TSTP Solution File: DAT137^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT137^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n026.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 19:51:36 EDT 2024
% Result : Theorem 11.68s 1.98s
% Output : Refutation 11.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 199
% Syntax : Number of formulae : 218 ( 18 unt; 194 typ; 0 def)
% Number of atoms : 314 ( 25 equ; 0 cnn)
% Maximal formula atoms : 2 ( 13 avg)
% Number of connectives : 16 ( 10 ~; 3 |; 0 &; 0 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 395 ( 394 >; 1 *; 0 +; 0 <<)
% Number of symbols : 193 ( 190 usr; 5 con; 0-6 aty)
% Number of variables : 199 ( 0 ^ 30 !; 0 ?; 199 :)
% ( 169 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
itself: $tType > $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
nat: $tType ).
thf(type_def_8,type,
coindu1593790203_llist: $tType > $tType ).
thf(type_def_9,type,
extended_enat: $tType ).
thf(type_def_10,type,
list: $tType > $tType ).
thf(type_def_11,type,
num: $tType ).
thf(func_def_0,type,
coindu1593790203_llist: $tType > $tType ).
thf(func_def_1,type,
extended_enat: $tType ).
thf(func_def_2,type,
list: $tType > $tType ).
thf(func_def_3,type,
num: $tType ).
thf(func_def_4,type,
nat: $tType ).
thf(func_def_5,type,
itself: $tType > $tType ).
thf(func_def_6,type,
type:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_7,type,
one:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_8,type,
numeral:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_9,type,
ring_1:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_10,type,
uminus:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_11,type,
ord:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_12,type,
ring_char_0:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_13,type,
neg_numeral:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_14,type,
order:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_15,type,
group_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_16,type,
linorder:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_17,type,
ab_group_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_18,type,
semiring_char_0:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_19,type,
semigroup_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_20,type,
comm_semiring_1:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_21,type,
linordered_idom:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_22,type,
linordered_field:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_23,type,
ab_semigroup_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_24,type,
linordered_semidom:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_25,type,
cancel_semigroup_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_26,type,
ordered_ab_group_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_27,type,
ordere779506340up_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_28,type,
ordere236663937imp_le:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_29,type,
ordere223160158up_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_30,type,
strict2144017051up_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_31,type,
condit1656338222tinuum:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_32,type,
coindu493225792length:
!>[X0: $tType] : ( nat > coindu1593790203_llist(X0) > extended_enat ) ).
thf(func_def_33,type,
coindu1542816657of_aux:
!>[X0: $tType] : ( list(X0) > coindu1593790203_llist(X0) > list(X0) ) ).
thf(func_def_34,type,
coindu1121789889_LCons:
!>[X0: $tType] : ( X0 > coindu1593790203_llist(X0) > coindu1593790203_llist(X0) ) ).
thf(func_def_35,type,
coindu1598213697e_LNil:
!>[X0: $tType] : coindu1593790203_llist(X0) ).
thf(func_def_36,type,
coindu1079202755ist_of:
!>[X0: $tType] : ( list(X0) > coindu1593790203_llist(X0) ) ).
thf(func_def_37,type,
coindu567634248member:
!>[X0: $tType] : ( X0 > coindu1593790203_llist(X0) > $o ) ).
thf(func_def_38,type,
one_one:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
plus_plus:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_40,type,
uminus_uminus:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_41,type,
if:
!>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).
thf(func_def_42,type,
count_list:
!>[X0: $tType] : ( list(X0) > X0 > nat ) ).
thf(func_def_43,type,
gen_length:
!>[X0: $tType] : ( nat > list(X0) > nat ) ).
thf(func_def_44,type,
cons:
!>[X0: $tType] : ( X0 > list(X0) > list(X0) ) ).
thf(func_def_45,type,
nil:
!>[X0: $tType] : list(X0) ).
thf(func_def_46,type,
member:
!>[X0: $tType] : ( list(X0) > X0 > $o ) ).
thf(func_def_47,type,
nth:
!>[X0: $tType] : ( list(X0) > nat > X0 ) ).
thf(func_def_48,type,
ord_lexordp_eq:
!>[X0: $tType] : ( list(X0) > list(X0) > $o ) ).
thf(func_def_49,type,
product_lists:
!>[X0: $tType] : ( list(list(X0)) > list(list(X0)) ) ).
thf(func_def_50,type,
sublists:
!>[X0: $tType] : ( list(X0) > list(list(X0)) ) ).
thf(func_def_51,type,
upt: nat > nat > list(nat) ).
thf(func_def_52,type,
suc: nat > nat ).
thf(func_def_53,type,
nat_triangle: nat > nat ).
thf(func_def_54,type,
bitM: num > num ).
thf(func_def_55,type,
inc: num > num ).
thf(func_def_56,type,
neg_numeral_dbl:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_57,type,
neg_numeral_dbl_dec:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_58,type,
neg_numeral_sub:
!>[X0: $tType] : ( num > num > X0 ) ).
thf(func_def_59,type,
bit0: num > num ).
thf(func_def_60,type,
one2: num ).
thf(func_def_61,type,
numeral_numeral:
!>[X0: $tType] : ( num > X0 ) ).
thf(func_def_62,type,
ring_1_iszero:
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_63,type,
ord_less:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_64,type,
type2:
!>[X0: $tType] : itself(X0) ).
thf(func_def_65,type,
prefixes:
!>[X0: $tType] : ( list(X0) > list(list(X0)) ) ).
thf(func_def_66,type,
ma: nat ).
thf(func_def_67,type,
na: nat ).
thf(func_def_71,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_72,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_73,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_74,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_75,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_76,type,
vNOT: $o > $o ).
thf(func_def_77,type,
vOR: $o > $o > $o ).
thf(func_def_78,type,
vAND: $o > $o > $o ).
thf(func_def_79,type,
iCOMB:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_80,type,
sP0:
!>[X0: $tType] : ( list(X0) > X0 > X0 > list(X0) > $o ) ).
thf(func_def_81,type,
sP1:
!>[X0: $tType] : ( list(X0) > list(X0) > $o ) ).
thf(func_def_82,type,
sP2:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > $o ) ).
thf(func_def_83,type,
sP3: nat > ( nat > $o ) > $o ).
thf(func_def_84,type,
sP4: ( nat > nat > $o ) > $o ).
thf(func_def_85,type,
sK5: list(nat) > nat ).
thf(func_def_86,type,
sK6: list(nat) > list(nat) ).
thf(func_def_87,type,
sK7:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_88,type,
sK8:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_89,type,
sK9:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_90,type,
sK10:
!>[X0: $tType] : ( ( nat > X0 ) > nat ) ).
thf(func_def_91,type,
sK11:
!>[X0: $tType] : ( ( nat > X0 ) > nat ) ).
thf(func_def_92,type,
sK12:
!>[X0: $tType] : ( list(X0) > list(X0) > X0 ) ).
thf(func_def_93,type,
sK13:
!>[X0: $tType] : ( list(X0) > list(X0) > X0 ) ).
thf(func_def_94,type,
sK14:
!>[X0: $tType] : ( list(X0) > list(X0) > list(X0) ) ).
thf(func_def_95,type,
sK15:
!>[X0: $tType] : ( list(X0) > list(X0) > list(X0) ) ).
thf(func_def_96,type,
sK16:
!>[X0: $tType] : ( list(X0) > X0 > X0 > list(X0) > list(X0) ) ).
thf(func_def_97,type,
sK17:
!>[X0: $tType] : ( list(X0) > list(X0) > X0 ) ).
thf(func_def_98,type,
sK18:
!>[X0: $tType] : ( list(X0) > list(X0) > X0 ) ).
thf(func_def_99,type,
sK19:
!>[X0: $tType] : ( list(X0) > list(X0) > list(X0) ) ).
thf(func_def_100,type,
sK20:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
thf(func_def_101,type,
sK21:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > X0 ) ).
thf(func_def_102,type,
sK22:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > X0 ) ).
thf(func_def_103,type,
sK23:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).
thf(func_def_104,type,
sK24:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).
thf(func_def_105,type,
sK25:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > X0 ) ).
thf(func_def_106,type,
sK26:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > X0 ) ).
thf(func_def_107,type,
sK27:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).
thf(func_def_108,type,
sK28:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).
thf(func_def_109,type,
sK29:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).
thf(func_def_110,type,
sK30:
!>[X0: $tType] : ( coindu1593790203_llist(X0) > X0 ) ).
thf(func_def_111,type,
sK31:
!>[X0: $tType] : ( coindu1593790203_llist(X0) > coindu1593790203_llist(X0) ) ).
thf(func_def_112,type,
sK32:
!>[X0: $tType] : ( list(X0) > X0 ) ).
thf(func_def_113,type,
sK33:
!>[X0: $tType] : ( list(X0) > X0 ) ).
thf(func_def_114,type,
sK34:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
thf(func_def_115,type,
sK35:
!>[X0: $tType] : ( list(X0) > X0 ) ).
thf(func_def_116,type,
sK36:
!>[X0: $tType] : ( list(X0) > X0 ) ).
thf(func_def_117,type,
sK37:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
thf(func_def_118,type,
sK38:
!>[X0: $tType] : ( list(X0) > X0 ) ).
thf(func_def_119,type,
sK39:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
thf(func_def_120,type,
sK40:
!>[X0: $tType] : ( list(list(X0)) > X0 ) ).
thf(func_def_121,type,
sK41:
!>[X0: $tType] : ( list(list(X0)) > list(X0) ) ).
thf(func_def_122,type,
sK42:
!>[X0: $tType] : ( list(list(X0)) > list(list(X0)) ) ).
thf(func_def_123,type,
sK43:
!>[X0: $tType] : ( list(list(X0)) > list(list(X0)) ) ).
thf(func_def_124,type,
sK44: ( nat > $o ) > nat ).
thf(func_def_125,type,
sK45: ( extended_enat > $o ) > extended_enat ).
thf(func_def_126,type,
sK46: ( nat > $o ) > nat ).
thf(func_def_127,type,
sK47: ( num > $o ) > num ).
thf(func_def_128,type,
sK48: ( list(nat) > $o ) > nat ).
thf(func_def_129,type,
sK49: ( list(nat) > $o ) > list(nat) ).
thf(func_def_130,type,
sK50: nat > nat > nat ).
thf(func_def_131,type,
sK51: nat > nat > nat ).
thf(func_def_132,type,
sK52: nat > nat > nat ).
thf(func_def_133,type,
sK53:
!>[X0: $tType] : ( ( list(X0) > $o ) > X0 ) ).
thf(func_def_134,type,
sK54:
!>[X0: $tType] : ( ( list(X0) > $o ) > list(X0) ) ).
thf(func_def_135,type,
sK55:
!>[X0: $tType] : ( ( list(X0) > $o ) > X0 ) ).
thf(func_def_136,type,
sK56:
!>[X0: $tType] : ( ( list(X0) > $o ) > X0 ) ).
thf(func_def_137,type,
sK57:
!>[X0: $tType] : ( ( list(X0) > $o ) > X0 ) ).
thf(func_def_138,type,
sK58:
!>[X0: $tType] : ( ( list(X0) > $o ) > list(X0) ) ).
thf(func_def_139,type,
sK59:
!>[X0: $tType] : ( ( list(X0) > $o ) > X0 ) ).
thf(func_def_140,type,
sK60:
!>[X0: $tType] : ( ( list(X0) > $o ) > X0 ) ).
thf(func_def_141,type,
sK61:
!>[X0: $tType] : ( ( list(X0) > $o ) > list(X0) ) ).
thf(func_def_142,type,
sK62:
!>[X0: $tType] : ( ( list(X0) > $o ) > X0 ) ).
thf(func_def_143,type,
sK63:
!>[X0: $tType] : ( ( list(X0) > $o ) > list(X0) ) ).
thf(func_def_144,type,
sK64: nat > ( nat > $o ) > nat ).
thf(func_def_145,type,
sK65: ( nat > $o ) > nat > nat ).
thf(func_def_146,type,
sK66: ( nat > nat > $o ) > nat ).
thf(func_def_147,type,
sK67: ( nat > nat > $o ) > nat ).
thf(func_def_148,type,
sK68: ( nat > nat > $o ) > nat ).
thf(func_def_149,type,
sK69: ( nat > nat > $o ) > nat ).
thf(func_def_150,type,
sK70:
!>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).
thf(func_def_151,type,
sK71:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).
thf(func_def_152,type,
sK72:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).
thf(func_def_153,type,
sK73:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > X0 ) ).
thf(func_def_154,type,
sK74:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).
thf(func_def_155,type,
sK75:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > X0 ) ).
thf(func_def_156,type,
sK76:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).
thf(func_def_157,type,
sK77:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > X0 ) ).
thf(func_def_158,type,
sK78:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).
thf(func_def_159,type,
sK79:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).
thf(func_def_160,type,
sK80:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).
thf(func_def_161,type,
sK81:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).
thf(func_def_162,type,
sK82:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > X0 ) ).
thf(func_def_163,type,
sK83:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).
thf(func_def_164,type,
sK84:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > X0 ) ).
thf(func_def_165,type,
sK85:
!>[X0: $tType] : ( ( list(X0) > list(X0) > $o ) > list(X0) ) ).
thf(func_def_166,type,
sK86:
!>[X0: $tType,X1: $tType] : ( ( list(X0) > list(X1) > $o ) > X0 ) ).
thf(func_def_167,type,
sK87:
!>[X0: $tType,X1: $tType] : ( ( list(X0) > list(X1) > $o ) > list(X0) ) ).
thf(func_def_168,type,
sK88:
!>[X0: $tType,X1: $tType] : ( ( list(X0) > list(X1) > $o ) > X1 ) ).
thf(func_def_169,type,
sK89:
!>[X0: $tType,X1: $tType] : ( ( list(X0) > list(X1) > $o ) > list(X1) ) ).
thf(func_def_170,type,
sK90:
!>[X0: $tType,X1: $tType] : ( ( list(X0) > list(X1) > $o ) > X1 ) ).
thf(func_def_171,type,
sK91:
!>[X0: $tType,X1: $tType] : ( ( list(X0) > list(X1) > $o ) > list(X1) ) ).
thf(func_def_172,type,
sK92:
!>[X0: $tType,X1: $tType] : ( ( list(X0) > list(X1) > $o ) > X0 ) ).
thf(func_def_173,type,
sK93:
!>[X0: $tType,X1: $tType] : ( ( list(X0) > list(X1) > $o ) > list(X0) ) ).
thf(func_def_174,type,
sK94:
!>[X0: $tType,X1: $tType] : ( ( ( X0 > X1 ) > list(X0) > list(X1) > $o ) > X0 > X1 ) ).
thf(func_def_175,type,
sK95:
!>[X0: $tType,X1: $tType] : ( ( ( X0 > X1 ) > list(X0) > list(X1) > $o ) > X0 ) ).
thf(func_def_176,type,
sK96:
!>[X0: $tType,X1: $tType] : ( ( ( X0 > X1 ) > list(X0) > list(X1) > $o ) > list(X0) ) ).
thf(func_def_177,type,
sK97:
!>[X0: $tType,X1: $tType] : ( ( ( X0 > X1 ) > list(X0) > list(X1) > $o ) > list(X1) ) ).
thf(func_def_178,type,
sK98:
!>[X0: $tType,X1: $tType] : ( ( ( X0 > X1 ) > list(X0) > list(X1) > $o ) > X0 > X1 ) ).
thf(func_def_179,type,
sK99:
!>[X0: $tType,X1: $tType] : ( ( ( X0 > X1 ) > list(X0) > list(X1) > $o ) > list(X1) ) ).
thf(func_def_180,type,
sK100:
!>[X0: $tType] : ( ( ( nat > X0 > X0 ) > nat > nat > X0 > $o ) > nat > X0 > X0 ) ).
thf(func_def_181,type,
sK101:
!>[X0: $tType] : ( ( ( nat > X0 > X0 ) > nat > nat > X0 > $o ) > nat ) ).
thf(func_def_182,type,
sK102:
!>[X0: $tType] : ( ( ( nat > X0 > X0 ) > nat > nat > X0 > $o ) > nat ) ).
thf(func_def_183,type,
sK103:
!>[X0: $tType] : ( ( ( nat > X0 > X0 ) > nat > nat > X0 > $o ) > X0 ) ).
thf(func_def_185,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_186,type,
vIMP: $o > $o > $o ).
thf(func_def_187,type,
sK105:
!>[X0: $tType] : ( coindu1593790203_llist(X0) > list(X0) > X0 > list(X0) ) ).
thf(func_def_188,type,
sK106: nat > nat > nat ).
thf(func_def_189,type,
sK107:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
thf(func_def_190,type,
sK108:
!>[X0: $tType] : ( coindu1593790203_llist(X0) > coindu1593790203_llist(X0) ) ).
thf(f27859,plain,
$false,
inference(subsumption_resolution,[],[f27849,f1417]) ).
thf(f1417,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0))) ),
inference(cnf_transformation,[],[f641]) ).
thf(f641,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0))) ),
inference(fool_elimination,[],[f640]) ).
thf(f640,plain,
! [X0: nat,X1: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0))),
inference(rectify,[],[f92]) ).
thf(f92,axiom,
! [X24: nat,X3: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X24),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X24))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_less__add__Suc2) ).
thf(f27849,plain,
$true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),ma),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),ma))),
inference(trivial_inequality_removal,[],[f27841]) ).
thf(f27841,plain,
( ( vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,ma),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),ma)))) != vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,ma),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),ma)))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),ma),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),ma))) ) ),
inference(superposition,[],[f1825,f1400]) ).
thf(f1400,plain,
! [X0: nat,X1: nat] :
( ( vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),X0),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,X0)),X1)) = vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
inference(cnf_transformation,[],[f1006]) ).
thf(f1006,plain,
! [X0: nat,X1: nat] :
( ( vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),X0),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,X0)),X1)) = vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
inference(ennf_transformation,[],[f611]) ).
thf(f611,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) )
=> ( vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),X0),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,X0)),X1)) = vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,X0),X1) ) ),
inference(fool_elimination,[],[f610]) ).
thf(f610,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)
=> ( vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),X0),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,X0)),X1)) = vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,X0),X1) ) ),
inference(rectify,[],[f30]) ).
thf(f30,axiom,
! [X24: nat,X25: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X24),X25)
=> ( vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,X24),X25) = vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),X24),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,X24)),X25)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_upt__conv__Cons) ).
thf(f1825,plain,
vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,ma),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),ma)))) != vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),ma),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,ma)),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),ma))))),
inference(backward_demodulation,[],[f1824,f1359]) ).
thf(f1359,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,suc,X1)) ),
inference(cnf_transformation,[],[f808]) ).
thf(f808,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,suc,X1)) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X3: nat,X4: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,suc,X4)) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_add__Suc__right) ).
thf(f1824,plain,
vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),ma),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,ma)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),vAPP(nat,nat,suc,ma))))) != vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,ma),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),ma)))),
inference(backward_demodulation,[],[f1181,f1358]) ).
thf(f1358,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0)),X1) ),
inference(cnf_transformation,[],[f807]) ).
thf(f807,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0)),X1) ),
inference(rectify,[],[f10]) ).
thf(f10,axiom,
! [X3: nat,X4: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X4)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X3)),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_add__Suc) ).
thf(f1181,plain,
vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),ma),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,ma)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),vAPP(nat,nat,suc,ma))))) != vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,ma),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,na)),ma))),
inference(cnf_transformation,[],[f775]) ).
thf(f775,plain,
vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),ma),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,ma)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),vAPP(nat,nat,suc,ma))))) != vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,ma),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,na)),ma))),
inference(flattening,[],[f292]) ).
thf(f292,negated_conjecture,
vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),ma),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,ma)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),vAPP(nat,nat,suc,ma))))) != vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,ma),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,na)),ma))),
inference(negated_conjecture,[],[f291]) ).
thf(f291,conjecture,
vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(list(nat),list(nat),vAPP(nat,sTfun(list(nat),list(nat)),cons(nat),ma),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,vAPP(nat,nat,suc,ma)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),na),vAPP(nat,nat,suc,ma))))) = vAPP(list(nat),coindu1593790203_llist(nat),coindu1079202755ist_of(nat),vAPP(nat,list(nat),vAPP(nat,sTfun(nat,list(nat)),upt,ma),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,na)),ma))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : DAT137^1 : TPTP v8.2.0. Released v7.0.0.
% 0.09/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.09/0.30 % Computer : n026.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Sun May 19 23:31:52 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.09/0.30 % (19079)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.33 % (19082)WARNING: value z3 for option sas not known
% 0.15/0.33 % (19085)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)
% 0.15/0.33 % (19083)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.33 % (19084)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)
% 0.15/0.33 % (19082)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)
% 0.15/0.33 % (19080)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.33 % (19081)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.33 % (19086)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)
% 0.15/0.36 % (19086)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.36 % Exception at run slice level
% 0.15/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.37 % Exception at run slice level
% 0.15/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.37 % Exception at run slice level
% 0.15/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.38 % (19087)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.15/0.38 % (19088)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)
% 0.15/0.39 % (19089)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)
% 0.15/0.41 % (19087)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.41 % Exception at run slice level
% 0.15/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.42 % (19088)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.43 % (19090)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)
% 11.68/1.97 % (19089)First to succeed.
% 11.68/1.98 % (19089)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-19079"
% 11.68/1.98 % (19089)Refutation found. Thanks to Tanya!
% 11.68/1.98 % SZS status Theorem for theBenchmark
% 11.68/1.98 % SZS output start Proof for theBenchmark
% See solution above
% 11.68/1.98 % (19089)------------------------------
% 11.68/1.98 % (19089)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 11.68/1.98 % (19089)Termination reason: Refutation
% 11.68/1.98
% 11.68/1.98 % (19089)Memory used [KB]: 9258
% 11.68/1.98 % (19089)Time elapsed: 1.591 s
% 11.68/1.98 % (19089)Instructions burned: 3475 (million)
% 11.68/1.98 % (19079)Success in time 1.665 s
%------------------------------------------------------------------------------