X1,X0) ),
inference(flattening,[],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( ? [X2] :
( relation(X2)
& function(X2)
& ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ~ in(X3,X0)
| ~ in(X3,X0)
| ? [X5] :
( subset_complement(the_carrier(X1),X5) != X4
& X3 = X5
& element(X5,powerset(the_carrier(X1))) ) )
& ( ( in(X3,X0)
& in(X3,X0)
& ! [X6] :
( subset_complement(the_carrier(X1),X6) = X4
| X3 != X6
| ~ element(X6,powerset(the_carrier(X1))) ) )
| ~ in(ordered_pair(X3,X4),X2) ) ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f128]) ).
fof(f130,plain,
! [X0,X1] :
( ( relation(sK12(X0,X1))
& function(sK12(X0,X1))
& ! [X3,X4] :
( ( in(ordered_pair(X3,X4),sK12(X0,X1))
| ~ in(X3,X0)
| ~ in(X3,X0)
| ( subset_complement(the_carrier(X1),sK13(X1,X3,X4)) != X4
& sK13(X1,X3,X4) = X3
& element(sK13(X1,X3,X4),powerset(the_carrier(X1))) ) )
& ( ( in(X3,X0)
& in(X3,X0)
& ! [X6] :
( subset_complement(the_carrier(X1),X6) = X4
| X3 != X6
| ~ element(X6,powerset(the_carrier(X1))) ) )
| ~ in(ordered_pair(X3,X4),sK12(X0,X1)) ) ) )
| ~ sP1(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X2,sK12(X0,X1)),skolemize(X5,sK13(X1,X3,X4))],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( sP1(X1,X0)
| ( sK15(X0,X1) != sK16(X0,X1)
& in(sK14(X0,X1),X1)
& ! [X5] :
( subset_complement(the_carrier(X0),X5) = sK15(X0,X1)
| sK14(X0,X1) != X5
| ~ element(X5,powerset(the_carrier(X0))) )
& in(sK14(X0,X1),X1)
& ! [X6] :
( subset_complement(the_carrier(X0),X6) = sK16(X0,X1)
| sK14(X0,X1) != X6
| ~ element(X6,powerset(the_carrier(X0))) ) )
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X2,sK14(X0,X1)),skolemize(X3,sK15(X0,X1)),skolemize(X4,sK16(X0,X1))],[f118]) ).
fof(f132,plain,
! [X0] :
( ! [X1,X2] :
( ( ( ( X2 = apply(X0,X1)
| ~ in(ordered_pair(X1,X2),X0) )
& ( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 ) )
| ~ in(X1,relation_dom(X0)) )
& ( ( ( X2 = apply(X0,X1)
| empty_set != X2 )
& ( X2 = empty_set
| apply(X0,X1) != X2 ) )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f103]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f104]) ).
fof(f134,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f133]) ).
fof(f135,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK17(X0,X1),X3),X0)
| ~ in(sK17(X0,X1),X1) )
& ( in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X0)
| in(sK17(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK19(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18,sK19]),skolemize(X2,sK17(X0,X1)),skolemize(X4,sK18(X0,X1)),skolemize(X7,sK19(X0,X5))],[f134]) ).
fof(f136,plain,
! [X0] : element(sK20(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X1,sK20(X0))],[f42]) ).
fof(f145,plain,
! [X2,X0,X1] :
( element(sK2(X0,X1,X2),powerset(the_carrier(X1)))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f121]) ).
fof(f146,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| sK2(X0,X1,X2) = X2 ),
inference(cnf_transformation,[],[f121]) ).
fof(f147,plain,
! [X2,X0,X1] :
( subset_complement(the_carrier(X1),sK2(X0,X1,X2)) != X0
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f121]) ).
fof(f148,plain,
element(sK4,powerset(powerset(the_carrier(sK3)))),
inference(cnf_transformation,[],[f123]) ).
fof(f149,plain,
one_sorted_str(sK3),
inference(cnf_transformation,[],[f123]) ).
fof(f151,plain,
! [X6,X7,X5] :
( X6 = X7
| ~ in(X5,sK4)
| element(sK7(X5,X6),powerset(the_carrier(sK3)))
| sP0(X7,sK3,X5) ),
inference(cnf_transformation,[],[f123]) ).
fof(f152,plain,
! [X6,X7,X5] :
( sP0(X7,sK3,X5)
| ~ in(X5,sK4)
| sK7(X5,X6) = X5
| X6 = X7 ),
inference(cnf_transformation,[],[f123]) ).
fof(f154,plain,
! [X2] :
( relation_dom(X2) != sK4
| ~ function(X2)
| ~ relation(X2)
| in(sK5(X2),sK4) ),
inference(cnf_transformation,[],[f123]) ).
fof(f155,plain,
! [X2] :
( ~ relation(X2)
| ~ function(X2)
| relation_dom(X2) != sK4
| element(sK6(X2),powerset(the_carrier(sK3))) ),
inference(cnf_transformation,[],[f123]) ).
fof(f156,plain,
! [X2] :
( relation_dom(X2) != sK4
| ~ function(X2)
| ~ relation(X2)
| sK5(X2) = sK6(X2) ),
inference(cnf_transformation,[],[f123]) ).
fof(f157,plain,
! [X2] :
( ~ relation(X2)
| ~ function(X2)
| relation_dom(X2) != sK4
| apply(X2,sK5(X2)) != subset_complement(the_carrier(sK3),sK6(X2)) ),
inference(cnf_transformation,[],[f123]) ).
fof(f196,plain,
! [X3,X0,X1,X6,X4] :
( subset_complement(the_carrier(X1),X6) = X4
| X3 != X6
| ~ element(X6,powerset(the_carrier(X1)))
| ~ in(ordered_pair(X3,X4),sK12(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f197,plain,
! [X3,X0,X1,X4] :
( in(X3,X0)
| ~ in(ordered_pair(X3,X4),sK12(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f200,plain,
! [X3,X0,X1,X4] :
( in(ordered_pair(X3,X4),sK12(X0,X1))
| ~ in(X3,X0)
| ~ in(X3,X0)
| sK13(X1,X3,X4) = X3
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f201,plain,
! [X3,X0,X1,X4] :
( in(ordered_pair(X3,X4),sK12(X0,X1))
| ~ in(X3,X0)
| ~ in(X3,X0)
| subset_complement(the_carrier(X1),sK13(X1,X3,X4)) != X4
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f202,plain,
! [X0,X1] :
( function(sK12(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f203,plain,
! [X0,X1] :
( relation(sK12(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f204,plain,
! [X0,X1,X6] :
( sP1(X1,X0)
| subset_complement(the_carrier(X0),X6) = sK16(X0,X1)
| sK14(X0,X1) != X6
| ~ element(X6,powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f131]) ).
fof(f205,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| in(sK14(X0,X1),X1)
| ~ one_sorted_str(X0)
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f206,plain,
! [X0,X1,X5] :
( sP1(X1,X0)
| subset_complement(the_carrier(X0),X5) = sK15(X0,X1)
| sK14(X0,X1) != X5
| ~ element(X5,powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f131]) ).
fof(f208,plain,
! [X0,X1] :
( sK15(X0,X1) != sK16(X0,X1)
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f131]) ).
fof(f215,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f216,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK19(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f217,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f218,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(ordered_pair(sK17(X0,X1),sK18(X0,X1)),X0)
| in(sK17(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f219,plain,
! [X3,X0,X1] :
( relation_dom(X0) = X1
| ~ in(ordered_pair(sK17(X0,X1),X3),X0)
| ~ in(sK17(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f220,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f37]) ).
fof(f221,plain,
! [X0] : element(sK20(X0),X0),
inference(cnf_transformation,[],[f136]) ).
fof(f249,plain,
! [X3,X0,X1,X4] :
( in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),sK12(X0,X1))
| ~ in(X3,X0)
| ~ in(X3,X0)
| subset_complement(the_carrier(X1),sK13(X1,X3,X4)) != X4
| ~ sP1(X0,X1) ),
inference(definition_unfolding,[],[f201,f220]) ).
fof(f250,plain,
! [X3,X0,X1,X4] :
( in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),sK12(X0,X1))
| ~ in(X3,X0)
| ~ in(X3,X0)
| sK13(X1,X3,X4) = X3
| ~ sP1(X0,X1) ),
inference(definition_unfolding,[],[f200,f220]) ).
fof(f253,plain,
! [X3,X0,X1,X4] :
( ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),sK12(X0,X1))
| in(X3,X0)
| ~ sP1(X0,X1) ),
inference(definition_unfolding,[],[f197,f220]) ).
fof(f254,plain,
! [X3,X0,X1,X6,X4] :
( subset_complement(the_carrier(X1),X6) = X4
| X3 != X6
| ~ element(X6,powerset(the_carrier(X1)))
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),sK12(X0,X1))
| ~ sP1(X0,X1) ),
inference(definition_unfolding,[],[f196,f220]) ).
fof(f255,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(definition_unfolding,[],[f215,f220]) ).
fof(f257,plain,
! [X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK17(X0,X1),X3),singleton(sK17(X0,X1))),X0)
| relation_dom(X0) = X1
| ~ in(sK17(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f219,f220]) ).
fof(f258,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK17(X0,X1),sK18(X0,X1)),singleton(sK17(X0,X1))),X0)
| relation_dom(X0) = X1
| in(sK17(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f218,f220]) ).
fof(f259,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f217,f220]) ).
fof(f260,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK19(X0,X5)),singleton(X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f216,f220]) ).
fof(f263,plain,
! [X0,X1,X6,X4] :
( ~ in(unordered_pair(unordered_pair(X6,X4),singleton(X6)),sK12(X0,X1))
| ~ element(X6,powerset(the_carrier(X1)))
| subset_complement(the_carrier(X1),X6) = X4
| ~ sP1(X0,X1) ),
inference(equality_resolution,[],[f254]) ).
fof(f264,plain,
! [X0,X1] :
( ~ element(sK14(X0,X1),powerset(the_carrier(X0)))
| sK15(X0,X1) = subset_complement(the_carrier(X0),sK14(X0,X1))
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f206]) ).
fof(f265,plain,
! [X0,X1] :
( ~ element(sK14(X0,X1),powerset(the_carrier(X0)))
| sK16(X0,X1) = subset_complement(the_carrier(X0),sK14(X0,X1))
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f204]) ).
fof(f269,plain,
! [X0,X6,X5] :
( ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f259]) ).
fof(f270,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK19(X0,X5)),singleton(X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f260]) ).
fof(f271,definition,
! [X2] : sF28(X2) = apply(X2,sK5(X2)),
introduced(definition,[new_symbols(definition,[sF28])],[function_definition]) ).
fof(f272,plain,
! [X2] : apply(X2,sK5(X2)) = sF28(X2),
inference(reorient_equations,[],[f271]) ).
fof(f273,definition,
sF29 = the_carrier(sK3),
introduced(definition,[new_symbols(definition,[sF29])],[function_definition]) ).
fof(f274,plain,
the_carrier(sK3) = sF29,
inference(reorient_equations,[],[f273]) ).
fof(f275,definition,
! [X2] : sF30(X2) = subset_complement(sF29,sK6(X2)),
introduced(definition,[new_symbols(definition,[sF30])],[function_definition]) ).
fof(f276,plain,
! [X2] : subset_complement(sF29,sK6(X2)) = sF30(X2),
inference(reorient_equations,[],[f275]) ).
fof(f277,plain,
! [X2] :
( sF28(X2) != sF30(X2)
| ~ function(X2)
| relation_dom(X2) != sK4
| ~ relation(X2) ),
inference(definition_folding,[],[f157,f276,f274,f272]) ).
fof(f278,definition,
sF31 = powerset(sF29),
introduced(definition,[new_symbols(definition,[sF31])],[function_definition]) ).
fof(f279,plain,
powerset(sF29) = sF31,
inference(reorient_equations,[],[f278]) ).
fof(f280,plain,
! [X2] :
( relation_dom(X2) != sK4
| ~ function(X2)
| ~ relation(X2)
| element(sK6(X2),sF31) ),
inference(definition_folding,[],[f155,f279,f274]) ).
fof(f284,plain,
! [X6,X7,X5] :
( element(sK7(X5,X6),sF31)
| sP0(X7,sK3,X5)
| ~ in(X5,sK4)
| X6 = X7 ),
inference(definition_folding,[],[f151,f279,f274]) ).
fof(f285,definition,
! [X11] : sF33(X11) = subset_complement(sF29,X11),
introduced(definition,[new_symbols(definition,[sF33])],[function_definition]) ).
fof(f286,plain,
! [X11] : subset_complement(sF29,X11) = sF33(X11),
inference(reorient_equations,[],[f285]) ).
fof(f288,definition,
sF34 = powerset(sF31),
introduced(definition,[new_symbols(definition,[sF34])],[function_definition]) ).
fof(f289,plain,
powerset(sF31) = sF34,
inference(reorient_equations,[],[f288]) ).
fof(f290,plain,
element(sK4,sF34),
inference(definition_folding,[],[f148,f289,f279,f274]) ).
fof(f292,plain,
! [X3,X0,X1,X4] :
( in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),sK12(X0,X1))
| ~ in(X3,X0)
| sK13(X1,X3,X4) = X3
| ~ sP1(X0,X1) ),
inference(duplicate_literal_removal,[],[f250]) ).
fof(f293,plain,
! [X3,X0,X1,X4] :
( subset_complement(the_carrier(X1),sK13(X1,X3,X4)) != X4
| ~ in(X3,X0)
| in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),sK12(X0,X1))
| ~ sP1(X0,X1) ),
inference(duplicate_literal_removal,[],[f249]) ).
fof(f294,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| apply(X0,X1) = X2
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f255,f269]) ).
fof(f304,plain,
! [X0] : sF30(X0) = sF33(sK6(X0)),
inference(superposition,[],[f286,f276]) ).
fof(f305,plain,
! [X0] :
( ~ element(X0,powerset(powerset(sF29)))
| in(sK14(sK3,X0),X0)
| ~ one_sorted_str(sK3)
| sP1(X0,sK3) ),
inference(superposition,[],[f205,f274]) ).
fof(f306,plain,
! [X0] :
( ~ element(X0,powerset(powerset(sF29)))
| in(sK14(sK3,X0),X0)
| sP1(X0,sK3) ),
inference(forward_subsumption_resolution,[],[f305,f149]) ).
fof(f307,plain,
! [X0] :
( ~ element(X0,powerset(sF31))
| in(sK14(sK3,X0),X0)
| sP1(X0,sK3) ),
inference(forward_demodulation,[],[f306,f279]) ).
fof(f308,plain,
! [X0] :
( in(sK14(sK3,X0),X0)
| ~ element(X0,sF34)
| sP1(X0,sK3) ),
inference(forward_demodulation,[],[f307,f289]) ).
fof(f312,definition,
( spl35_1
<=> sP1(sK4,sK3) ),
introduced(definition,[new_symbols(definition,[spl35_1])],[avatar_definition]) ).
fof(f313,plain,
( ~ sP1(sK4,sK3)
| spl35_1 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f314,plain,
( sP1(sK4,sK3)
| ~ spl35_1 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f316,definition,
( spl35_2
<=> element(sK14(sK3,sK4),sF31) ),
introduced(definition,[new_symbols(definition,[spl35_2])],[avatar_definition]) ).
fof(f317,plain,
( element(sK14(sK3,sK4),sF31)
| ~ spl35_2 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f318,plain,
( ~ element(sK14(sK3,sK4),sF31)
| spl35_2 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f324,plain,
! [X0] :
( ~ element(sK14(sK3,X0),powerset(sF29))
| sK16(sK3,X0) = subset_complement(sF29,sK14(sK3,X0))
| sP1(X0,sK3)
| ~ one_sorted_str(sK3)
| ~ element(X0,powerset(powerset(sF29))) ),
inference(superposition,[],[f265,f274]) ).
fof(f325,plain,
! [X0] :
( ~ element(sK14(sK3,X0),powerset(sF29))
| sK16(sK3,X0) = subset_complement(sF29,sK14(sK3,X0))
| sP1(X0,sK3)
| ~ element(X0,powerset(powerset(sF29))) ),
inference(forward_subsumption_resolution,[],[f324,f149]) ).
fof(f326,plain,
! [X0] :
( ~ element(sK14(sK3,X0),sF31)
| sK16(sK3,X0) = subset_complement(sF29,sK14(sK3,X0))
| sP1(X0,sK3)
| ~ element(X0,powerset(powerset(sF29))) ),
inference(forward_demodulation,[],[f325,f279]) ).
fof(f327,plain,
! [X0] :
( sK16(sK3,X0) = sF33(sK14(sK3,X0))
| ~ element(sK14(sK3,X0),sF31)
| sP1(X0,sK3)
| ~ element(X0,powerset(powerset(sF29))) ),
inference(forward_demodulation,[],[f326,f286]) ).
fof(f328,plain,
! [X0] :
( ~ element(X0,powerset(sF31))
| sK16(sK3,X0) = sF33(sK14(sK3,X0))
| ~ element(sK14(sK3,X0),sF31)
| sP1(X0,sK3) ),
inference(forward_demodulation,[],[f327,f279]) ).
fof(f329,plain,
! [X0] :
( ~ element(sK14(sK3,X0),sF31)
| sK16(sK3,X0) = sF33(sK14(sK3,X0))
| ~ element(X0,sF34)
| sP1(X0,sK3) ),
inference(forward_demodulation,[],[f328,f289]) ).
fof(f330,plain,
! [X0] :
( ~ element(sK14(sK3,X0),powerset(sF29))
| subset_complement(sF29,sK14(sK3,X0)) = sK15(sK3,X0)
| sP1(X0,sK3)
| ~ one_sorted_str(sK3)
| ~ element(X0,powerset(powerset(sF29))) ),
inference(superposition,[],[f264,f274]) ).
fof(f331,plain,
! [X0] :
( ~ element(sK14(sK3,X0),powerset(sF29))
| subset_complement(sF29,sK14(sK3,X0)) = sK15(sK3,X0)
| sP1(X0,sK3)
| ~ element(X0,powerset(powerset(sF29))) ),
inference(forward_subsumption_resolution,[],[f330,f149]) ).
fof(f332,plain,
! [X0] :
( ~ element(sK14(sK3,X0),sF31)
| subset_complement(sF29,sK14(sK3,X0)) = sK15(sK3,X0)
| sP1(X0,sK3)
| ~ element(X0,powerset(powerset(sF29))) ),
inference(forward_demodulation,[],[f331,f279]) ).
fof(f333,plain,
! [X0] :
( sF33(sK14(sK3,X0)) = sK15(sK3,X0)
| ~ element(sK14(sK3,X0),sF31)
| sP1(X0,sK3)
| ~ element(X0,powerset(powerset(sF29))) ),
inference(forward_demodulation,[],[f332,f286]) ).
fof(f334,plain,
! [X0] :
( ~ element(X0,powerset(sF31))
| sF33(sK14(sK3,X0)) = sK15(sK3,X0)
| ~ element(sK14(sK3,X0),sF31)
| sP1(X0,sK3) ),
inference(forward_demodulation,[],[f333,f279]) ).
fof(f335,plain,
! [X0] :
( ~ element(sK14(sK3,X0),sF31)
| sF33(sK14(sK3,X0)) = sK15(sK3,X0)
| ~ element(X0,sF34)
| sP1(X0,sK3) ),
inference(forward_demodulation,[],[f334,f289]) ).
fof(f339,plain,
! [X2,X0,X1] :
( ~ in(X0,sK4)
| sK7(X0,X1) = X0
| X1 = X2
| sK2(X2,sK3,X0) = X0 ),
inference(resolution,[],[f152,f146]) ).
fof(f340,plain,
! [X0,X1] :
( sK14(sK3,sK4) = sK7(sK14(sK3,sK4),X0)
| X0 = X1
| sK14(sK3,sK4) = sK2(X1,sK3,sK14(sK3,sK4))
| ~ element(sK4,sF34)
| sP1(sK4,sK3) ),
inference(resolution,[],[f339,f308]) ).
fof(f343,plain,
! [X0,X1] :
( sK14(sK3,sK4) = sK7(sK14(sK3,sK4),X0)
| X0 = X1
| sK14(sK3,sK4) = sK2(X1,sK3,sK14(sK3,sK4))
| sP1(sK4,sK3) ),
inference(forward_subsumption_resolution,[],[f340,f290]) ).
fof(f345,definition,
( spl35_4
<=> ! [X0,X1] :
( sK14(sK3,sK4) = sK7(sK14(sK3,sK4),X0)
| sK14(sK3,sK4) = sK2(X1,sK3,sK14(sK3,sK4))
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[spl35_4])],[avatar_definition]) ).
fof(f346,plain,
( ! [X0,X1] :
( sK14(sK3,sK4) = sK7(sK14(sK3,sK4),X0)
| sK14(sK3,sK4) = sK2(X1,sK3,sK14(sK3,sK4))
| X0 = X1 )
| ~ spl35_4 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f347,plain,
( spl35_1
| spl35_4 ),
inference(avatar_split_clause,[],[f343,f345,f312]) ).
fof(f348,plain,
! [X2,X0,X1] :
( subset_complement(sF29,sK13(sK3,X0,X1)) != X1
| ~ in(X0,X2)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK12(X2,sK3))
| ~ sP1(X2,sK3) ),
inference(superposition,[],[f293,f274]) ).
fof(f349,plain,
! [X2,X0,X1] :
( sF33(sK13(sK3,X0,X1)) != X1
| ~ in(X0,X2)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK12(X2,sK3))
| ~ sP1(X2,sK3) ),
inference(forward_demodulation,[],[f348,f286]) ).
fof(f351,plain,
! [X0,X1] :
( element(sK2(X0,sK3,X1),powerset(sF29))
| ~ sP0(X0,sK3,X1) ),
inference(superposition,[],[f145,f274]) ).
fof(f352,plain,
! [X0,X1] :
( element(sK2(X0,sK3,X1),sF31)
| ~ sP0(X0,sK3,X1) ),
inference(forward_demodulation,[],[f351,f279]) ).
fof(f396,plain,
! [X2,X0,X1] :
( element(sK7(X1,X2),sF31)
| ~ in(X1,sK4)
| X0 = X2
| sK2(X0,sK3,X1) = X1 ),
inference(resolution,[],[f284,f146]) ).
fof(f409,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(sK12(X1,X2)))
| ~ relation(sK12(X1,X2))
| ~ element(X0,powerset(the_carrier(X2)))
| subset_complement(the_carrier(X2),X0) = sK19(sK12(X1,X2),X0)
| ~ sP1(X1,X2) ),
inference(resolution,[],[f270,f263]) ).
fof(f425,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(sK12(X1,X2)))
| ~ element(X0,powerset(the_carrier(X2)))
| subset_complement(the_carrier(X2),X0) = sK19(sK12(X1,X2),X0)
| ~ sP1(X1,X2) ),
inference(forward_subsumption_resolution,[],[f409,f203]) ).
fof(f509,plain,
! [X2,X3,X0,X1] :
( ~ in(sK17(sK12(X0,X1),X2),X0)
| sK17(sK12(X0,X1),X2) = sK13(X1,sK17(sK12(X0,X1),X2),X3)
| ~ sP1(X0,X1)
| relation_dom(sK12(X0,X1)) = X2
| ~ in(sK17(sK12(X0,X1),X2),X2)
| ~ relation(sK12(X0,X1)) ),
inference(resolution,[],[f292,f257]) ).
fof(f516,plain,
! [X2,X3,X0,X1] :
( ~ in(sK17(sK12(X0,X1),X2),X2)
| sK17(sK12(X0,X1),X2) = sK13(X1,sK17(sK12(X0,X1),X2),X3)
| ~ sP1(X0,X1)
| relation_dom(sK12(X0,X1)) = X2
| ~ in(sK17(sK12(X0,X1),X2),X0) ),
inference(forward_subsumption_resolution,[],[f509,f203]) ).
fof(f546,plain,
! [X2,X0,X1] :
( relation_dom(sK12(X0,X1)) = X2
| in(sK17(sK12(X0,X1),X2),X2)
| ~ relation(sK12(X0,X1))
| in(sK17(sK12(X0,X1),X2),X0)
| ~ sP1(X0,X1) ),
inference(resolution,[],[f258,f253]) ).
fof(f561,plain,
! [X2,X0,X1] :
( in(sK17(sK12(X0,X1),X2),X2)
| in(sK17(sK12(X0,X1),X2),X0)
| relation_dom(sK12(X0,X1)) = X2
| ~ sP1(X0,X1) ),
inference(forward_subsumption_resolution,[],[f546,f203]) ).
fof(f572,plain,
! [X0,X1] :
( in(sK17(sK12(X0,X1),X0),X0)
| relation_dom(sK12(X0,X1)) = X0
| ~ sP1(X0,X1) ),
inference(factoring,[],[f561]) ).
fof(f642,plain,
! [X2,X0,X1] :
( sK17(sK12(X0,X1),X0) = sK13(X1,sK17(sK12(X0,X1),X0),X2)
| ~ sP1(X0,X1)
| relation_dom(sK12(X0,X1)) = X0
| ~ in(sK17(sK12(X0,X1),X0),X0)
| relation_dom(sK12(X0,X1)) = X0
| ~ sP1(X0,X1) ),
inference(resolution,[],[f516,f572]) ).
fof(f646,plain,
! [X2,X0,X1] :
( sK17(sK12(X0,X1),X0) = sK13(X1,sK17(sK12(X0,X1),X0),X2)
| ~ sP1(X0,X1)
| relation_dom(sK12(X0,X1)) = X0
| ~ in(sK17(sK12(X0,X1),X0),X0) ),
inference(duplicate_literal_removal,[],[f642]) ).
fof(f648,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1)
| sK17(sK12(X0,X1),X0) = sK13(X1,sK17(sK12(X0,X1),X0),X2)
| relation_dom(sK12(X0,X1)) = X0 ),
inference(forward_subsumption_resolution,[],[f646,f572]) ).
fof(f649,plain,
( ! [X0] :
( sK17(sK12(sK4,sK3),sK4) = sK13(sK3,sK17(sK12(sK4,sK3),sK4),X0)
| sK4 = relation_dom(sK12(sK4,sK3)) )
| ~ spl35_1 ),
inference(resolution,[],[f648,f314]) ).
fof(f651,definition,
( spl35_17
<=> sK4 = relation_dom(sK12(sK4,sK3)) ),
introduced(definition,[new_symbols(definition,[spl35_17])],[avatar_definition]) ).
fof(f652,plain,
( sK4 != relation_dom(sK12(sK4,sK3))
| spl35_17 ),
inference(avatar_component_clause,[],[f651]) ).
fof(f653,plain,
( sK4 = relation_dom(sK12(sK4,sK3))
| ~ spl35_17 ),
inference(avatar_component_clause,[],[f651]) ).
fof(f655,definition,
( spl35_18
<=> ! [X0] : sK17(sK12(sK4,sK3),sK4) = sK13(sK3,sK17(sK12(sK4,sK3),sK4),X0) ),
introduced(definition,[new_symbols(definition,[spl35_18])],[avatar_definition]) ).
fof(f656,plain,
( ! [X0] : sK17(sK12(sK4,sK3),sK4) = sK13(sK3,sK17(sK12(sK4,sK3),sK4),X0)
| ~ spl35_18 ),
inference(avatar_component_clause,[],[f655]) ).
fof(f657,plain,
( spl35_17
| spl35_18
| ~ spl35_1 ),
inference(avatar_split_clause,[],[f649,f312,f655,f651]) ).
fof(f659,plain,
( ! [X2,X0,X1] :
( element(sK14(sK3,sK4),sF31)
| ~ in(sK14(sK3,sK4),sK4)
| X0 = X1
| sK14(sK3,sK4) = sK2(X1,sK3,sK14(sK3,sK4))
| sK14(sK3,sK4) = sK2(X2,sK3,sK14(sK3,sK4))
| X0 = X2 )
| ~ spl35_4 ),
inference(superposition,[],[f396,f346]) ).
fof(f671,plain,
( ! [X2,X0,X1] :
( ~ in(sK14(sK3,sK4),sK4)
| X0 = X1
| sK14(sK3,sK4) = sK2(X1,sK3,sK14(sK3,sK4))
| sK14(sK3,sK4) = sK2(X2,sK3,sK14(sK3,sK4))
| X0 = X2 )
| spl35_2
| ~ spl35_4 ),
inference(forward_subsumption_resolution,[],[f659,f318]) ).
fof(f675,definition,
( spl35_19
<=> in(sK14(sK3,sK4),sK4) ),
introduced(definition,[new_symbols(definition,[spl35_19])],[avatar_definition]) ).
fof(f676,plain,
( in(sK14(sK3,sK4),sK4)
| ~ spl35_19 ),
inference(avatar_component_clause,[],[f675]) ).
fof(f677,plain,
( ~ in(sK14(sK3,sK4),sK4)
| spl35_19 ),
inference(avatar_component_clause,[],[f675]) ).
fof(f683,definition,
( spl35_21
<=> ! [X2,X0,X1] :
( X0 = X1
| X0 = X2
| sK14(sK3,sK4) = sK2(X2,sK3,sK14(sK3,sK4))
| sK14(sK3,sK4) = sK2(X1,sK3,sK14(sK3,sK4)) ) ),
introduced(definition,[new_symbols(definition,[spl35_21])],[avatar_definition]) ).
fof(f684,plain,
( ! [X2,X0,X1] :
( X0 = X1
| X0 = X2
| sK14(sK3,sK4) = sK2(X2,sK3,sK14(sK3,sK4))
| sK14(sK3,sK4) = sK2(X1,sK3,sK14(sK3,sK4)) )
| ~ spl35_21 ),
inference(avatar_component_clause,[],[f683]) ).
fof(f685,plain,
( spl35_21
| ~ spl35_19
| spl35_2
| ~ spl35_4 ),
inference(avatar_split_clause,[],[f671,f345,f316,f675,f683]) ).
fof(f686,plain,
( ~ element(sK4,sF34)
| sP1(sK4,sK3)
| spl35_19 ),
inference(resolution,[],[f677,f308]) ).
fof(f687,plain,
( sP1(sK4,sK3)
| spl35_19 ),
inference(forward_subsumption_resolution,[],[f686,f290]) ).
fof(f688,plain,
( $false
| spl35_1
| spl35_19 ),
inference(forward_subsumption_resolution,[],[f687,f313]) ).
fof(f689,plain,
( spl35_1
| spl35_19 ),
inference(avatar_contradiction_clause,[],[f688]) ).
fof(f692,plain,
( ! [X0] :
( ~ in(X0,sK4)
| ~ element(X0,powerset(the_carrier(sK3)))
| subset_complement(the_carrier(sK3),X0) = sK19(sK12(sK4,sK3),X0)
| ~ sP1(sK4,sK3) )
| ~ spl35_17 ),
inference(superposition,[],[f425,f653]) ).
fof(f695,plain,
( sK4 != sK4
| ~ function(sK12(sK4,sK3))
| ~ relation(sK12(sK4,sK3))
| element(sK6(sK12(sK4,sK3)),sF31)
| ~ spl35_17 ),
inference(superposition,[],[f280,f653]) ).
fof(f697,plain,
( sK4 != sK4
| ~ function(sK12(sK4,sK3))
| ~ relation(sK12(sK4,sK3))
| in(sK5(sK12(sK4,sK3)),sK4)
| ~ spl35_17 ),
inference(superposition,[],[f154,f653]) ).
fof(f698,plain,
( sK4 != sK4
| ~ function(sK12(sK4,sK3))
| ~ relation(sK12(sK4,sK3))
| sK6(sK12(sK4,sK3)) = sK5(sK12(sK4,sK3))
| ~ spl35_17 ),
inference(superposition,[],[f156,f653]) ).
fof(f699,plain,
( ~ function(sK12(sK4,sK3))
| ~ relation(sK12(sK4,sK3))
| sK6(sK12(sK4,sK3)) = sK5(sK12(sK4,sK3))
| ~ spl35_17 ),
inference(trivial_inequality_removal,[],[f698]) ).
fof(f700,plain,
( ~ function(sK12(sK4,sK3))
| ~ relation(sK12(sK4,sK3))
| in(sK5(sK12(sK4,sK3)),sK4)
| ~ spl35_17 ),
inference(trivial_inequality_removal,[],[f697]) ).
fof(f701,plain,
( ~ function(sK12(sK4,sK3))
| ~ relation(sK12(sK4,sK3))
| element(sK6(sK12(sK4,sK3)),sF31)
| ~ spl35_17 ),
inference(trivial_inequality_removal,[],[f695]) ).
fof(f703,definition,
( spl35_22
<=> sK6(sK12(sK4,sK3)) = sK5(sK12(sK4,sK3)) ),
introduced(definition,[new_symbols(definition,[spl35_22])],[avatar_definition]) ).
fof(f705,plain,
( sK6(sK12(sK4,sK3)) = sK5(sK12(sK4,sK3))
| ~ spl35_22 ),
inference(avatar_component_clause,[],[f703]) ).
fof(f707,definition,
( spl35_23
<=> relation(sK12(sK4,sK3)) ),
introduced(definition,[new_symbols(definition,[spl35_23])],[avatar_definition]) ).
fof(f708,plain,
( relation(sK12(sK4,sK3))
| ~ spl35_23 ),
inference(avatar_component_clause,[],[f707]) ).
fof(f709,plain,
( ~ relation(sK12(sK4,sK3))
| spl35_23 ),
inference(avatar_component_clause,[],[f707]) ).
fof(f711,definition,
( spl35_24
<=> function(sK12(sK4,sK3)) ),
introduced(definition,[new_symbols(definition,[spl35_24])],[avatar_definition]) ).
fof(f712,plain,
( function(sK12(sK4,sK3))
| ~ spl35_24 ),
inference(avatar_component_clause,[],[f711]) ).
fof(f713,plain,
( ~ function(sK12(sK4,sK3))
| spl35_24 ),
inference(avatar_component_clause,[],[f711]) ).
fof(f714,plain,
( spl35_22
| ~ spl35_23
| ~ spl35_24
| ~ spl35_17 ),
inference(avatar_split_clause,[],[f699,f651,f711,f707,f703]) ).
fof(f716,definition,
( spl35_25
<=> in(sK5(sK12(sK4,sK3)),sK4) ),
introduced(definition,[new_symbols(definition,[spl35_25])],[avatar_definition]) ).
fof(f718,plain,
( in(sK5(sK12(sK4,sK3)),sK4)
| ~ spl35_25 ),
inference(avatar_component_clause,[],[f716]) ).
fof(f719,plain,
( spl35_25
| ~ spl35_23
| ~ spl35_24
| ~ spl35_17 ),
inference(avatar_split_clause,[],[f700,f651,f711,f707,f716]) ).
fof(f725,definition,
( spl35_27
<=> element(sK6(sK12(sK4,sK3)),sF31) ),
introduced(definition,[new_symbols(definition,[spl35_27])],[avatar_definition]) ).
fof(f727,plain,
( element(sK6(sK12(sK4,sK3)),sF31)
| ~ spl35_27 ),
inference(avatar_component_clause,[],[f725]) ).
fof(f728,plain,
( spl35_27
| ~ spl35_23
| ~ spl35_24
| ~ spl35_17 ),
inference(avatar_split_clause,[],[f701,f651,f711,f707,f725]) ).
fof(f739,plain,
( ~ sP1(sK4,sK3)
| spl35_23 ),
inference(resolution,[],[f709,f203]) ).
fof(f740,plain,
( $false
| ~ spl35_1
| spl35_23 ),
inference(forward_subsumption_resolution,[],[f739,f314]) ).
fof(f741,plain,
( ~ spl35_1
| spl35_23 ),
inference(avatar_contradiction_clause,[],[f740]) ).
fof(f1052,plain,
( ! [X0,X1] :
( sK14(sK3,sK4) != sK14(sK3,sK4)
| X0 = X1
| X0 = X1
| sK14(sK3,sK4) = sK2(X0,sK3,sK14(sK3,sK4)) )
| ~ spl35_21 ),
inference(equality_factoring,[],[f684]) ).
fof(f1053,plain,
( ! [X0,X1] :
( sK14(sK3,sK4) != sK14(sK3,sK4)
| X0 = X1
| sK14(sK3,sK4) = sK2(X0,sK3,sK14(sK3,sK4)) )
| ~ spl35_21 ),
inference(duplicate_literal_removal,[],[f1052]) ).
fof(f1054,plain,
( ! [X0,X1] :
( X0 = X1
| sK14(sK3,sK4) = sK2(X0,sK3,sK14(sK3,sK4)) )
| ~ spl35_21 ),
inference(trivial_inequality_removal,[],[f1053]) ).
fof(f1214,plain,
( ! [X0,X1] :
( element(sK14(sK3,sK4),sF31)
| ~ sP0(X0,sK3,sK14(sK3,sK4))
| X0 = X1 )
| ~ spl35_21 ),
inference(superposition,[],[f352,f1054]) ).
fof(f1218,plain,
( ! [X0] :
( sK14(sK3,sK4) != X0
| sK14(sK3,sK4) = sK2(X0,sK3,sK14(sK3,sK4)) )
| ~ spl35_21 ),
inference(equality_factoring,[],[f1054]) ).
fof(f1220,plain,
( ! [X0] : sK14(sK3,sK4) = sK2(X0,sK3,sK14(sK3,sK4))
| ~ spl35_21 ),
inference(forward_subsumption_resolution,[],[f1218,f1054]) ).
fof(f1223,plain,
( ! [X0,X1] :
( ~ sP0(X0,sK3,sK14(sK3,sK4))
| X0 = X1 )
| spl35_2
| ~ spl35_21 ),
inference(forward_subsumption_resolution,[],[f1214,f318]) ).
fof(f1271,plain,
( ! [X0] :
( ~ in(X0,sK4)
| ~ element(X0,powerset(the_carrier(sK3)))
| subset_complement(the_carrier(sK3),X0) = sK19(sK12(sK4,sK3),X0) )
| ~ spl35_1
| ~ spl35_17 ),
inference(forward_subsumption_resolution,[],[f692,f314]) ).
fof(f1273,plain,
( ! [X0] :
( ~ element(X0,powerset(sF29))
| ~ in(X0,sK4)
| subset_complement(the_carrier(sK3),X0) = sK19(sK12(sK4,sK3),X0) )
| ~ spl35_1
| ~ spl35_17 ),
inference(forward_demodulation,[],[f1271,f274]) ).
fof(f1275,plain,
( ! [X0] :
( ~ element(X0,sF31)
| ~ in(X0,sK4)
| subset_complement(the_carrier(sK3),X0) = sK19(sK12(sK4,sK3),X0) )
| ~ spl35_1
| ~ spl35_17 ),
inference(forward_demodulation,[],[f1273,f279]) ).
fof(f1277,plain,
( ! [X0] :
( subset_complement(sF29,X0) = sK19(sK12(sK4,sK3),X0)
| ~ element(X0,sF31)
| ~ in(X0,sK4) )
| ~ spl35_1
| ~ spl35_17 ),
inference(forward_demodulation,[],[f1275,f274]) ).
fof(f1279,plain,
( ! [X0] :
( ~ in(X0,sK4)
| ~ element(X0,sF31)
| sF33(X0) = sK19(sK12(sK4,sK3),X0) )
| ~ spl35_1
| ~ spl35_17 ),
inference(forward_demodulation,[],[f1277,f286]) ).
fof(f1280,plain,
( ~ sP1(sK4,sK3)
| spl35_24 ),
inference(resolution,[],[f713,f202]) ).
fof(f1281,plain,
( $false
| ~ spl35_1
| spl35_24 ),
inference(forward_subsumption_resolution,[],[f1280,f314]) ).
fof(f1282,plain,
( ~ spl35_1
| spl35_24 ),
inference(avatar_contradiction_clause,[],[f1281]) ).
fof(f1283,plain,
( element(sK5(sK12(sK4,sK3)),sF31)
| ~ spl35_22
| ~ spl35_27 ),
inference(forward_demodulation,[],[f727,f705]) ).
fof(f1287,plain,
( sF33(sK5(sK12(sK4,sK3))) = sF30(sK12(sK4,sK3))
| ~ spl35_22 ),
inference(superposition,[],[f304,f705]) ).
fof(f1316,plain,
( ~ element(sK5(sK12(sK4,sK3)),sF31)
| sF33(sK5(sK12(sK4,sK3))) = sK19(sK12(sK4,sK3),sK5(sK12(sK4,sK3)))
| ~ spl35_1
| ~ spl35_17
| ~ spl35_25 ),
inference(resolution,[],[f1279,f718]) ).
fof(f1323,plain,
( sF33(sK5(sK12(sK4,sK3))) = sK19(sK12(sK4,sK3),sK5(sK12(sK4,sK3)))
| ~ spl35_1
| ~ spl35_17
| ~ spl35_22
| ~ spl35_25
| ~ spl35_27 ),
inference(forward_subsumption_resolution,[],[f1316,f1283]) ).
fof(f1324,plain,
( sF30(sK12(sK4,sK3)) = sK19(sK12(sK4,sK3),sK5(sK12(sK4,sK3)))
| ~ spl35_1
| ~ spl35_17
| ~ spl35_22
| ~ spl35_25
| ~ spl35_27 ),
inference(forward_demodulation,[],[f1323,f1287]) ).
fof(f1325,plain,
( in(unordered_pair(unordered_pair(sK5(sK12(sK4,sK3)),sF30(sK12(sK4,sK3))),singleton(sK5(sK12(sK4,sK3)))),sK12(sK4,sK3))
| ~ in(sK5(sK12(sK4,sK3)),relation_dom(sK12(sK4,sK3)))
| ~ relation(sK12(sK4,sK3))
| ~ spl35_1
| ~ spl35_17
| ~ spl35_22
| ~ spl35_25
| ~ spl35_27 ),
inference(superposition,[],[f270,f1324]) ).
fof(f1326,plain,
( in(unordered_pair(unordered_pair(sK5(sK12(sK4,sK3)),sF30(sK12(sK4,sK3))),singleton(sK5(sK12(sK4,sK3)))),sK12(sK4,sK3))
| ~ in(sK5(sK12(sK4,sK3)),relation_dom(sK12(sK4,sK3)))
| ~ spl35_1
| ~ spl35_17
| ~ spl35_22
| ~ spl35_23
| ~ spl35_25
| ~ spl35_27 ),
inference(forward_subsumption_resolution,[],[f1325,f708]) ).
fof(f1327,plain,
( ~ in(sK5(sK12(sK4,sK3)),sK4)
| in(unordered_pair(unordered_pair(sK5(sK12(sK4,sK3)),sF30(sK12(sK4,sK3))),singleton(sK5(sK12(sK4,sK3)))),sK12(sK4,sK3))
| ~ spl35_1
| ~ spl35_17
| ~ spl35_22
| ~ spl35_23
| ~ spl35_25
| ~ spl35_27 ),
inference(forward_demodulation,[],[f1326,f653]) ).
fof(f1328,plain,
( in(unordered_pair(unordered_pair(sK5(sK12(sK4,sK3)),sF30(sK12(sK4,sK3))),singleton(sK5(sK12(sK4,sK3)))),sK12(sK4,sK3))
| ~ spl35_1
| ~ spl35_17
| ~ spl35_22
| ~ spl35_23
| ~ spl35_25
| ~ spl35_27 ),
inference(forward_subsumption_resolution,[],[f1327,f718]) ).
fof(f1331,plain,
( sF30(sK12(sK4,sK3)) = apply(sK12(sK4,sK3),sK5(sK12(sK4,sK3)))
| ~ relation(sK12(sK4,sK3))
| ~ function(sK12(sK4,sK3))
| ~ spl35_1
| ~ spl35_17
| ~ spl35_22
| ~ spl35_23
| ~ spl35_25
| ~ spl35_27 ),
inference(resolution,[],[f1328,f294]) ).
fof(f1336,plain,
( sF30(sK12(sK4,sK3)) = apply(sK12(sK4,sK3),sK5(sK12(sK4,sK3)))
| ~ function(sK12(sK4,sK3))
| ~ spl35_1
| ~ spl35_17
| ~ spl35_22
| ~ spl35_23
| ~ spl35_25
| ~ spl35_27 ),
inference(forward_subsumption_resolution,[],[f1331,f708]) ).
fof(f1339,plain,
( sF30(sK12(sK4,sK3)) = apply(sK12(sK4,sK3),sK5(sK12(sK4,sK3)))
| ~ spl35_1
| ~ spl35_17
| ~ spl35_22
| ~ spl35_23
| ~ spl35_24
| ~ spl35_25
| ~ spl35_27 ),
inference(forward_subsumption_resolution,[],[f1336,f712]) ).
fof(f1341,plain,
( sF30(sK12(sK4,sK3)) = sF28(sK12(sK4,sK3))
| ~ spl35_1
| ~ spl35_17
| ~ spl35_22
| ~ spl35_23
| ~ spl35_24
| ~ spl35_25
| ~ spl35_27 ),
inference(forward_demodulation,[],[f1339,f272]) ).
fof(f1348,plain,
( sF28(sK12(sK4,sK3)) != sF28(sK12(sK4,sK3))
| ~ function(sK12(sK4,sK3))
| sK4 != relation_dom(sK12(sK4,sK3))
| ~ relation(sK12(sK4,sK3))
| ~ spl35_1
| ~ spl35_17
| ~ spl35_22
| ~ spl35_23
| ~ spl35_24
| ~ spl35_25
| ~ spl35_27 ),
inference(superposition,[],[f277,f1341]) ).
fof(f1349,plain,
( ~ function(sK12(sK4,sK3))
| sK4 != relation_dom(sK12(sK4,sK3))
| ~ relation(sK12(sK4,sK3))
| ~ spl35_1
| ~ spl35_17
| ~ spl35_22
| ~ spl35_23
| ~ spl35_24
| ~ spl35_25
| ~ spl35_27 ),
inference(trivial_inequality_removal,[],[f1348]) ).
fof(f1350,plain,
( sK4 != relation_dom(sK12(sK4,sK3))
| ~ relation(sK12(sK4,sK3))
| ~ spl35_1
| ~ spl35_17
| ~ spl35_22
| ~ spl35_23
| ~ spl35_24
| ~ spl35_25
| ~ spl35_27 ),
inference(forward_subsumption_resolution,[],[f1349,f712]) ).
fof(f1351,plain,
( ~ relation(sK12(sK4,sK3))
| ~ spl35_1
| ~ spl35_17
| ~ spl35_22
| ~ spl35_23
| ~ spl35_24
| ~ spl35_25
| ~ spl35_27 ),
inference(forward_subsumption_resolution,[],[f1350,f653]) ).
fof(f1352,plain,
( $false
| ~ spl35_1
| ~ spl35_17
| ~ spl35_22
| ~ spl35_23
| ~ spl35_24
| ~ spl35_25
| ~ spl35_27 ),
inference(forward_subsumption_resolution,[],[f1351,f708]) ).
fof(f1353,plain,
( ~ spl35_1
| ~ spl35_17
| ~ spl35_22
| ~ spl35_23
| ~ spl35_24
| ~ spl35_25
| ~ spl35_27 ),
inference(avatar_contradiction_clause,[],[f1352]) ).
fof(f1354,plain,
( ! [X0,X1] :
( sF33(sK17(sK12(sK4,sK3),sK4)) != X0
| ~ in(sK17(sK12(sK4,sK3),sK4),X1)
| in(unordered_pair(unordered_pair(sK17(sK12(sK4,sK3),sK4),X0),singleton(sK17(sK12(sK4,sK3),sK4))),sK12(X1,sK3))
| ~ sP1(X1,sK3) )
| ~ spl35_18 ),
inference(superposition,[],[f349,f656]) ).
fof(f1674,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(sK17(sK12(sK4,sK3),sK4),sF33(sK17(sK12(sK4,sK3),sK4))),singleton(sK17(sK12(sK4,sK3),sK4))),sK12(X0,sK3))
| ~ in(sK17(sK12(sK4,sK3),sK4),X0)
| ~ sP1(X0,sK3) )
| ~ spl35_18 ),
inference(equality_resolution,[],[f1354]) ).
fof(f1675,plain,
( ~ in(sK17(sK12(sK4,sK3),sK4),sK4)
| ~ sP1(sK4,sK3)
| sK4 = relation_dom(sK12(sK4,sK3))
| ~ in(sK17(sK12(sK4,sK3),sK4),sK4)
| ~ relation(sK12(sK4,sK3))
| ~ spl35_18 ),
inference(resolution,[],[f1674,f257]) ).
fof(f1684,plain,
( ~ in(sK17(sK12(sK4,sK3),sK4),sK4)
| ~ sP1(sK4,sK3)
| sK4 = relation_dom(sK12(sK4,sK3))
| ~ relation(sK12(sK4,sK3))
| ~ spl35_18 ),
inference(duplicate_literal_removal,[],[f1675]) ).
fof(f1688,plain,
( ~ sP1(sK4,sK3)
| sK4 = relation_dom(sK12(sK4,sK3))
| ~ relation(sK12(sK4,sK3))
| ~ spl35_18 ),
inference(forward_subsumption_resolution,[],[f1684,f572]) ).
fof(f1691,plain,
( sK4 = relation_dom(sK12(sK4,sK3))
| ~ relation(sK12(sK4,sK3))
| ~ spl35_1
| ~ spl35_18 ),
inference(forward_subsumption_resolution,[],[f1688,f314]) ).
fof(f1693,plain,
( ~ relation(sK12(sK4,sK3))
| ~ spl35_1
| spl35_17
| ~ spl35_18 ),
inference(forward_subsumption_resolution,[],[f1691,f652]) ).
fof(f1694,plain,
( $false
| ~ spl35_1
| spl35_17
| ~ spl35_18
| ~ spl35_23 ),
inference(forward_subsumption_resolution,[],[f1693,f708]) ).
fof(f1695,plain,
( ~ spl35_1
| spl35_17
| ~ spl35_18
| ~ spl35_23 ),
inference(avatar_contradiction_clause,[],[f1694]) ).
fof(f1935,plain,
( ! [X0] :
( subset_complement(the_carrier(sK3),sK14(sK3,sK4)) != X0
| ~ sP0(X0,sK3,sK14(sK3,sK4)) )
| ~ spl35_21 ),
inference(superposition,[],[f147,f1220]) ).
fof(f1936,plain,
( ! [X0] : ~ sP0(X0,sK3,sK14(sK3,sK4))
| spl35_2
| ~ spl35_21 ),
inference(forward_subsumption_resolution,[],[f1935,f1223]) ).
fof(f1941,plain,
( ! [X0,X1] :
( element(sK7(sK14(sK3,sK4),X1),sF31)
| ~ in(sK14(sK3,sK4),sK4)
| X0 = X1 )
| spl35_2
| ~ spl35_21 ),
inference(resolution,[],[f1936,f284]) ).
fof(f1942,plain,
( ! [X0,X1] :
( ~ in(sK14(sK3,sK4),sK4)
| sK14(sK3,sK4) = sK7(sK14(sK3,sK4),X0)
| X0 = X1 )
| spl35_2
| ~ spl35_21 ),
inference(resolution,[],[f1936,f152]) ).
fof(f1943,plain,
( ! [X0,X1] :
( sK14(sK3,sK4) = sK7(sK14(sK3,sK4),X0)
| X0 = X1 )
| spl35_2
| ~ spl35_19
| ~ spl35_21 ),
inference(forward_subsumption_resolution,[],[f1942,f676]) ).
fof(f1944,plain,
( ! [X0,X1] :
( element(sK7(sK14(sK3,sK4),X1),sF31)
| X0 = X1 )
| spl35_2
| ~ spl35_19
| ~ spl35_21 ),
inference(forward_subsumption_resolution,[],[f1941,f676]) ).
fof(f1952,plain,
( ! [X2,X0,X1] :
( element(sK14(sK3,sK4),sF31)
| X0 = X1
| X0 = X2 )
| spl35_2
| ~ spl35_19
| ~ spl35_21 ),
inference(superposition,[],[f1944,f1943]) ).
fof(f2191,plain,
( ! [X2,X0,X1] :
( X0 = X1
| X0 = X2 )
| spl35_2
| ~ spl35_19
| ~ spl35_21 ),
inference(forward_subsumption_resolution,[],[f1952,f318]) ).
fof(f3676,plain,
( ! [X0,X1] :
( X1 != X1
| X0 = X1 )
| spl35_2
| ~ spl35_19
| ~ spl35_21 ),
inference(equality_factoring,[],[f2191]) ).
fof(f3677,plain,
( ! [X0,X1] : X0 = X1
| spl35_2
| ~ spl35_19
| ~ spl35_21 ),
inference(trivial_inequality_removal,[],[f3676]) ).
fof(f3975,plain,
( ! [X0] : ~ element(X0,sF31)
| spl35_2
| ~ spl35_19
| ~ spl35_21 ),
inference(superposition,[],[f318,f3677]) ).
fof(f4377,plain,
( ! [X0,X1] : element(X0,X1)
| spl35_2
| ~ spl35_19
| ~ spl35_21 ),
inference(superposition,[],[f221,f3677]) ).
fof(f4578,plain,
( sF33(sK14(sK3,sK4)) = sK15(sK3,sK4)
| ~ element(sK4,sF34)
| sP1(sK4,sK3)
| ~ spl35_2 ),
inference(resolution,[],[f317,f335]) ).
fof(f4579,plain,
( sF33(sK14(sK3,sK4)) = sK16(sK3,sK4)
| ~ element(sK4,sF34)
| sP1(sK4,sK3)
| ~ spl35_2 ),
inference(resolution,[],[f317,f329]) ).
fof(f4582,plain,
( sF33(sK14(sK3,sK4)) = sK16(sK3,sK4)
| sP1(sK4,sK3)
| ~ spl35_2 ),
inference(forward_subsumption_resolution,[],[f4579,f290]) ).
fof(f4583,plain,
( sF33(sK14(sK3,sK4)) = sK15(sK3,sK4)
| sP1(sK4,sK3)
| ~ spl35_2 ),
inference(forward_subsumption_resolution,[],[f4578,f290]) ).
fof(f4584,plain,
( sF33(sK14(sK3,sK4)) = sK16(sK3,sK4)
| spl35_1
| ~ spl35_2 ),
inference(forward_subsumption_resolution,[],[f4582,f313]) ).
fof(f4585,plain,
( sF33(sK14(sK3,sK4)) = sK15(sK3,sK4)
| spl35_1
| ~ spl35_2 ),
inference(forward_subsumption_resolution,[],[f4583,f313]) ).
fof(f4586,plain,
( sK15(sK3,sK4) = sK16(sK3,sK4)
| spl35_1
| ~ spl35_2 ),
inference(forward_demodulation,[],[f4585,f4584]) ).
fof(f4590,plain,
( sK15(sK3,sK4) != sK15(sK3,sK4)
| sP1(sK4,sK3)
| ~ one_sorted_str(sK3)
| ~ element(sK4,powerset(powerset(the_carrier(sK3))))
| spl35_1
| ~ spl35_2 ),
inference(superposition,[],[f208,f4586]) ).
fof(f4591,plain,
( sP1(sK4,sK3)
| ~ one_sorted_str(sK3)
| ~ element(sK4,powerset(powerset(the_carrier(sK3))))
| spl35_1
| ~ spl35_2 ),
inference(trivial_inequality_removal,[],[f4590]) ).
fof(f4592,plain,
( ~ one_sorted_str(sK3)
| ~ element(sK4,powerset(powerset(the_carrier(sK3))))
| spl35_1
| ~ spl35_2 ),
inference(forward_subsumption_resolution,[],[f4591,f313]) ).
fof(f4593,plain,
( ~ element(sK4,powerset(powerset(the_carrier(sK3))))
| spl35_1
| ~ spl35_2 ),
inference(forward_subsumption_resolution,[],[f4592,f149]) ).
fof(f4594,plain,
( ~ element(sK4,powerset(powerset(sF29)))
| spl35_1
| ~ spl35_2 ),
inference(forward_demodulation,[],[f4593,f274]) ).
fof(f4595,plain,
( ~ element(sK4,powerset(sF31))
| spl35_1
| ~ spl35_2 ),
inference(forward_demodulation,[],[f4594,f279]) ).
fof(f4596,plain,
( ~ element(sK4,sF34)
| spl35_1
| ~ spl35_2 ),
inference(forward_demodulation,[],[f4595,f289]) ).
fof(f4597,plain,
( $false
| spl35_1
| ~ spl35_2 ),
inference(forward_subsumption_resolution,[],[f4596,f290]) ).
fof(f4598,plain,
( spl35_1
| ~ spl35_2 ),
inference(avatar_contradiction_clause,[],[f4597]) ).
fof(f4656,plain,
( $false
| spl35_2
| ~ spl35_19
| ~ spl35_21 ),
inference(forward_subsumption_resolution,[],[f3975,f4377]) ).
fof(f4657,plain,
( spl35_2
| ~ spl35_19
| ~ spl35_21 ),
inference(avatar_contradiction_clause,[],[f4656]) ).
cnf(s2,plain,
( spl35_1
| spl35_4 ),
inference(sat_conversion,[],[f347]) ).
cnf(s11,plain,
( ~ spl35_1
| spl35_17
| spl35_18 ),
inference(sat_conversion,[],[f657]) ).
cnf(s13,plain,
( spl35_2
| ~ spl35_4
| ~ spl35_19
| spl35_21 ),
inference(sat_conversion,[],[f685]) ).
cnf(s14,plain,
( spl35_1
| spl35_19 ),
inference(sat_conversion,[],[f689]) ).
cnf(s15,plain,
( ~ spl35_17
| spl35_22
| ~ spl35_23
| ~ spl35_24 ),
inference(sat_conversion,[],[f714]) ).
cnf(s16,plain,
( ~ spl35_17
| ~ spl35_23
| ~ spl35_24
| spl35_25 ),
inference(sat_conversion,[],[f719]) ).
cnf(s18,plain,
( ~ spl35_17
| ~ spl35_23
| ~ spl35_24
| spl35_27 ),
inference(sat_conversion,[],[f728]) ).
cnf(s19,plain,
( ~ spl35_1
| spl35_23 ),
inference(sat_conversion,[],[f741]) ).
cnf(s28,plain,
( ~ spl35_1
| spl35_24 ),
inference(sat_conversion,[],[f1282]) ).
cnf(s29,plain,
( ~ spl35_1
| ~ spl35_17
| ~ spl35_22
| ~ spl35_23
| ~ spl35_24
| ~ spl35_25
| ~ spl35_27 ),
inference(sat_conversion,[],[f1353]) ).
cnf(s40,plain,
( ~ spl35_1
| spl35_17
| ~ spl35_18
| ~ spl35_23 ),
inference(sat_conversion,[],[f1695]) ).
cnf(s79,plain,
( spl35_1
| ~ spl35_2 ),
inference(sat_conversion,[],[f4598]) ).
cnf(s102,plain,
( spl35_2
| ~ spl35_19
| ~ spl35_21 ),
inference(sat_conversion,[],[f4657]) ).
cnf(s104,plain,
spl35_1,
inference(rat,[],[s13,s102,s2,s14,s79]) ).
cnf(s105,plain,
spl35_24,
inference(rat,[],[s28,s104]) ).
cnf(s106,plain,
spl35_23,
inference(rat,[],[s19,s104]) ).
cnf(s107,plain,
spl35_17,
inference(rat,[],[s11,s40,s104,s106]) ).
cnf(s108,plain,
spl35_27,
inference(rat,[],[s18,s106,s105,s107]) ).
cnf(s110,plain,
spl35_25,
inference(rat,[],[s16,s106,s105,s107]) ).
cnf(s111,plain,
spl35_22,
inference(rat,[],[s15,s105,s106,s107]) ).
cnf(s112,plain,
$false,
inference(rat,[],[s29,s108,s110,s105,s106,s104,s111,s107]) ).
fof(f4661,plain,
$false,
inference(avatar_sat_refutation,[],[s112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU334+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n002.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 04:50:45 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 9.45/2.18 % (4152450)Detected formulas, will run a generic FOF schedule.
% 9.45/2.18 % (4152458)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1671905963:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.45/2.18 % (4152456)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=3470636119:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.45/2.18 % (4152455)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=1195853668:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.45/2.18 % (4152458)Instruction limit reached!
% 9.45/2.18 % (4152458)------------------------------
% 9.45/2.18 % (4152458)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.18 % (4152458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.18 % (4152458)CaDiCaL version: 2.1.3
% 9.45/2.18 % (4152458)Termination reason: Instruction limit
% 9.45/2.19 % (4152458)Termination phase: Saturation
% 9.45/2.19 % (4152458)Time elapsed: 0.036 s
% 9.45/2.19 % (4152458)Peak memory usage: 89 MB
% 9.45/2.19 % (4152458)Instructions burned: 109 (million)
% 9.45/2.19 % (4152457)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=358980010:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.45/2.19 % (4152459)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2487949780:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.45/2.19 % (4152461)dis-21_1_sil=8000:lcm=predicate:random_seed=36091983: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)
% 9.45/2.19 % (4152460)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2260020542:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.45/2.19 % (4152460)Instruction limit reached!
% 9.45/2.19 % (4152460)------------------------------
% 9.45/2.19 % (4152460)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (4152460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (4152460)CaDiCaL version: 2.1.3
% 9.45/2.19 % (4152460)Termination reason: Instruction limit
% 9.45/2.19 % (4152460)Termination phase: Saturation
% 9.45/2.19 % (4152460)Time elapsed: 0.070 s
% 9.45/2.19 % (4152460)Peak memory usage: 90 MB
% 9.45/2.19 % (4152460)Instructions burned: 141 (million)
% 9.45/2.19 % (4152459)Instruction limit reached!
% 9.45/2.19 % (4152459)------------------------------
% 9.45/2.19 % (4152459)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (4152459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (4152459)CaDiCaL version: 2.1.3
% 9.45/2.19 % (4152459)Termination reason: Instruction limit
% 9.45/2.19 % (4152459)Termination phase: Saturation
% 9.45/2.19 % (4152459)Time elapsed: 0.073 s
% 9.45/2.19 % (4152459)Peak memory usage: 88 MB
% 9.45/2.19 % (4152459)Instructions burned: 120 (million)
% 9.45/2.19 % (4152461)Instruction limit reached!
% 9.45/2.19 % (4152461)------------------------------
% 9.45/2.19 % (4152461)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (4152461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (4152461)CaDiCaL version: 2.1.3
% 9.45/2.19 % (4152461)Termination reason: Instruction limit
% 9.45/2.19 % (4152461)Termination phase: Saturation
% 9.45/2.19 % (4152461)Time elapsed: 0.082 s
% 9.45/2.19 % (4152461)Peak memory usage: 90 MB
% 9.45/2.19 % (4152461)Instructions burned: 130 (million)
% 9.45/2.19 % (4152469)lrs+10_1_sil=8000:sp=occurrence:random_seed=1114917233:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 9.45/2.19 % (4152469)Instruction limit reached!
% 9.45/2.19 % (4152469)------------------------------
% 9.45/2.19 % (4152469)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (4152469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (4152469)CaDiCaL version: 2.1.3
% 9.45/2.19 % (4152469)Termination reason: Instruction limit
% 9.45/2.19 % (4152469)Termination phase: Saturation
% 9.45/2.19 % (4152469)Time elapsed: 0.085 s
% 9.45/2.19 % (4152469)Peak memory usage: 91 MB
% 9.45/2.19 % (4152469)Instructions burned: 286 (million)
% 9.45/2.19 % (4152471)lrs+1011_1_sil=32000:sp=occurrence:random_seed=839359854:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 9.45/2.19 % (4152470)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1387653249:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 9.45/2.19 % (4152472)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=3552256336:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 9.45/2.19 % (4152470)Instruction limit reached!
% 9.45/2.19 % (4152470)------------------------------
% 9.45/2.19 % (4152470)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (4152470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (4152470)CaDiCaL version: 2.1.3
% 9.45/2.19 % (4152470)Termination reason: Instruction limit
% 9.45/2.19 % (4152470)Termination phase: Saturation
% 9.45/2.19 % (4152470)Time elapsed: 0.090 s
% 9.45/2.19 % (4152470)Peak memory usage: 89 MB
% 9.45/2.19 % (4152470)Instructions burned: 159 (million)
% 9.45/2.19 % (4152474)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2437049556:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 9.45/2.19 % (4152474)Refutation not found, incomplete strategy
% 9.45/2.19 % (4152474)------------------------------
% 9.45/2.19 % (4152474)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (4152474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (4152474)CaDiCaL version: 2.1.3
% 9.45/2.19 % (4152474)Termination reason: Refutation not found, incomplete strategy
% 9.45/2.19 % (4152474)Time elapsed: 0.058 s
% 9.45/2.19 % (4152474)Peak memory usage: 89 MB
% 9.45/2.19 % (4152474)Instructions burned: 191 (million)
% 9.45/2.19 % (4152472)Instruction limit reached!
% 9.45/2.19 % (4152472)------------------------------
% 9.45/2.19 % (4152472)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (4152472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (4152472)CaDiCaL version: 2.1.3
% 9.45/2.19 % (4152472)Termination reason: Instruction limit
% 9.45/2.19 % (4152472)Termination phase: Saturation
% 9.45/2.19 % (4152472)Time elapsed: 0.151 s
% 9.45/2.19 % (4152472)Peak memory usage: 90 MB
% 9.45/2.19 % (4152472)Instructions burned: 249 (million)
% 9.45/2.19 % (4152471)Instruction limit reached!
% 9.45/2.19 % (4152471)------------------------------
% 9.45/2.19 % (4152471)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (4152471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (4152471)CaDiCaL version: 2.1.3
% 9.45/2.19 % (4152471)Termination reason: Instruction limit
% 9.45/2.19 % (4152471)Termination phase: Saturation
% 9.45/2.19 % (4152471)Time elapsed: 0.213 s
% 9.45/2.19 % (4152471)Peak memory usage: 91 MB
% 9.45/2.19 % (4152471)Instructions burned: 325 (million)
% 9.45/2.19 % (4152479)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1893845440:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 9.45/2.19 % (4152474)------------------------------
% 9.45/2.19 % (4152474)------------------------------
% 9.45/2.19 % (4152480)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1872247629:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 9.45/2.19 % (4152481)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1441562762:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 9.45/2.19 % (4152480)Instruction limit reached!
% 9.45/2.19 % (4152480)------------------------------
% 9.45/2.19 % (4152480)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (4152480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (4152480)CaDiCaL version: 2.1.3
% 9.45/2.19 % (4152480)Termination reason: Instruction limit
% 9.45/2.19 % (4152480)Termination phase: Saturation
% 9.45/2.19 % (4152480)Time elapsed: 0.081 s
% 9.45/2.19 % (4152480)Peak memory usage: 90 MB
% 9.45/2.19 % (4152480)Instructions burned: 113 (million)
% 9.45/2.19 % (4152483)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3235982786:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 9.45/2.19 % (4152481)Instruction limit reached!
% 9.45/2.19 % (4152481)------------------------------
% 9.45/2.19 % (4152481)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (4152481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (4152481)CaDiCaL version: 2.1.3
% 9.45/2.19 % (4152481)Termination reason: Instruction limit
% 9.45/2.19 % (4152481)Termination phase: Saturation
% 9.45/2.19 % (4152481)Time elapsed: 0.066 s
% 9.45/2.19 % (4152481)Peak memory usage: 88 MB
% 9.45/2.19 % (4152481)Instructions burned: 128 (million)
% 9.45/2.19 % (4152483)Instruction limit reached!
% 9.45/2.19 % (4152483)------------------------------
% 9.45/2.19 % (4152483)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (4152483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (4152483)CaDiCaL version: 2.1.3
% 9.45/2.19 % (4152483)Termination reason: Instruction limit
% 9.45/2.19 % (4152483)Termination phase: Saturation
% 9.45/2.19 % (4152483)Time elapsed: 0.035 s
% 9.45/2.19 % (4152483)Peak memory usage: 89 MB
% 9.45/2.19 % (4152483)Instructions burned: 118 (million)
% 9.45/2.19 % (4152486)lrs+10_1_sil=8000:sp=occurrence:random_seed=3846711692:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 9.45/2.19 % (4152489)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1784491786:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 9.45/2.19 % (4152488)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=866985359:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 9.45/2.19 % (4152455)First to succeed.
% 9.45/2.19 % (4152455)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4152450"
% 9.45/2.19 % (4152488)Instruction limit reached!
% 9.45/2.19 % (4152488)------------------------------
% 9.45/2.19 % (4152488)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (4152488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (4152488)CaDiCaL version: 2.1.3
% 9.45/2.19 % (4152488)Termination reason: Instruction limit
% 9.45/2.19 % (4152488)Termination phase: Saturation
% 9.45/2.19 % (4152488)Time elapsed: 0.249 s
% 9.45/2.19 % (4152488)Peak memory usage: 92 MB
% 9.45/2.19 % (4152488)Instructions burned: 438 (million)
% 9.45/2.19 % (4152456)Also succeeded, but the first one will report.
% 9.45/2.19 % (4152455)Refutation found. Thanks to Tanya!
% 9.45/2.19 % SZS status Theorem for theBenchmark
% 9.45/2.19 % SZS output start Proof for theBenchmark
% See solution above
% 9.99/2.38 % (4152455)------------------------------
% 9.99/2.38 % (4152455)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.99/2.38 % (4152455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.99/2.38 % (4152455)CaDiCaL version: 2.1.3
% 9.99/2.38 % (4152455)Termination reason: Refutation
% 9.99/2.38 % (4152455)Time elapsed: 0.915 s
% 9.99/2.38 % (4152455)Peak memory usage: 132 MB
% 9.99/2.38 % (4152455)Instructions burned: 1388 (million)
% 9.99/2.38 % (4152455)------------------------------
% 9.99/2.38 % (4152455)------------------------------
% 9.99/2.38 % (4152450)Success in time 1.336 s
% 9.99/2.38 % Vampire exiting
%------------------------------------------------------------------------------