%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU332+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 : n010.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 1.38s 1.21s
% Output : Refutation 3.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 16
% Syntax : Number of formulae : 165 ( 10 unt; 14 def)
% Number of atoms : 828 ( 208 equ)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 1104 ( 441 ~; 481 |; 137 &)
% ( 19 <=>; 24 =>; 0 <=; 2 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 13 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 3 con; 0-4 aty)
% Number of variables : 390 ( 0 sgn 292 !; 98 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( ( one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ! [X2] :
? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,cartesian_product2(X1,X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,X1)
& ! [X7] :
( element(X7,powerset(the_carrier(X0)))
=> ( X7 = X5
=> X6 = subset_complement(the_carrier(X0),X7) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e4_7_2__tops_2__1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ( one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ! [X2] :
? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,cartesian_product2(X1,X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,X1)
& ! [X7] :
( element(X7,powerset(the_carrier(X0)))
=> ( X7 = X5
=> X6 = subset_complement(the_carrier(X0),X7) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f33,axiom,
! [X0,X1] :
( ( one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ! [X2] :
( ! [X3,X4,X5] :
( ( X3 = X4
& ? [X6,X7] :
( ordered_pair(X6,X7) = X4
& in(X6,X1)
& ! [X8] :
( element(X8,powerset(the_carrier(X0)))
=> ( X8 = X6
=> X7 = subset_complement(the_carrier(X0),X8) ) ) )
& X3 = X5
& ? [X9,X10] :
( ordered_pair(X9,X10) = X5
& in(X9,X1)
& ! [X11] :
( element(X11,powerset(the_carrier(X0)))
=> ( X11 = X9
=> X10 = subset_complement(the_carrier(X0),X11) ) ) ) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,cartesian_product2(X1,X2))
& X5 = X4
& ? [X12,X13] :
( ordered_pair(X12,X13) = X4
& in(X12,X1)
& ! [X14] :
( element(X14,powerset(the_carrier(X0)))
=> ( X14 = X12
=> X13 = subset_complement(the_carrier(X0),X14) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e4_7_2__tops_2__2) ).
fof(f34,plain,
! [X0,X1] :
( ( one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ! [X2] :
( ! [X3,X4,X5] :
( ( X3 = X4
& ? [X6,X7] :
( ordered_pair(X6,X7) = X4
& in(X6,X1)
& ! [X8] :
( element(X8,powerset(the_carrier(X0)))
=> ( X8 = X6
=> X7 = subset_complement(the_carrier(X0),X8) ) ) )
& X3 = X5
& ? [X9,X10] :
( ordered_pair(X9,X10) = X5
& in(X9,X1)
& ! [X11] :
( element(X11,powerset(the_carrier(X0)))
=> ( X11 = X9
=> X10 = subset_complement(the_carrier(X0),X11) ) ) ) )
=> X4 = X5 )
=> ? [X12] :
! [X13] :
( in(X13,X12)
<=> ? [X14] :
( in(X14,cartesian_product2(X1,X2))
& X13 = X14
& ? [X15,X16] :
( ordered_pair(X15,X16) = X13
& in(X15,X1)
& ! [X17] :
( element(X17,powerset(the_carrier(X0)))
=> ( X15 = X17
=> subset_complement(the_carrier(X0),X17) = X16 ) ) ) ) ) ) ),
inference(rectify,[],[f33]) ).
fof(f51,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( in(X4,X3)
<~> ( in(X4,cartesian_product2(X1,X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,X1)
& ! [X7] :
( X6 = subset_complement(the_carrier(X0),X7)
| X5 != X7
| ~ element(X7,powerset(the_carrier(X0))) ) ) ) )
& one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f52,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( in(X4,X3)
<~> ( in(X4,cartesian_product2(X1,X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,X1)
& ! [X7] :
( X6 = subset_complement(the_carrier(X0),X7)
| X5 != X7
| ~ element(X7,powerset(the_carrier(X0))) ) ) ) )
& one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(flattening,[],[f51]) ).
fof(f69,plain,
! [X0,X1] :
( ! [X2] :
( ? [X12] :
! [X13] :
( in(X13,X12)
<=> ? [X14] :
( in(X14,cartesian_product2(X1,X2))
& X13 = X14
& ? [X15,X16] :
( ordered_pair(X15,X16) = X13
& in(X15,X1)
& ! [X17] :
( subset_complement(the_carrier(X0),X17) = X16
| X15 != X17
| ~ element(X17,powerset(the_carrier(X0))) ) ) ) )
| ? [X3,X4,X5] :
( X4 != X5
& X3 = X4
& ? [X6,X7] :
( ordered_pair(X6,X7) = X4
& in(X6,X1)
& ! [X8] :
( X7 = subset_complement(the_carrier(X0),X8)
| X6 != X8
| ~ element(X8,powerset(the_carrier(X0))) ) )
& X3 = X5
& ? [X9,X10] :
( ordered_pair(X9,X10) = X5
& in(X9,X1)
& ! [X11] :
( X10 = subset_complement(the_carrier(X0),X11)
| X9 != X11
| ~ element(X11,powerset(the_carrier(X0))) ) ) ) )
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(ennf_transformation,[],[f34]) ).
fof(f70,plain,
! [X0,X1] :
( ! [X2] :
( ? [X12] :
! [X13] :
( in(X13,X12)
<=> ? [X14] :
( in(X14,cartesian_product2(X1,X2))
& X13 = X14
& ? [X15,X16] :
( ordered_pair(X15,X16) = X13
& in(X15,X1)
& ! [X17] :
( subset_complement(the_carrier(X0),X17) = X16
| X15 != X17
| ~ element(X17,powerset(the_carrier(X0))) ) ) ) )
| ? [X3,X4,X5] :
( X4 != X5
& X3 = X4
& ? [X6,X7] :
( ordered_pair(X6,X7) = X4
& in(X6,X1)
& ! [X8] :
( X7 = subset_complement(the_carrier(X0),X8)
| X6 != X8
| ~ element(X8,powerset(the_carrier(X0))) ) )
& X3 = X5
& ? [X9,X10] :
( ordered_pair(X9,X10) = X5
& in(X9,X1)
& ! [X11] :
( X10 = subset_complement(the_carrier(X0),X11)
| X9 != X11
| ~ element(X11,powerset(the_carrier(X0))) ) ) ) )
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(flattening,[],[f69]) ).
fof(f71,definition,
! [X5,X1,X0] :
( ? [X9,X10] :
( ordered_pair(X9,X10) = X5
& in(X9,X1)
& ! [X11] :
( X10 = subset_complement(the_carrier(X0),X11)
| X9 != X11
| ~ element(X11,powerset(the_carrier(X0))) ) )
| ~ sP0(X5,X1,X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f72,definition,
! [X2,X1,X0] :
( ? [X12] :
! [X13] :
( in(X13,X12)
<=> ? [X14] :
( in(X14,cartesian_product2(X1,X2))
& X13 = X14
& ? [X15,X16] :
( ordered_pair(X15,X16) = X13
& in(X15,X1)
& ! [X17] :
( subset_complement(the_carrier(X0),X17) = X16
| X15 != X17
| ~ element(X17,powerset(the_carrier(X0))) ) ) ) )
| ~ sP1(X2,X1,X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f73,plain,
! [X0,X1] :
( ! [X2] :
( sP1(X2,X1,X0)
| ? [X3,X4,X5] :
( X4 != X5
& X3 = X4
& ? [X6,X7] :
( ordered_pair(X6,X7) = X4
& in(X6,X1)
& ! [X8] :
( X7 = subset_complement(the_carrier(X0),X8)
| X6 != X8
| ~ element(X8,powerset(the_carrier(X0))) ) )
& X3 = X5
& sP0(X5,X1,X0) ) )
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(definition_folding,[],[f70,f72,f71]) ).
fof(f74,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( ( ~ in(X4,cartesian_product2(X1,X2))
| ! [X5,X6] :
( ordered_pair(X5,X6) != X4
| ~ in(X5,X1)
| ? [X7] :
( subset_complement(the_carrier(X0),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(X0))) ) )
| ~ in(X4,X3) )
& ( ( in(X4,cartesian_product2(X1,X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,X1)
& ! [X7] :
( X6 = subset_complement(the_carrier(X0),X7)
| X5 != X7
| ~ element(X7,powerset(the_carrier(X0))) ) ) )
| in(X4,X3) ) )
& one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(nnf_transformation,[],[f52]) ).
fof(f75,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( ( ~ in(X4,cartesian_product2(X1,X2))
| ! [X5,X6] :
( ordered_pair(X5,X6) != X4
| ~ in(X5,X1)
| ? [X7] :
( subset_complement(the_carrier(X0),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(X0))) ) )
| ~ in(X4,X3) )
& ( ( in(X4,cartesian_product2(X1,X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,X1)
& ! [X7] :
( X6 = subset_complement(the_carrier(X0),X7)
| X5 != X7
| ~ element(X7,powerset(the_carrier(X0))) ) ) )
| in(X4,X3) ) )
& one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( ( ~ in(X4,cartesian_product2(X1,X2))
| ! [X5,X6] :
( ordered_pair(X5,X6) != X4
| ~ in(X5,X1)
| ? [X7] :
( subset_complement(the_carrier(X0),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(X0))) ) )
| ~ in(X4,X3) )
& ( ( in(X4,cartesian_product2(X1,X2))
& ? [X8,X9] :
( ordered_pair(X8,X9) = X4
& in(X8,X1)
& ! [X10] :
( subset_complement(the_carrier(X0),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(X0))) ) ) )
| in(X4,X3) ) )
& one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(rectify,[],[f75]) ).
fof(f77,plain,
( ! [X3] :
( ( ~ in(sK5(X3),cartesian_product2(sK3,sK4))
| ! [X5,X6] :
( ordered_pair(X5,X6) != sK5(X3)
| ~ in(X5,sK3)
| ( subset_complement(the_carrier(sK2),sK6(X5,X6)) != X6
& sK6(X5,X6) = X5
& element(sK6(X5,X6),powerset(the_carrier(sK2))) ) )
| ~ in(sK5(X3),X3) )
& ( ( in(sK5(X3),cartesian_product2(sK3,sK4))
& sK5(X3) = ordered_pair(sK7(X3),sK8(X3))
& in(sK7(X3),sK3)
& ! [X10] :
( sK8(X3) = subset_complement(the_carrier(sK2),X10)
| sK7(X3) != X10
| ~ element(X10,powerset(the_carrier(sK2))) ) )
| in(sK5(X3),X3) ) )
& one_sorted_str(sK2)
& element(sK3,powerset(powerset(the_carrier(sK2)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X4,sK5(X3)),skolemize(X7,sK6(X5,X6)),skolemize(X8,sK7(X3)),skolemize(X9,sK8(X3))],[f76]) ).
fof(f81,plain,
! [X2,X1,X0] :
( ? [X12] :
! [X13] :
( ( in(X13,X12)
| ! [X14] :
( ~ in(X14,cartesian_product2(X1,X2))
| X13 != X14
| ! [X15,X16] :
( ordered_pair(X15,X16) != X13
| ~ in(X15,X1)
| ? [X17] :
( subset_complement(the_carrier(X0),X17) != X16
& X15 = X17
& element(X17,powerset(the_carrier(X0))) ) ) ) )
& ( ? [X14] :
( in(X14,cartesian_product2(X1,X2))
& X13 = X14
& ? [X15,X16] :
( ordered_pair(X15,X16) = X13
& in(X15,X1)
& ! [X17] :
( subset_complement(the_carrier(X0),X17) = X16
| X15 != X17
| ~ element(X17,powerset(the_carrier(X0))) ) ) )
| ~ in(X13,X12) ) )
| ~ sP1(X2,X1,X0) ),
inference(nnf_transformation,[],[f72]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ! [X5] :
( ~ in(X5,cartesian_product2(X1,X0))
| X4 != X5
| ! [X6,X7] :
( ordered_pair(X6,X7) != X4
| ~ in(X6,X1)
| ? [X8] :
( subset_complement(the_carrier(X2),X8) != X7
& X6 = X8
& element(X8,powerset(the_carrier(X2))) ) ) ) )
& ( ? [X9] :
( in(X9,cartesian_product2(X1,X0))
& X4 = X9
& ? [X10,X11] :
( ordered_pair(X10,X11) = X4
& in(X10,X1)
& ! [X12] :
( subset_complement(the_carrier(X2),X12) = X11
| X10 != X12
| ~ element(X12,powerset(the_carrier(X2))) ) ) )
| ~ in(X4,X3) ) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f81]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ! [X4] :
( ( in(X4,sK12(X0,X1,X2))
| ! [X5] :
( ~ in(X5,cartesian_product2(X1,X0))
| X4 != X5
| ! [X6,X7] :
( ordered_pair(X6,X7) != X4
| ~ in(X6,X1)
| ( subset_complement(the_carrier(X2),sK13(X2,X6,X7)) != X7
& sK13(X2,X6,X7) = X6
& element(sK13(X2,X6,X7),powerset(the_carrier(X2))) ) ) ) )
& ( ( in(sK14(X0,X1,X2,X4),cartesian_product2(X1,X0))
& sK14(X0,X1,X2,X4) = X4
& ordered_pair(sK15(X1,X2,X4),sK16(X1,X2,X4)) = X4
& in(sK15(X1,X2,X4),X1)
& ! [X12] :
( subset_complement(the_carrier(X2),X12) = sK16(X1,X2,X4)
| sK15(X1,X2,X4) != X12
| ~ element(X12,powerset(the_carrier(X2))) ) )
| ~ in(X4,sK12(X0,X1,X2)) ) )
| ~ sP1(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15,sK16]),skolemize(X3,sK12(X0,X1,X2)),skolemize(X8,sK13(X2,X6,X7)),skolemize(X9,sK14(X0,X1,X2,X4)),skolemize(X10,sK15(X1,X2,X4)),skolemize(X11,sK16(X1,X2,X4))],[f82]) ).
fof(f87,plain,
! [X0,X1] :
( ! [X2] :
( sP1(X2,X1,X0)
| ( sK20(X0,X1) != sK21(X0,X1)
& sK19(X0,X1) = sK20(X0,X1)
& sK20(X0,X1) = ordered_pair(sK22(X0,X1),sK23(X0,X1))
& in(sK22(X0,X1),X1)
& ! [X8] :
( subset_complement(the_carrier(X0),X8) = sK23(X0,X1)
| sK22(X0,X1) != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& sK19(X0,X1) = sK21(X0,X1)
& sP0(sK21(X0,X1),X1,X0) ) )
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20,sK21,sK22,sK23]),skolemize(X3,sK19(X0,X1)),skolemize(X4,sK20(X0,X1)),skolemize(X5,sK21(X0,X1)),skolemize(X6,sK22(X0,X1)),skolemize(X7,sK23(X0,X1))],[f73]) ).
fof(f88,plain,
element(sK3,powerset(powerset(the_carrier(sK2)))),
inference(cnf_transformation,[],[f77]) ).
fof(f89,plain,
one_sorted_str(sK2),
inference(cnf_transformation,[],[f77]) ).
fof(f90,plain,
! [X3,X10] :
( sK8(X3) = subset_complement(the_carrier(sK2),X10)
| sK7(X3) != X10
| ~ element(X10,powerset(the_carrier(sK2)))
| in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f77]) ).
fof(f91,plain,
! [X3] :
( in(sK7(X3),sK3)
| in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f77]) ).
fof(f92,plain,
! [X3] :
( in(sK5(X3),X3)
| sK5(X3) = ordered_pair(sK7(X3),sK8(X3)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f93,plain,
! [X3] :
( in(sK5(X3),cartesian_product2(sK3,sK4))
| in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f77]) ).
fof(f94,plain,
! [X3,X6,X5] :
( element(sK6(X5,X6),powerset(the_carrier(sK2)))
| ordered_pair(X5,X6) != sK5(X3)
| ~ in(X5,sK3)
| ~ in(sK5(X3),cartesian_product2(sK3,sK4))
| ~ in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f77]) ).
fof(f95,plain,
! [X3,X6,X5] :
( ordered_pair(X5,X6) != sK5(X3)
| ~ in(sK5(X3),cartesian_product2(sK3,sK4))
| ~ in(X5,sK3)
| sK6(X5,X6) = X5
| ~ in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f77]) ).
fof(f96,plain,
! [X3,X6,X5] :
( ordered_pair(X5,X6) != sK5(X3)
| ~ in(sK5(X3),cartesian_product2(sK3,sK4))
| ~ in(X5,sK3)
| subset_complement(the_carrier(sK2),sK6(X5,X6)) != X6
| ~ in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f77]) ).
fof(f136,plain,
! [X2,X0,X1,X4,X12] :
( subset_complement(the_carrier(X2),X12) = sK16(X1,X2,X4)
| sK15(X1,X2,X4) != X12
| ~ element(X12,powerset(the_carrier(X2)))
| ~ in(X4,sK12(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f137,plain,
! [X2,X0,X1,X4] :
( in(sK15(X1,X2,X4),X1)
| ~ in(X4,sK12(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f138,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK12(X0,X1,X2))
| ordered_pair(sK15(X1,X2,X4),sK16(X1,X2,X4)) = X4
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f139,plain,
! [X2,X0,X1,X4] :
( sK14(X0,X1,X2,X4) = X4
| ~ in(X4,sK12(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f140,plain,
! [X2,X0,X1,X4] :
( in(sK14(X0,X1,X2,X4),cartesian_product2(X1,X0))
| ~ in(X4,sK12(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f141,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( in(X4,sK12(X0,X1,X2))
| ~ in(X5,cartesian_product2(X1,X0))
| X4 != X5
| ordered_pair(X6,X7) != X4
| ~ in(X6,X1)
| element(sK13(X2,X6,X7),powerset(the_carrier(X2)))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f142,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( in(X4,sK12(X0,X1,X2))
| ~ in(X5,cartesian_product2(X1,X0))
| X4 != X5
| ordered_pair(X6,X7) != X4
| ~ in(X6,X1)
| sK13(X2,X6,X7) = X6
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f143,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( in(X4,sK12(X0,X1,X2))
| ~ in(X5,cartesian_product2(X1,X0))
| X4 != X5
| ordered_pair(X6,X7) != X4
| ~ in(X6,X1)
| subset_complement(the_carrier(X2),sK13(X2,X6,X7)) != X7
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f148,plain,
! [X2,X0,X1] :
( sP1(X2,X1,X0)
| sK19(X0,X1) = sK21(X0,X1)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f87]) ).
fof(f152,plain,
! [X2,X0,X1] :
( sP1(X2,X1,X0)
| sK19(X0,X1) = sK20(X0,X1)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f87]) ).
fof(f153,plain,
! [X2,X0,X1] :
( sK20(X0,X1) != sK21(X0,X1)
| sP1(X2,X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f87]) ).
fof(f154,plain,
! [X3] :
( ~ element(sK7(X3),powerset(the_carrier(sK2)))
| sK8(X3) = subset_complement(the_carrier(sK2),sK7(X3))
| in(sK5(X3),X3) ),
inference(equality_resolution,[],[f90]) ).
fof(f155,plain,
! [X2,X0,X1,X6,X7,X5] :
( in(X5,sK12(X0,X1,X2))
| ~ in(X5,cartesian_product2(X1,X0))
| ordered_pair(X6,X7) != X5
| ~ in(X6,X1)
| subset_complement(the_carrier(X2),sK13(X2,X6,X7)) != X7
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f143]) ).
fof(f156,plain,
! [X2,X0,X1,X6,X7] :
( subset_complement(the_carrier(X2),sK13(X2,X6,X7)) != X7
| ~ in(ordered_pair(X6,X7),cartesian_product2(X1,X0))
| ~ in(X6,X1)
| in(ordered_pair(X6,X7),sK12(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f155]) ).
fof(f157,plain,
! [X2,X0,X1,X6,X7,X5] :
( in(X5,sK12(X0,X1,X2))
| ~ in(X5,cartesian_product2(X1,X0))
| ordered_pair(X6,X7) != X5
| ~ in(X6,X1)
| sK13(X2,X6,X7) = X6
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f142]) ).
fof(f158,plain,
! [X2,X0,X1,X6,X7] :
( sK13(X2,X6,X7) = X6
| ~ in(ordered_pair(X6,X7),cartesian_product2(X1,X0))
| ~ in(X6,X1)
| in(ordered_pair(X6,X7),sK12(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f157]) ).
fof(f159,plain,
! [X2,X0,X1,X6,X7,X5] :
( in(X5,sK12(X0,X1,X2))
| ~ in(X5,cartesian_product2(X1,X0))
| ordered_pair(X6,X7) != X5
| ~ in(X6,X1)
| element(sK13(X2,X6,X7),powerset(the_carrier(X2)))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f141]) ).
fof(f160,plain,
! [X2,X0,X1,X6,X7] :
( element(sK13(X2,X6,X7),powerset(the_carrier(X2)))
| ~ in(ordered_pair(X6,X7),cartesian_product2(X1,X0))
| ~ in(X6,X1)
| in(ordered_pair(X6,X7),sK12(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f159]) ).
fof(f161,plain,
! [X2,X0,X1,X4] :
( ~ element(sK15(X1,X2,X4),powerset(the_carrier(X2)))
| sK16(X1,X2,X4) = subset_complement(the_carrier(X2),sK15(X1,X2,X4))
| ~ in(X4,sK12(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f136]) ).
fof(f171,plain,
! [X2,X3,X0,X1] :
( in(X0,cartesian_product2(X2,X1))
| ~ in(X0,sK12(X1,X2,X3))
| ~ sP1(X1,X2,X3)
| ~ in(X0,sK12(X1,X2,X3))
| ~ sP1(X1,X2,X3) ),
inference(superposition,[],[f140,f139]) ).
fof(f172,plain,
! [X2,X3,X0,X1] :
( in(X0,cartesian_product2(X2,X1))
| ~ in(X0,sK12(X1,X2,X3))
| ~ sP1(X1,X2,X3) ),
inference(duplicate_literal_removal,[],[f171]) ).
fof(f180,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ in(ordered_pair(X0,X2),cartesian_product2(X3,X4))
| element(X0,powerset(the_carrier(X1)))
| ~ in(X0,X3)
| in(ordered_pair(X0,X2),sK12(X4,X3,X1))
| ~ sP1(X4,X3,X1)
| ~ in(ordered_pair(X0,X2),cartesian_product2(X5,X6))
| ~ in(X0,X5)
| in(ordered_pair(X0,X2),sK12(X6,X5,X1))
| ~ sP1(X6,X5,X1) ),
inference(superposition,[],[f160,f158]) ).
fof(f189,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ in(ordered_pair(X0,X2),cartesian_product2(X3,X4))
| subset_complement(the_carrier(X1),X0) != X2
| ~ in(X0,X3)
| in(ordered_pair(X0,X2),sK12(X4,X3,X1))
| ~ sP1(X4,X3,X1)
| ~ in(ordered_pair(X0,X2),cartesian_product2(X5,X6))
| ~ in(X0,X5)
| in(ordered_pair(X0,X2),sK12(X6,X5,X1))
| ~ sP1(X6,X5,X1) ),
inference(superposition,[],[f156,f158]) ).
fof(f201,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| element(X0,powerset(the_carrier(X4)))
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),sK12(X3,X2,X4))
| ~ sP1(X3,X2,X4)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),sK12(X3,X2,X4))
| ~ sP1(X3,X2,X4) ),
inference(factoring,[],[f180]) ).
fof(f203,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| element(X0,powerset(the_carrier(X4)))
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),sK12(X3,X2,X4))
| ~ sP1(X3,X2,X4) ),
inference(duplicate_literal_removal,[],[f201]) ).
fof(f205,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| subset_complement(the_carrier(X4),X0) != X1
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),sK12(X3,X2,X4))
| ~ sP1(X3,X2,X4)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),sK12(X3,X2,X4))
| ~ sP1(X3,X2,X4) ),
inference(factoring,[],[f189]) ).
fof(f207,plain,
! [X2,X3,X0,X1,X4] :
( subset_complement(the_carrier(X4),X0) != X1
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),sK12(X3,X2,X4))
| ~ sP1(X3,X2,X4) ),
inference(duplicate_literal_removal,[],[f205]) ).
fof(f215,definition,
( spl24_1
<=> ! [X2] :
( ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(X2,sK3,sK2))
| ~ sP1(X2,sK3,sK2) ) ),
introduced(definition,[new_symbols(definition,[spl24_1])],[avatar_definition]) ).
fof(f216,plain,
( ! [X2] :
( ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(X2,sK3,sK2))
| ~ sP1(X2,sK3,sK2) )
| ~ spl24_1 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f218,definition,
( spl24_2
<=> sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) ),
introduced(definition,[new_symbols(definition,[spl24_2])],[avatar_definition]) ).
fof(f220,plain,
( sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))))
| ~ spl24_2 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f222,definition,
( spl24_3
<=> sP1(sK4,sK3,sK2) ),
introduced(definition,[new_symbols(definition,[spl24_3])],[avatar_definition]) ).
fof(f223,plain,
( sP1(sK4,sK3,sK2)
| ~ spl24_3 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f224,plain,
( ~ sP1(sK4,sK3,sK2)
| spl24_3 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f226,definition,
( spl24_4
<=> sK5(sK12(sK4,sK3,sK2)) = ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) ),
introduced(definition,[new_symbols(definition,[spl24_4])],[avatar_definition]) ).
fof(f227,plain,
( sK5(sK12(sK4,sK3,sK2)) != ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2)))
| spl24_4 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f228,plain,
( sK5(sK12(sK4,sK3,sK2)) = ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2)))
| ~ spl24_4 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f235,plain,
( sK20(sK2,sK3) = sK19(sK2,sK3)
| ~ one_sorted_str(sK2)
| ~ element(sK3,powerset(powerset(the_carrier(sK2))))
| spl24_3 ),
inference(resolution,[],[f224,f152]) ).
fof(f236,plain,
( sK19(sK2,sK3) = sK21(sK2,sK3)
| ~ one_sorted_str(sK2)
| ~ element(sK3,powerset(powerset(the_carrier(sK2))))
| spl24_3 ),
inference(resolution,[],[f224,f148]) ).
fof(f241,plain,
( sK19(sK2,sK3) = sK21(sK2,sK3)
| ~ element(sK3,powerset(powerset(the_carrier(sK2))))
| spl24_3 ),
inference(forward_subsumption_resolution,[],[f236,f89]) ).
fof(f242,plain,
( sK20(sK2,sK3) = sK19(sK2,sK3)
| ~ element(sK3,powerset(powerset(the_carrier(sK2))))
| spl24_3 ),
inference(forward_subsumption_resolution,[],[f235,f89]) ).
fof(f246,plain,
( sK19(sK2,sK3) = sK21(sK2,sK3)
| spl24_3 ),
inference(forward_subsumption_resolution,[],[f241,f88]) ).
fof(f247,plain,
( sK20(sK2,sK3) = sK19(sK2,sK3)
| spl24_3 ),
inference(forward_subsumption_resolution,[],[f242,f88]) ).
fof(f257,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,subset_complement(the_carrier(X1),X0)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| in(ordered_pair(X0,subset_complement(the_carrier(X1),X0)),sK12(X3,X2,X1))
| ~ sP1(X3,X2,X1) ),
inference(equality_resolution,[],[f207]) ).
fof(f258,plain,
( sK20(sK2,sK3) = sK21(sK2,sK3)
| spl24_3 ),
inference(superposition,[],[f247,f246]) ).
fof(f261,plain,
( ! [X0] :
( sK20(sK2,sK3) != sK20(sK2,sK3)
| sP1(X0,sK3,sK2)
| ~ one_sorted_str(sK2)
| ~ element(sK3,powerset(powerset(the_carrier(sK2)))) )
| spl24_3 ),
inference(superposition,[],[f153,f258]) ).
fof(f262,plain,
( ! [X0] :
( sP1(X0,sK3,sK2)
| ~ one_sorted_str(sK2)
| ~ element(sK3,powerset(powerset(the_carrier(sK2)))) )
| spl24_3 ),
inference(trivial_inequality_removal,[],[f261]) ).
fof(f263,plain,
( ! [X0] :
( sP1(X0,sK3,sK2)
| ~ element(sK3,powerset(powerset(the_carrier(sK2)))) )
| spl24_3 ),
inference(forward_subsumption_resolution,[],[f262,f89]) ).
fof(f264,plain,
( ! [X0] : sP1(X0,sK3,sK2)
| spl24_3 ),
inference(forward_subsumption_resolution,[],[f263,f88]) ).
fof(f265,plain,
( $false
| spl24_3 ),
inference(resolution,[],[f264,f224]) ).
fof(f266,plain,
spl24_3,
inference(avatar_contradiction_clause,[],[f265]) ).
fof(f278,definition,
( spl24_6
<=> element(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2))) ),
introduced(definition,[new_symbols(definition,[spl24_6])],[avatar_definition]) ).
fof(f279,plain,
( element(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ~ spl24_6 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f280,plain,
( ~ element(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| spl24_6 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f298,definition,
( spl24_10
<=> in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3) ),
introduced(definition,[new_symbols(definition,[spl24_10])],[avatar_definition]) ).
fof(f299,plain,
( in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ~ spl24_10 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f300,plain,
( ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| spl24_10 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f302,definition,
( spl24_11
<=> ! [X0] :
( ~ in(sK5(X0),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0),X0)
| sK5(X0) != sK5(sK12(sK4,sK3,sK2)) ) ),
introduced(definition,[new_symbols(definition,[spl24_11])],[avatar_definition]) ).
fof(f303,plain,
( ! [X0] :
( sK5(X0) != sK5(sK12(sK4,sK3,sK2))
| ~ in(sK5(X0),X0)
| ~ in(sK5(X0),cartesian_product2(sK3,sK4)) )
| ~ spl24_11 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f316,plain,
( ! [X2,X0,X1] :
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(X2)))
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(X0,X1))
| ~ in(sK7(sK12(sK4,sK3,sK2)),X0)
| in(sK5(sK12(sK4,sK3,sK2)),sK12(X1,X0,X2))
| ~ sP1(X1,X0,X2) )
| ~ spl24_4 ),
inference(superposition,[],[f203,f228]) ).
fof(f358,definition,
( spl24_15
<=> sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) ),
introduced(definition,[new_symbols(definition,[spl24_15])],[avatar_definition]) ).
fof(f360,plain,
( sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))))
| ~ spl24_15 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f367,plain,
( ! [X0] :
( ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(X0,sK3,sK2))
| ~ sP1(X0,sK3,sK2) )
| spl24_10 ),
inference(resolution,[],[f300,f137]) ).
fof(f368,plain,
( spl24_1
| spl24_10 ),
inference(avatar_split_clause,[],[f367,f298,f215]) ).
fof(f380,plain,
( ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ spl24_11 ),
inference(equality_resolution,[],[f303]) ).
fof(f394,definition,
( spl24_17
<=> in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl24_17])],[avatar_definition]) ).
fof(f396,plain,
( ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| spl24_17 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f398,definition,
( spl24_18
<=> in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
introduced(definition,[new_symbols(definition,[spl24_18])],[avatar_definition]) ).
fof(f399,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ~ spl24_18 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f400,plain,
( ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| spl24_18 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f401,plain,
( ~ spl24_17
| ~ spl24_18
| ~ spl24_11 ),
inference(avatar_split_clause,[],[f380,f302,f398,f394]) ).
fof(f424,plain,
( ! [X0,X1] :
( ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(X0,X1))
| ~ in(sK7(sK12(sK4,sK3,sK2)),X0)
| in(sK5(sK12(sK4,sK3,sK2)),sK12(X1,X0,sK2))
| ~ sP1(X1,X0,sK2)
| sK8(sK12(sK4,sK3,sK2)) = subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2)))
| in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) )
| ~ spl24_4 ),
inference(resolution,[],[f316,f154]) ).
fof(f425,plain,
( ! [X0,X1] :
( ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(X0,X1))
| ~ in(sK7(sK12(sK4,sK3,sK2)),X0)
| in(sK5(sK12(sK4,sK3,sK2)),sK12(X1,X0,sK2))
| ~ sP1(X1,X0,sK2)
| sK8(sK12(sK4,sK3,sK2)) = subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) )
| ~ spl24_4
| spl24_18 ),
inference(forward_subsumption_resolution,[],[f424,f400]) ).
fof(f427,definition,
( spl24_19
<=> sK8(sK12(sK4,sK3,sK2)) = subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) ),
introduced(definition,[new_symbols(definition,[spl24_19])],[avatar_definition]) ).
fof(f429,plain,
( sK8(sK12(sK4,sK3,sK2)) = subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2)))
| ~ spl24_19 ),
inference(avatar_component_clause,[],[f427]) ).
fof(f431,definition,
( spl24_20
<=> ! [X0,X1] :
( ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(X0,X1))
| ~ sP1(X1,X0,sK2)
| in(sK5(sK12(sK4,sK3,sK2)),sK12(X1,X0,sK2))
| ~ in(sK7(sK12(sK4,sK3,sK2)),X0) ) ),
introduced(definition,[new_symbols(definition,[spl24_20])],[avatar_definition]) ).
fof(f432,plain,
( ! [X0,X1] :
( ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(X0,X1))
| ~ sP1(X1,X0,sK2)
| in(sK5(sK12(sK4,sK3,sK2)),sK12(X1,X0,sK2))
| ~ in(sK7(sK12(sK4,sK3,sK2)),X0) )
| ~ spl24_20 ),
inference(avatar_component_clause,[],[f431]) ).
fof(f433,plain,
( spl24_19
| spl24_20
| ~ spl24_4
| spl24_18 ),
inference(avatar_split_clause,[],[f425,f398,f226,f431,f427]) ).
fof(f434,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),cartesian_product2(X0,X1))
| ~ in(sK7(sK12(sK4,sK3,sK2)),X0)
| in(ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),sK12(X1,X0,sK2))
| ~ sP1(X1,X0,sK2) )
| ~ spl24_19 ),
inference(superposition,[],[f257,f429]) ).
fof(f452,plain,
( ! [X0,X1] :
( ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(X0,X1))
| ~ in(sK7(sK12(sK4,sK3,sK2)),X0)
| in(ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),sK12(X1,X0,sK2))
| ~ sP1(X1,X0,sK2) )
| ~ spl24_4
| ~ spl24_19 ),
inference(forward_demodulation,[],[f434,f228]) ).
fof(f453,plain,
( ! [X0,X1] :
( in(sK5(sK12(sK4,sK3,sK2)),sK12(X1,X0,sK2))
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(X0,X1))
| ~ in(sK7(sK12(sK4,sK3,sK2)),X0)
| ~ sP1(X1,X0,sK2) )
| ~ spl24_4
| ~ spl24_19 ),
inference(forward_demodulation,[],[f452,f228]) ).
fof(f454,plain,
( spl24_20
| ~ spl24_4
| ~ spl24_19 ),
inference(avatar_split_clause,[],[f453,f427,f226,f431]) ).
fof(f458,plain,
( ~ sP1(sK4,sK3,sK2)
| in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ~ spl24_20 ),
inference(resolution,[],[f432,f93]) ).
fof(f460,plain,
( ~ sP1(sK4,sK3,sK2)
| in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ spl24_20 ),
inference(duplicate_literal_removal,[],[f458]) ).
fof(f461,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ spl24_3
| ~ spl24_20 ),
inference(forward_subsumption_resolution,[],[f460,f223]) ).
fof(f469,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ~ spl24_3
| ~ spl24_20 ),
inference(forward_subsumption_resolution,[],[f461,f91]) ).
fof(f470,plain,
( spl24_18
| ~ spl24_3
| ~ spl24_20 ),
inference(avatar_split_clause,[],[f469,f431,f222,f398]) ).
fof(f477,plain,
( ! [X0] :
( ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,X0))
| ~ sP1(sK4,sK3,X0) )
| spl24_17 ),
inference(resolution,[],[f396,f172]) ).
fof(f487,plain,
( sK5(sK12(sK4,sK3,sK2)) = ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))))
| ~ sP1(sK4,sK3,sK2)
| ~ spl24_18 ),
inference(resolution,[],[f399,f138]) ).
fof(f494,plain,
( sK5(sK12(sK4,sK3,sK2)) = ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))))
| ~ spl24_3
| ~ spl24_18 ),
inference(forward_subsumption_resolution,[],[f487,f223]) ).
fof(f499,plain,
( ~ sP1(sK4,sK3,sK2)
| spl24_17
| ~ spl24_18 ),
inference(resolution,[],[f477,f399]) ).
fof(f501,plain,
( $false
| ~ spl24_3
| spl24_17
| ~ spl24_18 ),
inference(forward_subsumption_resolution,[],[f499,f223]) ).
fof(f502,plain,
( ~ spl24_3
| spl24_17
| ~ spl24_18 ),
inference(avatar_contradiction_clause,[],[f501]) ).
fof(f555,plain,
( ~ sP1(sK4,sK3,sK2)
| ~ spl24_1
| ~ spl24_18 ),
inference(resolution,[],[f216,f399]) ).
fof(f558,plain,
( $false
| ~ spl24_1
| ~ spl24_3
| ~ spl24_18 ),
inference(forward_subsumption_resolution,[],[f555,f223]) ).
fof(f559,plain,
( ~ spl24_1
| ~ spl24_3
| ~ spl24_18 ),
inference(avatar_contradiction_clause,[],[f558]) ).
fof(f584,plain,
( ! [X0] :
( sK5(X0) != sK5(sK12(sK4,sK3,sK2))
| ~ in(sK5(X0),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))))
| ~ in(sK5(X0),X0) )
| ~ spl24_3
| ~ spl24_18 ),
inference(superposition,[],[f95,f494]) ).
fof(f585,plain,
( ! [X0] :
( sK5(X0) != sK5(sK12(sK4,sK3,sK2))
| ~ in(sK5(X0),cartesian_product2(sK3,sK4))
| sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))))
| ~ in(sK5(X0),X0) )
| ~ spl24_3
| ~ spl24_10
| ~ spl24_18 ),
inference(forward_subsumption_resolution,[],[f584,f299]) ).
fof(f587,plain,
( spl24_15
| spl24_11
| ~ spl24_3
| ~ spl24_10
| ~ spl24_18 ),
inference(avatar_split_clause,[],[f585,f398,f298,f222,f302,f358]) ).
fof(f592,plain,
( ! [X0] :
( element(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| sK5(X0) != ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ~ in(sK5(X0),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0),X0) )
| ~ spl24_15 ),
inference(superposition,[],[f94,f360]) ).
fof(f593,plain,
( ! [X0] :
( sK5(X0) != ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ~ in(sK5(X0),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0),X0) )
| spl24_6
| ~ spl24_15 ),
inference(forward_subsumption_resolution,[],[f592,f280]) ).
fof(f594,plain,
( ! [X0] :
( sK5(X0) != ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))))
| ~ in(sK5(X0),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0),X0) )
| spl24_6
| ~ spl24_10
| ~ spl24_15 ),
inference(forward_subsumption_resolution,[],[f593,f299]) ).
fof(f595,plain,
( ! [X0] :
( sK5(X0) != sK5(sK12(sK4,sK3,sK2))
| ~ in(sK5(X0),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0),X0) )
| ~ spl24_3
| spl24_6
| ~ spl24_10
| ~ spl24_15
| ~ spl24_18 ),
inference(forward_demodulation,[],[f594,f494]) ).
fof(f596,plain,
( spl24_11
| ~ spl24_3
| spl24_6
| ~ spl24_10
| ~ spl24_15
| ~ spl24_18 ),
inference(avatar_split_clause,[],[f595,f398,f358,f298,f278,f222,f302]) ).
fof(f600,plain,
( sK5(sK12(sK4,sK3,sK2)) = ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2)))
| spl24_18 ),
inference(resolution,[],[f400,f92]) ).
fof(f601,plain,
( $false
| spl24_4
| spl24_18 ),
inference(forward_subsumption_resolution,[],[f600,f227]) ).
fof(f602,plain,
( spl24_4
| spl24_18 ),
inference(avatar_contradiction_clause,[],[f601]) ).
fof(f616,plain,
( sK5(sK12(sK4,sK3,sK2)) = ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))))
| ~ sP1(sK4,sK3,sK2)
| ~ spl24_18 ),
inference(resolution,[],[f399,f138]) ).
fof(f624,plain,
( sK5(sK12(sK4,sK3,sK2)) = ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))))
| ~ spl24_3
| ~ spl24_18 ),
inference(forward_subsumption_resolution,[],[f616,f223]) ).
fof(f627,plain,
( ! [X0] :
( sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(X0,sK3,sK2))
| ~ sP1(X0,sK3,sK2) )
| ~ spl24_6 ),
inference(resolution,[],[f279,f161]) ).
fof(f628,plain,
( spl24_1
| spl24_2
| ~ spl24_6 ),
inference(avatar_split_clause,[],[f627,f278,f218,f215]) ).
fof(f676,plain,
( ! [X0] :
( sK5(X0) != sK5(sK12(sK4,sK3,sK2))
| ~ in(sK5(X0),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) != subset_complement(the_carrier(sK2),sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))))
| ~ in(sK5(X0),X0) )
| ~ spl24_3
| ~ spl24_18 ),
inference(superposition,[],[f96,f624]) ).
fof(f678,plain,
( ! [X0] :
( sK5(X0) != sK5(sK12(sK4,sK3,sK2))
| ~ in(sK5(X0),cartesian_product2(sK3,sK4))
| sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) != subset_complement(the_carrier(sK2),sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))))
| ~ in(sK5(X0),X0) )
| ~ spl24_3
| ~ spl24_10
| ~ spl24_18 ),
inference(forward_subsumption_resolution,[],[f676,f299]) ).
fof(f679,plain,
( ! [X0] :
( sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) != subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))))
| sK5(X0) != sK5(sK12(sK4,sK3,sK2))
| ~ in(sK5(X0),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0),X0) )
| ~ spl24_3
| ~ spl24_10
| ~ spl24_15
| ~ spl24_18 ),
inference(forward_demodulation,[],[f678,f360]) ).
fof(f680,plain,
( ! [X0] :
( sK5(X0) != sK5(sK12(sK4,sK3,sK2))
| ~ in(sK5(X0),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0),X0) )
| ~ spl24_2
| ~ spl24_3
| ~ spl24_10
| ~ spl24_15
| ~ spl24_18 ),
inference(forward_subsumption_resolution,[],[f679,f220]) ).
fof(f681,plain,
( spl24_11
| ~ spl24_2
| ~ spl24_3
| ~ spl24_10
| ~ spl24_15
| ~ spl24_18 ),
inference(avatar_split_clause,[],[f680,f398,f358,f298,f222,f218,f302]) ).
cnf(s3,plain,
spl24_3,
inference(sat_conversion,[],[f266]) ).
cnf(s17,plain,
( spl24_1
| spl24_10 ),
inference(sat_conversion,[],[f368]) ).
cnf(s20,plain,
( ~ spl24_11
| ~ spl24_17
| ~ spl24_18 ),
inference(sat_conversion,[],[f401]) ).
cnf(s22,plain,
( ~ spl24_4
| spl24_18
| spl24_19
| spl24_20 ),
inference(sat_conversion,[],[f433]) ).
cnf(s25,plain,
( ~ spl24_4
| ~ spl24_19
| spl24_20 ),
inference(sat_conversion,[],[f454]) ).
cnf(s29,plain,
( ~ spl24_3
| spl24_18
| ~ spl24_20 ),
inference(sat_conversion,[],[f470]) ).
cnf(s31,plain,
( ~ spl24_3
| spl24_17
| ~ spl24_18 ),
inference(sat_conversion,[],[f502]) ).
cnf(s39,plain,
( ~ spl24_1
| ~ spl24_3
| ~ spl24_18 ),
inference(sat_conversion,[],[f559]) ).
cnf(s42,plain,
( ~ spl24_3
| ~ spl24_10
| spl24_11
| spl24_15
| ~ spl24_18 ),
inference(sat_conversion,[],[f587]) ).
cnf(s44,plain,
( ~ spl24_3
| spl24_6
| ~ spl24_10
| spl24_11
| ~ spl24_15
| ~ spl24_18 ),
inference(sat_conversion,[],[f596]) ).
cnf(s46,plain,
( spl24_4
| spl24_18 ),
inference(sat_conversion,[],[f602]) ).
cnf(s51,plain,
( spl24_1
| spl24_2
| ~ spl24_6 ),
inference(sat_conversion,[],[f628]) ).
cnf(s54,plain,
( ~ spl24_2
| ~ spl24_3
| ~ spl24_10
| spl24_11
| ~ spl24_15
| ~ spl24_18 ),
inference(sat_conversion,[],[f681]) ).
cnf(s56,plain,
( ~ spl24_18
| spl24_6
| ~ spl24_10 ),
inference(rat,[],[s44,s42,s20,s31,s3]) ).
cnf(s57,plain,
( spl24_18
| spl24_20
| ~ spl24_4 ),
inference(rat,[],[s25,s22]) ).
cnf(s58,plain,
spl24_18,
inference(rat,[],[s57,s29,s46,s3]) ).
cnf(s59,plain,
spl24_17,
inference(rat,[],[s31,s3,s58]) ).
cnf(s60,plain,
~ spl24_11,
inference(rat,[],[s20,s58,s59]) ).
cnf(s61,plain,
spl24_1,
inference(rat,[],[s54,s42,s51,s56,s17,s3,s60,s58]) ).
cnf(s62,plain,
$false,
inference(rat,[],[s39,s3,s58,s61]) ).
fof(f682,plain,
$false,
inference(avatar_sat_refutation,[],[s62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU332+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n010.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 04:44:17 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 1.38/1.21 % (1560076)Detected formulas, will run a generic FOF schedule.
% 1.38/1.21 % (1560187)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2916878220:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.38/1.21 % (1560187)First to succeed.
% 1.38/1.21 % (1560187)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1560076"
% 1.38/1.21 % (1560185)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1831463124:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.38/1.21 % (1560183)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=3175424796:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.38/1.21 % (1560186)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2941657451:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.38/1.21 % (1560188)dis-21_1_sil=8000:lcm=predicate:random_seed=1052775283: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)
% 1.38/1.21 % (1560184)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=3521391024:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.38/1.21 % (1560182)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=832223002:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.38/1.21 % (1560186)Also succeeded, but the first one will report.
% 1.38/1.21 % (1560185)Instruction limit reached!
% 1.38/1.21 % (1560185)------------------------------
% 1.38/1.21 % (1560185)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.38/1.21 % (1560185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/1.21 % (1560185)CaDiCaL version: 2.1.3
% 1.38/1.21 % (1560185)Termination reason: Instruction limit
% 1.38/1.21 % (1560185)Termination phase: Saturation
% 1.38/1.21 % (1560185)Time elapsed: 0.061 s
% 1.38/1.21 % (1560185)Peak memory usage: 89 MB
% 1.38/1.21 % (1560185)Instructions burned: 110 (million)
% 1.38/1.21 % (1560188)Instruction limit reached!
% 1.38/1.21 % (1560188)------------------------------
% 1.38/1.21 % (1560188)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.38/1.21 % (1560188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/1.21 % (1560188)CaDiCaL version: 2.1.3
% 1.38/1.21 % (1560188)Termination reason: Instruction limit
% 1.38/1.21 % (1560188)Termination phase: Saturation
% 1.38/1.21 % (1560188)Time elapsed: 0.084 s
% 1.38/1.21 % (1560188)Peak memory usage: 89 MB
% 1.38/1.21 % (1560188)Instructions burned: 131 (million)
% 1.38/1.21 % (1560187)Refutation found. Thanks to Tanya!
% 1.38/1.21 % SZS status Theorem for theBenchmark
% 1.38/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 3.17/1.50 % (1560187)------------------------------
% 3.17/1.50 % (1560187)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.50 % (1560187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.50 % (1560187)CaDiCaL version: 2.1.3
% 3.17/1.50 % (1560187)Termination reason: Refutation
% 3.17/1.50 % (1560187)Time elapsed: 0.029 s
% 3.17/1.50 % (1560187)Peak memory usage: 90 MB
% 3.17/1.50 % (1560187)Instructions burned: 75 (million)
% 3.17/1.50 % (1560187)------------------------------
% 3.17/1.50 % (1560187)------------------------------
% 3.17/1.50 % (1560076)Success in time 0.339 s
% 3.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------