TSTP Solution File: ITP101^2 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP101^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:51:41 EDT 2024
% Result : Theorem 6.23s 1.30s
% Output : Refutation 6.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 170
% Syntax : Number of formulae : 188 ( 13 unt; 166 typ; 0 def)
% Number of atoms : 522 ( 57 equ; 0 cnn)
% Maximal formula atoms : 10 ( 23 avg)
% Number of connectives : 73 ( 23 ~; 11 |; 15 &; 0 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 371 ( 370 >; 1 *; 0 +; 0 <<)
% Number of symbols : 168 ( 165 usr; 5 con; 0-6 aty)
% Number of variables : 184 ( 0 ^ 8 !; 0 ?; 184 :)
% ( 176 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
list: $tType > $tType ).
thf(type_def_7,type,
nat: $tType ).
thf(type_def_8,type,
set: $tType > $tType ).
thf(type_def_9,type,
a: $tType ).
thf(func_def_0,type,
list: $tType > $tType ).
thf(func_def_1,type,
set: $tType > $tType ).
thf(func_def_2,type,
nat: $tType ).
thf(func_def_3,type,
a: $tType ).
thf(func_def_4,type,
type:
!>[X0: $tType] : $o ).
thf(func_def_5,type,
size:
!>[X0: $tType] : $o ).
thf(func_def_6,type,
one:
!>[X0: $tType] : $o ).
thf(func_def_7,type,
minus:
!>[X0: $tType] : $o ).
thf(func_def_8,type,
ord:
!>[X0: $tType] : $o ).
thf(func_def_9,type,
order:
!>[X0: $tType] : $o ).
thf(func_def_10,type,
group_add:
!>[X0: $tType] : $o ).
thf(func_def_11,type,
no_bot:
!>[X0: $tType] : $o ).
thf(func_def_12,type,
no_top:
!>[X0: $tType] : $o ).
thf(func_def_13,type,
linorder:
!>[X0: $tType] : $o ).
thf(func_def_14,type,
preorder:
!>[X0: $tType] : $o ).
thf(func_def_15,type,
wellorder:
!>[X0: $tType] : $o ).
thf(func_def_16,type,
dense_order:
!>[X0: $tType] : $o ).
thf(func_def_17,type,
dense_linorder:
!>[X0: $tType] : $o ).
thf(func_def_18,type,
ordered_ab_group_add:
!>[X0: $tType] : $o ).
thf(func_def_19,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
thf(func_def_20,type,
condit1037483654norder:
!>[X0: $tType] : $o ).
thf(func_def_21,type,
minus_minus:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_22,type,
one_one:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
if:
!>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).
thf(func_def_24,type,
list_asc:
!>[X0: $tType] : ( list(X0) > $o ) ).
thf(func_def_25,type,
list_desc:
!>[X0: $tType] : ( list(X0) > $o ) ).
thf(func_def_26,type,
list_strict_asc:
!>[X0: $tType] : ( list(X0) > $o ) ).
thf(func_def_27,type,
list_strict_desc:
!>[X0: $tType] : ( list(X0) > $o ) ).
thf(func_def_28,type,
listIn521021761append:
!>[X0: $tType] : ( list(X0) > ( nat > X0 ) > nat > X0 ) ).
thf(func_def_29,type,
append:
!>[X0: $tType] : ( list(X0) > list(X0) > list(X0) ) ).
thf(func_def_30,type,
butlast:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
thf(func_def_31,type,
set2:
!>[X0: $tType] : ( list(X0) > set(X0) ) ).
thf(func_def_32,type,
list_ex:
!>[X0: $tType] : ( ( X0 > $o ) > list(X0) > $o ) ).
thf(func_def_33,type,
list_update:
!>[X0: $tType] : ( list(X0) > nat > X0 > list(X0) ) ).
thf(func_def_34,type,
nth:
!>[X0: $tType] : ( list(X0) > nat > X0 ) ).
thf(func_def_35,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
thf(func_def_36,type,
ord_less:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_37,type,
ord_less_eq:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_38,type,
collect:
!>[X0: $tType] : ( ( X0 > $o ) > set(X0) ) ).
thf(func_def_39,type,
member:
!>[X0: $tType] : ( X0 > set(X0) > $o ) ).
thf(func_def_40,type,
f: nat > a ).
thf(func_def_41,type,
g: nat > a ).
thf(func_def_42,type,
x: nat ).
thf(func_def_43,type,
xs: list(a) ).
thf(func_def_44,type,
ys: list(a) ).
thf(func_def_48,type,
vOR: $o > $o > $o ).
thf(func_def_49,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_50,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_51,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_52,type,
vAND: $o > $o > $o ).
thf(func_def_53,type,
vNOT: $o > $o ).
thf(func_def_54,type,
vIMP: $o > $o > $o ).
thf(func_def_55,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_56,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_57,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_58,type,
sP0:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_59,type,
sP1:
!>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).
thf(func_def_60,type,
sP2:
!>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).
thf(func_def_61,type,
sP3:
!>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).
thf(func_def_62,type,
sP4:
!>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).
thf(func_def_63,type,
sP5: nat > ( nat > $o ) > $o ).
thf(func_def_64,type,
sK6:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_65,type,
sK7:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_66,type,
sK8:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_67,type,
sK9:
!>[X0: $tType] : ( X0 > X0 > ( X0 > $o ) > X0 ) ).
thf(func_def_68,type,
sK10:
!>[X0: $tType] : ( ( X0 > $o ) > X0 > X0 > X0 ) ).
thf(func_def_69,type,
sK11:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_70,type,
sK12:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_71,type,
sK13:
!>[X0: $tType] : ( X0 > X0 > X0 > X0 ) ).
thf(func_def_72,type,
sK14:
!>[X0: $tType] : ( X0 > X0 > X0 > X0 ) ).
thf(func_def_73,type,
sK15:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_74,type,
sK16:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_75,type,
sK17:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_76,type,
sK18:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_77,type,
sK19:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_78,type,
sK20:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_79,type,
sK21:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_80,type,
sK22:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_81,type,
sK23:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_82,type,
sK24:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_83,type,
sK25:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_84,type,
sK26:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_85,type,
sK27:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_86,type,
sK28:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_87,type,
sK29:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_88,type,
sK30:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_89,type,
sK31:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_90,type,
sK32:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_91,type,
sK33:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_92,type,
sK34:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_93,type,
sK35:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_94,type,
sK36:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_95,type,
sK37:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_96,type,
sK38:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_97,type,
sK39:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_98,type,
sK40:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_99,type,
sK41:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_100,type,
sK42:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_101,type,
sK43:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_102,type,
sK44:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_103,type,
sK45:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_104,type,
sK46:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_105,type,
sK47:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_106,type,
sK48:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_107,type,
sK49:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_108,type,
sK50:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_109,type,
sK51:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_110,type,
sK52:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_111,type,
sK53:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_112,type,
sK54:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_113,type,
sK55:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_114,type,
sK56:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_115,type,
sK57:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_116,type,
sK58:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_117,type,
sK59:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_118,type,
sK60:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_119,type,
sK61:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_120,type,
sK62:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_121,type,
sK63:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_122,type,
sK64:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_123,type,
sK65:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_124,type,
sK66:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_125,type,
sK67:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_126,type,
sK68:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_127,type,
sK69:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_128,type,
sK70:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_129,type,
sK71:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_130,type,
sK72:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_131,type,
sK73: ( nat > $o ) > nat ).
thf(func_def_132,type,
sK74: ( nat > $o ) > nat ).
thf(func_def_133,type,
sK75:
!>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_134,type,
sK76:
!>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_135,type,
sK77:
!>[X0: $tType,X1: $tType] : ( X1 > X0 ) ).
thf(func_def_136,type,
sK78:
!>[X0: $tType,X1: $tType] : ( X1 > X0 ) ).
thf(func_def_137,type,
sK79:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_138,type,
sK80:
!>[X0: $tType] : ( nat > list(X0) ) ).
thf(func_def_139,type,
sK81:
!>[X0: $tType] : ( list(X0) > list(X0) > nat ) ).
thf(func_def_140,type,
sK82:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_141,type,
sK83:
!>[X0: $tType] : ( ( list(X0) > $o ) > list(X0) ) ).
thf(func_def_142,type,
sK84: nat > ( nat > $o ) > nat ).
thf(func_def_143,type,
sK85: ( nat > $o ) > nat > nat ).
thf(func_def_144,type,
sK86: ( nat > nat ) > nat ).
thf(func_def_145,type,
sK87: ( nat > nat ) > nat ).
thf(func_def_146,type,
sK88: ( nat > $o ) > nat ).
thf(func_def_147,type,
sK89: nat > ( nat > $o ) > nat ).
thf(func_def_148,type,
sK90:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_149,type,
sK91:
!>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).
thf(func_def_150,type,
sK92:
!>[X0: $tType] : ( ( X0 > $o ) > list(X0) > nat ) ).
thf(func_def_151,type,
sK93:
!>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).
thf(func_def_152,type,
sK94:
!>[X0: $tType] : ( ( X0 > $o ) > list(X0) > X0 ) ).
thf(func_def_153,type,
sK95:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > list(X0) > X0 ) ).
thf(func_def_154,type,
sK96:
!>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).
thf(func_def_155,type,
sK97:
!>[X0: $tType] : ( nat > ( X0 > nat ) > ( X0 > $o ) > X0 ) ).
thf(func_def_157,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_158,type,
sK99:
!>[X0: $tType] : ( list(X0) > list(X0) > list(X0) > list(X0) > list(X0) ) ).
thf(func_def_159,type,
sK100:
!>[X0: $tType] : ( list(X0) > set(X0) > X0 ) ).
thf(func_def_160,type,
sK101:
!>[X0: $tType] : ( X0 > list(X0) > nat ) ).
thf(func_def_161,type,
sK102:
!>[X0: $tType] : ( list(X0) > ( X0 > $o ) > X0 ) ).
thf(func_def_162,type,
sK103:
!>[X0: $tType] : ( list(X0) > ( X0 > $o ) > nat ) ).
thf(func_def_163,type,
sK104:
!>[X0: $tType] : ( nat > ( nat > X0 > $o ) > nat ) ).
thf(func_def_164,type,
sK105:
!>[X0: $tType] : ( nat > ( nat > X0 > $o ) > list(X0) ) ).
thf(f13045,plain,
$false,
inference(subsumption_resolution,[],[f13018,f1352]) ).
thf(f1352,plain,
vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),xs),x) != vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),ys),x),
inference(cnf_transformation,[],[f825]) ).
thf(f825,plain,
vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),xs),x) != vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),ys),x),
inference(flattening,[],[f288]) ).
thf(f288,negated_conjecture,
vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),xs),x) != vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),ys),x),
inference(negated_conjecture,[],[f287]) ).
thf(f287,conjecture,
vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),xs),x) = vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),ys),x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
thf(f13018,plain,
vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),xs),x) = vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),ys),x),
inference(trivial_inequality_removal,[],[f12997]) ).
thf(f12997,plain,
( ( $true != $true )
| ( vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),xs),x) = vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),ys),x) ) ),
inference(superposition,[],[f2282,f2283]) ).
thf(f2283,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),x),vAPP(list(a),nat,size_size(list(a)),xs)),
inference(forward_demodulation,[],[f1358,f1353]) ).
thf(f1353,plain,
vAPP(list(a),nat,size_size(list(a)),xs) = vAPP(list(a),nat,size_size(list(a)),ys),
inference(cnf_transformation,[],[f284]) ).
thf(f284,axiom,
vAPP(list(a),nat,size_size(list(a)),xs) = vAPP(list(a),nat,size_size(list(a)),ys),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f1358,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),x),vAPP(list(a),nat,size_size(list(a)),ys)) = $true,
inference(cnf_transformation,[],[f294]) ).
thf(f294,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),x),vAPP(list(a),nat,size_size(list(a)),ys)) = $true,
inference(fool_elimination,[],[f293]) ).
thf(f293,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),x),vAPP(list(a),nat,size_size(list(a)),ys)),
inference(rectify,[],[f286]) ).
thf(f286,axiom,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),x),vAPP(list(a),nat,size_size(list(a)),ys)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(f2282,plain,
! [X0: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),xs)) )
| ( vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),xs),X0) = vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),ys),X0) ) ),
inference(forward_demodulation,[],[f2278,f1353]) ).
thf(f2278,plain,
! [X0: nat] :
( ( vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),xs),X0) = vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),ys),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys)) ) ),
inference(duplicate_literal_removal,[],[f1354]) ).
thf(f1354,plain,
! [X0: nat] :
( ( vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),xs),X0) = vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),ys),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys)) ) ),
inference(cnf_transformation,[],[f873]) ).
thf(f873,plain,
! [X0: nat] :
( ( ( ( ( vAPP(nat,a,f,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(list(a),nat,size_size(list(a)),xs))) = vAPP(nat,a,g,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys)) ) )
& ( ( vAPP(nat,a,g,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys))) = vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),xs),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys)) ) ) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys)) ) )
& ( ( ( ( vAPP(nat,a,f,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(list(a),nat,size_size(list(a)),xs))) = vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),ys),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys)) ) )
& ( ( vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),xs),X0) = vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),ys),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys)) ) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys)) ) ) ),
inference(ennf_transformation,[],[f826]) ).
thf(f826,plain,
! [X0: nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys)) )
=> ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys)) )
=> ( vAPP(nat,a,f,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(list(a),nat,size_size(list(a)),xs))) = vAPP(nat,a,g,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys))) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys)) )
=> ( vAPP(nat,a,g,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys))) = vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),xs),X0) ) ) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys)) )
=> ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys)) )
=> ( vAPP(nat,a,f,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(list(a),nat,size_size(list(a)),xs))) = vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),ys),X0) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys)) )
=> ( vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),xs),X0) = vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),ys),X0) ) ) ) ) ),
inference(flattening,[],[f292]) ).
thf(f292,plain,
! [X0: nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys)) )
=> ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys)) )
=> ( vAPP(nat,a,f,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(list(a),nat,size_size(list(a)),xs))) = vAPP(nat,a,g,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys))) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys)) )
=> ( vAPP(nat,a,g,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys))) = vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),xs),X0) ) ) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys)) )
=> ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys)) )
=> ( vAPP(nat,a,f,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(list(a),nat,size_size(list(a)),xs))) = vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),ys),X0) ) )
& ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys)) )
=> ( vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),xs),X0) = vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),ys),X0) ) ) ) ) ),
inference(fool_elimination,[],[f291]) ).
thf(f291,plain,
! [X0: nat] :
( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys))
=> ( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys))
=> ( vAPP(nat,a,f,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(list(a),nat,size_size(list(a)),xs))) = vAPP(nat,a,g,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys))) ) )
& ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys))
=> ( vAPP(nat,a,g,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys))) = vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),xs),X0) ) ) ) )
& ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys))
=> ( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys))
=> ( vAPP(nat,a,f,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(list(a),nat,size_size(list(a)),xs))) = vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),ys),X0) ) )
& ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(a),nat,size_size(list(a)),ys))
=> ( vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),xs),X0) = vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),ys),X0) ) ) ) ) ),
inference(rectify,[],[f285]) ).
thf(f285,axiom,
! [X60: nat] :
( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X60),vAPP(list(a),nat,size_size(list(a)),ys))
=> ( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X60),vAPP(list(a),nat,size_size(list(a)),ys))
=> ( vAPP(nat,a,f,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X60),vAPP(list(a),nat,size_size(list(a)),xs))) = vAPP(nat,a,g,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X60),vAPP(list(a),nat,size_size(list(a)),ys))) ) )
& ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X60),vAPP(list(a),nat,size_size(list(a)),ys))
=> ( vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),xs),X60) = vAPP(nat,a,g,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X60),vAPP(list(a),nat,size_size(list(a)),ys))) ) ) ) )
& ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X60),vAPP(list(a),nat,size_size(list(a)),ys))
=> ( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X60),vAPP(list(a),nat,size_size(list(a)),ys))
=> ( vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),ys),X60) = vAPP(nat,a,f,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X60),vAPP(list(a),nat,size_size(list(a)),xs))) ) )
& ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X60),vAPP(list(a),nat,size_size(list(a)),ys))
=> ( vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),xs),X60) = vAPP(nat,a,vAPP(list(a),sTfun(nat,a),nth(a),ys),X60) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ITP101^2 : TPTP v8.2.0. Released v7.5.0.
% 0.03/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.37 % Computer : n028.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sat May 18 17:39:23 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.16/0.37 % (9435)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.41 % (9438)WARNING: value z3 for option sas not known
% 0.24/0.41 % (9439)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.24/0.41 % (9437)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.24/0.41 % (9436)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.24/0.41 % (9438)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.24/0.41 % (9440)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.24/0.41 % (9442)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.24/0.41 % (9441)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.24/0.46 % (9442)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.24/0.46 % Exception at run slice level
% 0.24/0.46 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.24/0.46 % Exception at run slice level
% 0.24/0.46 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.24/0.47 % Exception at run slice level
% 0.24/0.47 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.24/0.48 % (9444)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.24/0.48 % (9443)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.24/0.48 % (9445)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.24/0.51 % (9444)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.04/0.54 % (9443)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.18/0.55 % Exception at run slice level
% 1.18/0.55 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 1.18/0.56 % (9446)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 6.23/1.29 % (9445)First to succeed.
% 6.23/1.30 % (9445)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9435"
% 6.23/1.30 % (9445)Refutation found. Thanks to Tanya!
% 6.23/1.30 % SZS status Theorem for theBenchmark
% 6.23/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 6.23/1.30 % (9445)------------------------------
% 6.23/1.30 % (9445)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 6.23/1.30 % (9445)Termination reason: Refutation
% 6.23/1.30
% 6.23/1.30 % (9445)Memory used [KB]: 4918
% 6.23/1.30 % (9445)Time elapsed: 0.815 s
% 6.23/1.30 % (9445)Instructions burned: 1666 (million)
% 6.23/1.30 % (9435)Success in time 0.903 s
%------------------------------------------------------------------------------