%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU286+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : 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 12:48:10 PM UTC 2026
% Result : Theorem 3.38s 1.61s
% Output : Refutation 5.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 32
% Syntax : Number of formulae : 257 ( 15 unt; 30 def)
% Number of atoms : 1092 ( 175 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 1364 ( 529 ~; 604 |; 183 &)
% ( 30 <=>; 16 =>; 0 <=; 2 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 31 ( 29 usr; 23 prp; 0-4 aty)
% Number of functors : 23 ( 23 usr; 4 con; 0-4 aty)
% Number of variables : 461 ( 0 sgn 339 !; 122 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( ( ~ empty(X0)
& relation(X1) )
=> ! [X2] :
? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,cartesian_product2(X0,X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,X0)
& ? [X7] :
( X5 = X7
& in(X6,X7)
& ! [X8] :
( in(X8,X7)
=> in(ordered_pair(X6,X8),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e10_24__wellord2__1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ( ~ empty(X0)
& relation(X1) )
=> ! [X2] :
? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,cartesian_product2(X0,X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,X0)
& ? [X7] :
( X5 = X7
& in(X6,X7)
& ! [X8] :
( in(X8,X7)
=> in(ordered_pair(X6,X8),X1) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f20,axiom,
! [X0,X1] :
( ( ~ empty(X0)
& relation(X1) )
=> ! [X2] :
( ! [X3,X4,X5] :
( ( X3 = X4
& ? [X6,X7] :
( ordered_pair(X6,X7) = X4
& in(X6,X0)
& ? [X8] :
( X6 = X8
& in(X7,X8)
& ! [X9] :
( in(X9,X8)
=> in(ordered_pair(X7,X9),X1) ) ) )
& X3 = X5
& ? [X10,X11] :
( ordered_pair(X10,X11) = X5
& in(X10,X0)
& ? [X12] :
( X10 = X12
& in(X11,X12)
& ! [X13] :
( in(X13,X12)
=> in(ordered_pair(X11,X13),X1) ) ) ) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,cartesian_product2(X0,X2))
& X5 = X4
& ? [X14,X15] :
( ordered_pair(X14,X15) = X4
& in(X14,X0)
& ? [X16] :
( X14 = X16
& in(X15,X16)
& ! [X17] :
( in(X17,X16)
=> in(ordered_pair(X15,X17),X1) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e10_24__wellord2__2) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ empty(X0)
& relation(X1) )
=> ! [X2] :
( ! [X3,X4,X5] :
( ( X3 = X4
& ? [X6,X7] :
( ordered_pair(X6,X7) = X4
& in(X6,X0)
& ? [X8] :
( X6 = X8
& in(X7,X8)
& ! [X9] :
( in(X9,X8)
=> in(ordered_pair(X7,X9),X1) ) ) )
& X3 = X5
& ? [X10,X11] :
( ordered_pair(X10,X11) = X5
& in(X10,X0)
& ? [X12] :
( X10 = X12
& in(X11,X12)
& ! [X13] :
( in(X13,X12)
=> in(ordered_pair(X11,X13),X1) ) ) ) )
=> X4 = X5 )
=> ? [X14] :
! [X15] :
( in(X15,X14)
<=> ? [X16] :
( in(X16,cartesian_product2(X0,X2))
& X15 = X16
& ? [X17,X18] :
( ordered_pair(X17,X18) = X15
& in(X17,X0)
& ? [X19] :
( X17 = X19
& in(X18,X19)
& ! [X20] :
( in(X20,X19)
=> in(ordered_pair(X18,X20),X1) ) ) ) ) ) ) ),
inference(rectify,[],[f20]) ).
fof(f25,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( in(X4,X3)
<~> ( in(X4,cartesian_product2(X0,X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,X0)
& ? [X7] :
( X5 = X7
& in(X6,X7)
& ! [X8] :
( in(ordered_pair(X6,X8),X1)
| ~ in(X8,X7) ) ) ) ) )
& ~ empty(X0)
& relation(X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f26,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( in(X4,X3)
<~> ( in(X4,cartesian_product2(X0,X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,X0)
& ? [X7] :
( X5 = X7
& in(X6,X7)
& ! [X8] :
( in(ordered_pair(X6,X8),X1)
| ~ in(X8,X7) ) ) ) ) )
& ~ empty(X0)
& relation(X1) ),
inference(flattening,[],[f25]) ).
fof(f35,plain,
! [X0,X1] :
( ! [X2] :
( ? [X14] :
! [X15] :
( in(X15,X14)
<=> ? [X16] :
( in(X16,cartesian_product2(X0,X2))
& X15 = X16
& ? [X17,X18] :
( ordered_pair(X17,X18) = X15
& in(X17,X0)
& ? [X19] :
( X17 = X19
& in(X18,X19)
& ! [X20] :
( in(ordered_pair(X18,X20),X1)
| ~ in(X20,X19) ) ) ) ) )
| ? [X3,X4,X5] :
( X4 != X5
& X3 = X4
& ? [X6,X7] :
( ordered_pair(X6,X7) = X4
& in(X6,X0)
& ? [X8] :
( X6 = X8
& in(X7,X8)
& ! [X9] :
( in(ordered_pair(X7,X9),X1)
| ~ in(X9,X8) ) ) )
& X3 = X5
& ? [X10,X11] :
( ordered_pair(X10,X11) = X5
& in(X10,X0)
& ? [X12] :
( X10 = X12
& in(X11,X12)
& ! [X13] :
( in(ordered_pair(X11,X13),X1)
| ~ in(X13,X12) ) ) ) ) )
| empty(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f36,plain,
! [X0,X1] :
( ! [X2] :
( ? [X14] :
! [X15] :
( in(X15,X14)
<=> ? [X16] :
( in(X16,cartesian_product2(X0,X2))
& X15 = X16
& ? [X17,X18] :
( ordered_pair(X17,X18) = X15
& in(X17,X0)
& ? [X19] :
( X17 = X19
& in(X18,X19)
& ! [X20] :
( in(ordered_pair(X18,X20),X1)
| ~ in(X20,X19) ) ) ) ) )
| ? [X3,X4,X5] :
( X4 != X5
& X3 = X4
& ? [X6,X7] :
( ordered_pair(X6,X7) = X4
& in(X6,X0)
& ? [X8] :
( X6 = X8
& in(X7,X8)
& ! [X9] :
( in(ordered_pair(X7,X9),X1)
| ~ in(X9,X8) ) ) )
& X3 = X5
& ? [X10,X11] :
( ordered_pair(X10,X11) = X5
& in(X10,X0)
& ? [X12] :
( X10 = X12
& in(X11,X12)
& ! [X13] :
( in(ordered_pair(X11,X13),X1)
| ~ in(X13,X12) ) ) ) ) )
| empty(X0)
| ~ relation(X1) ),
inference(flattening,[],[f35]) ).
fof(f37,definition,
! [X5,X0,X1] :
( ? [X10,X11] :
( ordered_pair(X10,X11) = X5
& in(X10,X0)
& ? [X12] :
( X10 = X12
& in(X11,X12)
& ! [X13] :
( in(ordered_pair(X11,X13),X1)
| ~ in(X13,X12) ) ) )
| ~ sP0(X5,X0,X1) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f38,definition,
! [X4,X0,X1] :
( ? [X6,X7] :
( ordered_pair(X6,X7) = X4
& in(X6,X0)
& ? [X8] :
( X6 = X8
& in(X7,X8)
& ! [X9] :
( in(ordered_pair(X7,X9),X1)
| ~ in(X9,X8) ) ) )
| ~ sP1(X4,X0,X1) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f39,definition,
! [X2,X0,X15,X1] :
( sP2(X2,X0,X15,X1)
<=> ? [X16] :
( in(X16,cartesian_product2(X0,X2))
& X15 = X16
& ? [X17,X18] :
( ordered_pair(X17,X18) = X15
& in(X17,X0)
& ? [X19] :
( X17 = X19
& in(X18,X19)
& ! [X20] :
( in(ordered_pair(X18,X20),X1)
| ~ in(X20,X19) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f40,definition,
! [X1,X0,X2] :
( ? [X14] :
! [X15] :
( in(X15,X14)
<=> sP2(X2,X0,X15,X1) )
| ~ sP3(X1,X0,X2) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f41,plain,
! [X0,X1] :
( ! [X2] :
( sP3(X1,X0,X2)
| ? [X3,X4,X5] :
( X4 != X5
& X3 = X4
& sP1(X4,X0,X1)
& X3 = X5
& sP0(X5,X0,X1) ) )
| empty(X0)
| ~ relation(X1) ),
inference(definition_folding,[],[f36,f40,f39,f38,f37]) ).
fof(f42,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( ( ~ in(X4,cartesian_product2(X0,X2))
| ! [X5,X6] :
( ordered_pair(X5,X6) != X4
| ~ in(X5,X0)
| ! [X7] :
( X5 != X7
| ~ in(X6,X7)
| ? [X8] :
( ~ in(ordered_pair(X6,X8),X1)
& in(X8,X7) ) ) )
| ~ in(X4,X3) )
& ( ( in(X4,cartesian_product2(X0,X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,X0)
& ? [X7] :
( X5 = X7
& in(X6,X7)
& ! [X8] :
( in(ordered_pair(X6,X8),X1)
| ~ in(X8,X7) ) ) ) )
| in(X4,X3) ) )
& ~ empty(X0)
& relation(X1) ),
inference(nnf_transformation,[],[f26]) ).
fof(f43,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( ( ~ in(X4,cartesian_product2(X0,X2))
| ! [X5,X6] :
( ordered_pair(X5,X6) != X4
| ~ in(X5,X0)
| ! [X7] :
( X5 != X7
| ~ in(X6,X7)
| ? [X8] :
( ~ in(ordered_pair(X6,X8),X1)
& in(X8,X7) ) ) )
| ~ in(X4,X3) )
& ( ( in(X4,cartesian_product2(X0,X2))
& ? [X5,X6] :
( ordered_pair(X5,X6) = X4
& in(X5,X0)
& ? [X7] :
( X5 = X7
& in(X6,X7)
& ! [X8] :
( in(ordered_pair(X6,X8),X1)
| ~ in(X8,X7) ) ) ) )
| in(X4,X3) ) )
& ~ empty(X0)
& relation(X1) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( ( ~ in(X4,cartesian_product2(X0,X2))
| ! [X5,X6] :
( ordered_pair(X5,X6) != X4
| ~ in(X5,X0)
| ! [X7] :
( X5 != X7
| ~ in(X6,X7)
| ? [X8] :
( ~ in(ordered_pair(X6,X8),X1)
& in(X8,X7) ) ) )
| ~ in(X4,X3) )
& ( ( in(X4,cartesian_product2(X0,X2))
& ? [X9,X10] :
( ordered_pair(X9,X10) = X4
& in(X9,X0)
& ? [X11] :
( X9 = X11
& in(X10,X11)
& ! [X12] :
( in(ordered_pair(X10,X12),X1)
| ~ in(X12,X11) ) ) ) )
| in(X4,X3) ) )
& ~ empty(X0)
& relation(X1) ),
inference(rectify,[],[f43]) ).
fof(f45,plain,
( ! [X3] :
( ( ~ in(sK7(X3),cartesian_product2(sK4,sK6))
| ! [X5,X6] :
( ordered_pair(X5,X6) != sK7(X3)
| ~ in(X5,sK4)
| ! [X7] :
( X5 != X7
| ~ in(X6,X7)
| ( ~ in(ordered_pair(X6,sK8(X6,X7)),sK5)
& in(sK8(X6,X7),X7) ) ) )
| ~ in(sK7(X3),X3) )
& ( ( in(sK7(X3),cartesian_product2(sK4,sK6))
& sK7(X3) = ordered_pair(sK9(X3),sK10(X3))
& in(sK9(X3),sK4)
& sK9(X3) = sK11(X3)
& in(sK10(X3),sK11(X3))
& ! [X12] :
( in(ordered_pair(sK10(X3),X12),sK5)
| ~ in(X12,sK11(X3)) ) )
| in(sK7(X3),X3) ) )
& ~ empty(sK4)
& relation(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X4,sK7(X3)),skolemize(X8,sK8(X6,X7)),skolemize(X9,sK9(X3)),skolemize(X10,sK10(X3)),skolemize(X11,sK11(X3))],[f44]) ).
fof(f54,plain,
! [X1,X0,X2] :
( ? [X14] :
! [X15] :
( ( in(X15,X14)
| ~ sP2(X2,X0,X15,X1) )
& ( sP2(X2,X0,X15,X1)
| ~ in(X15,X14) ) )
| ~ sP3(X1,X0,X2) ),
inference(nnf_transformation,[],[f40]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ~ sP2(X2,X1,X4,X0) )
& ( sP2(X2,X1,X4,X0)
| ~ in(X4,X3) ) )
| ~ sP3(X0,X1,X2) ),
inference(rectify,[],[f54]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ! [X4] :
( ( in(X4,sK20(X0,X1,X2))
| ~ sP2(X2,X1,X4,X0) )
& ( sP2(X2,X1,X4,X0)
| ~ in(X4,sK20(X0,X1,X2)) ) )
| ~ sP3(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X3,sK20(X0,X1,X2))],[f55]) ).
fof(f57,plain,
! [X2,X0,X15,X1] :
( ( sP2(X2,X0,X15,X1)
| ! [X16] :
( ~ in(X16,cartesian_product2(X0,X2))
| X15 != X16
| ! [X17,X18] :
( ordered_pair(X17,X18) != X15
| ~ in(X17,X0)
| ! [X19] :
( X17 != X19
| ~ in(X18,X19)
| ? [X20] :
( ~ in(ordered_pair(X18,X20),X1)
& in(X20,X19) ) ) ) ) )
& ( ? [X16] :
( in(X16,cartesian_product2(X0,X2))
& X15 = X16
& ? [X17,X18] :
( ordered_pair(X17,X18) = X15
& in(X17,X0)
& ? [X19] :
( X17 = X19
& in(X18,X19)
& ! [X20] :
( in(ordered_pair(X18,X20),X1)
| ~ in(X20,X19) ) ) ) )
| ~ sP2(X2,X0,X15,X1) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( ( sP2(X0,X1,X2,X3)
| ! [X4] :
( ~ in(X4,cartesian_product2(X1,X0))
| X2 != X4
| ! [X5,X6] :
( ordered_pair(X5,X6) != X2
| ~ in(X5,X1)
| ! [X7] :
( X5 != X7
| ~ in(X6,X7)
| ? [X8] :
( ~ in(ordered_pair(X6,X8),X3)
& in(X8,X7) ) ) ) ) )
& ( ? [X9] :
( in(X9,cartesian_product2(X1,X0))
& X2 = X9
& ? [X10,X11] :
( ordered_pair(X10,X11) = X2
& in(X10,X1)
& ? [X12] :
( X10 = X12
& in(X11,X12)
& ! [X13] :
( in(ordered_pair(X11,X13),X3)
| ~ in(X13,X12) ) ) ) )
| ~ sP2(X0,X1,X2,X3) ) ),
inference(rectify,[],[f57]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( ( sP2(X0,X1,X2,X3)
| ! [X4] :
( ~ in(X4,cartesian_product2(X1,X0))
| X2 != X4
| ! [X5,X6] :
( ordered_pair(X5,X6) != X2
| ~ in(X5,X1)
| ! [X7] :
( X5 != X7
| ~ in(X6,X7)
| ( ~ in(ordered_pair(X6,sK21(X3,X6,X7)),X3)
& in(sK21(X3,X6,X7),X7) ) ) ) ) )
& ( ( in(sK22(X0,X1,X2,X3),cartesian_product2(X1,X0))
& sK22(X0,X1,X2,X3) = X2
& ordered_pair(sK23(X1,X2,X3),sK24(X1,X2,X3)) = X2
& in(sK23(X1,X2,X3),X1)
& sK23(X1,X2,X3) = sK25(X1,X2,X3)
& in(sK24(X1,X2,X3),sK25(X1,X2,X3))
& ! [X13] :
( in(ordered_pair(sK24(X1,X2,X3),X13),X3)
| ~ in(X13,sK25(X1,X2,X3)) ) )
| ~ sP2(X0,X1,X2,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21,sK22,sK23,sK24,sK25]),skolemize(X8,sK21(X3,X6,X7)),skolemize(X9,sK22(X0,X1,X2,X3)),skolemize(X10,sK23(X1,X2,X3)),skolemize(X11,sK24(X1,X2,X3)),skolemize(X12,sK25(X1,X2,X3))],[f58]) ).
fof(f66,plain,
! [X0,X1] :
( ! [X2] :
( sP3(X1,X0,X2)
| ( sK33(X0,X1) != sK34(X0,X1)
& sK32(X0,X1) = sK33(X0,X1)
& sP1(sK33(X0,X1),X0,X1)
& sK32(X0,X1) = sK34(X0,X1)
& sP0(sK34(X0,X1),X0,X1) ) )
| empty(X0)
| ~ relation(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32,sK33,sK34]),skolemize(X3,sK32(X0,X1)),skolemize(X4,sK33(X0,X1)),skolemize(X5,sK34(X0,X1))],[f41]) ).
fof(f67,plain,
relation(sK5),
inference(cnf_transformation,[],[f45]) ).
fof(f68,plain,
~ empty(sK4),
inference(cnf_transformation,[],[f45]) ).
fof(f69,plain,
! [X3,X12] :
( in(ordered_pair(sK10(X3),X12),sK5)
| ~ in(X12,sK11(X3))
| in(sK7(X3),X3) ),
inference(cnf_transformation,[],[f45]) ).
fof(f70,plain,
! [X3] :
( in(sK10(X3),sK11(X3))
| in(sK7(X3),X3) ),
inference(cnf_transformation,[],[f45]) ).
fof(f71,plain,
! [X3] :
( in(sK7(X3),X3)
| sK9(X3) = sK11(X3) ),
inference(cnf_transformation,[],[f45]) ).
fof(f72,plain,
! [X3] :
( in(sK9(X3),sK4)
| in(sK7(X3),X3) ),
inference(cnf_transformation,[],[f45]) ).
fof(f73,plain,
! [X3] :
( sK7(X3) = ordered_pair(sK9(X3),sK10(X3))
| in(sK7(X3),X3) ),
inference(cnf_transformation,[],[f45]) ).
fof(f74,plain,
! [X3] :
( in(sK7(X3),cartesian_product2(sK4,sK6))
| in(sK7(X3),X3) ),
inference(cnf_transformation,[],[f45]) ).
fof(f75,plain,
! [X3,X6,X7,X5] :
( ~ in(sK7(X3),cartesian_product2(sK4,sK6))
| ordered_pair(X5,X6) != sK7(X3)
| ~ in(X5,sK4)
| X5 != X7
| ~ in(X6,X7)
| in(sK8(X6,X7),X7)
| ~ in(sK7(X3),X3) ),
inference(cnf_transformation,[],[f45]) ).
fof(f76,plain,
! [X3,X6,X7,X5] :
( ~ in(sK7(X3),cartesian_product2(sK4,sK6))
| ordered_pair(X5,X6) != sK7(X3)
| ~ in(X5,sK4)
| X5 != X7
| ~ in(X6,X7)
| ~ in(ordered_pair(X6,sK8(X6,X7)),sK5)
| ~ in(sK7(X3),X3) ),
inference(cnf_transformation,[],[f45]) ).
fof(f110,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK20(X0,X1,X2))
| sP2(X2,X1,X4,X0)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f56]) ).
fof(f111,plain,
! [X2,X0,X1,X4] :
( in(X4,sK20(X0,X1,X2))
| ~ sP2(X2,X1,X4,X0)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f56]) ).
fof(f112,plain,
! [X2,X3,X0,X1,X13] :
( ~ in(X13,sK25(X1,X2,X3))
| in(ordered_pair(sK24(X1,X2,X3),X13),X3)
| ~ sP2(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f59]) ).
fof(f113,plain,
! [X2,X3,X0,X1] :
( ~ sP2(X0,X1,X2,X3)
| in(sK24(X1,X2,X3),sK25(X1,X2,X3)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f114,plain,
! [X2,X3,X0,X1] :
( ~ sP2(X0,X1,X2,X3)
| sK23(X1,X2,X3) = sK25(X1,X2,X3) ),
inference(cnf_transformation,[],[f59]) ).
fof(f115,plain,
! [X2,X3,X0,X1] :
( ~ sP2(X0,X1,X2,X3)
| in(sK23(X1,X2,X3),X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f116,plain,
! [X2,X3,X0,X1] :
( ~ sP2(X0,X1,X2,X3)
| ordered_pair(sK23(X1,X2,X3),sK24(X1,X2,X3)) = X2 ),
inference(cnf_transformation,[],[f59]) ).
fof(f117,plain,
! [X2,X3,X0,X1] :
( ~ sP2(X0,X1,X2,X3)
| sK22(X0,X1,X2,X3) = X2 ),
inference(cnf_transformation,[],[f59]) ).
fof(f118,plain,
! [X2,X3,X0,X1] :
( in(sK22(X0,X1,X2,X3),cartesian_product2(X1,X0))
| ~ sP2(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f59]) ).
fof(f119,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( sP2(X0,X1,X2,X3)
| ~ in(X4,cartesian_product2(X1,X0))
| X2 != X4
| ordered_pair(X5,X6) != X2
| ~ in(X5,X1)
| X5 != X7
| ~ in(X6,X7)
| in(sK21(X3,X6,X7),X7) ),
inference(cnf_transformation,[],[f59]) ).
fof(f120,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( sP2(X0,X1,X2,X3)
| ~ in(X4,cartesian_product2(X1,X0))
| X2 != X4
| ordered_pair(X5,X6) != X2
| ~ in(X5,X1)
| X5 != X7
| ~ in(X6,X7)
| ~ in(ordered_pair(X6,sK21(X3,X6,X7)),X3) ),
inference(cnf_transformation,[],[f59]) ).
fof(f132,plain,
! [X2,X0,X1] :
( sP3(X1,X0,X2)
| sK32(X0,X1) = sK34(X0,X1)
| empty(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f134,plain,
! [X2,X0,X1] :
( sP3(X1,X0,X2)
| sK32(X0,X1) = sK33(X0,X1)
| empty(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f135,plain,
! [X2,X0,X1] :
( sK33(X0,X1) != sK34(X0,X1)
| sP3(X1,X0,X2)
| empty(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f136,plain,
! [X3,X6,X7] :
( ~ in(sK7(X3),cartesian_product2(sK4,sK6))
| sK7(X3) != ordered_pair(X7,X6)
| ~ in(X7,sK4)
| ~ in(X6,X7)
| ~ in(ordered_pair(X6,sK8(X6,X7)),sK5)
| ~ in(sK7(X3),X3) ),
inference(equality_resolution,[],[f76]) ).
fof(f137,plain,
! [X3,X6,X7] :
( ~ in(sK7(X3),cartesian_product2(sK4,sK6))
| sK7(X3) != ordered_pair(X7,X6)
| ~ in(X7,sK4)
| ~ in(X6,X7)
| in(sK8(X6,X7),X7)
| ~ in(sK7(X3),X3) ),
inference(equality_resolution,[],[f75]) ).
fof(f138,plain,
! [X3,X0,X1,X6,X7,X4,X5] :
( sP2(X0,X1,X4,X3)
| ~ in(X4,cartesian_product2(X1,X0))
| ordered_pair(X5,X6) != X4
| ~ in(X5,X1)
| X5 != X7
| ~ in(X6,X7)
| ~ in(ordered_pair(X6,sK21(X3,X6,X7)),X3) ),
inference(equality_resolution,[],[f120]) ).
fof(f139,plain,
! [X3,X0,X1,X6,X7,X5] :
( sP2(X0,X1,ordered_pair(X5,X6),X3)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X1,X0))
| ~ in(X5,X1)
| X5 != X7
| ~ in(X6,X7)
| ~ in(ordered_pair(X6,sK21(X3,X6,X7)),X3) ),
inference(equality_resolution,[],[f138]) ).
fof(f140,plain,
! [X3,X0,X1,X6,X7] :
( ~ in(ordered_pair(X6,sK21(X3,X6,X7)),X3)
| ~ in(ordered_pair(X7,X6),cartesian_product2(X1,X0))
| ~ in(X7,X1)
| ~ in(X6,X7)
| sP2(X0,X1,ordered_pair(X7,X6),X3) ),
inference(equality_resolution,[],[f139]) ).
fof(f141,plain,
! [X3,X0,X1,X6,X7,X4,X5] :
( sP2(X0,X1,X4,X3)
| ~ in(X4,cartesian_product2(X1,X0))
| ordered_pair(X5,X6) != X4
| ~ in(X5,X1)
| X5 != X7
| ~ in(X6,X7)
| in(sK21(X3,X6,X7),X7) ),
inference(equality_resolution,[],[f119]) ).
fof(f142,plain,
! [X3,X0,X1,X6,X7,X5] :
( sP2(X0,X1,ordered_pair(X5,X6),X3)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X1,X0))
| ~ in(X5,X1)
| X5 != X7
| ~ in(X6,X7)
| in(sK21(X3,X6,X7),X7) ),
inference(equality_resolution,[],[f141]) ).
fof(f143,plain,
! [X3,X0,X1,X6,X7] :
( ~ in(ordered_pair(X7,X6),cartesian_product2(X1,X0))
| sP2(X0,X1,ordered_pair(X7,X6),X3)
| ~ in(X7,X1)
| ~ in(X6,X7)
| in(sK21(X3,X6,X7),X7) ),
inference(equality_resolution,[],[f142]) ).
fof(f144,definition,
sF35 = cartesian_product2(sK4,sK6),
introduced(definition,[new_symbols(definition,[sF35])],[function_definition]) ).
fof(f145,plain,
cartesian_product2(sK4,sK6) = sF35,
inference(reorient_equations,[],[f144]) ).
fof(f146,definition,
! [X6,X7] : sF36(X6,X7) = ordered_pair(X6,sK8(X6,X7)),
introduced(definition,[new_symbols(definition,[sF36])],[function_definition]) ).
fof(f147,plain,
! [X6,X7] : ordered_pair(X6,sK8(X6,X7)) = sF36(X6,X7),
inference(reorient_equations,[],[f146]) ).
fof(f148,plain,
! [X3,X6,X7] :
( sK7(X3) != ordered_pair(X7,X6)
| ~ in(sK7(X3),sF35)
| ~ in(X7,sK4)
| ~ in(X6,X7)
| ~ in(sF36(X6,X7),sK5)
| ~ in(sK7(X3),X3) ),
inference(definition_folding,[],[f136,f147,f145]) ).
fof(f149,plain,
! [X3,X6,X7] :
( sK7(X3) != ordered_pair(X7,X6)
| ~ in(sK7(X3),sF35)
| ~ in(X7,sK4)
| ~ in(X6,X7)
| in(sK8(X6,X7),X7)
| ~ in(sK7(X3),X3) ),
inference(definition_folding,[],[f137,f145]) ).
fof(f150,plain,
! [X3] :
( in(sK7(X3),sF35)
| in(sK7(X3),X3) ),
inference(definition_folding,[],[f74,f145]) ).
fof(f151,definition,
! [X3] : sF37(X3) = ordered_pair(sK9(X3),sK10(X3)),
introduced(definition,[new_symbols(definition,[sF37])],[function_definition]) ).
fof(f152,plain,
! [X3] : ordered_pair(sK9(X3),sK10(X3)) = sF37(X3),
inference(reorient_equations,[],[f151]) ).
fof(f153,plain,
! [X3] :
( in(sK7(X3),X3)
| sK7(X3) = sF37(X3) ),
inference(definition_folding,[],[f73,f152]) ).
fof(f154,definition,
! [X3,X12] : sF38(X3,X12) = ordered_pair(sK10(X3),X12),
introduced(definition,[new_symbols(definition,[sF38])],[function_definition]) ).
fof(f155,plain,
! [X3,X12] : ordered_pair(sK10(X3),X12) = sF38(X3,X12),
inference(reorient_equations,[],[f154]) ).
fof(f156,plain,
! [X3,X12] :
( ~ in(X12,sK11(X3))
| in(sF38(X3,X12),sK5)
| in(sK7(X3),X3) ),
inference(definition_folding,[],[f69,f155]) ).
fof(f163,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(sF38(X0,sK21(X1,sK10(X0),X2)),X1)
| ~ in(ordered_pair(X2,sK10(X0)),cartesian_product2(X3,X4))
| ~ in(X2,X3)
| ~ in(sK10(X0),X2)
| sP2(X4,X3,ordered_pair(X2,sK10(X0)),X1) ),
inference(superposition,[],[f140,f155]) ).
fof(f177,plain,
! [X2,X0,X1] :
( sP2(sK6,sK4,ordered_pair(X0,X1),X2)
| in(sK21(X2,X1,X0),X0)
| ~ in(X0,sK4)
| ~ in(X1,X0)
| ~ in(ordered_pair(X0,X1),sF35) ),
inference(superposition,[],[f143,f145]) ).
fof(f219,plain,
! [X2,X0,X1] :
( sP2(X0,X1,sK7(sK20(X2,X1,X0)),X2)
| ~ sP3(X2,X1,X0)
| sK9(sK20(X2,X1,X0)) = sK11(sK20(X2,X1,X0)) ),
inference(resolution,[],[f110,f71]) ).
fof(f241,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1,X2)
| sK9(sK20(X0,X1,X2)) = sK11(sK20(X0,X1,X2))
| sK23(X1,sK7(sK20(X0,X1,X2)),X0) = sK25(X1,sK7(sK20(X0,X1,X2)),X0) ),
inference(resolution,[],[f219,f114]) ).
fof(f242,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1,X2)
| sK9(sK20(X0,X1,X2)) = sK11(sK20(X0,X1,X2))
| sK7(sK20(X0,X1,X2)) = ordered_pair(sK23(X1,sK7(sK20(X0,X1,X2)),X0),sK24(X1,sK7(sK20(X0,X1,X2)),X0)) ),
inference(resolution,[],[f219,f116]) ).
fof(f357,definition,
( spl39_2
<=> sK32(sK4,sK5) = sK34(sK4,sK5) ),
introduced(definition,[new_symbols(definition,[spl39_2])],[avatar_definition]) ).
fof(f358,plain,
( sK32(sK4,sK5) != sK34(sK4,sK5)
| spl39_2 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f359,plain,
( sK32(sK4,sK5) = sK34(sK4,sK5)
| ~ spl39_2 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f373,definition,
( spl39_3
<=> sK34(sK4,sK5) = sK33(sK4,sK5) ),
introduced(definition,[new_symbols(definition,[spl39_3])],[avatar_definition]) ).
fof(f375,plain,
( sK34(sK4,sK5) = sK33(sK4,sK5)
| ~ spl39_3 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f380,definition,
( spl39_4
<=> sK9(sK20(sK5,sK4,sK6)) = sK11(sK20(sK5,sK4,sK6)) ),
introduced(definition,[new_symbols(definition,[spl39_4])],[avatar_definition]) ).
fof(f381,plain,
( sK9(sK20(sK5,sK4,sK6)) != sK11(sK20(sK5,sK4,sK6))
| spl39_4 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f382,plain,
( sK9(sK20(sK5,sK4,sK6)) = sK11(sK20(sK5,sK4,sK6))
| ~ spl39_4 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f384,definition,
( spl39_5
<=> sP2(sK6,sK4,sK7(sK20(sK5,sK4,sK6)),sK5) ),
introduced(definition,[new_symbols(definition,[spl39_5])],[avatar_definition]) ).
fof(f385,plain,
( sP2(sK6,sK4,sK7(sK20(sK5,sK4,sK6)),sK5)
| ~ spl39_5 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f386,plain,
( ~ sP2(sK6,sK4,sK7(sK20(sK5,sK4,sK6)),sK5)
| spl39_5 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f388,definition,
( spl39_6
<=> in(sK7(sK20(sK5,sK4,sK6)),sF35) ),
introduced(definition,[new_symbols(definition,[spl39_6])],[avatar_definition]) ).
fof(f389,plain,
( ~ in(sK7(sK20(sK5,sK4,sK6)),sF35)
| spl39_6 ),
inference(avatar_component_clause,[],[f388]) ).
fof(f390,plain,
( in(sK7(sK20(sK5,sK4,sK6)),sF35)
| ~ spl39_6 ),
inference(avatar_component_clause,[],[f388]) ).
fof(f399,definition,
( spl39_7
<=> sP3(sK5,sK4,sK6) ),
introduced(definition,[new_symbols(definition,[spl39_7])],[avatar_definition]) ).
fof(f400,plain,
( sP3(sK5,sK4,sK6)
| ~ spl39_7 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f401,plain,
( ~ sP3(sK5,sK4,sK6)
| spl39_7 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f406,plain,
( sK32(sK4,sK5) = sK33(sK4,sK5)
| empty(sK4)
| ~ relation(sK5)
| spl39_7 ),
inference(resolution,[],[f401,f134]) ).
fof(f408,plain,
( sK32(sK4,sK5) = sK33(sK4,sK5)
| ~ relation(sK5)
| spl39_7 ),
inference(forward_subsumption_resolution,[],[f406,f68]) ).
fof(f409,plain,
( sK32(sK4,sK5) = sK33(sK4,sK5)
| spl39_7 ),
inference(forward_subsumption_resolution,[],[f408,f67]) ).
fof(f410,plain,
( sK34(sK4,sK5) = sK33(sK4,sK5)
| ~ spl39_2
| spl39_7 ),
inference(forward_demodulation,[],[f409,f359]) ).
fof(f411,plain,
( spl39_3
| ~ spl39_2
| spl39_7 ),
inference(avatar_split_clause,[],[f410,f399,f357,f373]) ).
fof(f412,plain,
( in(sK10(sK20(sK5,sK4,sK6)),sK9(sK20(sK5,sK4,sK6)))
| in(sK7(sK20(sK5,sK4,sK6)),sK20(sK5,sK4,sK6))
| ~ spl39_4 ),
inference(superposition,[],[f70,f382]) ).
fof(f413,plain,
( ! [X0] :
( ~ in(X0,sK9(sK20(sK5,sK4,sK6)))
| in(sF38(sK20(sK5,sK4,sK6),X0),sK5)
| in(sK7(sK20(sK5,sK4,sK6)),sK20(sK5,sK4,sK6)) )
| ~ spl39_4 ),
inference(superposition,[],[f156,f382]) ).
fof(f431,definition,
( spl39_8
<=> in(sK7(sK20(sK5,sK4,sK6)),sK20(sK5,sK4,sK6)) ),
introduced(definition,[new_symbols(definition,[spl39_8])],[avatar_definition]) ).
fof(f432,plain,
( ~ in(sK7(sK20(sK5,sK4,sK6)),sK20(sK5,sK4,sK6))
| spl39_8 ),
inference(avatar_component_clause,[],[f431]) ).
fof(f433,plain,
( in(sK7(sK20(sK5,sK4,sK6)),sK20(sK5,sK4,sK6))
| ~ spl39_8 ),
inference(avatar_component_clause,[],[f431]) ).
fof(f495,definition,
( spl39_22
<=> ! [X0] :
( ~ in(X0,sK9(sK20(sK5,sK4,sK6)))
| in(sF38(sK20(sK5,sK4,sK6),X0),sK5) ) ),
introduced(definition,[new_symbols(definition,[spl39_22])],[avatar_definition]) ).
fof(f496,plain,
( ! [X0] :
( in(sF38(sK20(sK5,sK4,sK6),X0),sK5)
| ~ in(X0,sK9(sK20(sK5,sK4,sK6))) )
| ~ spl39_22 ),
inference(avatar_component_clause,[],[f495]) ).
fof(f497,plain,
( spl39_8
| spl39_22
| ~ spl39_4 ),
inference(avatar_split_clause,[],[f413,f380,f495,f431]) ).
fof(f499,definition,
( spl39_23
<=> in(sK10(sK20(sK5,sK4,sK6)),sK9(sK20(sK5,sK4,sK6))) ),
introduced(definition,[new_symbols(definition,[spl39_23])],[avatar_definition]) ).
fof(f501,plain,
( in(sK10(sK20(sK5,sK4,sK6)),sK9(sK20(sK5,sK4,sK6)))
| ~ spl39_23 ),
inference(avatar_component_clause,[],[f499]) ).
fof(f502,plain,
( spl39_8
| spl39_23
| ~ spl39_4 ),
inference(avatar_split_clause,[],[f412,f380,f499,f431]) ).
fof(f520,plain,
( sK9(sK20(sK5,sK4,sK6)) = sK11(sK20(sK5,sK4,sK6))
| sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5) = sK25(sK4,sK7(sK20(sK5,sK4,sK6)),sK5)
| ~ spl39_7 ),
inference(resolution,[],[f400,f241]) ).
fof(f522,plain,
( sK9(sK20(sK5,sK4,sK6)) = sK11(sK20(sK5,sK4,sK6))
| sK7(sK20(sK5,sK4,sK6)) = ordered_pair(sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5))
| ~ spl39_7 ),
inference(resolution,[],[f400,f242]) ).
fof(f526,definition,
( spl39_28
<=> sK7(sK20(sK5,sK4,sK6)) = sK22(sK6,sK4,sK7(sK20(sK5,sK4,sK6)),sK5) ),
introduced(definition,[new_symbols(definition,[spl39_28])],[avatar_definition]) ).
fof(f528,plain,
( sK7(sK20(sK5,sK4,sK6)) = sK22(sK6,sK4,sK7(sK20(sK5,sK4,sK6)),sK5)
| ~ spl39_28 ),
inference(avatar_component_clause,[],[f526]) ).
fof(f530,definition,
( spl39_29
<=> sK7(sK20(sK5,sK4,sK6)) = sF37(sK20(sK5,sK4,sK6)) ),
introduced(definition,[new_symbols(definition,[spl39_29])],[avatar_definition]) ).
fof(f531,plain,
( sK7(sK20(sK5,sK4,sK6)) != sF37(sK20(sK5,sK4,sK6))
| spl39_29 ),
inference(avatar_component_clause,[],[f530]) ).
fof(f532,plain,
( sK7(sK20(sK5,sK4,sK6)) = sF37(sK20(sK5,sK4,sK6))
| ~ spl39_29 ),
inference(avatar_component_clause,[],[f530]) ).
fof(f534,plain,
( sK7(sK20(sK5,sK4,sK6)) = ordered_pair(sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5))
| spl39_4
| ~ spl39_7 ),
inference(forward_subsumption_resolution,[],[f522,f381]) ).
fof(f536,definition,
( spl39_30
<=> sK7(sK20(sK5,sK4,sK6)) = ordered_pair(sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5)) ),
introduced(definition,[new_symbols(definition,[spl39_30])],[avatar_definition]) ).
fof(f538,plain,
( sK7(sK20(sK5,sK4,sK6)) = ordered_pair(sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5))
| ~ spl39_30 ),
inference(avatar_component_clause,[],[f536]) ).
fof(f540,plain,
( sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5) = sK25(sK4,sK7(sK20(sK5,sK4,sK6)),sK5)
| spl39_4
| ~ spl39_7 ),
inference(forward_subsumption_resolution,[],[f520,f381]) ).
fof(f542,definition,
( spl39_31
<=> sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5) = sK25(sK4,sK7(sK20(sK5,sK4,sK6)),sK5) ),
introduced(definition,[new_symbols(definition,[spl39_31])],[avatar_definition]) ).
fof(f544,plain,
( sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5) = sK25(sK4,sK7(sK20(sK5,sK4,sK6)),sK5)
| ~ spl39_31 ),
inference(avatar_component_clause,[],[f542]) ).
fof(f546,plain,
( spl39_30
| spl39_4
| ~ spl39_7 ),
inference(avatar_split_clause,[],[f534,f399,f380,f536]) ).
fof(f547,plain,
( spl39_31
| spl39_4
| ~ spl39_7 ),
inference(avatar_split_clause,[],[f540,f399,f380,f542]) ).
fof(f549,plain,
( ! [X0] :
( sK33(sK4,sK5) != sK33(sK4,sK5)
| sP3(sK5,sK4,X0)
| empty(sK4)
| ~ relation(sK5) )
| ~ spl39_3 ),
inference(superposition,[],[f135,f375]) ).
fof(f550,plain,
( ! [X0] :
( sP3(sK5,sK4,X0)
| empty(sK4)
| ~ relation(sK5) )
| ~ spl39_3 ),
inference(trivial_inequality_removal,[],[f549]) ).
fof(f551,plain,
( ! [X0] :
( sP3(sK5,sK4,X0)
| ~ relation(sK5) )
| ~ spl39_3 ),
inference(forward_subsumption_resolution,[],[f550,f68]) ).
fof(f553,plain,
( ! [X0] : sP3(sK5,sK4,X0)
| ~ spl39_3 ),
inference(forward_subsumption_resolution,[],[f551,f67]) ).
fof(f563,plain,
( $false
| ~ spl39_3
| spl39_7 ),
inference(resolution,[],[f401,f553]) ).
fof(f565,plain,
( sK32(sK4,sK5) = sK34(sK4,sK5)
| empty(sK4)
| ~ relation(sK5)
| spl39_7 ),
inference(resolution,[],[f401,f132]) ).
fof(f566,plain,
( ~ spl39_3
| spl39_7 ),
inference(avatar_contradiction_clause,[],[f563]) ).
fof(f570,plain,
( empty(sK4)
| ~ relation(sK5)
| spl39_2
| spl39_7 ),
inference(forward_subsumption_resolution,[],[f565,f358]) ).
fof(f571,plain,
( ~ relation(sK5)
| spl39_2
| spl39_7 ),
inference(forward_subsumption_resolution,[],[f570,f68]) ).
fof(f572,plain,
( $false
| spl39_2
| spl39_7 ),
inference(forward_subsumption_resolution,[],[f571,f67]) ).
fof(f573,plain,
( spl39_2
| spl39_7 ),
inference(avatar_contradiction_clause,[],[f572]) ).
fof(f583,definition,
( spl39_33
<=> in(sK9(sK20(sK5,sK4,sK6)),sK4) ),
introduced(definition,[new_symbols(definition,[spl39_33])],[avatar_definition]) ).
fof(f584,plain,
( in(sK9(sK20(sK5,sK4,sK6)),sK4)
| ~ spl39_33 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f585,plain,
( ~ in(sK9(sK20(sK5,sK4,sK6)),sK4)
| spl39_33 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f587,definition,
( spl39_34
<=> ! [X0] :
( sK7(X0) != sK7(sK20(sK5,sK4,sK6))
| ~ in(sK7(X0),X0)
| ~ in(sK7(X0),sF35) ) ),
introduced(definition,[new_symbols(definition,[spl39_34])],[avatar_definition]) ).
fof(f588,plain,
( ! [X0] :
( sK7(X0) != sK7(sK20(sK5,sK4,sK6))
| ~ in(sK7(X0),X0)
| ~ in(sK7(X0),sF35) )
| ~ spl39_34 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f623,plain,
( sP2(sK6,sK4,sK7(sK20(sK5,sK4,sK6)),sK5)
| ~ sP3(sK5,sK4,sK6)
| ~ spl39_8 ),
inference(resolution,[],[f433,f110]) ).
fof(f624,plain,
( ~ sP3(sK5,sK4,sK6)
| spl39_5
| ~ spl39_8 ),
inference(forward_subsumption_resolution,[],[f623,f386]) ).
fof(f625,plain,
( $false
| spl39_5
| ~ spl39_7
| ~ spl39_8 ),
inference(forward_subsumption_resolution,[],[f624,f400]) ).
fof(f626,plain,
( spl39_5
| ~ spl39_7
| ~ spl39_8 ),
inference(avatar_contradiction_clause,[],[f625]) ).
fof(f629,plain,
( sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5) = sK25(sK4,sK7(sK20(sK5,sK4,sK6)),sK5)
| ~ spl39_5 ),
inference(resolution,[],[f385,f114]) ).
fof(f631,plain,
( sK7(sK20(sK5,sK4,sK6)) = ordered_pair(sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5))
| ~ spl39_5 ),
inference(resolution,[],[f385,f116]) ).
fof(f632,plain,
( sK7(sK20(sK5,sK4,sK6)) = sK22(sK6,sK4,sK7(sK20(sK5,sK4,sK6)),sK5)
| ~ spl39_5 ),
inference(resolution,[],[f385,f117]) ).
fof(f661,plain,
( spl39_28
| ~ spl39_5 ),
inference(avatar_split_clause,[],[f632,f384,f526]) ).
fof(f662,plain,
( spl39_30
| ~ spl39_5 ),
inference(avatar_split_clause,[],[f631,f384,f536]) ).
fof(f663,plain,
( spl39_31
| ~ spl39_5 ),
inference(avatar_split_clause,[],[f629,f384,f542]) ).
fof(f666,plain,
( ! [X0] :
( sK7(X0) != sK7(sK20(sK5,sK4,sK6))
| ~ in(sK7(X0),sF35)
| ~ in(sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),sK4)
| ~ in(sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5))
| ~ in(sF36(sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5)),sK5)
| ~ in(sK7(X0),X0) )
| ~ spl39_30 ),
inference(superposition,[],[f148,f538]) ).
fof(f667,plain,
( ! [X0] :
( sK7(X0) != sK7(sK20(sK5,sK4,sK6))
| ~ in(sK7(X0),sF35)
| ~ in(sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),sK4)
| ~ in(sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5))
| in(sK8(sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5)),sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5))
| ~ in(sK7(X0),X0) )
| ~ spl39_30 ),
inference(superposition,[],[f149,f538]) ).
fof(f671,definition,
( spl39_42
<=> in(sK8(sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5)),sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5)) ),
introduced(definition,[new_symbols(definition,[spl39_42])],[avatar_definition]) ).
fof(f673,plain,
( in(sK8(sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5)),sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5))
| ~ spl39_42 ),
inference(avatar_component_clause,[],[f671]) ).
fof(f675,definition,
( spl39_43
<=> in(sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5)) ),
introduced(definition,[new_symbols(definition,[spl39_43])],[avatar_definition]) ).
fof(f679,definition,
( spl39_44
<=> in(sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),sK4) ),
introduced(definition,[new_symbols(definition,[spl39_44])],[avatar_definition]) ).
fof(f682,plain,
( spl39_42
| ~ spl39_43
| ~ spl39_44
| spl39_34
| ~ spl39_30 ),
inference(avatar_split_clause,[],[f667,f536,f587,f679,f675,f671]) ).
fof(f684,definition,
( spl39_45
<=> in(sF36(sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5)),sK5) ),
introduced(definition,[new_symbols(definition,[spl39_45])],[avatar_definition]) ).
fof(f686,plain,
( ~ in(sF36(sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5)),sK5)
| spl39_45 ),
inference(avatar_component_clause,[],[f684]) ).
fof(f687,plain,
( ~ spl39_45
| ~ spl39_43
| ~ spl39_44
| spl39_34
| ~ spl39_30 ),
inference(avatar_split_clause,[],[f666,f536,f587,f679,f675,f684]) ).
fof(f700,plain,
( ! [X0,X1] :
( ~ in(X0,sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5))
| in(ordered_pair(sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),X0),sK5)
| ~ sP2(X1,sK4,sK7(sK20(sK5,sK4,sK6)),sK5) )
| ~ spl39_31 ),
inference(superposition,[],[f112,f544]) ).
fof(f702,definition,
( spl39_48
<=> ! [X1] : ~ sP2(X1,sK4,sK7(sK20(sK5,sK4,sK6)),sK5) ),
introduced(definition,[new_symbols(definition,[spl39_48])],[avatar_definition]) ).
fof(f703,plain,
( ! [X1] : ~ sP2(X1,sK4,sK7(sK20(sK5,sK4,sK6)),sK5)
| ~ spl39_48 ),
inference(avatar_component_clause,[],[f702]) ).
fof(f705,definition,
( spl39_49
<=> ! [X0] :
( ~ in(X0,sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5))
| in(ordered_pair(sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),X0),sK5) ) ),
introduced(definition,[new_symbols(definition,[spl39_49])],[avatar_definition]) ).
fof(f706,plain,
( ! [X0] :
( in(ordered_pair(sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),X0),sK5)
| ~ in(X0,sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5)) )
| ~ spl39_49 ),
inference(avatar_component_clause,[],[f705]) ).
fof(f707,plain,
( spl39_48
| spl39_49
| ~ spl39_31 ),
inference(avatar_split_clause,[],[f700,f542,f705,f702]) ).
fof(f742,plain,
( ! [X2,X0,X1] :
( ~ in(sK21(sK5,sK10(sK20(sK5,sK4,sK6)),X0),sK9(sK20(sK5,sK4,sK6)))
| ~ in(ordered_pair(X0,sK10(sK20(sK5,sK4,sK6))),cartesian_product2(X1,X2))
| ~ in(X0,X1)
| ~ in(sK10(sK20(sK5,sK4,sK6)),X0)
| sP2(X2,X1,ordered_pair(X0,sK10(sK20(sK5,sK4,sK6))),sK5) )
| ~ spl39_22 ),
inference(resolution,[],[f496,f163]) ).
fof(f745,plain,
( in(sK7(sK20(sK5,sK4,sK6)),cartesian_product2(sK4,sK6))
| ~ sP2(sK6,sK4,sK7(sK20(sK5,sK4,sK6)),sK5)
| ~ spl39_28 ),
inference(superposition,[],[f118,f528]) ).
fof(f750,plain,
( in(sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),sK25(sK4,sK7(sK20(sK5,sK4,sK6)),sK5))
| ~ spl39_5 ),
inference(resolution,[],[f385,f113]) ).
fof(f752,plain,
( in(sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),sK4)
| ~ spl39_5 ),
inference(resolution,[],[f385,f115]) ).
fof(f763,plain,
( spl39_44
| ~ spl39_5 ),
inference(avatar_split_clause,[],[f752,f384,f679]) ).
fof(f764,plain,
( in(sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5))
| ~ spl39_5
| ~ spl39_31 ),
inference(forward_demodulation,[],[f750,f544]) ).
fof(f769,plain,
( in(sK7(sK20(sK5,sK4,sK6)),sF35)
| spl39_8 ),
inference(resolution,[],[f432,f150]) ).
fof(f781,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),cartesian_product2(X0,X1))
| ~ in(sK9(sK20(sK5,sK4,sK6)),X0)
| ~ in(sK10(sK20(sK5,sK4,sK6)),sK9(sK20(sK5,sK4,sK6)))
| sP2(X1,X0,ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sK5)
| sP2(sK6,sK4,ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sK5)
| ~ in(sK9(sK20(sK5,sK4,sK6)),sK4)
| ~ in(sK10(sK20(sK5,sK4,sK6)),sK9(sK20(sK5,sK4,sK6)))
| ~ in(ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sF35) )
| ~ spl39_22 ),
inference(resolution,[],[f742,f177]) ).
fof(f782,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),cartesian_product2(X0,X1))
| ~ in(sK9(sK20(sK5,sK4,sK6)),X0)
| ~ in(sK10(sK20(sK5,sK4,sK6)),sK9(sK20(sK5,sK4,sK6)))
| sP2(X1,X0,ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sK5)
| sP2(sK6,sK4,ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sK5)
| ~ in(sK9(sK20(sK5,sK4,sK6)),sK4)
| ~ in(ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sF35) )
| ~ spl39_22 ),
inference(duplicate_literal_removal,[],[f781]) ).
fof(f786,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),cartesian_product2(X0,X1))
| ~ in(sK9(sK20(sK5,sK4,sK6)),X0)
| sP2(X1,X0,ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sK5)
| sP2(sK6,sK4,ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sK5)
| ~ in(sK9(sK20(sK5,sK4,sK6)),sK4)
| ~ in(ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sF35) )
| ~ spl39_22
| ~ spl39_23 ),
inference(forward_subsumption_resolution,[],[f782,f501]) ).
fof(f790,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),cartesian_product2(X0,X1))
| ~ in(sK9(sK20(sK5,sK4,sK6)),X0)
| sP2(X1,X0,ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sK5)
| sP2(sK6,sK4,ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sK5)
| ~ in(ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sF35) )
| ~ spl39_22
| ~ spl39_23
| ~ spl39_33 ),
inference(forward_subsumption_resolution,[],[f786,f584]) ).
fof(f794,plain,
( ! [X0,X1] :
( ~ in(sF37(sK20(sK5,sK4,sK6)),cartesian_product2(X0,X1))
| ~ in(sK9(sK20(sK5,sK4,sK6)),X0)
| sP2(X1,X0,ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sK5)
| sP2(sK6,sK4,ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sK5)
| ~ in(ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sF35) )
| ~ spl39_22
| ~ spl39_23
| ~ spl39_33 ),
inference(forward_demodulation,[],[f790,f152]) ).
fof(f798,plain,
( ! [X0,X1] :
( ~ in(sK7(sK20(sK5,sK4,sK6)),cartesian_product2(X0,X1))
| ~ in(sK9(sK20(sK5,sK4,sK6)),X0)
| sP2(X1,X0,ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sK5)
| sP2(sK6,sK4,ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sK5)
| ~ in(ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sF35) )
| ~ spl39_22
| ~ spl39_23
| ~ spl39_29
| ~ spl39_33 ),
inference(forward_demodulation,[],[f794,f532]) ).
fof(f802,plain,
( ! [X0,X1] :
( sP2(X1,X0,sF37(sK20(sK5,sK4,sK6)),sK5)
| ~ in(sK7(sK20(sK5,sK4,sK6)),cartesian_product2(X0,X1))
| ~ in(sK9(sK20(sK5,sK4,sK6)),X0)
| sP2(sK6,sK4,ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sK5)
| ~ in(ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sF35) )
| ~ spl39_22
| ~ spl39_23
| ~ spl39_29
| ~ spl39_33 ),
inference(forward_demodulation,[],[f798,f152]) ).
fof(f806,plain,
( ! [X0,X1] :
( sP2(X1,X0,sK7(sK20(sK5,sK4,sK6)),sK5)
| ~ in(sK7(sK20(sK5,sK4,sK6)),cartesian_product2(X0,X1))
| ~ in(sK9(sK20(sK5,sK4,sK6)),X0)
| sP2(sK6,sK4,ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sK5)
| ~ in(ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sF35) )
| ~ spl39_22
| ~ spl39_23
| ~ spl39_29
| ~ spl39_33 ),
inference(forward_demodulation,[],[f802,f532]) ).
fof(f810,plain,
( ! [X0,X1] :
( sP2(sK6,sK4,sF37(sK20(sK5,sK4,sK6)),sK5)
| sP2(X1,X0,sK7(sK20(sK5,sK4,sK6)),sK5)
| ~ in(sK7(sK20(sK5,sK4,sK6)),cartesian_product2(X0,X1))
| ~ in(sK9(sK20(sK5,sK4,sK6)),X0)
| ~ in(ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sF35) )
| ~ spl39_22
| ~ spl39_23
| ~ spl39_29
| ~ spl39_33 ),
inference(forward_demodulation,[],[f806,f152]) ).
fof(f814,plain,
( ! [X0,X1] :
( sP2(sK6,sK4,sK7(sK20(sK5,sK4,sK6)),sK5)
| sP2(X1,X0,sK7(sK20(sK5,sK4,sK6)),sK5)
| ~ in(sK7(sK20(sK5,sK4,sK6)),cartesian_product2(X0,X1))
| ~ in(sK9(sK20(sK5,sK4,sK6)),X0)
| ~ in(ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sF35) )
| ~ spl39_22
| ~ spl39_23
| ~ spl39_29
| ~ spl39_33 ),
inference(forward_demodulation,[],[f810,f532]) ).
fof(f818,plain,
( ! [X0,X1] :
( sP2(X1,X0,sK7(sK20(sK5,sK4,sK6)),sK5)
| ~ in(sK7(sK20(sK5,sK4,sK6)),cartesian_product2(X0,X1))
| ~ in(sK9(sK20(sK5,sK4,sK6)),X0)
| ~ in(ordered_pair(sK9(sK20(sK5,sK4,sK6)),sK10(sK20(sK5,sK4,sK6))),sF35) )
| spl39_5
| ~ spl39_22
| ~ spl39_23
| ~ spl39_29
| ~ spl39_33 ),
inference(forward_subsumption_resolution,[],[f814,f386]) ).
fof(f820,plain,
( ! [X0,X1] :
( ~ in(sF37(sK20(sK5,sK4,sK6)),sF35)
| sP2(X1,X0,sK7(sK20(sK5,sK4,sK6)),sK5)
| ~ in(sK7(sK20(sK5,sK4,sK6)),cartesian_product2(X0,X1))
| ~ in(sK9(sK20(sK5,sK4,sK6)),X0) )
| spl39_5
| ~ spl39_22
| ~ spl39_23
| ~ spl39_29
| ~ spl39_33 ),
inference(forward_demodulation,[],[f818,f152]) ).
fof(f822,plain,
( ! [X0,X1] :
( ~ in(sK7(sK20(sK5,sK4,sK6)),sF35)
| sP2(X1,X0,sK7(sK20(sK5,sK4,sK6)),sK5)
| ~ in(sK7(sK20(sK5,sK4,sK6)),cartesian_product2(X0,X1))
| ~ in(sK9(sK20(sK5,sK4,sK6)),X0) )
| spl39_5
| ~ spl39_22
| ~ spl39_23
| ~ spl39_29
| ~ spl39_33 ),
inference(forward_demodulation,[],[f820,f532]) ).
fof(f824,plain,
( ! [X0,X1] :
( sP2(X1,X0,sK7(sK20(sK5,sK4,sK6)),sK5)
| ~ in(sK7(sK20(sK5,sK4,sK6)),cartesian_product2(X0,X1))
| ~ in(sK9(sK20(sK5,sK4,sK6)),X0) )
| spl39_5
| ~ spl39_6
| ~ spl39_22
| ~ spl39_23
| ~ spl39_29
| ~ spl39_33 ),
inference(forward_subsumption_resolution,[],[f822,f390]) ).
fof(f826,definition,
( spl39_50
<=> ! [X0,X1] :
( sP2(X1,X0,sK7(sK20(sK5,sK4,sK6)),sK5)
| ~ in(sK9(sK20(sK5,sK4,sK6)),X0)
| ~ in(sK7(sK20(sK5,sK4,sK6)),cartesian_product2(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl39_50])],[avatar_definition]) ).
fof(f827,plain,
( ! [X0,X1] :
( ~ in(sK7(sK20(sK5,sK4,sK6)),cartesian_product2(X0,X1))
| ~ in(sK9(sK20(sK5,sK4,sK6)),X0)
| sP2(X1,X0,sK7(sK20(sK5,sK4,sK6)),sK5) )
| ~ spl39_50 ),
inference(avatar_component_clause,[],[f826]) ).
fof(f829,plain,
( spl39_50
| spl39_5
| ~ spl39_6
| ~ spl39_22
| ~ spl39_23
| ~ spl39_29
| ~ spl39_33 ),
inference(avatar_split_clause,[],[f824,f583,f530,f499,f495,f388,f384,f826]) ).
fof(f833,plain,
( ~ in(sK7(sK20(sK5,sK4,sK6)),sF35)
| ~ in(sK9(sK20(sK5,sK4,sK6)),sK4)
| sP2(sK6,sK4,sK7(sK20(sK5,sK4,sK6)),sK5)
| ~ spl39_50 ),
inference(superposition,[],[f827,f145]) ).
fof(f834,plain,
( ~ in(sK9(sK20(sK5,sK4,sK6)),sK4)
| sP2(sK6,sK4,sK7(sK20(sK5,sK4,sK6)),sK5)
| ~ spl39_6
| ~ spl39_50 ),
inference(forward_subsumption_resolution,[],[f833,f390]) ).
fof(f835,plain,
( sP2(sK6,sK4,sK7(sK20(sK5,sK4,sK6)),sK5)
| ~ spl39_6
| ~ spl39_33
| ~ spl39_50 ),
inference(forward_subsumption_resolution,[],[f834,f584]) ).
fof(f836,plain,
( $false
| spl39_5
| ~ spl39_6
| ~ spl39_33
| ~ spl39_50 ),
inference(forward_subsumption_resolution,[],[f835,f386]) ).
fof(f837,plain,
( spl39_5
| ~ spl39_6
| ~ spl39_33
| ~ spl39_50 ),
inference(avatar_contradiction_clause,[],[f836]) ).
fof(f839,plain,
( $false
| spl39_6
| spl39_8 ),
inference(forward_subsumption_resolution,[],[f769,f389]) ).
fof(f840,plain,
( spl39_6
| spl39_8 ),
inference(avatar_contradiction_clause,[],[f839]) ).
fof(f844,plain,
( spl39_43
| ~ spl39_5
| ~ spl39_31 ),
inference(avatar_split_clause,[],[f764,f542,f384,f675]) ).
fof(f847,plain,
( in(sK7(sK20(sK5,sK4,sK6)),cartesian_product2(sK4,sK6))
| ~ spl39_5
| ~ spl39_28 ),
inference(forward_subsumption_resolution,[],[f745,f385]) ).
fof(f849,plain,
( in(sK7(sK20(sK5,sK4,sK6)),sF35)
| ~ spl39_5
| ~ spl39_28 ),
inference(forward_demodulation,[],[f847,f145]) ).
fof(f852,plain,
( $false
| ~ spl39_5
| spl39_6
| ~ spl39_28 ),
inference(forward_subsumption_resolution,[],[f849,f389]) ).
fof(f853,plain,
( ~ spl39_5
| spl39_6
| ~ spl39_28 ),
inference(avatar_contradiction_clause,[],[f852]) ).
fof(f856,plain,
( ~ in(sK7(sK20(sK5,sK4,sK6)),sK20(sK5,sK4,sK6))
| ~ in(sK7(sK20(sK5,sK4,sK6)),sF35)
| ~ spl39_34 ),
inference(equality_resolution,[],[f588]) ).
fof(f857,plain,
( ~ in(sK7(sK20(sK5,sK4,sK6)),sF35)
| ~ spl39_8
| ~ spl39_34 ),
inference(forward_subsumption_resolution,[],[f856,f433]) ).
fof(f858,plain,
( $false
| ~ spl39_6
| ~ spl39_8
| ~ spl39_34 ),
inference(forward_subsumption_resolution,[],[f857,f390]) ).
fof(f859,plain,
( ~ spl39_6
| ~ spl39_8
| ~ spl39_34 ),
inference(avatar_contradiction_clause,[],[f858]) ).
fof(f887,plain,
( ! [X0] :
( ~ in(sK8(sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),X0),sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5))
| in(sF36(sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),X0),sK5) )
| ~ spl39_49 ),
inference(superposition,[],[f706,f147]) ).
fof(f923,plain,
( in(sF36(sK24(sK4,sK7(sK20(sK5,sK4,sK6)),sK5),sK23(sK4,sK7(sK20(sK5,sK4,sK6)),sK5)),sK5)
| ~ spl39_42
| ~ spl39_49 ),
inference(resolution,[],[f887,f673]) ).
fof(f924,plain,
( $false
| ~ spl39_42
| spl39_45
| ~ spl39_49 ),
inference(forward_subsumption_resolution,[],[f923,f686]) ).
fof(f925,plain,
( ~ spl39_42
| spl39_45
| ~ spl39_49 ),
inference(avatar_contradiction_clause,[],[f924]) ).
fof(f926,plain,
( $false
| ~ spl39_5
| ~ spl39_48 ),
inference(resolution,[],[f703,f385]) ).
fof(f931,plain,
( ~ spl39_5
| ~ spl39_48 ),
inference(avatar_contradiction_clause,[],[f926]) ).
fof(f938,plain,
( sK9(sK20(sK5,sK4,sK6)) = sK11(sK20(sK5,sK4,sK6))
| spl39_8 ),
inference(resolution,[],[f432,f71]) ).
fof(f939,plain,
( in(sK9(sK20(sK5,sK4,sK6)),sK4)
| spl39_8 ),
inference(resolution,[],[f432,f72]) ).
fof(f941,plain,
( sK7(sK20(sK5,sK4,sK6)) = sF37(sK20(sK5,sK4,sK6))
| spl39_8 ),
inference(resolution,[],[f432,f153]) ).
fof(f942,plain,
( ~ sP2(sK6,sK4,sK7(sK20(sK5,sK4,sK6)),sK5)
| ~ sP3(sK5,sK4,sK6)
| spl39_8 ),
inference(resolution,[],[f432,f111]) ).
fof(f943,plain,
( ~ sP3(sK5,sK4,sK6)
| ~ spl39_5
| spl39_8 ),
inference(forward_subsumption_resolution,[],[f942,f385]) ).
fof(f944,plain,
( $false
| spl39_4
| spl39_8 ),
inference(forward_subsumption_resolution,[],[f938,f381]) ).
fof(f945,plain,
( spl39_4
| spl39_8 ),
inference(avatar_contradiction_clause,[],[f944]) ).
fof(f946,plain,
( $false
| ~ spl39_5
| ~ spl39_7
| spl39_8 ),
inference(forward_subsumption_resolution,[],[f943,f400]) ).
fof(f947,plain,
( ~ spl39_5
| ~ spl39_7
| spl39_8 ),
inference(avatar_contradiction_clause,[],[f946]) ).
fof(f951,plain,
( $false
| spl39_8
| spl39_33 ),
inference(forward_subsumption_resolution,[],[f939,f585]) ).
fof(f952,plain,
( spl39_8
| spl39_33 ),
inference(avatar_contradiction_clause,[],[f951]) ).
fof(f964,plain,
( $false
| spl39_8
| spl39_29 ),
inference(forward_subsumption_resolution,[],[f941,f531]) ).
fof(f965,plain,
( spl39_8
| spl39_29 ),
inference(avatar_contradiction_clause,[],[f964]) ).
cnf(s5,plain,
( ~ spl39_2
| spl39_3
| spl39_7 ),
inference(sat_conversion,[],[f411]) ).
cnf(s18,plain,
( ~ spl39_4
| spl39_8
| spl39_22 ),
inference(sat_conversion,[],[f497]) ).
cnf(s19,plain,
( ~ spl39_4
| spl39_8
| spl39_23 ),
inference(sat_conversion,[],[f502]) ).
cnf(s27,plain,
( spl39_4
| ~ spl39_7
| spl39_30 ),
inference(sat_conversion,[],[f546]) ).
cnf(s28,plain,
( spl39_4
| ~ spl39_7
| spl39_31 ),
inference(sat_conversion,[],[f547]) ).
cnf(s29,plain,
( ~ spl39_3
| spl39_7 ),
inference(sat_conversion,[],[f566]) ).
cnf(s30,plain,
( spl39_2
| spl39_7 ),
inference(sat_conversion,[],[f573]) ).
cnf(s34,plain,
( spl39_5
| ~ spl39_7
| ~ spl39_8 ),
inference(sat_conversion,[],[f626]) ).
cnf(s39,plain,
( ~ spl39_5
| spl39_28 ),
inference(sat_conversion,[],[f661]) ).
cnf(s40,plain,
( ~ spl39_5
| spl39_30 ),
inference(sat_conversion,[],[f662]) ).
cnf(s41,plain,
( ~ spl39_5
| spl39_31 ),
inference(sat_conversion,[],[f663]) ).
cnf(s42,plain,
( ~ spl39_30
| spl39_34
| spl39_42
| ~ spl39_43
| ~ spl39_44 ),
inference(sat_conversion,[],[f682]) ).
cnf(s43,plain,
( ~ spl39_30
| spl39_34
| ~ spl39_43
| ~ spl39_44
| ~ spl39_45 ),
inference(sat_conversion,[],[f687]) ).
cnf(s46,plain,
( ~ spl39_31
| spl39_48
| spl39_49 ),
inference(sat_conversion,[],[f707]) ).
cnf(s50,plain,
( ~ spl39_5
| spl39_44 ),
inference(sat_conversion,[],[f763]) ).
cnf(s53,plain,
( spl39_5
| ~ spl39_6
| ~ spl39_22
| ~ spl39_23
| ~ spl39_29
| ~ spl39_33
| spl39_50 ),
inference(sat_conversion,[],[f829]) ).
cnf(s54,plain,
( spl39_5
| ~ spl39_6
| ~ spl39_33
| ~ spl39_50 ),
inference(sat_conversion,[],[f837]) ).
cnf(s55,plain,
( spl39_6
| spl39_8 ),
inference(sat_conversion,[],[f840]) ).
cnf(s57,plain,
( ~ spl39_5
| ~ spl39_31
| spl39_43 ),
inference(sat_conversion,[],[f844]) ).
cnf(s60,plain,
( ~ spl39_5
| spl39_6
| ~ spl39_28 ),
inference(sat_conversion,[],[f853]) ).
cnf(s61,plain,
( ~ spl39_6
| ~ spl39_8
| ~ spl39_34 ),
inference(sat_conversion,[],[f859]) ).
cnf(s65,plain,
( ~ spl39_42
| spl39_45
| ~ spl39_49 ),
inference(sat_conversion,[],[f925]) ).
cnf(s66,plain,
( ~ spl39_5
| ~ spl39_48 ),
inference(sat_conversion,[],[f931]) ).
cnf(s67,plain,
( spl39_4
| spl39_8 ),
inference(sat_conversion,[],[f945]) ).
cnf(s68,plain,
( ~ spl39_5
| ~ spl39_7
| spl39_8 ),
inference(sat_conversion,[],[f947]) ).
cnf(s71,plain,
( spl39_8
| spl39_33 ),
inference(sat_conversion,[],[f952]) ).
cnf(s72,plain,
( spl39_8
| spl39_29 ),
inference(sat_conversion,[],[f965]) ).
cnf(s76,plain,
( spl39_4
| ~ spl39_7 ),
inference(rat,[],[s65,s42,s43,s61,s60,s46,s39,s50,s66,s57,s34,s27,s28,s67]) ).
cnf(s77,plain,
( ~ spl39_5
| ~ spl39_7 ),
inference(rat,[],[s65,s42,s43,s61,s60,s57,s46,s39,s40,s41,s50,s66,s68]) ).
cnf(s78,plain,
~ spl39_7,
inference(rat,[],[s53,s54,s18,s19,s55,s71,s72,s34,s77,s76]) ).
cnf(s79,plain,
spl39_2,
inference(rat,[],[s30,s78]) ).
cnf(s80,plain,
~ spl39_3,
inference(rat,[],[s29,s78]) ).
cnf(s81,plain,
$false,
inference(rat,[],[s5,s79,s78,s80]) ).
fof(f994,plain,
$false,
inference(avatar_sat_refutation,[],[s81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU286+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 04:33:13 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.38/1.61 % (4145553)Detected formulas, will run a generic FOF schedule.
% 3.38/1.61 % (4145558)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=1712894684:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.38/1.61 % (4145563)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2097018837:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.38/1.61 % (4145559)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=3428172297:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.38/1.61 % (4145561)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1175856070:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.38/1.61 % (4145562)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3630993800:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.38/1.61 % (4145560)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=2401101511:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.38/1.61 % (4145561)Refutation not found, incomplete strategy
% 3.38/1.61 % (4145561)------------------------------
% 3.38/1.61 % (4145561)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.61 % (4145561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.61 % (4145561)CaDiCaL version: 2.1.3
% 3.38/1.61 % (4145561)Termination reason: Refutation not found, incomplete strategy
% 3.38/1.61 % (4145561)Time elapsed: 0.008 s
% 3.38/1.61 % (4145561)Peak memory usage: 88 MB
% 3.38/1.61 % (4145561)Instructions burned: 10 (million)
% 3.38/1.61 % (4145564)dis-21_1_sil=8000:lcm=predicate:random_seed=3144987191: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)
% 3.38/1.61 % (4145562)Instruction limit reached!
% 3.38/1.61 % (4145562)------------------------------
% 3.38/1.61 % (4145562)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.61 % (4145562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.61 % (4145562)CaDiCaL version: 2.1.3
% 3.38/1.61 % (4145562)Termination reason: Instruction limit
% 3.38/1.61 % (4145562)Termination phase: Saturation
% 3.38/1.61 % (4145562)Time elapsed: 0.075 s
% 3.38/1.61 % (4145562)Peak memory usage: 88 MB
% 3.38/1.61 % (4145562)Instructions burned: 119 (million)
% 3.38/1.61 % (4145564)Instruction limit reached!
% 3.38/1.61 % (4145564)------------------------------
% 3.38/1.61 % (4145564)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.61 % (4145564)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.61 % (4145564)CaDiCaL version: 2.1.3
% 3.38/1.61 % (4145564)Termination reason: Instruction limit
% 3.38/1.61 % (4145564)Termination phase: Saturation
% 3.38/1.61 % (4145564)Time elapsed: 0.072 s
% 3.38/1.61 % (4145564)Peak memory usage: 89 MB
% 3.38/1.61 % (4145564)Instructions burned: 130 (million)
% 3.38/1.61 % (4145563)Instruction limit reached!
% 3.38/1.61 % (4145563)------------------------------
% 3.38/1.61 % (4145563)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.61 % (4145563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.61 % (4145563)CaDiCaL version: 2.1.3
% 3.38/1.61 % (4145563)Termination reason: Instruction limit
% 3.38/1.61 % (4145563)Termination phase: Saturation
% 3.38/1.61 % (4145563)Time elapsed: 0.099 s
% 3.38/1.61 % (4145563)Peak memory usage: 90 MB
% 3.38/1.61 % (4145563)Instructions burned: 140 (million)
% 3.38/1.61 % (4145573)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1781970820:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.38/1.61 % (4145572)lrs+10_1_sil=8000:sp=occurrence:random_seed=438425342:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.38/1.61 % (4145573)Refutation not found, incomplete strategy
% 3.38/1.61 % (4145573)------------------------------
% 3.38/1.61 % (4145573)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.61 % (4145573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.61 % (4145573)CaDiCaL version: 2.1.3
% 3.38/1.61 % (4145573)Termination reason: Refutation not found, incomplete strategy
% 3.38/1.61 % (4145573)Time elapsed: 0.004 s
% 3.38/1.61 % (4145573)Peak memory usage: 89 MB
% 3.38/1.61 % (4145573)Instructions burned: 4 (million)
% 3.38/1.61 % (4145574)lrs+1011_1_sil=32000:sp=occurrence:random_seed=268742178:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.38/1.61 % (4145561)------------------------------
% 3.38/1.61 % (4145561)------------------------------
% 3.38/1.61 % (4145572)Instruction limit reached!
% 3.38/1.61 % (4145572)------------------------------
% 3.38/1.61 % (4145572)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.61 % (4145572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.61 % (4145572)CaDiCaL version: 2.1.3
% 3.38/1.61 % (4145572)Termination reason: Instruction limit
% 3.38/1.61 % (4145572)Termination phase: Saturation
% 3.38/1.61 % (4145572)Time elapsed: 0.156 s
% 3.38/1.61 % (4145572)Peak memory usage: 92 MB
% 3.38/1.61 % (4145572)Instructions burned: 285 (million)
% 3.38/1.61 % (4145578)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=475837498:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 3.38/1.61 % (4145578)Refutation not found, incomplete strategy
% 3.38/1.61 % (4145578)------------------------------
% 3.38/1.61 % (4145578)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.61 % (4145578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.61 % (4145578)CaDiCaL version: 2.1.3
% 3.38/1.61 % (4145578)Termination reason: Refutation not found, incomplete strategy
% 3.38/1.61 % (4145578)Time elapsed: 0.005 s
% 3.38/1.61 % (4145578)Peak memory usage: 88 MB
% 3.38/1.61 % (4145578)Instructions burned: 6 (million)
% 3.38/1.61 % (4145574)Instruction limit reached!
% 3.38/1.61 % (4145574)------------------------------
% 3.38/1.61 % (4145574)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.61 % (4145574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.61 % (4145574)CaDiCaL version: 2.1.3
% 3.38/1.61 % (4145574)Termination reason: Instruction limit
% 3.38/1.61 % (4145574)Termination phase: Saturation
% 3.38/1.61 % (4145574)Time elapsed: 0.194 s
% 3.38/1.61 % (4145574)Peak memory usage: 92 MB
% 3.38/1.61 % (4145574)Instructions burned: 326 (million)
% 3.38/1.61 % (4145573)------------------------------
% 3.38/1.61 % (4145573)------------------------------
% 3.38/1.61 % (4145558)First to succeed.
% 3.38/1.61 % (4145558)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4145553"
% 3.38/1.61 % (4145579)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1373742031:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 3.38/1.61 % (4145579)Refutation not found, incomplete strategy
% 3.38/1.61 % (4145579)------------------------------
% 3.38/1.61 % (4145579)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.61 % (4145579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.61 % (4145579)CaDiCaL version: 2.1.3
% 3.38/1.61 % (4145579)Termination reason: Refutation not found, incomplete strategy
% 3.38/1.61 % (4145579)Time elapsed: 0.008 s
% 3.38/1.61 % (4145579)Peak memory usage: 88 MB
% 3.38/1.61 % (4145579)Instructions burned: 9 (million)
% 3.38/1.61 % (4145581)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3986811072:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 3.38/1.61 % (4145582)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2625924099:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 3.38/1.61 % (4145558)Refutation found. Thanks to Tanya!
% 3.38/1.61 % SZS status Theorem for theBenchmark
% 3.38/1.61 % SZS output start Proof for theBenchmark
% See solution above
% 5.98/1.79 % (4145558)------------------------------
% 5.98/1.79 % (4145558)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.98/1.79 % (4145558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.98/1.79 % (4145558)CaDiCaL version: 2.1.3
% 5.98/1.79 % (4145558)Termination reason: Refutation
% 5.98/1.79 % (4145558)Time elapsed: 0.505 s
% 5.98/1.79 % (4145558)Peak memory usage: 131 MB
% 5.98/1.79 % (4145558)Instructions burned: 1134 (million)
% 5.98/1.79 % (4145558)------------------------------
% 5.98/1.79 % (4145558)------------------------------
% 5.98/1.79 % (4145553)Success in time 0.774 s
% 5.98/1.79 % Vampire exiting
%------------------------------------------------------------------------------