%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU329+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 : n001.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 12:48:22 PM UTC 2026
% Result : Theorem 2.68s 1.30s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 4
% Syntax : Number of formulae : 104 ( 5 unt; 2 def)
% Number of atoms : 772 ( 185 equ)
% Maximal formula atoms : 23 ( 7 avg)
% Number of connectives : 1123 ( 455 ~; 498 |; 137 &)
% ( 7 <=>; 24 =>; 0 <=; 2 <~>)
% Maximal formula depth : 20 ( 11 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 3 con; 0-4 aty)
% Number of variables : 474 ( 376 !; 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(complements_of_subsets(the_carrier(X0),X1),X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,complements_of_subsets(the_carrier(X0),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_1__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(complements_of_subsets(the_carrier(X0),X1),X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,complements_of_subsets(the_carrier(X0),X1))
& ! [X7] :
( element(X7,powerset(the_carrier(X0)))
=> ( X7 = X5
=> X6 = subset_complement(the_carrier(X0),X7) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f35,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,complements_of_subsets(the_carrier(X0),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,complements_of_subsets(the_carrier(X0),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(complements_of_subsets(the_carrier(X0),X1),X2))
& X5 = X4
& ? [X12,X13] :
( ordered_pair(X12,X13) = X4
& in(X12,complements_of_subsets(the_carrier(X0),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_1__tops_2__2) ).
fof(f36,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,complements_of_subsets(the_carrier(X0),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,complements_of_subsets(the_carrier(X0),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(complements_of_subsets(the_carrier(X0),X1),X2))
& X13 = X14
& ? [X15,X16] :
( ordered_pair(X15,X16) = X13
& in(X15,complements_of_subsets(the_carrier(X0),X1))
& ! [X17] :
( element(X17,powerset(the_carrier(X0)))
=> ( X15 = X17
=> subset_complement(the_carrier(X0),X17) = X16 ) ) ) ) ) ) ),
inference(rectify,[],[f35]) ).
fof(f37,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( in(X4,X3)
<~> ( in(X4,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,complements_of_subsets(the_carrier(X0),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(f38,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( in(X4,X3)
<~> ( in(X4,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,complements_of_subsets(the_carrier(X0),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,[],[f37]) ).
fof(f41,plain,
! [X0,X1] :
( ! [X2] :
( ? [X12] :
! [X13] :
( in(X13,X12)
<=> ? [X14] :
( in(X14,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
& X13 = X14
& ? [X15,X16] :
( ordered_pair(X15,X16) = X13
& in(X15,complements_of_subsets(the_carrier(X0),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,complements_of_subsets(the_carrier(X0),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,complements_of_subsets(the_carrier(X0),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,[],[f36]) ).
fof(f42,plain,
! [X0,X1] :
( ! [X2] :
( ? [X12] :
! [X13] :
( in(X13,X12)
<=> ? [X14] :
( in(X14,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
& X13 = X14
& ? [X15,X16] :
( ordered_pair(X15,X16) = X13
& in(X15,complements_of_subsets(the_carrier(X0),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,complements_of_subsets(the_carrier(X0),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,complements_of_subsets(the_carrier(X0),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,[],[f41]) ).
fof(f49,definition,
! [X5,X1,X0] :
( ? [X9,X10] :
( ordered_pair(X9,X10) = X5
& in(X9,complements_of_subsets(the_carrier(X0),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(f50,definition,
! [X2,X1,X0] :
( ? [X12] :
! [X13] :
( in(X13,X12)
<=> ? [X14] :
( in(X14,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
& X13 = X14
& ? [X15,X16] :
( ordered_pair(X15,X16) = X13
& in(X15,complements_of_subsets(the_carrier(X0),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(f51,plain,
! [X0,X1] :
( ! [X2] :
( sP1(X2,X1,X0)
| ? [X3,X4,X5] :
( X4 != X5
& X3 = X4
& ? [X6,X7] :
( ordered_pair(X6,X7) = X4
& in(X6,complements_of_subsets(the_carrier(X0),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,[],[f42,f50,f49]) ).
fof(f52,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( ( ~ in(X4,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
| ! [X5,X6] :
( ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X0),X1))
| ? [X7] :
( subset_complement(the_carrier(X0),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(X0))) ) )
| ~ in(X4,X3) )
& ( ( in(X4,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,complements_of_subsets(the_carrier(X0),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,[],[f38]) ).
fof(f53,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( ( ~ in(X4,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
| ! [X5,X6] :
( ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X0),X1))
| ? [X7] :
( subset_complement(the_carrier(X0),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(X0))) ) )
| ~ in(X4,X3) )
& ( ( in(X4,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,complements_of_subsets(the_carrier(X0),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,[],[f52]) ).
fof(f54,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( ( ~ in(X4,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
| ! [X5,X6] :
( ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X0),X1))
| ? [X7] :
( subset_complement(the_carrier(X0),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(X0))) ) )
| ~ in(X4,X3) )
& ( ( in(X4,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
& ? [X8,X9] :
( ordered_pair(X8,X9) = X4
& in(X8,complements_of_subsets(the_carrier(X0),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,[],[f53]) ).
fof(f55,plain,
( ! [X3] :
( ( ~ in(sK5(X3),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ! [X5,X6] :
( ordered_pair(X5,X6) != sK5(X3)
| ~ in(X5,complements_of_subsets(the_carrier(sK2),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(complements_of_subsets(the_carrier(sK2),sK3),sK4))
& sK5(X3) = ordered_pair(sK7(X3),sK8(X3))
& in(sK7(X3),complements_of_subsets(the_carrier(sK2),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))],[f54]) ).
fof(f56,plain,
! [X2,X1,X0] :
( ? [X12] :
! [X13] :
( ( in(X13,X12)
| ! [X14] :
( ~ in(X14,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
| X13 != X14
| ! [X15,X16] :
( ordered_pair(X15,X16) != X13
| ~ in(X15,complements_of_subsets(the_carrier(X0),X1))
| ? [X17] :
( subset_complement(the_carrier(X0),X17) != X16
& X15 = X17
& element(X17,powerset(the_carrier(X0))) ) ) ) )
& ( ? [X14] :
( in(X14,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
& X13 = X14
& ? [X15,X16] :
( ordered_pair(X15,X16) = X13
& in(X15,complements_of_subsets(the_carrier(X0),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,[],[f50]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ! [X5] :
( ~ in(X5,cartesian_product2(complements_of_subsets(the_carrier(X2),X1),X0))
| X4 != X5
| ! [X6,X7] :
( ordered_pair(X6,X7) != X4
| ~ in(X6,complements_of_subsets(the_carrier(X2),X1))
| ? [X8] :
( subset_complement(the_carrier(X2),X8) != X7
& X6 = X8
& element(X8,powerset(the_carrier(X2))) ) ) ) )
& ( ? [X9] :
( in(X9,cartesian_product2(complements_of_subsets(the_carrier(X2),X1),X0))
& X4 = X9
& ? [X10,X11] :
( ordered_pair(X10,X11) = X4
& in(X10,complements_of_subsets(the_carrier(X2),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,[],[f56]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ! [X4] :
( ( in(X4,sK9(X0,X1,X2))
| ! [X5] :
( ~ in(X5,cartesian_product2(complements_of_subsets(the_carrier(X2),X1),X0))
| X4 != X5
| ! [X6,X7] :
( ordered_pair(X6,X7) != X4
| ~ in(X6,complements_of_subsets(the_carrier(X2),X1))
| ( subset_complement(the_carrier(X2),sK10(X2,X6,X7)) != X7
& sK10(X2,X6,X7) = X6
& element(sK10(X2,X6,X7),powerset(the_carrier(X2))) ) ) ) )
& ( ( in(sK11(X0,X1,X2,X4),cartesian_product2(complements_of_subsets(the_carrier(X2),X1),X0))
& sK11(X0,X1,X2,X4) = X4
& ordered_pair(sK12(X1,X2,X4),sK13(X1,X2,X4)) = X4
& in(sK12(X1,X2,X4),complements_of_subsets(the_carrier(X2),X1))
& ! [X12] :
( subset_complement(the_carrier(X2),X12) = sK13(X1,X2,X4)
| sK12(X1,X2,X4) != X12
| ~ element(X12,powerset(the_carrier(X2))) ) )
| ~ in(X4,sK9(X0,X1,X2)) ) )
| ~ sP1(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13]),skolemize(X3,sK9(X0,X1,X2)),skolemize(X8,sK10(X2,X6,X7)),skolemize(X9,sK11(X0,X1,X2,X4)),skolemize(X10,sK12(X1,X2,X4)),skolemize(X11,sK13(X1,X2,X4))],[f57]) ).
fof(f62,plain,
! [X0,X1] :
( ! [X2] :
( sP1(X2,X1,X0)
| ( sK17(X0,X1) != sK18(X0,X1)
& sK16(X0,X1) = sK17(X0,X1)
& sK17(X0,X1) = ordered_pair(sK19(X0,X1),sK20(X0,X1))
& in(sK19(X0,X1),complements_of_subsets(the_carrier(X0),X1))
& ! [X8] :
( subset_complement(the_carrier(X0),X8) = sK20(X0,X1)
| sK19(X0,X1) != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& sK16(X0,X1) = sK18(X0,X1)
& sP0(sK18(X0,X1),X1,X0) ) )
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19,sK20]),skolemize(X3,sK16(X0,X1)),skolemize(X4,sK17(X0,X1)),skolemize(X5,sK18(X0,X1)),skolemize(X6,sK19(X0,X1)),skolemize(X7,sK20(X0,X1))],[f51]) ).
fof(f65,plain,
element(sK3,powerset(powerset(the_carrier(sK2)))),
inference(cnf_transformation,[],[f55]) ).
fof(f66,plain,
one_sorted_str(sK2),
inference(cnf_transformation,[],[f55]) ).
fof(f67,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,[],[f55]) ).
fof(f68,plain,
! [X3] :
( in(sK7(X3),complements_of_subsets(the_carrier(sK2),sK3))
| in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f55]) ).
fof(f69,plain,
! [X3] :
( sK5(X3) = ordered_pair(sK7(X3),sK8(X3))
| in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f55]) ).
fof(f70,plain,
! [X3] :
( in(sK5(X3),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f55]) ).
fof(f71,plain,
! [X3,X6,X5] :
( ordered_pair(X5,X6) != sK5(X3)
| ~ in(sK5(X3),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(X5,complements_of_subsets(the_carrier(sK2),sK3))
| element(sK6(X5,X6),powerset(the_carrier(sK2)))
| ~ in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f55]) ).
fof(f72,plain,
! [X3,X6,X5] :
( ordered_pair(X5,X6) != sK5(X3)
| ~ in(sK5(X3),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(X5,complements_of_subsets(the_carrier(sK2),sK3))
| sK6(X5,X6) = X5
| ~ in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f55]) ).
fof(f73,plain,
! [X3,X6,X5] :
( subset_complement(the_carrier(sK2),sK6(X5,X6)) != X6
| ordered_pair(X5,X6) != sK5(X3)
| ~ in(X5,complements_of_subsets(the_carrier(sK2),sK3))
| ~ in(sK5(X3),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f55]) ).
fof(f76,plain,
! [X2,X0,X1,X4,X12] :
( subset_complement(the_carrier(X2),X12) = sK13(X1,X2,X4)
| sK12(X1,X2,X4) != X12
| ~ element(X12,powerset(the_carrier(X2)))
| ~ in(X4,sK9(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f77,plain,
! [X2,X0,X1,X4] :
( in(sK12(X1,X2,X4),complements_of_subsets(the_carrier(X2),X1))
| ~ in(X4,sK9(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f78,plain,
! [X2,X0,X1,X4] :
( ordered_pair(sK12(X1,X2,X4),sK13(X1,X2,X4)) = X4
| ~ in(X4,sK9(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f79,plain,
! [X2,X0,X1,X4] :
( sK11(X0,X1,X2,X4) = X4
| ~ in(X4,sK9(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f80,plain,
! [X2,X0,X1,X4] :
( in(sK11(X0,X1,X2,X4),cartesian_product2(complements_of_subsets(the_carrier(X2),X1),X0))
| ~ in(X4,sK9(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f81,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( in(X4,sK9(X0,X1,X2))
| ~ in(X5,cartesian_product2(complements_of_subsets(the_carrier(X2),X1),X0))
| X4 != X5
| ordered_pair(X6,X7) != X4
| ~ in(X6,complements_of_subsets(the_carrier(X2),X1))
| element(sK10(X2,X6,X7),powerset(the_carrier(X2)))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f82,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( in(X4,sK9(X0,X1,X2))
| ~ in(X5,cartesian_product2(complements_of_subsets(the_carrier(X2),X1),X0))
| X4 != X5
| ordered_pair(X6,X7) != X4
| ~ in(X6,complements_of_subsets(the_carrier(X2),X1))
| sK10(X2,X6,X7) = X6
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f83,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( in(X4,sK9(X0,X1,X2))
| ~ in(X5,cartesian_product2(complements_of_subsets(the_carrier(X2),X1),X0))
| X4 != X5
| ordered_pair(X6,X7) != X4
| ~ in(X6,complements_of_subsets(the_carrier(X2),X1))
| subset_complement(the_carrier(X2),sK10(X2,X6,X7)) != X7
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f88,plain,
! [X2,X0,X1] :
( sK16(X0,X1) = sK18(X0,X1)
| sP1(X2,X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f62]) ).
fof(f92,plain,
! [X2,X0,X1] :
( sK16(X0,X1) = sK17(X0,X1)
| sP1(X2,X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f62]) ).
fof(f93,plain,
! [X2,X0,X1] :
( sK17(X0,X1) != sK18(X0,X1)
| sP1(X2,X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f62]) ).
fof(f103,plain,
! [X3] :
( sK8(X3) = subset_complement(the_carrier(sK2),sK7(X3))
| ~ element(sK7(X3),powerset(the_carrier(sK2)))
| in(sK5(X3),X3) ),
inference(equality_resolution,[],[f67]) ).
fof(f104,plain,
! [X2,X0,X1,X6,X7,X5] :
( in(X5,sK9(X0,X1,X2))
| ~ in(X5,cartesian_product2(complements_of_subsets(the_carrier(X2),X1),X0))
| ordered_pair(X6,X7) != X5
| ~ in(X6,complements_of_subsets(the_carrier(X2),X1))
| subset_complement(the_carrier(X2),sK10(X2,X6,X7)) != X7
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f83]) ).
fof(f105,plain,
! [X2,X0,X1,X6,X7] :
( subset_complement(the_carrier(X2),sK10(X2,X6,X7)) != X7
| ~ in(ordered_pair(X6,X7),cartesian_product2(complements_of_subsets(the_carrier(X2),X1),X0))
| ~ in(X6,complements_of_subsets(the_carrier(X2),X1))
| in(ordered_pair(X6,X7),sK9(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f104]) ).
fof(f106,plain,
! [X2,X0,X1,X6,X7,X5] :
( in(X5,sK9(X0,X1,X2))
| ~ in(X5,cartesian_product2(complements_of_subsets(the_carrier(X2),X1),X0))
| ordered_pair(X6,X7) != X5
| ~ in(X6,complements_of_subsets(the_carrier(X2),X1))
| sK10(X2,X6,X7) = X6
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f82]) ).
fof(f107,plain,
! [X2,X0,X1,X6,X7] :
( ~ in(ordered_pair(X6,X7),cartesian_product2(complements_of_subsets(the_carrier(X2),X1),X0))
| in(ordered_pair(X6,X7),sK9(X0,X1,X2))
| ~ in(X6,complements_of_subsets(the_carrier(X2),X1))
| sK10(X2,X6,X7) = X6
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f106]) ).
fof(f108,plain,
! [X2,X0,X1,X6,X7,X5] :
( in(X5,sK9(X0,X1,X2))
| ~ in(X5,cartesian_product2(complements_of_subsets(the_carrier(X2),X1),X0))
| ordered_pair(X6,X7) != X5
| ~ in(X6,complements_of_subsets(the_carrier(X2),X1))
| element(sK10(X2,X6,X7),powerset(the_carrier(X2)))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f81]) ).
fof(f109,plain,
! [X2,X0,X1,X6,X7] :
( ~ in(ordered_pair(X6,X7),cartesian_product2(complements_of_subsets(the_carrier(X2),X1),X0))
| in(ordered_pair(X6,X7),sK9(X0,X1,X2))
| ~ in(X6,complements_of_subsets(the_carrier(X2),X1))
| element(sK10(X2,X6,X7),powerset(the_carrier(X2)))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f108]) ).
fof(f110,plain,
! [X2,X0,X1,X4] :
( sK13(X1,X2,X4) = subset_complement(the_carrier(X2),sK12(X1,X2,X4))
| ~ element(sK12(X1,X2,X4),powerset(the_carrier(X2)))
| ~ in(X4,sK9(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f76]) ).
fof(f147,plain,
! [X2,X3,X0,X1] :
( sK16(X0,X1) != sK17(X0,X1)
| sP1(X2,X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| sP1(X3,X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(superposition,[],[f93,f88]) ).
fof(f148,plain,
! [X2,X3,X0,X1] :
( sK16(X0,X1) != sK17(X0,X1)
| sP1(X2,X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| sP1(X3,X1,X0) ),
inference(duplicate_literal_removal,[],[f147]) ).
fof(f149,plain,
! [X2,X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0)
| sP1(X2,X1,X0)
| sP1(X3,X1,X0) ),
inference(forward_subsumption_resolution,[],[f148,f92]) ).
fof(f155,plain,
! [X0,X1] :
( ~ one_sorted_str(sK2)
| sP1(X0,sK3,sK2)
| sP1(X1,sK3,sK2) ),
inference(resolution,[],[f149,f65]) ).
fof(f159,plain,
! [X0,X1] :
( sP1(X1,sK3,sK2)
| sP1(X0,sK3,sK2) ),
inference(forward_subsumption_resolution,[],[f155,f66]) ).
fof(f160,plain,
! [X2,X3,X0,X1,X4] :
( sK5(X3) != X0
| ~ in(sK5(X3),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK12(X1,X2,X0),complements_of_subsets(the_carrier(sK2),sK3))
| element(sK6(sK12(X1,X2,X0),sK13(X1,X2,X0)),powerset(the_carrier(sK2)))
| ~ in(sK5(X3),X3)
| ~ in(X0,sK9(X4,X1,X2))
| ~ sP1(X4,X1,X2) ),
inference(superposition,[],[f71,f78]) ).
fof(f161,plain,
! [X2,X3,X0,X1,X4] :
( sK5(X3) != X0
| ~ in(sK5(X3),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK12(X1,X2,X0),complements_of_subsets(the_carrier(sK2),sK3))
| sK12(X1,X2,X0) = sK6(sK12(X1,X2,X0),sK13(X1,X2,X0))
| ~ in(sK5(X3),X3)
| ~ in(X0,sK9(X4,X1,X2))
| ~ sP1(X4,X1,X2) ),
inference(superposition,[],[f72,f78]) ).
fof(f162,plain,
! [X2,X3,X0,X1] :
( element(sK6(sK12(X1,X2,sK5(X0)),sK13(X1,X2,sK5(X0))),powerset(the_carrier(sK2)))
| ~ in(sK12(X1,X2,sK5(X0)),complements_of_subsets(the_carrier(sK2),sK3))
| ~ in(sK5(X0),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X0),X0)
| ~ in(sK5(X0),sK9(X3,X1,X2))
| ~ sP1(X3,X1,X2) ),
inference(equality_resolution,[],[f160]) ).
fof(f164,plain,
! [X2,X3,X0,X1] :
( in(X0,cartesian_product2(complements_of_subsets(the_carrier(X3),X2),X1))
| ~ in(X0,sK9(X1,X2,X3))
| ~ sP1(X1,X2,X3)
| ~ in(X0,sK9(X1,X2,X3))
| ~ sP1(X1,X2,X3) ),
inference(superposition,[],[f80,f79]) ).
fof(f166,plain,
! [X2,X3,X0,X1] :
( in(X0,cartesian_product2(complements_of_subsets(the_carrier(X3),X2),X1))
| ~ in(X0,sK9(X1,X2,X3))
| ~ sP1(X1,X2,X3) ),
inference(duplicate_literal_removal,[],[f164]) ).
fof(f167,plain,
! [X2,X3,X0,X1] :
( sK12(X1,X2,sK5(X0)) = sK6(sK12(X1,X2,sK5(X0)),sK13(X1,X2,sK5(X0)))
| ~ in(sK12(X1,X2,sK5(X0)),complements_of_subsets(the_carrier(sK2),sK3))
| ~ in(sK5(X0),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X0),X0)
| ~ in(sK5(X0),sK9(X3,X1,X2))
| ~ sP1(X3,X1,X2) ),
inference(equality_resolution,[],[f161]) ).
fof(f182,plain,
! [X2,X3,X0,X1,X4] :
( element(sK12(X0,X1,sK5(X2)),powerset(the_carrier(sK2)))
| ~ in(sK12(X0,X1,sK5(X2)),complements_of_subsets(the_carrier(sK2),sK3))
| ~ in(sK5(X2),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X2),X2)
| ~ in(sK5(X2),sK9(X3,X0,X1))
| ~ sP1(X3,X0,X1)
| ~ in(sK12(X0,X1,sK5(X2)),complements_of_subsets(the_carrier(sK2),sK3))
| ~ in(sK5(X2),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X2),X2)
| ~ in(sK5(X2),sK9(X4,X0,X1))
| ~ sP1(X4,X0,X1) ),
inference(superposition,[],[f162,f167]) ).
fof(f183,plain,
! [X2,X3,X0,X1,X4] :
( sK13(X0,X1,sK5(X2)) != subset_complement(the_carrier(sK2),sK12(X0,X1,sK5(X2)))
| sK5(X3) != ordered_pair(sK12(X0,X1,sK5(X2)),sK13(X0,X1,sK5(X2)))
| ~ in(sK12(X0,X1,sK5(X2)),complements_of_subsets(the_carrier(sK2),sK3))
| ~ in(sK5(X3),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X3),X3)
| ~ in(sK12(X0,X1,sK5(X2)),complements_of_subsets(the_carrier(sK2),sK3))
| ~ in(sK5(X2),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X2),X2)
| ~ in(sK5(X2),sK9(X4,X0,X1))
| ~ sP1(X4,X0,X1) ),
inference(superposition,[],[f73,f167]) ).
fof(f184,plain,
! [X2,X3,X0,X1,X4] :
( sK13(X0,X1,sK5(X2)) != subset_complement(the_carrier(sK2),sK12(X0,X1,sK5(X2)))
| sK5(X3) != ordered_pair(sK12(X0,X1,sK5(X2)),sK13(X0,X1,sK5(X2)))
| ~ in(sK12(X0,X1,sK5(X2)),complements_of_subsets(the_carrier(sK2),sK3))
| ~ in(sK5(X3),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X3),X3)
| ~ in(sK5(X2),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X2),X2)
| ~ in(sK5(X2),sK9(X4,X0,X1))
| ~ sP1(X4,X0,X1) ),
inference(duplicate_literal_removal,[],[f183]) ).
fof(f185,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(sK12(X0,X1,sK5(X2)),complements_of_subsets(the_carrier(sK2),sK3))
| element(sK12(X0,X1,sK5(X2)),powerset(the_carrier(sK2)))
| ~ in(sK5(X2),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X2),X2)
| ~ in(sK5(X2),sK9(X3,X0,X1))
| ~ sP1(X3,X0,X1)
| ~ in(sK5(X2),sK9(X4,X0,X1))
| ~ sP1(X4,X0,X1) ),
inference(duplicate_literal_removal,[],[f182]) ).
fof(f199,plain,
! [X2,X3,X0,X1] :
( ~ in(sK5(X0),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| in(sK5(X0),sK9(X3,X2,X1))
| ~ in(sK7(X0),complements_of_subsets(the_carrier(X1),X2))
| sK7(X0) = sK10(X1,sK7(X0),sK8(X0))
| ~ sP1(X3,X2,X1)
| in(sK5(X0),X0) ),
inference(superposition,[],[f107,f69]) ).
fof(f206,plain,
! [X2,X3,X0,X1] :
( element(sK10(X1,sK7(X0),sK8(X0)),powerset(the_carrier(X1)))
| in(sK5(X0),sK9(X3,X2,X1))
| ~ in(sK7(X0),complements_of_subsets(the_carrier(X1),X2))
| ~ in(sK5(X0),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| ~ sP1(X3,X2,X1)
| in(sK5(X0),X0) ),
inference(superposition,[],[f109,f69]) ).
fof(f215,plain,
! [X0] :
( in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ in(sK7(X0),complements_of_subsets(the_carrier(sK2),sK3))
| sK7(X0) = sK10(sK2,sK7(X0),sK8(X0))
| ~ sP1(sK4,sK3,sK2)
| in(sK5(X0),X0)
| in(sK5(X0),X0) ),
inference(resolution,[],[f199,f70]) ).
fof(f217,plain,
! [X0] :
( in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ in(sK7(X0),complements_of_subsets(the_carrier(sK2),sK3))
| sK7(X0) = sK10(sK2,sK7(X0),sK8(X0))
| ~ sP1(sK4,sK3,sK2)
| in(sK5(X0),X0) ),
inference(duplicate_literal_removal,[],[f215]) ).
fof(f218,plain,
! [X0] :
( sK7(X0) = sK10(sK2,sK7(X0),sK8(X0))
| in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ sP1(sK4,sK3,sK2)
| in(sK5(X0),X0) ),
inference(forward_subsumption_resolution,[],[f217,f68]) ).
fof(f219,plain,
! [X2,X0,X1] :
( sK8(X0) != subset_complement(the_carrier(sK2),sK7(X0))
| ~ in(ordered_pair(sK7(X0),sK8(X0)),cartesian_product2(complements_of_subsets(the_carrier(sK2),X1),X2))
| ~ in(sK7(X0),complements_of_subsets(the_carrier(sK2),X1))
| in(ordered_pair(sK7(X0),sK8(X0)),sK9(X2,X1,sK2))
| ~ sP1(X2,X1,sK2)
| in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ sP1(sK4,sK3,sK2)
| in(sK5(X0),X0) ),
inference(superposition,[],[f105,f218]) ).
fof(f220,plain,
! [X2,X0,X1] :
( element(sK7(X0),powerset(the_carrier(sK2)))
| in(sK5(X0),sK9(X1,X2,sK2))
| ~ in(sK7(X0),complements_of_subsets(the_carrier(sK2),X2))
| ~ in(sK5(X0),cartesian_product2(complements_of_subsets(the_carrier(sK2),X2),X1))
| ~ sP1(X1,X2,sK2)
| in(sK5(X0),X0)
| in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ sP1(sK4,sK3,sK2)
| in(sK5(X0),X0) ),
inference(superposition,[],[f206,f218]) ).
fof(f221,plain,
! [X2,X0,X1] :
( ~ in(sK5(X0),cartesian_product2(complements_of_subsets(the_carrier(sK2),X2),X1))
| in(sK5(X0),sK9(X1,X2,sK2))
| ~ in(sK7(X0),complements_of_subsets(the_carrier(sK2),X2))
| element(sK7(X0),powerset(the_carrier(sK2)))
| ~ sP1(X1,X2,sK2)
| in(sK5(X0),X0)
| in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ sP1(sK4,sK3,sK2) ),
inference(duplicate_literal_removal,[],[f220]) ).
fof(f258,plain,
! [X0] :
( in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ in(sK7(X0),complements_of_subsets(the_carrier(sK2),sK3))
| element(sK7(X0),powerset(the_carrier(sK2)))
| ~ sP1(sK4,sK3,sK2)
| in(sK5(X0),X0)
| in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ sP1(sK4,sK3,sK2)
| in(sK5(X0),X0) ),
inference(resolution,[],[f221,f70]) ).
fof(f262,plain,
! [X0] :
( in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ in(sK7(X0),complements_of_subsets(the_carrier(sK2),sK3))
| element(sK7(X0),powerset(the_carrier(sK2)))
| ~ sP1(sK4,sK3,sK2)
| in(sK5(X0),X0) ),
inference(duplicate_literal_removal,[],[f258]) ).
fof(f263,plain,
! [X0] :
( in(sK5(X0),sK9(sK4,sK3,sK2))
| element(sK7(X0),powerset(the_carrier(sK2)))
| ~ sP1(sK4,sK3,sK2)
| in(sK5(X0),X0) ),
inference(forward_subsumption_resolution,[],[f262,f68]) ).
fof(f278,plain,
! [X2,X0,X1] :
( sK8(X0) != sK8(X0)
| ~ in(ordered_pair(sK7(X0),sK8(X0)),cartesian_product2(complements_of_subsets(the_carrier(sK2),X1),X2))
| ~ in(sK7(X0),complements_of_subsets(the_carrier(sK2),X1))
| in(ordered_pair(sK7(X0),sK8(X0)),sK9(X2,X1,sK2))
| ~ sP1(X2,X1,sK2)
| in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ sP1(sK4,sK3,sK2)
| in(sK5(X0),X0)
| ~ element(sK7(X0),powerset(the_carrier(sK2)))
| in(sK5(X0),X0) ),
inference(superposition,[],[f219,f103]) ).
fof(f279,plain,
! [X2,X0,X1] :
( sK8(X0) != sK8(X0)
| ~ in(ordered_pair(sK7(X0),sK8(X0)),cartesian_product2(complements_of_subsets(the_carrier(sK2),X1),X2))
| ~ in(sK7(X0),complements_of_subsets(the_carrier(sK2),X1))
| in(ordered_pair(sK7(X0),sK8(X0)),sK9(X2,X1,sK2))
| ~ sP1(X2,X1,sK2)
| in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ sP1(sK4,sK3,sK2)
| in(sK5(X0),X0)
| ~ element(sK7(X0),powerset(the_carrier(sK2))) ),
inference(duplicate_literal_removal,[],[f278]) ).
fof(f280,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair(sK7(X0),sK8(X0)),cartesian_product2(complements_of_subsets(the_carrier(sK2),X1),X2))
| ~ in(sK7(X0),complements_of_subsets(the_carrier(sK2),X1))
| in(ordered_pair(sK7(X0),sK8(X0)),sK9(X2,X1,sK2))
| ~ sP1(X2,X1,sK2)
| in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ sP1(sK4,sK3,sK2)
| in(sK5(X0),X0)
| ~ element(sK7(X0),powerset(the_carrier(sK2))) ),
inference(trivial_inequality_removal,[],[f279]) ).
fof(f281,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair(sK7(X0),sK8(X0)),cartesian_product2(complements_of_subsets(the_carrier(sK2),X1),X2))
| ~ in(sK7(X0),complements_of_subsets(the_carrier(sK2),X1))
| in(ordered_pair(sK7(X0),sK8(X0)),sK9(X2,X1,sK2))
| ~ sP1(X2,X1,sK2)
| in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ sP1(sK4,sK3,sK2)
| in(sK5(X0),X0) ),
inference(forward_subsumption_resolution,[],[f280,f263]) ).
fof(f285,plain,
! [X2,X0,X1] :
( ~ in(sK5(X0),cartesian_product2(complements_of_subsets(the_carrier(sK2),X1),X2))
| ~ in(sK7(X0),complements_of_subsets(the_carrier(sK2),X1))
| in(sK5(X0),sK9(X2,X1,sK2))
| ~ sP1(X2,X1,sK2)
| in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ sP1(sK4,sK3,sK2)
| in(sK5(X0),X0)
| in(sK5(X0),X0) ),
inference(superposition,[],[f281,f69]) ).
fof(f287,plain,
! [X2,X0,X1] :
( ~ in(sK5(X0),cartesian_product2(complements_of_subsets(the_carrier(sK2),X1),X2))
| ~ in(sK7(X0),complements_of_subsets(the_carrier(sK2),X1))
| in(sK5(X0),sK9(X2,X1,sK2))
| ~ sP1(X2,X1,sK2)
| in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ sP1(sK4,sK3,sK2)
| in(sK5(X0),X0) ),
inference(duplicate_literal_removal,[],[f285]) ).
fof(f289,plain,
! [X0] :
( ~ in(sK7(X0),complements_of_subsets(the_carrier(sK2),sK3))
| in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ sP1(sK4,sK3,sK2)
| in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ sP1(sK4,sK3,sK2)
| in(sK5(X0),X0)
| in(sK5(X0),X0) ),
inference(resolution,[],[f287,f70]) ).
fof(f293,plain,
! [X0] :
( ~ in(sK7(X0),complements_of_subsets(the_carrier(sK2),sK3))
| in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ sP1(sK4,sK3,sK2)
| in(sK5(X0),X0) ),
inference(duplicate_literal_removal,[],[f289]) ).
fof(f294,plain,
! [X0] :
( in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ sP1(sK4,sK3,sK2)
| in(sK5(X0),X0) ),
inference(forward_subsumption_resolution,[],[f293,f68]) ).
fof(f328,plain,
! [X2,X3,X0,X1,X4] :
( sK13(X0,sK2,sK5(X1)) != sK13(X0,sK2,sK5(X1))
| sK5(X2) != ordered_pair(sK12(X0,sK2,sK5(X1)),sK13(X0,sK2,sK5(X1)))
| ~ in(sK12(X0,sK2,sK5(X1)),complements_of_subsets(the_carrier(sK2),sK3))
| ~ in(sK5(X2),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X2),X2)
| ~ in(sK5(X1),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X1),X1)
| ~ in(sK5(X1),sK9(X3,X0,sK2))
| ~ sP1(X3,X0,sK2)
| ~ element(sK12(X0,sK2,sK5(X1)),powerset(the_carrier(sK2)))
| ~ in(sK5(X1),sK9(X4,X0,sK2))
| ~ sP1(X4,X0,sK2) ),
inference(superposition,[],[f184,f110]) ).
fof(f329,plain,
! [X2,X3,X0,X1,X4] :
( sK5(X2) != ordered_pair(sK12(X0,sK2,sK5(X1)),sK13(X0,sK2,sK5(X1)))
| ~ in(sK12(X0,sK2,sK5(X1)),complements_of_subsets(the_carrier(sK2),sK3))
| ~ in(sK5(X2),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X2),X2)
| ~ in(sK5(X1),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X1),X1)
| ~ in(sK5(X1),sK9(X3,X0,sK2))
| ~ sP1(X3,X0,sK2)
| ~ element(sK12(X0,sK2,sK5(X1)),powerset(the_carrier(sK2)))
| ~ in(sK5(X1),sK9(X4,X0,sK2))
| ~ sP1(X4,X0,sK2) ),
inference(trivial_inequality_removal,[],[f328]) ).
fof(f330,plain,
! [X2,X3,X0,X1,X4] :
( sK5(X2) != ordered_pair(sK12(X0,sK2,sK5(X1)),sK13(X0,sK2,sK5(X1)))
| ~ in(sK12(X0,sK2,sK5(X1)),complements_of_subsets(the_carrier(sK2),sK3))
| ~ in(sK5(X2),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X2),X2)
| ~ in(sK5(X1),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X1),X1)
| ~ in(sK5(X1),sK9(X3,X0,sK2))
| ~ sP1(X3,X0,sK2)
| ~ in(sK5(X1),sK9(X4,X0,sK2))
| ~ sP1(X4,X0,sK2) ),
inference(forward_subsumption_resolution,[],[f329,f185]) ).
fof(f334,plain,
! [X2,X3,X0,X1,X4,X5] :
( sK5(X0) != sK5(X1)
| ~ in(sK12(X2,sK2,sK5(X0)),complements_of_subsets(the_carrier(sK2),sK3))
| ~ in(sK5(X1),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X1),X1)
| ~ in(sK5(X0),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X0),X0)
| ~ in(sK5(X0),sK9(X3,X2,sK2))
| ~ sP1(X3,X2,sK2)
| ~ in(sK5(X0),sK9(X4,X2,sK2))
| ~ sP1(X4,X2,sK2)
| ~ in(sK5(X0),sK9(X5,X2,sK2))
| ~ sP1(X5,X2,sK2) ),
inference(superposition,[],[f330,f78]) ).
fof(f335,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(sK12(X0,sK2,sK5(X1)),complements_of_subsets(the_carrier(sK2),sK3))
| ~ in(sK5(X1),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X1),X1)
| ~ in(sK5(X1),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X1),X1)
| ~ in(sK5(X1),sK9(X2,X0,sK2))
| ~ sP1(X2,X0,sK2)
| ~ in(sK5(X1),sK9(X3,X0,sK2))
| ~ sP1(X3,X0,sK2)
| ~ in(sK5(X1),sK9(X4,X0,sK2))
| ~ sP1(X4,X0,sK2) ),
inference(equality_resolution,[],[f334]) ).
fof(f336,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(sK12(X0,sK2,sK5(X1)),complements_of_subsets(the_carrier(sK2),sK3))
| ~ in(sK5(X1),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X1),X1)
| ~ in(sK5(X1),sK9(X2,X0,sK2))
| ~ sP1(X2,X0,sK2)
| ~ in(sK5(X1),sK9(X3,X0,sK2))
| ~ sP1(X3,X0,sK2)
| ~ in(sK5(X1),sK9(X4,X0,sK2))
| ~ sP1(X4,X0,sK2) ),
inference(duplicate_literal_removal,[],[f335]) ).
fof(f337,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(sK5(X0),cartesian_product2(complements_of_subsets(the_carrier(sK2),sK3),sK4))
| ~ in(sK5(X0),X0)
| ~ in(sK5(X0),sK9(X1,sK3,sK2))
| ~ sP1(X1,sK3,sK2)
| ~ in(sK5(X0),sK9(X2,sK3,sK2))
| ~ sP1(X2,sK3,sK2)
| ~ in(sK5(X0),sK9(X3,sK3,sK2))
| ~ sP1(X3,sK3,sK2)
| ~ in(sK5(X0),sK9(X4,sK3,sK2))
| ~ sP1(X4,sK3,sK2) ),
inference(resolution,[],[f336,f77]) ).
fof(f342,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ in(sK5(X0),sK9(X1,sK3,sK2))
| ~ sP1(X1,sK3,sK2)
| ~ in(sK5(X0),sK9(X2,sK3,sK2))
| ~ sP1(X2,sK3,sK2)
| ~ in(sK5(X0),sK9(X3,sK3,sK2))
| ~ sP1(X3,sK3,sK2)
| ~ in(sK5(X0),sK9(X4,sK3,sK2))
| ~ sP1(X4,sK3,sK2)
| ~ in(sK5(X0),X0)
| ~ sP1(sK4,sK3,sK2) ),
inference(resolution,[],[f337,f166]) ).
fof(f350,plain,
! [X2,X3,X0,X1] :
( ~ in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ in(sK5(X0),sK9(X1,sK3,sK2))
| ~ sP1(X1,sK3,sK2)
| ~ in(sK5(X0),sK9(X2,sK3,sK2))
| ~ sP1(X2,sK3,sK2)
| ~ in(sK5(X0),sK9(X3,sK3,sK2))
| ~ sP1(X3,sK3,sK2)
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK5(X0),X0)
| ~ sP1(sK4,sK3,sK2) ),
inference(factoring,[],[f342]) ).
fof(f352,plain,
! [X2,X3,X0,X1] :
( ~ in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ in(sK5(X0),sK9(X1,sK3,sK2))
| ~ sP1(X1,sK3,sK2)
| ~ in(sK5(X0),sK9(X2,sK3,sK2))
| ~ sP1(X2,sK3,sK2)
| ~ in(sK5(X0),sK9(X3,sK3,sK2))
| ~ sP1(X3,sK3,sK2)
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK5(X0),X0) ),
inference(duplicate_literal_removal,[],[f350]) ).
fof(f362,plain,
! [X2,X0,X1] :
( ~ in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ in(sK5(X0),sK9(X1,sK3,sK2))
| ~ sP1(X1,sK3,sK2)
| ~ in(sK5(X0),sK9(X2,sK3,sK2))
| ~ sP1(X2,sK3,sK2)
| ~ sP1(sK4,sK3,sK2)
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK5(X0),X0) ),
inference(factoring,[],[f352]) ).
fof(f364,plain,
! [X2,X0,X1] :
( ~ in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ in(sK5(X0),sK9(X1,sK3,sK2))
| ~ sP1(X1,sK3,sK2)
| ~ in(sK5(X0),sK9(X2,sK3,sK2))
| ~ sP1(X2,sK3,sK2)
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK5(X0),X0) ),
inference(duplicate_literal_removal,[],[f362]) ).
fof(f374,plain,
! [X0,X1] :
( ~ in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ in(sK5(X0),sK9(X1,sK3,sK2))
| ~ sP1(X1,sK3,sK2)
| ~ sP1(sK4,sK3,sK2)
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK5(X0),X0) ),
inference(factoring,[],[f364]) ).
fof(f376,plain,
! [X0,X1] :
( ~ in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ in(sK5(X0),sK9(X1,sK3,sK2))
| ~ sP1(X1,sK3,sK2)
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK5(X0),X0) ),
inference(duplicate_literal_removal,[],[f374]) ).
fof(f383,plain,
! [X0] :
( ~ in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ sP1(sK4,sK3,sK2)
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK5(X0),X0) ),
inference(factoring,[],[f376]) ).
fof(f385,plain,
! [X0] :
( ~ in(sK5(X0),sK9(sK4,sK3,sK2))
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK5(X0),X0) ),
inference(duplicate_literal_removal,[],[f383]) ).
fof(f390,plain,
( ~ in(sK5(sK9(sK4,sK3,sK2)),sK9(sK4,sK3,sK2))
| ~ sP1(sK4,sK3,sK2) ),
inference(factoring,[],[f385]) ).
fof(f393,plain,
( ~ sP1(sK4,sK3,sK2)
| ~ sP1(sK4,sK3,sK2)
| in(sK5(sK9(sK4,sK3,sK2)),sK9(sK4,sK3,sK2)) ),
inference(resolution,[],[f390,f294]) ).
fof(f396,plain,
( ~ sP1(sK4,sK3,sK2)
| in(sK5(sK9(sK4,sK3,sK2)),sK9(sK4,sK3,sK2)) ),
inference(duplicate_literal_removal,[],[f393]) ).
fof(f398,plain,
~ sP1(sK4,sK3,sK2),
inference(forward_subsumption_resolution,[],[f396,f390]) ).
fof(f399,plain,
! [X0] : sP1(X0,sK3,sK2),
inference(resolution,[],[f398,f159]) ).
fof(f400,plain,
$false,
inference(resolution,[],[f399,f398]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU329+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n001.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 28 04:49:32 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.68/1.30 % (26733)Detected formulas, will run a generic FOF schedule.
% 2.68/1.30 % (26740)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=1872827509:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.30 % (26742)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2763462526:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.30 % (26739)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=3879204349:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.30 % (26741)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3900349529:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.30 % (26743)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3735577615:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.30 % (26744)dis-21_1_sil=8000:lcm=predicate:random_seed=3402436276: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)
% 2.68/1.30 % (26738)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=2203446934:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.30 % (26742)First to succeed.
% 2.68/1.30 % (26742)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-26733"
% 2.68/1.30 % (26741)Refutation not found, incomplete strategy
% 2.68/1.30 % (26741)------------------------------
% 2.68/1.30 % (26741)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.30 % (26741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.30 % (26741)CaDiCaL version: 2.1.3
% 2.68/1.30 % (26741)Termination reason: Refutation not found, incomplete strategy
% 2.68/1.30 % (26741)Time elapsed: 0.034 s
% 2.68/1.30 % (26741)Peak memory usage: 89 MB
% 2.68/1.30 % (26741)Instructions burned: 49 (million)
% 2.68/1.30 % (26744)Instruction limit reached!
% 2.68/1.30 % (26744)------------------------------
% 2.68/1.30 % (26744)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.30 % (26744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.30 % (26744)CaDiCaL version: 2.1.3
% 2.68/1.30 % (26744)Termination reason: Instruction limit
% 2.68/1.30 % (26744)Termination phase: Saturation
% 2.68/1.30 % (26744)Time elapsed: 0.056 s
% 2.68/1.30 % (26744)Peak memory usage: 88 MB
% 2.68/1.30 % (26744)Instructions burned: 130 (million)
% 2.68/1.30 % (26743)Also succeeded, but the first one will report.
% 2.68/1.30 % (26752)lrs+10_1_sil=8000:sp=occurrence:random_seed=48508209:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.68/1.30 % (26742)Refutation found. Thanks to Tanya!
% 2.68/1.30 % SZS status Theorem for theBenchmark
% 2.68/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.39 % (26742)------------------------------
% 3.53/1.39 % (26742)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.39 % (26742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.39 % (26742)CaDiCaL version: 2.1.3
% 3.53/1.39 % (26742)Termination reason: Refutation
% 3.53/1.39 % (26742)Time elapsed: 0.024 s
% 3.53/1.39 % (26742)Peak memory usage: 88 MB
% 3.53/1.39 % (26742)Instructions burned: 35 (million)
% 3.53/1.39 % (26742)------------------------------
% 3.53/1.39 % (26742)------------------------------
% 3.53/1.39 % (26733)Success in time 0.431 s
% 3.53/1.39 % Vampire exiting
%------------------------------------------------------------------------------