%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC344+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 01:03:33 PM UTC 2026
% Result : Theorem 3.25s 1.15s
% Output : Refutation 4.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 35
% Syntax : Number of formulae : 245 ( 34 unt; 32 def)
% Number of atoms : 1091 ( 173 equ)
% Maximal formula atoms : 46 ( 4 avg)
% Number of connectives : 1397 ( 551 ~; 620 |; 172 &)
% ( 22 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 38 ( 36 usr; 17 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-2 aty)
% Number of variables : 336 ( 0 sgn 258 !; 78 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X4,X2),X5) != X3
| ~ strictorderedP(X2)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X4
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X2
& lt(X6,X8) ) ) ) )
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(cons(X10,nil),X11) = X5
& ? [X12] :
( ssItem(X12)
& ? [X13] :
( ssList(X13)
& app(X13,cons(X12,nil)) = X2
& lt(X12,X10) ) ) ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( ? [X14] :
( ssList(X14)
& ? [X15] :
( ssList(X15)
& app(app(X14,X0),X15) = X1
& ! [X16] :
( ssItem(X16)
=> ! [X17] :
( ssList(X17)
=> ( app(X17,cons(X16,nil)) != X14
| ! [X18] :
( ssItem(X18)
=> ! [X19] :
( ssList(X19)
=> ( app(cons(X18,nil),X19) != X0
| ~ lt(X16,X18) ) ) ) ) ) )
& ! [X20] :
( ssItem(X20)
=> ! [X21] :
( ssList(X21)
=> ( app(cons(X20,nil),X21) != X15
| ! [X22] :
( ssItem(X22)
=> ! [X23] :
( ssList(X23)
=> ( app(X23,cons(X22,nil)) != X0
| ~ lt(X22,X20) ) ) ) ) ) )
& strictorderedP(X0) ) )
& ( nil != X0
| nil = X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X4,X2),X5) != X3
| ~ strictorderedP(X2)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X4
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X2
& lt(X6,X8) ) ) ) )
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(cons(X10,nil),X11) = X5
& ? [X12] :
( ssItem(X12)
& ? [X13] :
( ssList(X13)
& app(X13,cons(X12,nil)) = X2
& lt(X12,X10) ) ) ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( ? [X14] :
( ssList(X14)
& ? [X15] :
( ssList(X15)
& app(app(X14,X0),X15) = X1
& ! [X16] :
( ssItem(X16)
=> ! [X17] :
( ssList(X17)
=> ( app(X17,cons(X16,nil)) != X14
| ! [X18] :
( ssItem(X18)
=> ! [X19] :
( ssList(X19)
=> ( app(cons(X18,nil),X19) != X0
| ~ lt(X16,X18) ) ) ) ) ) )
& ! [X20] :
( ssItem(X20)
=> ! [X21] :
( ssList(X21)
=> ( app(cons(X20,nil),X21) != X15
| ! [X22] :
( ssItem(X22)
=> ! [X23] :
( ssList(X23)
=> ( app(X23,cons(X22,nil)) != X0
| ~ lt(X22,X20) ) ) ) ) ) )
& strictorderedP(X0) ) )
& ( nil != X0
| nil = X1 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( ? [X5] :
( app(app(X4,X2),X5) = X3
& strictorderedP(X2)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != X4
| ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != X2
| ~ lt(X6,X8) ) ) ) )
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(cons(X10,nil),X11) != X5
| ! [X12] :
( ~ ssItem(X12)
| ! [X13] :
( ~ ssList(X13)
| app(X13,cons(X12,nil)) != X2
| ~ lt(X12,X10) ) ) ) )
& ssList(X5) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( ! [X14] :
( ~ ssList(X14)
| ! [X15] :
( ~ ssList(X15)
| app(app(X14,X0),X15) != X1
| ? [X16] :
( ? [X17] :
( app(X17,cons(X16,nil)) = X14
& ? [X18] :
( ? [X19] :
( app(cons(X18,nil),X19) = X0
& lt(X16,X18)
& ssList(X19) )
& ssItem(X18) )
& ssList(X17) )
& ssItem(X16) )
| ? [X20] :
( ? [X21] :
( app(cons(X20,nil),X21) = X15
& ? [X22] :
( ? [X23] :
( app(X23,cons(X22,nil)) = X0
& lt(X22,X20)
& ssList(X23) )
& ssItem(X22) )
& ssList(X21) )
& ssItem(X20) )
| ~ strictorderedP(X0) ) )
| ( nil = X0
& nil != X1 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( ? [X5] :
( app(app(X4,X2),X5) = X3
& strictorderedP(X2)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != X4
| ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != X2
| ~ lt(X6,X8) ) ) ) )
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(cons(X10,nil),X11) != X5
| ! [X12] :
( ~ ssItem(X12)
| ! [X13] :
( ~ ssList(X13)
| app(X13,cons(X12,nil)) != X2
| ~ lt(X12,X10) ) ) ) )
& ssList(X5) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( ! [X14] :
( ~ ssList(X14)
| ! [X15] :
( ~ ssList(X15)
| app(app(X14,X0),X15) != X1
| ? [X16] :
( ? [X17] :
( app(X17,cons(X16,nil)) = X14
& ? [X18] :
( ? [X19] :
( app(cons(X18,nil),X19) = X0
& lt(X16,X18)
& ssList(X19) )
& ssItem(X18) )
& ssList(X17) )
& ssItem(X16) )
| ? [X20] :
( ? [X21] :
( app(cons(X20,nil),X21) = X15
& ? [X22] :
( ? [X23] :
( app(X23,cons(X22,nil)) = X0
& lt(X22,X20)
& ssList(X23) )
& ssItem(X22) )
& ssList(X21) )
& ssItem(X20) )
| ~ strictorderedP(X0) ) )
| ( nil = X0
& nil != X1 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f132,definition,
! [X15,X0] :
( ? [X20] :
( ? [X21] :
( app(cons(X20,nil),X21) = X15
& ? [X22] :
( ? [X23] :
( app(X23,cons(X22,nil)) = X0
& lt(X22,X20)
& ssList(X23) )
& ssItem(X22) )
& ssList(X21) )
& ssItem(X20) )
| ~ sP0(X15,X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f133,definition,
! [X1,X0] :
( ! [X14] :
( ~ ssList(X14)
| ! [X15] :
( ~ ssList(X15)
| app(app(X14,X0),X15) != X1
| ? [X16] :
( ? [X17] :
( app(X17,cons(X16,nil)) = X14
& ? [X18] :
( ? [X19] :
( app(cons(X18,nil),X19) = X0
& lt(X16,X18)
& ssList(X19) )
& ssItem(X18) )
& ssList(X17) )
& ssItem(X16) )
| sP0(X15,X0)
| ~ strictorderedP(X0) ) )
| ~ sP1(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f134,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( ? [X5] :
( app(app(X4,X2),X5) = X3
& strictorderedP(X2)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != X4
| ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != X2
| ~ lt(X6,X8) ) ) ) )
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(cons(X10,nil),X11) != X5
| ! [X12] :
( ~ ssItem(X12)
| ! [X13] :
( ~ ssList(X13)
| app(X13,cons(X12,nil)) != X2
| ~ lt(X12,X10) ) ) ) )
& ssList(X5) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( sP1(X1,X0)
| ( nil = X0
& nil != X1 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f99,f133,f132]) ).
fof(f135,plain,
! [X1,X0] :
( ! [X14] :
( ~ ssList(X14)
| ! [X15] :
( ~ ssList(X15)
| app(app(X14,X0),X15) != X1
| ? [X16] :
( ? [X17] :
( app(X17,cons(X16,nil)) = X14
& ? [X18] :
( ? [X19] :
( app(cons(X18,nil),X19) = X0
& lt(X16,X18)
& ssList(X19) )
& ssItem(X18) )
& ssList(X17) )
& ssItem(X16) )
| sP0(X15,X0)
| ~ strictorderedP(X0) ) )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f133]) ).
fof(f136,plain,
! [X0,X1] :
( ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X2
& ? [X6] :
( ? [X7] :
( app(cons(X6,nil),X7) = X1
& lt(X4,X6)
& ssList(X7) )
& ssItem(X6) )
& ssList(X5) )
& ssItem(X4) )
| sP0(X3,X1)
| ~ strictorderedP(X1) ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f135]) ).
fof(f137,plain,
! [X0,X1] :
( ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0
| ( app(sK3(X1,X2),cons(sK2(X1,X2),nil)) = X2
& app(cons(sK4(X1,X2),nil),sK5(X1,X2)) = X1
& lt(sK2(X1,X2),sK4(X1,X2))
& ssList(sK5(X1,X2))
& ssItem(sK4(X1,X2))
& ssList(sK3(X1,X2))
& ssItem(sK2(X1,X2)) )
| sP0(X3,X1)
| ~ strictorderedP(X1) ) )
| ~ sP1(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X4,sK2(X1,X2)),skolemize(X5,sK3(X1,X2)),skolemize(X6,sK4(X1,X2)),skolemize(X7,sK5(X1,X2))],[f136]) ).
fof(f138,plain,
! [X15,X0] :
( ? [X20] :
( ? [X21] :
( app(cons(X20,nil),X21) = X15
& ? [X22] :
( ? [X23] :
( app(X23,cons(X22,nil)) = X0
& lt(X22,X20)
& ssList(X23) )
& ssItem(X22) )
& ssList(X21) )
& ssItem(X20) )
| ~ sP0(X15,X0) ),
inference(nnf_transformation,[],[f132]) ).
fof(f139,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( app(cons(X2,nil),X3) = X0
& ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X1
& lt(X4,X2)
& ssList(X5) )
& ssItem(X4) )
& ssList(X3) )
& ssItem(X2) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f138]) ).
fof(f140,plain,
! [X0,X1] :
( ( app(cons(sK6(X0,X1),nil),sK7(X0,X1)) = X0
& app(sK9(X0,X1),cons(sK8(X0,X1),nil)) = X1
& lt(sK8(X0,X1),sK6(X0,X1))
& ssList(sK9(X0,X1))
& ssItem(sK8(X0,X1))
& ssList(sK7(X0,X1))
& ssItem(sK6(X0,X1)) )
| ~ sP0(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9]),skolemize(X2,sK6(X0,X1)),skolemize(X3,sK7(X0,X1)),skolemize(X4,sK8(X0,X1)),skolemize(X5,sK9(X0,X1))],[f139]) ).
fof(f141,plain,
( sK11 = sK13
& sK10 = sK12
& sK13 = app(app(sK14,sK12),sK15)
& strictorderedP(sK12)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != sK14
| ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != sK12
| ~ lt(X6,X8) ) ) ) )
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(cons(X10,nil),X11) != sK15
| ! [X12] :
( ~ ssItem(X12)
| ! [X13] :
( ~ ssList(X13)
| app(X13,cons(X12,nil)) != sK12
| ~ lt(X12,X10) ) ) ) )
& ssList(sK15)
& ssList(sK14)
& ( nil = sK13
| nil != sK12 )
& ( sP1(sK11,sK10)
| ( nil = sK10
& nil != sK11 ) )
& ssList(sK13)
& ssList(sK12)
& ssList(sK11)
& ssList(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13,sK14,sK15]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12),skolemize(X3,sK13),skolemize(X4,sK14),skolemize(X5,sK15)],[f134]) ).
fof(f144,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X1
| nil != X0 )
& ( ( nil = X1
& nil = X0 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f108]) ).
fof(f145,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X1
| nil != X0 )
& ( ( nil = X1
& nil = X0 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f144]) ).
fof(f153,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,X1),X3) != X0
| ssItem(sK2(X1,X2))
| sP0(X3,X1)
| ~ strictorderedP(X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
fof(f154,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,X1),X3) != X0
| ssList(sK3(X1,X2))
| sP0(X3,X1)
| ~ strictorderedP(X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
fof(f155,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,X1),X3) != X0
| ssItem(sK4(X1,X2))
| sP0(X3,X1)
| ~ strictorderedP(X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
fof(f156,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,X1),X3) != X0
| ssList(sK5(X1,X2))
| sP0(X3,X1)
| ~ strictorderedP(X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
fof(f157,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,X1),X3) != X0
| lt(sK2(X1,X2),sK4(X1,X2))
| sP0(X3,X1)
| ~ strictorderedP(X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
fof(f158,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,X1),X3) != X0
| app(cons(sK4(X1,X2),nil),sK5(X1,X2)) = X1
| sP0(X3,X1)
| ~ strictorderedP(X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
fof(f159,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,X1),X3) != X0
| app(sK3(X1,X2),cons(sK2(X1,X2),nil)) = X2
| sP0(X3,X1)
| ~ strictorderedP(X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
fof(f160,plain,
! [X0,X1] :
( ssItem(sK6(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
fof(f161,plain,
! [X0,X1] :
( ssList(sK7(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
fof(f162,plain,
! [X0,X1] :
( ssItem(sK8(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
fof(f163,plain,
! [X0,X1] :
( ssList(sK9(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
fof(f164,plain,
! [X0,X1] :
( lt(sK8(X0,X1),sK6(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
fof(f165,plain,
! [X0,X1] :
( app(sK9(X0,X1),cons(sK8(X0,X1),nil)) = X1
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
fof(f166,plain,
! [X0,X1] :
( app(cons(sK6(X0,X1),nil),sK7(X0,X1)) = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
fof(f167,plain,
ssList(sK10),
inference(cnf_transformation,[],[f141]) ).
fof(f171,plain,
( sP1(sK11,sK10)
| nil != sK11 ),
inference(cnf_transformation,[],[f141]) ).
fof(f172,plain,
( sP1(sK11,sK10)
| nil = sK10 ),
inference(cnf_transformation,[],[f141]) ).
fof(f173,plain,
( nil = sK13
| nil != sK12 ),
inference(cnf_transformation,[],[f141]) ).
fof(f174,plain,
ssList(sK14),
inference(cnf_transformation,[],[f141]) ).
fof(f175,plain,
ssList(sK15),
inference(cnf_transformation,[],[f141]) ).
fof(f176,plain,
! [X10,X11,X12,X13] :
( ~ ssItem(X10)
| ~ ssList(X11)
| app(cons(X10,nil),X11) != sK15
| ~ ssItem(X12)
| ~ ssList(X13)
| app(X13,cons(X12,nil)) != sK12
| ~ lt(X12,X10) ),
inference(cnf_transformation,[],[f141]) ).
fof(f177,plain,
! [X8,X6,X9,X7] :
( ~ ssItem(X6)
| ~ ssList(X7)
| app(X7,cons(X6,nil)) != sK14
| ~ ssItem(X8)
| ~ ssList(X9)
| app(cons(X8,nil),X9) != sK12
| ~ lt(X6,X8) ),
inference(cnf_transformation,[],[f141]) ).
fof(f178,plain,
strictorderedP(sK12),
inference(cnf_transformation,[],[f141]) ).
fof(f179,plain,
sK13 = app(app(sK14,sK12),sK15),
inference(cnf_transformation,[],[f141]) ).
fof(f180,plain,
sK10 = sK12,
inference(cnf_transformation,[],[f141]) ).
fof(f181,plain,
sK11 = sK13,
inference(cnf_transformation,[],[f141]) ).
fof(f194,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f195,plain,
! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f196,plain,
! [X0,X1] :
( nil = app(X0,X1)
| nil != X1
| nil != X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f203,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f228,plain,
( sP1(sK13,sK12)
| nil = sK12 ),
inference(definition_unfolding,[],[f172,f181,f180,f180]) ).
fof(f229,plain,
( sP1(sK13,sK12)
| nil != sK13 ),
inference(definition_unfolding,[],[f171,f181,f180,f181]) ).
fof(f231,plain,
ssList(sK12),
inference(definition_unfolding,[],[f167,f180]) ).
fof(f232,definition,
~ sP25(sK14),
introduced(definition,[new_symbols(definition,[sP25])],[inequality_splitting_name_introduction]) ).
fof(f233,definition,
~ sP26(sK12),
introduced(definition,[new_symbols(definition,[sP26])],[inequality_splitting_name_introduction]) ).
fof(f234,plain,
! [X8,X6,X9,X7] :
( ~ ssItem(X6)
| ~ ssList(X7)
| sP25(app(X7,cons(X6,nil)))
| ~ ssItem(X8)
| ~ ssList(X9)
| sP26(app(cons(X8,nil),X9))
| ~ lt(X6,X8) ),
inference(inequality_splitting,[],[f177,f233,f232]) ).
fof(f235,definition,
~ sP27(sK15),
introduced(definition,[new_symbols(definition,[sP27])],[inequality_splitting_name_introduction]) ).
fof(f236,definition,
~ sP28(sK12),
introduced(definition,[new_symbols(definition,[sP28])],[inequality_splitting_name_introduction]) ).
fof(f237,plain,
! [X10,X11,X12,X13] :
( ~ ssItem(X10)
| ~ ssList(X11)
| sP27(app(cons(X10,nil),X11))
| ~ ssItem(X12)
| ~ ssList(X13)
| sP28(app(X13,cons(X12,nil)))
| ~ lt(X12,X10) ),
inference(inequality_splitting,[],[f176,f236,f235]) ).
fof(f238,definition,
~ sP29(nil),
introduced(definition,[new_symbols(definition,[sP29])],[inequality_splitting_name_introduction]) ).
fof(f239,plain,
( nil = sK13
| sP29(sK12) ),
inference(inequality_splitting,[],[f173,f238]) ).
fof(f240,definition,
~ sP30(nil),
introduced(definition,[new_symbols(definition,[sP30])],[inequality_splitting_name_introduction]) ).
fof(f241,plain,
( sP1(sK13,sK12)
| sP30(sK13) ),
inference(inequality_splitting,[],[f229,f240]) ).
fof(f246,definition,
~ sP33(nil),
introduced(definition,[new_symbols(definition,[sP33])],[inequality_splitting_name_introduction]) ).
fof(f247,definition,
~ sP34(nil),
introduced(definition,[new_symbols(definition,[sP34])],[inequality_splitting_name_introduction]) ).
fof(f248,plain,
! [X0,X1] :
( nil = app(X0,X1)
| sP33(X1)
| sP34(X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(inequality_splitting,[],[f196,f247,f246]) ).
fof(f249,definition,
~ sP35(nil),
introduced(definition,[new_symbols(definition,[sP35])],[inequality_splitting_name_introduction]) ).
fof(f250,plain,
! [X0,X1] :
( sP35(app(X0,X1))
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(inequality_splitting,[],[f195,f249]) ).
fof(f251,definition,
~ sP36(nil),
introduced(definition,[new_symbols(definition,[sP36])],[inequality_splitting_name_introduction]) ).
fof(f252,plain,
! [X0,X1] :
( sP36(app(X0,X1))
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(inequality_splitting,[],[f194,f251]) ).
fof(f257,plain,
! [X2,X3,X1] :
( app(sK3(X1,X2),cons(sK2(X1,X2),nil)) = X2
| ~ ssList(X3)
| ~ ssList(X2)
| sP0(X3,X1)
| ~ strictorderedP(X1)
| ~ sP1(app(app(X2,X1),X3),X1) ),
inference(equality_resolution,[],[f159]) ).
fof(f258,plain,
! [X2,X3,X1] :
( app(cons(sK4(X1,X2),nil),sK5(X1,X2)) = X1
| ~ ssList(X3)
| ~ ssList(X2)
| sP0(X3,X1)
| ~ strictorderedP(X1)
| ~ sP1(app(app(X2,X1),X3),X1) ),
inference(equality_resolution,[],[f158]) ).
fof(f259,plain,
! [X2,X3,X1] :
( ~ sP1(app(app(X2,X1),X3),X1)
| ~ ssList(X3)
| lt(sK2(X1,X2),sK4(X1,X2))
| sP0(X3,X1)
| ~ strictorderedP(X1)
| ~ ssList(X2) ),
inference(equality_resolution,[],[f157]) ).
fof(f260,plain,
! [X2,X3,X1] :
( ~ sP1(app(app(X2,X1),X3),X1)
| ~ ssList(X3)
| ssList(sK5(X1,X2))
| sP0(X3,X1)
| ~ strictorderedP(X1)
| ~ ssList(X2) ),
inference(equality_resolution,[],[f156]) ).
fof(f261,plain,
! [X2,X3,X1] :
( ~ sP1(app(app(X2,X1),X3),X1)
| ~ ssList(X3)
| ssItem(sK4(X1,X2))
| sP0(X3,X1)
| ~ strictorderedP(X1)
| ~ ssList(X2) ),
inference(equality_resolution,[],[f155]) ).
fof(f262,plain,
! [X2,X3,X1] :
( ~ sP1(app(app(X2,X1),X3),X1)
| ~ ssList(X3)
| ssList(sK3(X1,X2))
| sP0(X3,X1)
| ~ strictorderedP(X1)
| ~ ssList(X2) ),
inference(equality_resolution,[],[f154]) ).
fof(f263,plain,
! [X2,X3,X1] :
( ~ sP1(app(app(X2,X1),X3),X1)
| ~ ssList(X3)
| ssItem(sK2(X1,X2))
| sP0(X3,X1)
| ~ strictorderedP(X1)
| ~ ssList(X2) ),
inference(equality_resolution,[],[f153]) ).
fof(f266,plain,
! [X8,X9] :
( sP26(app(cons(X8,nil),X9))
| ~ ssList(X9)
| sP39(X8) ),
inference(cnf_transformation,[],[f266_D]) ).
fof(f266_D,definition,
! [X8] :
( ! [X9] :
( sP26(app(cons(X8,nil),X9))
| ~ ssList(X9) )
<=> ~ sP39(X8) ),
introduced(definition,[new_symbols(definition,[sP39])],[general_splitting_component_introduction]) ).
fof(f267,plain,
! [X8,X6,X7] :
( ~ ssItem(X6)
| ~ ssList(X7)
| sP25(app(X7,cons(X6,nil)))
| ~ ssItem(X8)
| ~ lt(X6,X8)
| ~ sP39(X8) ),
inference(general_splitting,[],[f234,f266_D]) ).
fof(f268,plain,
! [X8,X6] :
( ~ lt(X6,X8)
| ~ ssItem(X8)
| ~ sP39(X8)
| sP40(X6) ),
inference(cnf_transformation,[],[f268_D]) ).
fof(f268_D,definition,
! [X6] :
( ! [X8] :
( ~ lt(X6,X8)
| ~ ssItem(X8)
| ~ sP39(X8) )
<=> ~ sP40(X6) ),
introduced(definition,[new_symbols(definition,[sP40])],[general_splitting_component_introduction]) ).
fof(f269,plain,
! [X6,X7] :
( sP25(app(X7,cons(X6,nil)))
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ sP40(X6) ),
inference(general_splitting,[],[f267,f268_D]) ).
fof(f270,plain,
! [X10,X11] :
( sP27(app(cons(X10,nil),X11))
| ~ ssList(X11)
| sP41(X10) ),
inference(cnf_transformation,[],[f270_D]) ).
fof(f270_D,definition,
! [X10] :
( ! [X11] :
( sP27(app(cons(X10,nil),X11))
| ~ ssList(X11) )
<=> ~ sP41(X10) ),
introduced(definition,[new_symbols(definition,[sP41])],[general_splitting_component_introduction]) ).
fof(f271,plain,
! [X10,X12,X13] :
( ~ ssItem(X10)
| ~ ssItem(X12)
| ~ ssList(X13)
| sP28(app(X13,cons(X12,nil)))
| ~ lt(X12,X10)
| ~ sP41(X10) ),
inference(general_splitting,[],[f237,f270_D]) ).
fof(f272,plain,
! [X10,X12] :
( ~ lt(X12,X10)
| ~ ssItem(X10)
| ~ sP41(X10)
| sP42(X12) ),
inference(cnf_transformation,[],[f272_D]) ).
fof(f272_D,definition,
! [X12] :
( ! [X10] :
( ~ lt(X12,X10)
| ~ ssItem(X10)
| ~ sP41(X10) )
<=> ~ sP42(X12) ),
introduced(definition,[new_symbols(definition,[sP42])],[general_splitting_component_introduction]) ).
fof(f273,plain,
! [X12,X13] :
( sP28(app(X13,cons(X12,nil)))
| ~ ssList(X13)
| ~ ssItem(X12)
| ~ sP42(X12) ),
inference(general_splitting,[],[f271,f272_D]) ).
fof(f276,definition,
( spl43_1
<=> sP30(sK13) ),
introduced(definition,[new_symbols(definition,[spl43_1])],[avatar_definition]) ).
fof(f278,plain,
( sP30(sK13)
| ~ spl43_1 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f280,definition,
( spl43_2
<=> sP1(sK13,sK12) ),
introduced(definition,[new_symbols(definition,[spl43_2])],[avatar_definition]) ).
fof(f282,plain,
( sP1(sK13,sK12)
| ~ spl43_2 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f283,plain,
( spl43_1
| spl43_2 ),
inference(avatar_split_clause,[],[f241,f280,f276]) ).
fof(f285,definition,
( spl43_3
<=> nil = sK12 ),
introduced(definition,[new_symbols(definition,[spl43_3])],[avatar_definition]) ).
fof(f287,plain,
( nil = sK12
| ~ spl43_3 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f288,plain,
( spl43_3
| spl43_2 ),
inference(avatar_split_clause,[],[f228,f280,f285]) ).
fof(f290,definition,
( spl43_4
<=> sP29(sK12) ),
introduced(definition,[new_symbols(definition,[spl43_4])],[avatar_definition]) ).
fof(f292,plain,
( sP29(sK12)
| ~ spl43_4 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f294,definition,
( spl43_5
<=> nil = sK13 ),
introduced(definition,[new_symbols(definition,[spl43_5])],[avatar_definition]) ).
fof(f296,plain,
( nil = sK13
| ~ spl43_5 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f297,plain,
( spl43_4
| spl43_5 ),
inference(avatar_split_clause,[],[f239,f294,f290]) ).
fof(f299,plain,
! [X0,X1] :
( ~ sP30(app(X0,X1))
| sP33(X1)
| sP34(X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(superposition,[],[f240,f248]) ).
fof(f306,plain,
( ~ sP1(sK13,sK12)
| ~ ssList(sK15)
| ssItem(sK4(sK12,sK14))
| sP0(sK15,sK12)
| ~ strictorderedP(sK12)
| ~ ssList(sK14) ),
inference(superposition,[],[f261,f179]) ).
fof(f308,plain,
( ~ sP1(sK13,sK12)
| ~ ssList(sK15)
| lt(sK2(sK12,sK14),sK4(sK12,sK14))
| sP0(sK15,sK12)
| ~ strictorderedP(sK12)
| ~ ssList(sK14) ),
inference(superposition,[],[f259,f179]) ).
fof(f316,plain,
( sP35(sK13)
| nil = sK15
| ~ ssList(sK15)
| ~ ssList(app(sK14,sK12)) ),
inference(superposition,[],[f250,f179]) ).
fof(f317,plain,
( sP36(sK13)
| nil = app(sK14,sK12)
| ~ ssList(sK15)
| ~ ssList(app(sK14,sK12)) ),
inference(superposition,[],[f252,f179]) ).
fof(f324,definition,
( spl43_6
<=> ssList(app(sK14,sK12)) ),
introduced(definition,[new_symbols(definition,[spl43_6])],[avatar_definition]) ).
fof(f325,plain,
( ssList(app(sK14,sK12))
| ~ spl43_6 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f326,plain,
( ~ ssList(app(sK14,sK12))
| spl43_6 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f359,plain,
( sP36(sK13)
| nil = app(sK14,sK12)
| ~ ssList(app(sK14,sK12)) ),
inference(forward_subsumption_resolution,[],[f317,f175]) ).
fof(f360,plain,
( sP35(sK13)
| nil = sK15
| ~ ssList(app(sK14,sK12)) ),
inference(forward_subsumption_resolution,[],[f316,f175]) ).
fof(f367,plain,
( ~ ssList(sK15)
| lt(sK2(sK12,sK14),sK4(sK12,sK14))
| sP0(sK15,sK12)
| ~ strictorderedP(sK12)
| ~ ssList(sK14)
| ~ spl43_2 ),
inference(forward_subsumption_resolution,[],[f308,f282]) ).
fof(f369,plain,
( ~ ssList(sK15)
| ssItem(sK4(sK12,sK14))
| sP0(sK15,sK12)
| ~ strictorderedP(sK12)
| ~ ssList(sK14)
| ~ spl43_2 ),
inference(forward_subsumption_resolution,[],[f306,f282]) ).
fof(f377,definition,
( spl43_14
<=> nil = app(sK14,sK12) ),
introduced(definition,[new_symbols(definition,[spl43_14])],[avatar_definition]) ).
fof(f379,plain,
( nil = app(sK14,sK12)
| ~ spl43_14 ),
inference(avatar_component_clause,[],[f377]) ).
fof(f381,definition,
( spl43_15
<=> sP36(sK13) ),
introduced(definition,[new_symbols(definition,[spl43_15])],[avatar_definition]) ).
fof(f383,plain,
( sP36(sK13)
| ~ spl43_15 ),
inference(avatar_component_clause,[],[f381]) ).
fof(f384,plain,
( ~ spl43_6
| spl43_14
| spl43_15 ),
inference(avatar_split_clause,[],[f359,f381,f377,f324]) ).
fof(f386,definition,
( spl43_16
<=> nil = sK15 ),
introduced(definition,[new_symbols(definition,[spl43_16])],[avatar_definition]) ).
fof(f388,plain,
( nil = sK15
| ~ spl43_16 ),
inference(avatar_component_clause,[],[f386]) ).
fof(f390,definition,
( spl43_17
<=> sP35(sK13) ),
introduced(definition,[new_symbols(definition,[spl43_17])],[avatar_definition]) ).
fof(f392,plain,
( sP35(sK13)
| ~ spl43_17 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f393,plain,
( ~ spl43_6
| spl43_16
| spl43_17 ),
inference(avatar_split_clause,[],[f360,f390,f386,f324]) ).
fof(f395,definition,
( spl43_18
<=> sP34(app(sK14,sK12)) ),
introduced(definition,[new_symbols(definition,[spl43_18])],[avatar_definition]) ).
fof(f396,plain,
( ~ sP34(app(sK14,sK12))
| spl43_18 ),
inference(avatar_component_clause,[],[f395]) ).
fof(f397,plain,
( sP34(app(sK14,sK12))
| ~ spl43_18 ),
inference(avatar_component_clause,[],[f395]) ).
fof(f417,plain,
( lt(sK2(sK12,sK14),sK4(sK12,sK14))
| sP0(sK15,sK12)
| ~ strictorderedP(sK12)
| ~ ssList(sK14)
| ~ spl43_2 ),
inference(forward_subsumption_resolution,[],[f367,f175]) ).
fof(f419,plain,
( ssItem(sK4(sK12,sK14))
| sP0(sK15,sK12)
| ~ strictorderedP(sK12)
| ~ ssList(sK14)
| ~ spl43_2 ),
inference(forward_subsumption_resolution,[],[f369,f175]) ).
fof(f426,plain,
( lt(sK2(sK12,sK14),sK4(sK12,sK14))
| sP0(sK15,sK12)
| ~ ssList(sK14)
| ~ spl43_2 ),
inference(forward_subsumption_resolution,[],[f417,f178]) ).
fof(f428,plain,
( ssItem(sK4(sK12,sK14))
| sP0(sK15,sK12)
| ~ ssList(sK14)
| ~ spl43_2 ),
inference(forward_subsumption_resolution,[],[f419,f178]) ).
fof(f446,plain,
( lt(sK2(sK12,sK14),sK4(sK12,sK14))
| sP0(sK15,sK12)
| ~ spl43_2 ),
inference(forward_subsumption_resolution,[],[f426,f174]) ).
fof(f448,plain,
( ssItem(sK4(sK12,sK14))
| sP0(sK15,sK12)
| ~ spl43_2 ),
inference(forward_subsumption_resolution,[],[f428,f174]) ).
fof(f452,definition,
( spl43_26
<=> sP0(sK15,sK12) ),
introduced(definition,[new_symbols(definition,[spl43_26])],[avatar_definition]) ).
fof(f453,plain,
( ~ sP0(sK15,sK12)
| spl43_26 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f454,plain,
( sP0(sK15,sK12)
| ~ spl43_26 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f456,definition,
( spl43_27
<=> lt(sK2(sK12,sK14),sK4(sK12,sK14)) ),
introduced(definition,[new_symbols(definition,[spl43_27])],[avatar_definition]) ).
fof(f458,plain,
( lt(sK2(sK12,sK14),sK4(sK12,sK14))
| ~ spl43_27 ),
inference(avatar_component_clause,[],[f456]) ).
fof(f459,plain,
( spl43_26
| spl43_27
| ~ spl43_2 ),
inference(avatar_split_clause,[],[f446,f280,f456,f452]) ).
fof(f466,definition,
( spl43_29
<=> ssItem(sK4(sK12,sK14)) ),
introduced(definition,[new_symbols(definition,[spl43_29])],[avatar_definition]) ).
fof(f468,plain,
( ssItem(sK4(sK12,sK14))
| ~ spl43_29 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f469,plain,
( spl43_26
| spl43_29
| ~ spl43_2 ),
inference(avatar_split_clause,[],[f448,f280,f466,f452]) ).
fof(f482,plain,
! [X0,X1] :
( ~ ssItem(sK6(X0,X1))
| ~ sP41(sK6(X0,X1))
| sP42(sK8(X0,X1))
| ~ sP0(X0,X1) ),
inference(resolution,[],[f272,f164]) ).
fof(f483,plain,
! [X0,X1] :
( ~ sP41(sK6(X0,X1))
| sP42(sK8(X0,X1))
| ~ sP0(X0,X1) ),
inference(forward_subsumption_resolution,[],[f482,f160]) ).
fof(f484,plain,
( ~ ssList(sK12)
| ~ ssList(sK14)
| spl43_6 ),
inference(resolution,[],[f326,f203]) ).
fof(f486,plain,
( ~ ssList(sK14)
| spl43_6 ),
inference(forward_subsumption_resolution,[],[f484,f231]) ).
fof(f487,plain,
( $false
| spl43_6 ),
inference(forward_subsumption_resolution,[],[f486,f174]) ).
fof(f488,plain,
spl43_6,
inference(avatar_contradiction_clause,[],[f487]) ).
fof(f501,plain,
! [X2,X0,X1] :
( sP26(X0)
| ~ ssList(sK5(X0,X1))
| sP39(sK4(X0,X1))
| ~ ssList(X2)
| ~ ssList(X1)
| sP0(X2,X0)
| ~ strictorderedP(X0)
| ~ sP1(app(app(X1,X0),X2),X0) ),
inference(superposition,[],[f266,f258]) ).
fof(f524,plain,
! [X2,X0,X1] :
( ~ sP1(app(app(X1,X0),X2),X0)
| sP39(sK4(X0,X1))
| ~ ssList(X2)
| ~ ssList(X1)
| sP0(X2,X0)
| ~ strictorderedP(X0)
| sP26(X0) ),
inference(forward_subsumption_resolution,[],[f501,f260]) ).
fof(f540,plain,
! [X0,X1] :
( sP27(X0)
| ~ ssList(sK7(X0,X1))
| sP41(sK6(X0,X1))
| ~ sP0(X0,X1) ),
inference(superposition,[],[f270,f166]) ).
fof(f551,plain,
! [X0,X1] :
( sP41(sK6(X0,X1))
| sP27(X0)
| ~ sP0(X0,X1) ),
inference(forward_subsumption_resolution,[],[f540,f161]) ).
fof(f557,plain,
( sP35(nil)
| ~ spl43_5
| ~ spl43_17 ),
inference(forward_demodulation,[],[f392,f296]) ).
fof(f566,plain,
( $false
| ~ spl43_5
| ~ spl43_17 ),
inference(forward_subsumption_resolution,[],[f557,f249]) ).
fof(f567,plain,
( ~ spl43_5
| ~ spl43_17 ),
inference(avatar_contradiction_clause,[],[f566]) ).
fof(f569,plain,
( sP34(nil)
| ~ spl43_14
| ~ spl43_18 ),
inference(forward_demodulation,[],[f397,f379]) ).
fof(f572,plain,
( $false
| ~ spl43_14
| ~ spl43_18 ),
inference(forward_subsumption_resolution,[],[f569,f247]) ).
fof(f573,plain,
( ~ spl43_14
| ~ spl43_18 ),
inference(avatar_contradiction_clause,[],[f572]) ).
fof(f580,plain,
! [X2,X0,X1] :
( sP25(X0)
| ~ ssList(sK3(X1,X0))
| ~ ssItem(sK2(X1,X0))
| ~ sP40(sK2(X1,X0))
| ~ ssList(X2)
| ~ ssList(X0)
| sP0(X2,X1)
| ~ strictorderedP(X1)
| ~ sP1(app(app(X0,X1),X2),X1) ),
inference(superposition,[],[f269,f257]) ).
fof(f584,plain,
! [X2,X0,X1] :
( sP25(X0)
| ~ ssItem(sK2(X1,X0))
| ~ sP40(sK2(X1,X0))
| ~ ssList(X2)
| ~ ssList(X0)
| sP0(X2,X1)
| ~ strictorderedP(X1)
| ~ sP1(app(app(X0,X1),X2),X1) ),
inference(forward_subsumption_resolution,[],[f580,f262]) ).
fof(f589,plain,
! [X2,X0,X1] :
( ~ sP1(app(app(X0,X1),X2),X1)
| ~ sP40(sK2(X1,X0))
| ~ ssList(X2)
| ~ ssList(X0)
| sP0(X2,X1)
| ~ strictorderedP(X1)
| sP25(X0) ),
inference(forward_subsumption_resolution,[],[f584,f263]) ).
fof(f597,plain,
! [X0,X1] :
( sP28(X0)
| ~ ssList(sK9(X1,X0))
| ~ ssItem(sK8(X1,X0))
| ~ sP42(sK8(X1,X0))
| ~ sP0(X1,X0) ),
inference(superposition,[],[f273,f165]) ).
fof(f599,plain,
! [X0,X1] :
( sP28(X0)
| ~ ssItem(sK8(X1,X0))
| ~ sP42(sK8(X1,X0))
| ~ sP0(X1,X0) ),
inference(forward_subsumption_resolution,[],[f597,f163]) ).
fof(f604,plain,
! [X0,X1] :
( ~ sP42(sK8(X1,X0))
| sP28(X0)
| ~ sP0(X1,X0) ),
inference(forward_subsumption_resolution,[],[f599,f162]) ).
fof(f805,plain,
! [X0,X1] :
( sP42(sK8(X0,X1))
| ~ sP0(X0,X1)
| sP27(X0)
| ~ sP0(X0,X1) ),
inference(resolution,[],[f483,f551]) ).
fof(f806,plain,
! [X0,X1] :
( sP42(sK8(X0,X1))
| ~ sP0(X0,X1)
| sP27(X0) ),
inference(duplicate_literal_removal,[],[f805]) ).
fof(f855,plain,
( sP36(nil)
| ~ spl43_5
| ~ spl43_15 ),
inference(superposition,[],[f383,f296]) ).
fof(f857,plain,
( $false
| ~ spl43_5
| ~ spl43_15 ),
inference(forward_subsumption_resolution,[],[f855,f251]) ).
fof(f858,plain,
( ~ spl43_5
| ~ spl43_15 ),
inference(avatar_contradiction_clause,[],[f857]) ).
fof(f992,plain,
( ~ sP30(sK13)
| sP33(sK15)
| sP34(app(sK14,sK12))
| ~ ssList(sK15)
| ~ ssList(app(sK14,sK12)) ),
inference(superposition,[],[f299,f179]) ).
fof(f1075,plain,
( ~ ssItem(sK4(sK12,sK14))
| ~ sP39(sK4(sK12,sK14))
| sP40(sK2(sK12,sK14))
| ~ spl43_27 ),
inference(resolution,[],[f458,f268]) ).
fof(f1084,plain,
( ~ sP39(sK4(sK12,sK14))
| sP40(sK2(sK12,sK14))
| ~ spl43_27
| ~ spl43_29 ),
inference(forward_subsumption_resolution,[],[f1075,f468]) ).
fof(f1091,definition,
( spl43_68
<=> sP40(sK2(sK12,sK14)) ),
introduced(definition,[new_symbols(definition,[spl43_68])],[avatar_definition]) ).
fof(f1093,plain,
( sP40(sK2(sK12,sK14))
| ~ spl43_68 ),
inference(avatar_component_clause,[],[f1091]) ).
fof(f1095,definition,
( spl43_69
<=> sP39(sK4(sK12,sK14)) ),
introduced(definition,[new_symbols(definition,[spl43_69])],[avatar_definition]) ).
fof(f1097,plain,
( ~ sP39(sK4(sK12,sK14))
| spl43_69 ),
inference(avatar_component_clause,[],[f1095]) ).
fof(f1098,plain,
( spl43_68
| ~ spl43_69
| ~ spl43_27
| ~ spl43_29 ),
inference(avatar_split_clause,[],[f1084,f466,f456,f1095,f1091]) ).
fof(f1472,plain,
( ~ sP1(sK13,sK12)
| sP39(sK4(sK12,sK14))
| ~ ssList(sK15)
| ~ ssList(sK14)
| sP0(sK15,sK12)
| ~ strictorderedP(sK12)
| sP26(sK12) ),
inference(superposition,[],[f524,f179]) ).
fof(f1480,plain,
( sP39(sK4(sK12,sK14))
| ~ ssList(sK15)
| ~ ssList(sK14)
| sP0(sK15,sK12)
| ~ strictorderedP(sK12)
| sP26(sK12)
| ~ spl43_2 ),
inference(forward_subsumption_resolution,[],[f1472,f282]) ).
fof(f1490,plain,
( ~ ssList(sK15)
| ~ ssList(sK14)
| sP0(sK15,sK12)
| ~ strictorderedP(sK12)
| sP26(sK12)
| ~ spl43_2
| spl43_69 ),
inference(forward_subsumption_resolution,[],[f1480,f1097]) ).
fof(f1496,plain,
( ~ ssList(sK14)
| sP0(sK15,sK12)
| ~ strictorderedP(sK12)
| sP26(sK12)
| ~ spl43_2
| spl43_69 ),
inference(forward_subsumption_resolution,[],[f1490,f175]) ).
fof(f1498,plain,
( sP0(sK15,sK12)
| ~ strictorderedP(sK12)
| sP26(sK12)
| ~ spl43_2
| spl43_69 ),
inference(forward_subsumption_resolution,[],[f1496,f174]) ).
fof(f1500,plain,
( ~ strictorderedP(sK12)
| sP26(sK12)
| ~ spl43_2
| spl43_26
| spl43_69 ),
inference(forward_subsumption_resolution,[],[f1498,f453]) ).
fof(f1501,plain,
( sP26(sK12)
| ~ spl43_2
| spl43_26
| spl43_69 ),
inference(forward_subsumption_resolution,[],[f1500,f178]) ).
fof(f1502,plain,
( $false
| ~ spl43_2
| spl43_26
| spl43_69 ),
inference(forward_subsumption_resolution,[],[f1501,f233]) ).
fof(f1503,plain,
( ~ spl43_2
| spl43_26
| spl43_69 ),
inference(avatar_contradiction_clause,[],[f1502]) ).
fof(f1514,plain,
( sP29(nil)
| ~ spl43_3
| ~ spl43_4 ),
inference(superposition,[],[f292,f287]) ).
fof(f1541,plain,
( $false
| ~ spl43_3
| ~ spl43_4 ),
inference(forward_subsumption_resolution,[],[f1514,f238]) ).
fof(f1542,plain,
( ~ spl43_3
| ~ spl43_4 ),
inference(avatar_contradiction_clause,[],[f1541]) ).
fof(f1642,plain,
( ~ sP1(sK13,sK12)
| ~ sP40(sK2(sK12,sK14))
| ~ ssList(sK15)
| ~ ssList(sK14)
| sP0(sK15,sK12)
| ~ strictorderedP(sK12)
| sP25(sK14) ),
inference(superposition,[],[f589,f179]) ).
fof(f1705,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sP27(X0)
| sP28(X1)
| ~ sP0(X0,X1) ),
inference(resolution,[],[f806,f604]) ).
fof(f1706,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sP27(X0)
| sP28(X1) ),
inference(duplicate_literal_removal,[],[f1705]) ).
fof(f1749,plain,
( sP27(sK15)
| sP28(sK12)
| ~ spl43_26 ),
inference(resolution,[],[f1706,f454]) ).
fof(f1750,plain,
( sP28(sK12)
| ~ spl43_26 ),
inference(forward_subsumption_resolution,[],[f1749,f235]) ).
fof(f1751,plain,
( $false
| ~ spl43_26 ),
inference(forward_subsumption_resolution,[],[f1750,f236]) ).
fof(f1752,plain,
~ spl43_26,
inference(avatar_contradiction_clause,[],[f1751]) ).
fof(f1757,plain,
( ~ sP40(sK2(sK12,sK14))
| ~ ssList(sK15)
| ~ ssList(sK14)
| sP0(sK15,sK12)
| ~ strictorderedP(sK12)
| sP25(sK14)
| ~ spl43_2 ),
inference(forward_subsumption_resolution,[],[f1642,f282]) ).
fof(f1763,plain,
( ~ ssList(sK15)
| ~ ssList(sK14)
| sP0(sK15,sK12)
| ~ strictorderedP(sK12)
| sP25(sK14)
| ~ spl43_2
| ~ spl43_68 ),
inference(forward_subsumption_resolution,[],[f1757,f1093]) ).
fof(f1776,plain,
( ~ ssList(sK14)
| sP0(sK15,sK12)
| ~ strictorderedP(sK12)
| sP25(sK14)
| ~ spl43_2
| ~ spl43_68 ),
inference(forward_subsumption_resolution,[],[f1763,f175]) ).
fof(f1785,plain,
( sP0(sK15,sK12)
| ~ strictorderedP(sK12)
| sP25(sK14)
| ~ spl43_2
| ~ spl43_68 ),
inference(forward_subsumption_resolution,[],[f1776,f174]) ).
fof(f1789,plain,
( ~ strictorderedP(sK12)
| sP25(sK14)
| ~ spl43_2
| spl43_26
| ~ spl43_68 ),
inference(forward_subsumption_resolution,[],[f1785,f453]) ).
fof(f1792,plain,
( sP25(sK14)
| ~ spl43_2
| spl43_26
| ~ spl43_68 ),
inference(forward_subsumption_resolution,[],[f1789,f178]) ).
fof(f1795,plain,
( $false
| ~ spl43_2
| spl43_26
| ~ spl43_68 ),
inference(forward_subsumption_resolution,[],[f1792,f232]) ).
fof(f1796,plain,
( ~ spl43_2
| spl43_26
| ~ spl43_68 ),
inference(avatar_contradiction_clause,[],[f1795]) ).
fof(f1839,plain,
( sP33(sK15)
| sP34(app(sK14,sK12))
| ~ ssList(sK15)
| ~ ssList(app(sK14,sK12))
| ~ spl43_1 ),
inference(forward_subsumption_resolution,[],[f992,f278]) ).
fof(f1876,plain,
( sP33(sK15)
| ~ ssList(sK15)
| ~ ssList(app(sK14,sK12))
| ~ spl43_1
| spl43_18 ),
inference(forward_subsumption_resolution,[],[f1839,f396]) ).
fof(f1901,plain,
( sP33(sK15)
| ~ ssList(app(sK14,sK12))
| ~ spl43_1
| spl43_18 ),
inference(forward_subsumption_resolution,[],[f1876,f175]) ).
fof(f1922,plain,
( sP33(sK15)
| ~ spl43_1
| ~ spl43_6
| spl43_18 ),
inference(forward_subsumption_resolution,[],[f1901,f325]) ).
fof(f1940,plain,
( sP33(nil)
| ~ spl43_1
| ~ spl43_6
| ~ spl43_16
| spl43_18 ),
inference(forward_demodulation,[],[f1922,f388]) ).
fof(f1951,plain,
( $false
| ~ spl43_1
| ~ spl43_6
| ~ spl43_16
| spl43_18 ),
inference(forward_subsumption_resolution,[],[f1940,f246]) ).
fof(f1952,plain,
( ~ spl43_1
| ~ spl43_6
| ~ spl43_16
| spl43_18 ),
inference(avatar_contradiction_clause,[],[f1951]) ).
cnf(s1,plain,
( spl43_1
| spl43_2 ),
inference(sat_conversion,[],[f283]) ).
cnf(s2,plain,
( spl43_2
| spl43_3 ),
inference(sat_conversion,[],[f288]) ).
cnf(s3,plain,
( spl43_4
| spl43_5 ),
inference(sat_conversion,[],[f297]) ).
cnf(s9,plain,
( ~ spl43_6
| spl43_14
| spl43_15 ),
inference(sat_conversion,[],[f384]) ).
cnf(s10,plain,
( ~ spl43_6
| spl43_16
| spl43_17 ),
inference(sat_conversion,[],[f393]) ).
cnf(s19,plain,
( ~ spl43_2
| spl43_26
| spl43_27 ),
inference(sat_conversion,[],[f459]) ).
cnf(s21,plain,
( ~ spl43_2
| spl43_26
| spl43_29 ),
inference(sat_conversion,[],[f469]) ).
cnf(s24,plain,
spl43_6,
inference(sat_conversion,[],[f488]) ).
cnf(s29,plain,
( ~ spl43_5
| ~ spl43_17 ),
inference(sat_conversion,[],[f567]) ).
cnf(s30,plain,
( ~ spl43_14
| ~ spl43_18 ),
inference(sat_conversion,[],[f573]) ).
cnf(s53,plain,
( ~ spl43_5
| ~ spl43_15 ),
inference(sat_conversion,[],[f858]) ).
cnf(s66,plain,
( ~ spl43_27
| ~ spl43_29
| spl43_68
| ~ spl43_69 ),
inference(sat_conversion,[],[f1098]) ).
cnf(s79,plain,
( ~ spl43_2
| spl43_26
| spl43_69 ),
inference(sat_conversion,[],[f1503]) ).
cnf(s83,plain,
( ~ spl43_3
| ~ spl43_4 ),
inference(sat_conversion,[],[f1542]) ).
cnf(s88,plain,
~ spl43_26,
inference(sat_conversion,[],[f1752]) ).
cnf(s94,plain,
( ~ spl43_2
| spl43_26
| ~ spl43_68 ),
inference(sat_conversion,[],[f1796]) ).
cnf(s97,plain,
( ~ spl43_1
| ~ spl43_6
| ~ spl43_16
| spl43_18 ),
inference(sat_conversion,[],[f1952]) ).
cnf(s98,plain,
( ~ spl43_2
| spl43_69 ),
inference(rat,[],[s79,s88]) ).
cnf(s109,plain,
( ~ spl43_2
| spl43_29 ),
inference(rat,[],[s21,s88]) ).
cnf(s111,plain,
( ~ spl43_2
| spl43_27 ),
inference(rat,[],[s19,s88]) ).
cnf(s117,plain,
( spl43_16
| spl43_17 ),
inference(rat,[],[s10,s24]) ).
cnf(s118,plain,
( spl43_14
| spl43_15 ),
inference(rat,[],[s9,s24]) ).
cnf(s124,plain,
~ spl43_2,
inference(rat,[],[s66,s111,s109,s98,s94,s88]) ).
cnf(s125,plain,
spl43_3,
inference(rat,[],[s2,s124]) ).
cnf(s126,plain,
spl43_1,
inference(rat,[],[s1,s124]) ).
cnf(s129,plain,
~ spl43_4,
inference(rat,[],[s83,s125]) ).
cnf(s136,plain,
spl43_5,
inference(rat,[],[s3,s129]) ).
cnf(s137,plain,
~ spl43_15,
inference(rat,[],[s53,s136]) ).
cnf(s138,plain,
~ spl43_17,
inference(rat,[],[s29,s136]) ).
cnf(s139,plain,
spl43_14,
inference(rat,[],[s118,s137]) ).
cnf(s140,plain,
spl43_16,
inference(rat,[],[s117,s138]) ).
cnf(s142,plain,
~ spl43_18,
inference(rat,[],[s30,s139]) ).
cnf(s148,plain,
$false,
inference(rat,[],[s97,s126,s24,s142,s140]) ).
fof(f1977,plain,
$false,
inference(avatar_sat_refutation,[],[s148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC344+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n011.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 09:11:30 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 3.25/1.15 % (3264660)Detected formulas, will run a generic FOF schedule.
% 3.25/1.15 % (3264669)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=685083207:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.25/1.15 % (3264669)Instruction limit reached!
% 3.25/1.15 % (3264669)------------------------------
% 3.25/1.15 % (3264669)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.15 % (3264669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.15 % (3264669)CaDiCaL version: 2.1.3
% 3.25/1.15 % (3264669)Termination reason: Instruction limit
% 3.25/1.15 % (3264669)Termination phase: Saturation
% 3.25/1.15 % (3264669)Time elapsed: 0.039 s
% 3.25/1.15 % (3264669)Peak memory usage: 88 MB
% 3.25/1.15 % (3264669)Instructions burned: 120 (million)
% 3.25/1.15 % (3264670)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1100995507:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.25/1.15 % (3264666)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=3134293851:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.25/1.15 % (3264665)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=1356455618:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.25/1.15 % (3264667)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=3937335470:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.25/1.15 % (3264668)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4237694449:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.25/1.15 % (3264671)dis-21_1_sil=8000:lcm=predicate:random_seed=2252915293: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)
% 3.25/1.15 % (3264668)First to succeed.
% 3.25/1.15 % (3264668)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3264660"
% 3.25/1.15 % (3264671)Instruction limit reached!
% 3.25/1.15 % (3264671)------------------------------
% 3.25/1.15 % (3264671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.15 % (3264671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.15 % (3264671)CaDiCaL version: 2.1.3
% 3.25/1.15 % (3264671)Termination reason: Instruction limit
% 3.25/1.15 % (3264671)Termination phase: Saturation
% 3.25/1.15 % (3264671)Time elapsed: 0.071 s
% 3.25/1.15 % (3264671)Peak memory usage: 90 MB
% 3.25/1.15 % (3264671)Instructions burned: 129 (million)
% 3.25/1.15 % (3264670)Instruction limit reached!
% 3.25/1.15 % (3264670)------------------------------
% 3.25/1.15 % (3264670)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.15 % (3264670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.15 % (3264670)CaDiCaL version: 2.1.3
% 3.25/1.15 % (3264670)Termination reason: Instruction limit
% 3.25/1.15 % (3264670)Termination phase: Saturation
% 3.25/1.15 % (3264670)Time elapsed: 0.093 s
% 3.25/1.15 % (3264670)Peak memory usage: 90 MB
% 3.25/1.15 % (3264670)Instructions burned: 140 (million)
% 3.25/1.15 % (3264673)lrs+10_1_sil=8000:sp=occurrence:random_seed=1737471487:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.25/1.15 % (3264673)Instruction limit reached!
% 3.25/1.15 % (3264673)------------------------------
% 3.25/1.15 % (3264673)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.15 % (3264673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.15 % (3264673)CaDiCaL version: 2.1.3
% 3.25/1.15 % (3264673)Termination reason: Instruction limit
% 3.25/1.15 % (3264673)Termination phase: Saturation
% 3.25/1.15 % (3264673)Time elapsed: 0.087 s
% 3.25/1.15 % (3264673)Peak memory usage: 92 MB
% 3.25/1.15 % (3264673)Instructions burned: 287 (million)
% 3.25/1.15 % (3264680)lrs+10_1_sil=32000:urr=on:br=off:random_seed=414712418:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.25/1.15 % (3264681)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1746974931:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.25/1.15 % (3264668)Refutation found. Thanks to Tanya!
% 3.25/1.15 % SZS status Theorem for theBenchmark
% 3.25/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 4.07/1.34 % (3264668)------------------------------
% 4.07/1.34 % (3264668)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.34 % (3264668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.34 % (3264668)CaDiCaL version: 2.1.3
% 4.07/1.34 % (3264668)Termination reason: Refutation
% 4.07/1.34 % (3264668)Time elapsed: 0.050 s
% 4.07/1.34 % (3264668)Peak memory usage: 90 MB
% 4.07/1.34 % (3264668)Instructions burned: 78 (million)
% 4.07/1.34 % (3264668)------------------------------
% 4.07/1.34 % (3264668)------------------------------
% 4.07/1.34 % (3264660)Success in time 0.484 s
% 4.07/1.34 % Vampire exiting
%------------------------------------------------------------------------------