%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC344+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n006.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 : Fri Sep 25 03:09:23 PM UTC 2026
% Result : Theorem 23.24s 5.43s
% Output : CNFRefutation 23.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 130 ( 13 unt; 2 def)
% Number of atoms : 854 ( 208 equ)
% Maximal formula atoms : 46 ( 6 avg)
% Number of connectives : 1114 ( 434 ~; 486 |; 166 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 353 ( 0 sgn 275 !; 78 ?; 116 :)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil = X1
| nil != X0 )
& ? [X14] :
( ? [X15] :
( strictorderedP(X0)
& ! [X20] :
( ssItem(X20)
=> ! [X21] :
( ssList(X21)
=> ( ! [X22] :
( ssItem(X22)
=> ! [X23] :
( ssList(X23)
=> ( ~ lt(X22,X20)
| app(X23,cons(X22,nil)) != X0 ) ) )
| app(cons(X20,nil),X21) != X15 ) ) )
& ! [X16] :
( ssItem(X16)
=> ! [X17] :
( ssList(X17)
=> ( ! [X18] :
( ssItem(X18)
=> ! [X19] :
( ssList(X19)
=> ( ~ lt(X16,X18)
| app(cons(X18,nil),X19) != X0 ) ) )
| app(X17,cons(X16,nil)) != X14 ) ) )
& app(app(X14,X0),X15) = X1
& ssList(X15) )
& ssList(X14) ) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( lt(X12,X10)
& app(X13,cons(X12,nil)) = X2
& ssList(X13) )
& ssItem(X12) )
& app(cons(X10,nil),X11) = X5
& ssList(X11) )
& ssItem(X10) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( lt(X6,X8)
& app(cons(X8,nil),X9) = X2
& ssList(X9) )
& ssItem(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ strictorderedP(X2)
| app(app(X4,X2),X5) != X3 ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil = X1
| nil != X0 )
& ? [X14] :
( ? [X15] :
( strictorderedP(X0)
& ! [X20] :
( ssItem(X20)
=> ! [X21] :
( ssList(X21)
=> ( ! [X22] :
( ssItem(X22)
=> ! [X23] :
( ssList(X23)
=> ( ~ lt(X22,X20)
| app(X23,cons(X22,nil)) != X0 ) ) )
| app(cons(X20,nil),X21) != X15 ) ) )
& ! [X16] :
( ssItem(X16)
=> ! [X17] :
( ssList(X17)
=> ( ! [X18] :
( ssItem(X18)
=> ! [X19] :
( ssList(X19)
=> ( ~ lt(X16,X18)
| app(cons(X18,nil),X19) != X0 ) ) )
| app(X17,cons(X16,nil)) != X14 ) ) )
& app(app(X14,X0),X15) = X1
& ssList(X15) )
& ssList(X14) ) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( lt(X12,X10)
& app(X13,cons(X12,nil)) = X2
& ssList(X13) )
& ssItem(X12) )
& app(cons(X10,nil),X11) = X5
& ssList(X11) )
& ssItem(X10) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( lt(X6,X8)
& app(cons(X8,nil),X9) = X2
& ssList(X9) )
& ssItem(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ strictorderedP(X2)
| app(app(X4,X2),X5) != X3 ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil != X1
& nil = X0 )
| ! [X14] :
( ! [X15] :
( ~ strictorderedP(X0)
| ? [X20] :
( ssItem(X20)
& ? [X21] :
( ssList(X21)
& ? [X22] :
( ssItem(X22)
& ? [X23] :
( ssList(X23)
& lt(X22,X20)
& app(X23,cons(X22,nil)) = X0 ) )
& app(cons(X20,nil),X21) = X15 ) )
| ? [X16] :
( ssItem(X16)
& ? [X17] :
( ssList(X17)
& ? [X18] :
( ssItem(X18)
& ? [X19] :
( ssList(X19)
& lt(X16,X18)
& app(cons(X18,nil),X19) = X0 ) )
& app(X17,cons(X16,nil)) = X14 ) )
| app(app(X14,X0),X15) != X1
| ~ ssList(X15) )
| ~ ssList(X14) ) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ lt(X12,X10)
| app(X13,cons(X12,nil)) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(cons(X10,nil),X11) != X5
| ~ ssList(X11) )
| ~ ssItem(X10) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ lt(X6,X8)
| app(cons(X8,nil),X9) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(X7,cons(X6,nil)) != X4
| ~ ssList(X7) )
| ~ ssItem(X6) )
& strictorderedP(X2)
& app(app(X4,X2),X5) = X3 ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil != X1
& nil = X0 )
| ! [X14] :
( ! [X15] :
( ~ strictorderedP(X0)
| ? [X20] :
( ssItem(X20)
& ? [X21] :
( ssList(X21)
& ? [X22] :
( ssItem(X22)
& ? [X23] :
( ssList(X23)
& lt(X22,X20)
& app(X23,cons(X22,nil)) = X0 ) )
& app(cons(X20,nil),X21) = X15 ) )
| ? [X16] :
( ssItem(X16)
& ? [X17] :
( ssList(X17)
& ? [X18] :
( ssItem(X18)
& ? [X19] :
( ssList(X19)
& lt(X16,X18)
& app(cons(X18,nil),X19) = X0 ) )
& app(X17,cons(X16,nil)) = X14 ) )
| app(app(X14,X0),X15) != X1
| ~ ssList(X15) )
| ~ ssList(X14) ) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ lt(X12,X10)
| app(X13,cons(X12,nil)) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(cons(X10,nil),X11) != X5
| ~ ssList(X11) )
| ~ ssItem(X10) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ lt(X6,X8)
| app(cons(X8,nil),X9) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(X7,cons(X6,nil)) != X4
| ~ ssList(X7) )
| ~ ssItem(X6) )
& strictorderedP(X2)
& app(app(X4,X2),X5) = X3 ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f158,plain,
! [X1,X0] :
( ~ sP1(X1,X0)
| ! [X14] :
( ! [X15] :
( ~ strictorderedP(X0)
| sP0(X15,X0)
| ? [X16] :
( ssItem(X16)
& ? [X17] :
( ssList(X17)
& ? [X18] :
( ssItem(X18)
& ? [X19] :
( ssList(X19)
& lt(X16,X18)
& app(cons(X18,nil),X19) = X0 ) )
& app(X17,cons(X16,nil)) = X14 ) )
| app(app(X14,X0),X15) != X1
| ~ ssList(X15) )
| ~ ssList(X14) ) ),
inference(nnf_transformation,[],[f156]) ).
fof(f159,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| ! [X2] :
( ! [X3] :
( ~ strictorderedP(X1)
| sP0(X3,X1)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& lt(X4,X6)
& app(cons(X6,nil),X7) = X1 ) )
& app(X5,cons(X4,nil)) = X2 ) )
| app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) ),
inference(rectify,[],[f158]) ).
fof(f160,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| ! [X2] :
( ! [X3] :
( ~ strictorderedP(X1)
| sP0(X3,X1)
| ( ssItem(sK2(X1,X2))
& ssList(sK3(X1,X2))
& ssItem(sK4(X1,X2))
& ssList(sK5(X1,X2))
& lt(sK2(X1,X2),sK4(X1,X2))
& app(cons(sK4(X1,X2),nil),sK5(X1,X2)) = X1
& app(sK3(X1,X2),cons(sK2(X1,X2),nil)) = X2 )
| app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) ),
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))],[f159]) ).
fof(f164,plain,
( ssList(sK10)
& ssList(sK11)
& ssList(sK12)
& ssList(sK13)
& ( ( nil != sK11
& nil = sK10 )
| sP1(sK11,sK10) )
& ( nil != sK12
| nil = sK13 )
& ssList(sK14)
& ssList(sK15)
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ lt(X12,X10)
| app(X13,cons(X12,nil)) != sK12
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(cons(X10,nil),X11) != sK15
| ~ ssList(X11) )
| ~ ssItem(X10) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ lt(X6,X8)
| app(cons(X8,nil),X9) != sK12
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(X7,cons(X6,nil)) != sK14
| ~ ssList(X7) )
| ~ ssItem(X6) )
& strictorderedP(sK12)
& sK13 = app(app(sK14,sK12),sK15)
& sK10 = sK12
& sK11 = sK13 ),
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)],[f157]) ).
fof(f178,plain,
! [X2,X3,X0,X1] :
( ~ sP1(X0,X1)
| ~ strictorderedP(X1)
| sP0(X3,X1)
| ssItem(sK2(X1,X2))
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(cnf_transformation,[],[f160]) ).
fof(f179,plain,
! [X2,X3,X0,X1] :
( ~ sP1(X0,X1)
| ~ strictorderedP(X1)
| sP0(X3,X1)
| ssList(sK3(X1,X2))
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(cnf_transformation,[],[f160]) ).
fof(f180,plain,
! [X2,X3,X0,X1] :
( ~ sP1(X0,X1)
| ~ strictorderedP(X1)
| sP0(X3,X1)
| ssItem(sK4(X1,X2))
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(cnf_transformation,[],[f160]) ).
fof(f181,plain,
! [X2,X3,X0,X1] :
( ~ sP1(X0,X1)
| ~ strictorderedP(X1)
| sP0(X3,X1)
| ssList(sK5(X1,X2))
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(cnf_transformation,[],[f160]) ).
fof(f182,plain,
! [X2,X3,X0,X1] :
( ~ sP1(X0,X1)
| ~ strictorderedP(X1)
| sP0(X3,X1)
| lt(sK2(X1,X2),sK4(X1,X2))
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(cnf_transformation,[],[f160]) ).
fof(f183,plain,
! [X2,X3,X0,X1] :
( ~ sP1(X0,X1)
| ~ strictorderedP(X1)
| sP0(X3,X1)
| app(cons(sK4(X1,X2),nil),sK5(X1,X2)) = X1
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(cnf_transformation,[],[f160]) ).
fof(f184,plain,
! [X2,X3,X0,X1] :
( ~ sP1(X0,X1)
| ~ strictorderedP(X1)
| sP0(X3,X1)
| app(sK3(X1,X2),cons(sK2(X1,X2),nil)) = X2
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(cnf_transformation,[],[f160]) ).
fof(f196,plain,
( nil != sK11
| sP1(sK11,sK10) ),
inference(cnf_transformation,[],[f164]) ).
fof(f197,plain,
( nil = sK10
| sP1(sK11,sK10) ),
inference(cnf_transformation,[],[f164]) ).
fof(f198,plain,
( nil != sK12
| nil = sK13 ),
inference(cnf_transformation,[],[f164]) ).
fof(f199,plain,
ssList(sK14),
inference(cnf_transformation,[],[f164]) ).
fof(f200,plain,
ssList(sK15),
inference(cnf_transformation,[],[f164]) ).
fof(f201,plain,
! [X10,X11,X12,X13] :
( ~ lt(X12,X10)
| app(X13,cons(X12,nil)) != sK12
| ~ ssList(X13)
| ~ ssItem(X12)
| app(cons(X10,nil),X11) != sK15
| ~ ssList(X11)
| ~ ssItem(X10) ),
inference(cnf_transformation,[],[f164]) ).
fof(f202,plain,
! [X8,X6,X9,X7] :
( ~ lt(X6,X8)
| app(cons(X8,nil),X9) != sK12
| ~ ssList(X9)
| ~ ssItem(X8)
| app(X7,cons(X6,nil)) != sK14
| ~ ssList(X7)
| ~ ssItem(X6) ),
inference(cnf_transformation,[],[f164]) ).
fof(f203,plain,
strictorderedP(sK12),
inference(cnf_transformation,[],[f164]) ).
fof(f204,plain,
sK13 = app(app(sK14,sK12),sK15),
inference(cnf_transformation,[],[f164]) ).
fof(f205,plain,
sK10 = sK12,
inference(cnf_transformation,[],[f164]) ).
fof(f206,plain,
sK11 = sK13,
inference(cnf_transformation,[],[f164]) ).
fof(f268,plain,
( nil = sK12
| sP1(sK13,sK12) ),
inference(definition_unfolding,[],[f197,f206,f205,f205]) ).
fof(f269,plain,
( nil != sK13
| sP1(sK13,sK12) ),
inference(definition_unfolding,[],[f196,f206,f205,f206]) ).
fof(f272,plain,
! [X2,X3,X1] :
( ~ sP1(app(app(X2,X1),X3),X1)
| ~ strictorderedP(X1)
| sP0(X3,X1)
| app(sK3(X1,X2),cons(sK2(X1,X2),nil)) = X2
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(equality_resolution,[],[f184]) ).
fof(f273,plain,
! [X2,X3,X1] :
( ~ sP1(app(app(X2,X1),X3),X1)
| ~ strictorderedP(X1)
| sP0(X3,X1)
| app(cons(sK4(X1,X2),nil),sK5(X1,X2)) = X1
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(equality_resolution,[],[f183]) ).
fof(f274,plain,
! [X2,X3,X1] :
( ~ sP1(app(app(X2,X1),X3),X1)
| ~ strictorderedP(X1)
| sP0(X3,X1)
| lt(sK2(X1,X2),sK4(X1,X2))
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(equality_resolution,[],[f182]) ).
fof(f275,plain,
! [X2,X3,X1] :
( ~ sP1(app(app(X2,X1),X3),X1)
| ~ strictorderedP(X1)
| sP0(X3,X1)
| ssList(sK5(X1,X2))
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(equality_resolution,[],[f181]) ).
fof(f276,plain,
! [X2,X3,X1] :
( ~ sP1(app(app(X2,X1),X3),X1)
| ~ strictorderedP(X1)
| sP0(X3,X1)
| ssItem(sK4(X1,X2))
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(equality_resolution,[],[f180]) ).
fof(f277,plain,
! [X2,X3,X1] :
( ~ sP1(app(app(X2,X1),X3),X1)
| ~ strictorderedP(X1)
| sP0(X3,X1)
| ssList(sK3(X1,X2))
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(equality_resolution,[],[f179]) ).
fof(f278,plain,
! [X2,X3,X1] :
( ~ sP1(app(app(X2,X1),X3),X1)
| ~ strictorderedP(X1)
| sP0(X3,X1)
| ssItem(sK2(X1,X2))
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(equality_resolution,[],[f178]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X2,X1)
| ( app(sK3(X1,X0),cons(sK2(X1,X0),nil)) = X0 )
| ~ strictorderedP(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ sP1(app(app(X0,X1),X2),X1) ),
inference(cnf_transformation,[],[f272]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X2,X1)
| ( app(cons(sK4(X1,X0),nil),sK5(X1,X0)) = X1 )
| ~ strictorderedP(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ sP1(app(app(X0,X1),X2),X1) ),
inference(cnf_transformation,[],[f273]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X2,X1)
| lt(sK2(X1,X0),sK4(X1,X0))
| ~ strictorderedP(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ sP1(app(app(X0,X1),X2),X1) ),
inference(cnf_transformation,[],[f274]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X2,X1)
| ssList(sK5(X1,X0))
| ~ strictorderedP(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ sP1(app(app(X0,X1),X2),X1) ),
inference(cnf_transformation,[],[f275]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X2,X1)
| ssItem(sK4(X1,X0))
| ~ strictorderedP(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ sP1(app(app(X0,X1),X2),X1) ),
inference(cnf_transformation,[],[f276]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X2,X1)
| ssList(sK3(X1,X0))
| ~ strictorderedP(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ sP1(app(app(X0,X1),X2),X1) ),
inference(cnf_transformation,[],[f277]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X2,X1)
| ssItem(sK2(X1,X0))
| ~ strictorderedP(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ sP1(app(app(X0,X1),X2),X1) ),
inference(cnf_transformation,[],[f278]) ).
tcf(c_63,negated_conjecture,
app(app(sK14,sK12),sK15) = sK13,
inference(cnf_transformation,[],[f204]) ).
tcf(c_64,negated_conjecture,
strictorderedP(sK12),
inference(cnf_transformation,[],[f203]) ).
tcf(c_65,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ssItem(X3)
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ lt(X3,X0)
| ( app(X2,cons(X3,nil)) != sK14 )
| ( app(cons(X0,nil),X1) != sK12 ) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_66,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ssItem(X3)
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ lt(X3,X0)
| ( app(X2,cons(X3,nil)) != sK12 )
| ( app(cons(X0,nil),X1) != sK15 ) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_67,negated_conjecture,
ssList(sK15),
inference(cnf_transformation,[],[f200]) ).
tcf(c_68,negated_conjecture,
ssList(sK14),
inference(cnf_transformation,[],[f199]) ).
tcf(c_69,negated_conjecture,
( ( nil = sK13 )
| ( nil != sK12 ) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_70,negated_conjecture,
( sP1(sK13,sK12)
| ( nil = sK12 ) ),
inference(cnf_transformation,[],[f268]) ).
tcf(c_71,negated_conjecture,
( sP1(sK13,sK12)
| ( nil != sK13 ) ),
inference(cnf_transformation,[],[f269]) ).
tcf(c_182,negated_conjecture,
sP1(sK13,sK12),
inference(global_subsumption_just,[status(thm)],[c_70,c_70,c_71,c_69]) ).
tcf(c_184,negated_conjecture,
sP1(sK13,sK12),
inference(global_subsumption_just,[status(thm)],[c_71,c_182]) ).
tcf(c_1294,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X2,X1)
| ssItem(sK2(X1,X0))
| ~ strictorderedP(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ( X1 != sK12 )
| ( app(app(X0,X1),X2) != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_184]) ).
tcf(c_1295,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK12)
| ssItem(sK2(sK12,X0))
| ~ strictorderedP(sK12)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X0,sK12),X1) != sK13 ) ),
inference(unflattening,[status(thm)],[c_1294]) ).
tcf(c_1297,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK12)
| ssItem(sK2(sK12,X0))
| ( app(app(X0,sK12),X1) != sK13 )
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(global_subsumption_just,[status(thm)],[c_1295,c_64,c_1295]) ).
tcf(c_1298,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK12)
| ssItem(sK2(sK12,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X0,sK12),X1) != sK13 ) ),
inference(renaming,[status(thm)],[c_1297]) ).
tcf(c_1315,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X2,X1)
| ssList(sK3(X1,X0))
| ~ strictorderedP(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ( X1 != sK12 )
| ( app(app(X0,X1),X2) != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_184]) ).
tcf(c_1316,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK12)
| ssList(sK3(sK12,X0))
| ~ strictorderedP(sK12)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X0,sK12),X1) != sK13 ) ),
inference(unflattening,[status(thm)],[c_1315]) ).
tcf(c_1318,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK12)
| ssList(sK3(sK12,X0))
| ( app(app(X0,sK12),X1) != sK13 )
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(global_subsumption_just,[status(thm)],[c_1316,c_64,c_1316]) ).
tcf(c_1319,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK12)
| ssList(sK3(sK12,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X0,sK12),X1) != sK13 ) ),
inference(renaming,[status(thm)],[c_1318]) ).
tcf(c_1336,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X2,X1)
| ssItem(sK4(X1,X0))
| ~ strictorderedP(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ( X1 != sK12 )
| ( app(app(X0,X1),X2) != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_184]) ).
tcf(c_1337,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK12)
| ssItem(sK4(sK12,X0))
| ~ strictorderedP(sK12)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X0,sK12),X1) != sK13 ) ),
inference(unflattening,[status(thm)],[c_1336]) ).
tcf(c_1339,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK12)
| ssItem(sK4(sK12,X0))
| ( app(app(X0,sK12),X1) != sK13 )
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(global_subsumption_just,[status(thm)],[c_1337,c_64,c_1337]) ).
tcf(c_1340,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK12)
| ssItem(sK4(sK12,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X0,sK12),X1) != sK13 ) ),
inference(renaming,[status(thm)],[c_1339]) ).
tcf(c_1357,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X2,X1)
| ssList(sK5(X1,X0))
| ~ strictorderedP(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ( X1 != sK12 )
| ( app(app(X0,X1),X2) != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_184]) ).
tcf(c_1358,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK12)
| ssList(sK5(sK12,X0))
| ~ strictorderedP(sK12)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X0,sK12),X1) != sK13 ) ),
inference(unflattening,[status(thm)],[c_1357]) ).
tcf(c_1360,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK12)
| ssList(sK5(sK12,X0))
| ( app(app(X0,sK12),X1) != sK13 )
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(global_subsumption_just,[status(thm)],[c_1358,c_64,c_1358]) ).
tcf(c_1361,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK12)
| ssList(sK5(sK12,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X0,sK12),X1) != sK13 ) ),
inference(renaming,[status(thm)],[c_1360]) ).
tcf(c_1378,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X2,X1)
| lt(sK2(X1,X0),sK4(X1,X0))
| ~ strictorderedP(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ( X1 != sK12 )
| ( app(app(X0,X1),X2) != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_184]) ).
tcf(c_1379,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK12)
| lt(sK2(sK12,X0),sK4(sK12,X0))
| ~ strictorderedP(sK12)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X0,sK12),X1) != sK13 ) ),
inference(unflattening,[status(thm)],[c_1378]) ).
tcf(c_1381,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK12)
| lt(sK2(sK12,X0),sK4(sK12,X0))
| ( app(app(X0,sK12),X1) != sK13 )
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(global_subsumption_just,[status(thm)],[c_1379,c_64,c_1379]) ).
tcf(c_1382,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK12)
| lt(sK2(sK12,X0),sK4(sK12,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X0,sK12),X1) != sK13 ) ),
inference(renaming,[status(thm)],[c_1381]) ).
tcf(c_1399,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X2,X1)
| ( app(cons(sK4(X1,X0),nil),sK5(X1,X0)) = X1 )
| ~ strictorderedP(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ( X1 != sK12 )
| ( app(app(X0,X1),X2) != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_184]) ).
tcf(c_1400,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK12)
| ( app(cons(sK4(sK12,X0),nil),sK5(sK12,X0)) = sK12 )
| ~ strictorderedP(sK12)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X0,sK12),X1) != sK13 ) ),
inference(unflattening,[status(thm)],[c_1399]) ).
tcf(c_1402,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK12)
| ( app(cons(sK4(sK12,X0),nil),sK5(sK12,X0)) = sK12 )
| ( app(app(X0,sK12),X1) != sK13 )
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(global_subsumption_just,[status(thm)],[c_1400,c_64,c_1400]) ).
tcf(c_1403,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK12)
| ( app(cons(sK4(sK12,X0),nil),sK5(sK12,X0)) = sK12 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X0,sK12),X1) != sK13 ) ),
inference(renaming,[status(thm)],[c_1402]) ).
tcf(c_1420,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X2,X1)
| ( app(sK3(X1,X0),cons(sK2(X1,X0),nil)) = X0 )
| ~ strictorderedP(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ( X1 != sK12 )
| ( app(app(X0,X1),X2) != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_184]) ).
tcf(c_1421,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK12)
| ( app(sK3(sK12,X0),cons(sK2(sK12,X0),nil)) = X0 )
| ~ strictorderedP(sK12)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X0,sK12),X1) != sK13 ) ),
inference(unflattening,[status(thm)],[c_1420]) ).
tcf(c_1423,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK12)
| ( app(sK3(sK12,X0),cons(sK2(sK12,X0),nil)) = X0 )
| ( app(app(X0,sK12),X1) != sK13 )
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(global_subsumption_just,[status(thm)],[c_1421,c_64,c_1421]) ).
tcf(c_1424,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK12)
| ( app(sK3(sK12,X0),cons(sK2(sK12,X0),nil)) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X0,sK12),X1) != sK13 ) ),
inference(renaming,[status(thm)],[c_1423]) ).
tcf(c_6079,plain,
( sP0(sK15,sK12)
| ssItem(sK2(sK12,sK14))
| ~ ssList(sK15)
| ~ ssList(sK14) ),
inference(superposition,[status(thm)],[c_63,c_1298]) ).
tcf(c_6080,plain,
( sP0(sK15,sK12)
| ssItem(sK2(sK12,sK14)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6079,c_67,c_68]) ).
tcf(c_6097,plain,
( sP0(sK15,sK12)
| ssList(sK3(sK12,sK14))
| ~ ssList(sK15)
| ~ ssList(sK14) ),
inference(superposition,[status(thm)],[c_63,c_1319]) ).
tcf(c_6098,plain,
( sP0(sK15,sK12)
| ssList(sK3(sK12,sK14)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6097,c_67,c_68]) ).
tcf(c_6115,plain,
( sP0(sK15,sK12)
| ssItem(sK4(sK12,sK14))
| ~ ssList(sK15)
| ~ ssList(sK14) ),
inference(superposition,[status(thm)],[c_63,c_1340]) ).
tcf(c_6116,plain,
( sP0(sK15,sK12)
| ssItem(sK4(sK12,sK14)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6115,c_67,c_68]) ).
tcf(c_6133,plain,
( sP0(sK15,sK12)
| ssList(sK5(sK12,sK14))
| ~ ssList(sK15)
| ~ ssList(sK14) ),
inference(superposition,[status(thm)],[c_63,c_1361]) ).
tcf(c_6134,plain,
( sP0(sK15,sK12)
| ssList(sK5(sK12,sK14)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6133,c_67,c_68]) ).
tcf(c_6191,plain,
( sP0(sK15,sK12)
| lt(sK2(sK12,sK14),sK4(sK12,sK14))
| ~ ssList(sK15)
| ~ ssList(sK14) ),
inference(superposition,[status(thm)],[c_63,c_1382]) ).
tcf(c_6192,plain,
( sP0(sK15,sK12)
| lt(sK2(sK12,sK14),sK4(sK12,sK14)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6191,c_67,c_68]) ).
tcf(c_6209,plain,
( sP0(sK15,sK12)
| ( app(cons(sK4(sK12,sK14),nil),sK5(sK12,sK14)) = sK12 )
| ~ ssList(sK15)
| ~ ssList(sK14) ),
inference(superposition,[status(thm)],[c_63,c_1403]) ).
tcf(c_6210,plain,
( sP0(sK15,sK12)
| ( app(cons(sK4(sK12,sK14),nil),sK5(sK12,sK14)) = sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6209,c_67,c_68]) ).
tcf(c_6227,plain,
( sP0(sK15,sK12)
| ( app(sK3(sK12,sK14),cons(sK2(sK12,sK14),nil)) = sK14 )
| ~ ssList(sK15)
| ~ ssList(sK14) ),
inference(superposition,[status(thm)],[c_63,c_1424]) ).
tcf(c_6228,plain,
( sP0(sK15,sK12)
| ( app(sK3(sK12,sK14),cons(sK2(sK12,sK14),nil)) = sK14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6227,c_67,c_68]) ).
tcf(c_18959,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(sK4(sK12,X0))
| ~ ssItem(sK2(sK12,X0))
| ~ lt(sK2(sK12,X0),sK4(sK12,X0))
| ( app(X2,cons(sK2(sK12,X0),nil)) != sK14 )
| ( app(cons(sK4(sK12,X0),nil),X1) != sK12 ) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_21773,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(sK4(sK12,X0))
| ~ ssItem(sK2(sK12,X0))
| ~ ssList(sK5(sK12,X0))
| ~ lt(sK2(sK12,X0),sK4(sK12,X0))
| ( app(X1,cons(sK2(sK12,X0),nil)) != sK14 )
| ( app(cons(sK4(sK12,X0),nil),sK5(sK12,X0)) != sK12 ) ),
inference(instantiation,[status(thm)],[c_18959]) ).
tcf(c_24847,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(sK8(sK15,X0))
| ~ ssItem(sK6(sK15,X0))
| ~ lt(sK8(sK15,X0),sK6(sK15,X0))
| ( app(X2,cons(sK8(sK15,X0),nil)) != sK12 )
| ( app(cons(sK6(sK15,X0),nil),X1) != sK15 ) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_35920,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ ssItem(sK8(sK15,sK12))
| ~ ssItem(sK6(sK15,sK12))
| ~ ssList(sK7(sK15,sK12))
| ~ lt(sK8(sK15,sK12),sK6(sK15,sK12))
| ( app(X0,cons(sK8(sK15,sK12),nil)) != sK12 )
| ( app(cons(sK6(sK15,sK12),nil),sK7(sK15,sK12)) != sK15 ) ),
inference(instantiation,[status(thm)],[c_24847]) ).
tcf(c_55163,plain,
( ~ ssItem(sK8(sK15,sK12))
| ~ ssItem(sK6(sK15,sK12))
| ~ ssList(sK9(sK15,sK12))
| ~ ssList(sK7(sK15,sK12))
| ~ lt(sK8(sK15,sK12),sK6(sK15,sK12))
| ( app(sK9(sK15,sK12),cons(sK8(sK15,sK12),nil)) != sK12 )
| ( app(cons(sK6(sK15,sK12),nil),sK7(sK15,sK12)) != sK15 ) ),
inference(instantiation,[status(thm)],[c_35920]) ).
tcf(c_56197,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ ssItem(sK4(sK12,sK14))
| ~ ssItem(sK2(sK12,sK14))
| ~ ssList(sK5(sK12,sK14))
| ~ lt(sK2(sK12,sK14),sK4(sK12,sK14))
| ( app(X0,cons(sK2(sK12,sK14),nil)) != sK14 )
| ( app(cons(sK4(sK12,sK14),nil),sK5(sK12,sK14)) != sK12 ) ),
inference(instantiation,[status(thm)],[c_21773]) ).
tcf(c_75102,plain,
( ~ ssItem(sK4(sK12,sK14))
| ~ ssItem(sK2(sK12,sK14))
| ~ ssList(sK5(sK12,sK14))
| ~ ssList(sK3(sK12,sK14))
| ~ lt(sK2(sK12,sK14),sK4(sK12,sK14))
| ( app(sK3(sK12,sK14),cons(sK2(sK12,sK14),nil)) != sK14 )
| ( app(cons(sK4(sK12,sK14),nil),sK5(sK12,sK14)) != sK12 ) ),
inference(instantiation,[status(thm)],[c_56197]) ).
fof(f155,definition,
! [X15,X0] :
( ~ sP0(X15,X0)
| ? [X20] :
( ssItem(X20)
& ? [X21] :
( ssList(X21)
& ? [X22] :
( ssItem(X22)
& ? [X23] :
( ssList(X23)
& lt(X22,X20)
& app(X23,cons(X22,nil)) = X0 ) )
& app(cons(X20,nil),X21) = X15 ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f156,definition,
! [X1,X0] :
( ~ sP1(X1,X0)
| ! [X14] :
( ! [X15] :
( ~ strictorderedP(X0)
| sP0(X15,X0)
| ? [X16] :
( ssItem(X16)
& ? [X17] :
( ssList(X17)
& ? [X18] :
( ssItem(X18)
& ? [X19] :
( ssList(X19)
& lt(X16,X18)
& app(cons(X18,nil),X19) = X0 ) )
& app(X17,cons(X16,nil)) = X14 ) )
| app(app(X14,X0),X15) != X1
| ~ ssList(X15) )
| ~ ssList(X14) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f157,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil != X1
& nil = X0 )
| sP1(X1,X0) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ lt(X12,X10)
| app(X13,cons(X12,nil)) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(cons(X10,nil),X11) != X5
| ~ ssList(X11) )
| ~ ssItem(X10) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ lt(X6,X8)
| app(cons(X8,nil),X9) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(X7,cons(X6,nil)) != X4
| ~ ssList(X7) )
| ~ ssItem(X6) )
& strictorderedP(X2)
& app(app(X4,X2),X5) = X3 ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(definition_folding,[],[f99,f156,f155]) ).
fof(f161,plain,
! [X15,X0] :
( ~ sP0(X15,X0)
| ? [X20] :
( ssItem(X20)
& ? [X21] :
( ssList(X21)
& ? [X22] :
( ssItem(X22)
& ? [X23] :
( ssList(X23)
& lt(X22,X20)
& app(X23,cons(X22,nil)) = X0 ) )
& app(cons(X20,nil),X21) = X15 ) ) ),
inference(nnf_transformation,[],[f155]) ).
fof(f162,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& lt(X4,X2)
& app(X5,cons(X4,nil)) = X1 ) )
& app(cons(X2,nil),X3) = X0 ) ) ),
inference(rectify,[],[f161]) ).
fof(f163,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ( ssItem(sK6(X0,X1))
& ssList(sK7(X0,X1))
& ssItem(sK8(X0,X1))
& ssList(sK9(X0,X1))
& lt(sK8(X0,X1),sK6(X0,X1))
& app(sK9(X0,X1),cons(sK8(X0,X1),nil)) = X1
& app(cons(sK6(X0,X1),nil),sK7(X0,X1)) = X0 ) ),
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))],[f162]) ).
fof(f185,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ssItem(sK6(X0,X1)) ),
inference(cnf_transformation,[],[f163]) ).
fof(f186,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ssList(sK7(X0,X1)) ),
inference(cnf_transformation,[],[f163]) ).
fof(f187,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ssItem(sK8(X0,X1)) ),
inference(cnf_transformation,[],[f163]) ).
fof(f188,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ssList(sK9(X0,X1)) ),
inference(cnf_transformation,[],[f163]) ).
fof(f189,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| lt(sK8(X0,X1),sK6(X0,X1)) ),
inference(cnf_transformation,[],[f163]) ).
fof(f190,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| app(sK9(X0,X1),cons(sK8(X0,X1),nil)) = X1 ),
inference(cnf_transformation,[],[f163]) ).
fof(f191,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| app(cons(sK6(X0,X1),nil),sK7(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( app(cons(sK6(X0,X1),nil),sK7(X0,X1)) = X0 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( app(sK9(X0,X1),cons(sK8(X0,X1),nil)) = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( lt(sK8(X0,X1),sK6(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ssList(sK9(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ssItem(sK8(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ssList(sK7(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( ssItem(sK6(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_7490,plain,
( ( app(sK9(sK15,sK12),cons(sK8(sK15,sK12),nil)) = sK12 )
| ~ sP0(sK15,sK12) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_7491,plain,
( ( app(cons(sK6(sK15,sK12),nil),sK7(sK15,sK12)) = sK15 )
| ~ sP0(sK15,sK12) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_7492,plain,
( lt(sK8(sK15,sK12),sK6(sK15,sK12))
| ~ sP0(sK15,sK12) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_7493,plain,
( ssItem(sK6(sK15,sK12))
| ~ sP0(sK15,sK12) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_7494,plain,
( ssList(sK7(sK15,sK12))
| ~ sP0(sK15,sK12) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_7495,plain,
( ssItem(sK8(sK15,sK12))
| ~ sP0(sK15,sK12) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_7496,plain,
( ssList(sK9(sK15,sK12))
| ~ sP0(sK15,sK12) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_75104,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_75102,c_55163,c_7490,c_7491,c_7492,c_7493,c_7494,c_7495,c_7496,c_6228,c_6210,c_6192,c_6134,c_6116,c_6098,c_6080]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC344+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.20/0.45 % Computer : n006.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Thu Sep 24 17:44:22 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.23/0.51 Running first-order theorem proving
% 0.23/0.51 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.52
% 0.23/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.52
% 0.23/0.52 % Detected problem language: tptp
% 0.23/0.54 % Proving...
% 23.24/5.43 % SZS status Started for theBenchmark.p
% 23.24/5.43 % SZS status Theorem for theBenchmark.p
% 23.24/5.43
% 23.24/5.43 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 23.24/5.43
% 23.24/5.43 % ------ iProver source info
% 23.24/5.43
% 23.24/5.43 % git: date: 2026-07-19 20:42:38 +0200
% 23.24/5.43 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 23.24/5.43 % git: non_committed_changes: false
% 23.24/5.43
% 23.24/5.43 % ------ Parsing...
% 23.24/5.43 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 23.24/5.43
% 23.24/5.43 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 23.24/5.43
% 23.24/5.43 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 23.24/5.43
% 23.24/5.43 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 23.24/5.43 % ------ Proving...
% 23.24/5.43 % ------ Problem Properties
% 23.24/5.43
% 23.24/5.43 %
% 23.24/5.43 % clauses 80
% 23.24/5.43 % conjectures 9
% 23.24/5.43 % EPR 20
% 23.24/5.43 % Horn 50
% 23.24/5.43 % unary 12
% 23.24/5.43 % binary 13
% 23.24/5.43 % lits 272
% 23.24/5.43 % lits eq 70
% 23.24/5.43 % fd_pure 0
% 23.24/5.43 % fd_pseudo 0
% 23.24/5.43 % fd_cond 15
% 23.24/5.43 % fd_pseudo_cond 7
% 23.24/5.43 % AC symbols 0
% 23.24/5.43
% 23.24/5.43 % ------ Schedule dynamic 5 is on
% 23.24/5.43
% 23.24/5.43 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 23.24/5.43
% 23.24/5.43
% 23.24/5.43 % ------
% 23.24/5.43 % Current options:
% 23.24/5.43 % ------
% 23.24/5.43
% 23.24/5.43
% 23.24/5.43 %
% 23.24/5.43
% 23.24/5.43 % ------ Proving...
% 23.24/5.43 %
% 23.24/5.43
% 23.24/5.43 % SZS status Theorem for theBenchmark.p
% 23.24/5.43
% 23.24/5.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 23.24/5.44
% 23.24/5.44
%------------------------------------------------------------------------------