TSTP Solution File: ITP026^2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP026^2 : 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 : n008.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 22:48:25 EDT 2024
% Result : Theorem 6.64s 1.32s
% Output : Refutation 6.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 183
% Syntax : Number of formulae : 258 ( 31 unt; 167 typ; 0 def)
% Number of atoms : 650 ( 127 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 160 ( 65 ~; 67 |; 1 &; 0 @)
% ( 3 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 9 ( 8 usr)
% Number of type conns : 355 ( 344 >; 11 *; 0 +; 0 <<)
% Number of symbols : 157 ( 154 usr; 14 con; 0-9 aty)
% Number of variables : 204 ( 0 ^ 65 !; 0 ?; 204 :)
% ( 139 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
carrier_ext: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
set: $tType > $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_8,type,
ring_ext: ( $tType * $tType ) > $tType ).
thf(type_def_9,type,
aGroup_ext: ( $tType * $tType ) > $tType ).
thf(type_def_10,type,
module_ext: ( $tType * $tType * $tType ) > $tType ).
thf(type_def_11,type,
product_unit: $tType ).
thf(type_def_12,type,
nat: $tType ).
thf(type_def_13,type,
a: $tType ).
thf(type_def_14,type,
b: $tType ).
thf(type_def_15,type,
c: $tType ).
thf(type_def_16,type,
e: $tType ).
thf(type_def_17,type,
f: $tType ).
thf(type_def_18,type,
d: $tType ).
thf(func_def_0,type,
carrier_ext: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
module_ext: ( $tType * $tType * $tType ) > $tType ).
thf(func_def_2,type,
aGroup_ext: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
ring_ext: ( $tType * $tType ) > $tType ).
thf(func_def_4,type,
product_unit: $tType ).
thf(func_def_5,type,
set: $tType > $tType ).
thf(func_def_6,type,
nat: $tType ).
thf(func_def_7,type,
f: $tType ).
thf(func_def_8,type,
e: $tType ).
thf(func_def_9,type,
d: $tType ).
thf(func_def_10,type,
c: $tType ).
thf(func_def_11,type,
b: $tType ).
thf(func_def_12,type,
a: $tType ).
thf(func_def_13,type,
type:
!>[X0: $tType] : $o ).
thf(func_def_14,type,
zero:
!>[X0: $tType] : $o ).
thf(func_def_15,type,
order:
!>[X0: $tType] : $o ).
thf(func_def_16,type,
group_add:
!>[X0: $tType] : $o ).
thf(func_def_17,type,
wellorder:
!>[X0: $tType] : $o ).
thf(func_def_18,type,
comm_monoid_diff:
!>[X0: $tType] : $o ).
thf(func_def_19,type,
ordered_ab_group_add:
!>[X0: $tType] : $o ).
thf(func_def_20,type,
cancel1352612707id_add:
!>[X0: $tType] : $o ).
thf(func_def_21,type,
canoni770627133id_add:
!>[X0: $tType] : $o ).
thf(func_def_22,type,
carrier:
!>[X0: $tType,X1: $tType] : ( carrier_ext(X0,X1) > set(X0) ) ).
thf(func_def_23,type,
ring:
!>[X0: $tType,X1: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > $o ) ).
thf(func_def_24,type,
zero2:
!>[X0: $tType,X1: $tType] : ( carrier_ext(X0,aGroup_ext(X0,X1)) > X0 ) ).
thf(func_def_25,type,
ideal:
!>[X0: $tType,X1: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > set(X0) > $o ) ).
thf(func_def_26,type,
annihilator:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > set(X0) ) ).
thf(func_def_27,type,
hom:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > carrier_ext(X4,aGroup_ext(X4,module_ext(X4,X0,X5))) > carrier_ext(sTfun(X2,X4),aGroup_ext(sTfun(X2,X4),module_ext(sTfun(X2,X4),X0,product_unit))) ) ).
thf(func_def_28,type,
module:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( carrier_ext(X0,aGroup_ext(X0,module_ext(X0,X1,X2))) > carrier_ext(X1,aGroup_ext(X1,ring_ext(X1,X3))) > $o ) ).
thf(func_def_29,type,
free_generator:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > set(X2) > $o ) ).
thf(func_def_30,type,
generator:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > set(X2) > $o ) ).
thf(func_def_31,type,
l_comb:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > nat > ( nat > X0 ) > ( nat > X2 ) > X2 ) ).
thf(func_def_32,type,
linear_span:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > set(X0) > set(X2) > set(X2) ) ).
thf(func_def_33,type,
mdl:
!>[X0: $tType,X1: $tType,X2: $tType] : ( carrier_ext(X0,aGroup_ext(X0,module_ext(X0,X1,X2))) > set(X0) > carrier_ext(X0,aGroup_ext(X0,module_ext(X0,X1,product_unit))) ) ).
thf(func_def_34,type,
misomorphic:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > carrier_ext(X4,aGroup_ext(X4,module_ext(X4,X0,X5))) > $o ) ).
thf(func_def_35,type,
quotie135653060odules:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > set(X2) > set(X2) > set(X0) ) ).
thf(func_def_36,type,
smodule_ideal_coeff:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > set(X0) > set(X2) ) ).
thf(func_def_37,type,
submodule:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > set(X2) > $o ) ).
thf(func_def_38,type,
algebr833503410le_fgs:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > set(X2) > set(X2) ) ).
thf(func_def_39,type,
pi:
!>[X0: $tType,X1: $tType] : ( set(X0) > ( X0 > set(X1) ) > set(sTfun(X0,X1)) ) ).
thf(func_def_40,type,
minus_minus:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_41,type,
zero_zero:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
suc: nat > nat ).
thf(func_def_43,type,
bot_bot:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
ord_less:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_45,type,
ord_less_eq:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_46,type,
collect:
!>[X0: $tType] : ( ( X0 > $o ) > set(X0) ) ).
thf(func_def_47,type,
insert:
!>[X0: $tType] : ( X0 > set(X0) > set(X0) ) ).
thf(func_def_48,type,
member:
!>[X0: $tType] : ( X0 > set(X0) > $o ) ).
thf(func_def_49,type,
h: set(a) ).
thf(func_def_50,type,
h1: set(a) ).
thf(func_def_51,type,
m: carrier_ext(a,aGroup_ext(a,module_ext(a,b,c))) ).
thf(func_def_52,type,
n: carrier_ext(e,aGroup_ext(e,module_ext(e,b,f))) ).
thf(func_def_53,type,
r: carrier_ext(b,aGroup_ext(b,ring_ext(b,d))) ).
thf(func_def_54,type,
g: nat > a ).
thf(func_def_55,type,
h2: a ).
thf(func_def_56,type,
m2: nat ).
thf(func_def_57,type,
t: nat > b ).
thf(func_def_58,type,
x: a ).
thf(func_def_59,type,
xa: nat ).
thf(func_def_63,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_64,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_65,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_66,type,
vAND: $o > $o > $o ).
thf(func_def_67,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_68,type,
vNOT: $o > $o ).
thf(func_def_69,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_70,type,
vOR: $o > $o > $o ).
thf(func_def_71,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_72,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_73,type,
vIMP: $o > $o > $o ).
thf(func_def_74,type,
sP0: nat > ( nat > $o ) > $o ).
thf(func_def_75,type,
sP1: ( nat > nat > $o ) > $o ).
thf(func_def_76,type,
sP2:
!>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > $o ) ).
thf(func_def_77,type,
sK3: nat > nat ).
thf(func_def_78,type,
sK4: nat > nat ).
thf(func_def_79,type,
sK5:
!>[X0: $tType] : ( ( nat > X0 ) > nat ) ).
thf(func_def_80,type,
sK6:
!>[X0: $tType] : ( ( nat > X0 ) > nat ) ).
thf(func_def_81,type,
sK7:
!>[X0: $tType] : ( ( nat > X0 ) > nat ) ).
thf(func_def_82,type,
sK8:
!>[X0: $tType] : ( ( nat > X0 ) > nat ) ).
thf(func_def_83,type,
sK9: nat > nat ).
thf(func_def_84,type,
sK10: a > set(a) > nat ).
thf(func_def_85,type,
sK11: a > set(a) > nat > a ).
thf(func_def_86,type,
sK12: a > set(a) > nat > b ).
thf(func_def_87,type,
sK13: ( nat > $o ) > nat ).
thf(func_def_88,type,
sK14: ( nat > $o ) > nat ).
thf(func_def_89,type,
sK15: ( nat > $o ) > nat ).
thf(func_def_90,type,
sK16:
!>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_91,type,
sK17:
!>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_92,type,
sK18: nat > ( nat > $o ) > nat ).
thf(func_def_93,type,
sK19: nat > ( nat > $o ) > nat ).
thf(func_def_94,type,
sK20: ( nat > $o ) > nat ).
thf(func_def_95,type,
sK21: ( nat > $o ) > nat ).
thf(func_def_96,type,
sK22: ( nat > $o ) > nat ).
thf(func_def_97,type,
sK23: ( nat > $o ) > nat ).
thf(func_def_98,type,
sK24: nat > nat > nat ).
thf(func_def_99,type,
sK25: nat > nat > nat ).
thf(func_def_100,type,
sK26: nat > nat ).
thf(func_def_101,type,
sK27: a > set(b) > nat ).
thf(func_def_102,type,
sK28: a > set(b) > nat > b ).
thf(func_def_103,type,
sK29: a > set(b) > nat > a ).
thf(func_def_104,type,
sK30:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_105,type,
sK31:
!>[X0: $tType] : ( set(X0) > set(X0) > X0 ) ).
thf(func_def_106,type,
sK32: ( nat > nat > $o ) > nat ).
thf(func_def_107,type,
sK33: ( nat > nat > $o ) > nat ).
thf(func_def_108,type,
sK34: ( nat > nat > $o ) > nat ).
thf(func_def_109,type,
sK35: ( nat > nat > $o ) > nat ).
thf(func_def_110,type,
sK36: ( nat > nat ) > nat ).
thf(func_def_111,type,
sK37: ( nat > nat ) > nat ).
thf(func_def_112,type,
sK38: ( nat > $o ) > nat ).
thf(func_def_113,type,
sK39: nat > ( nat > $o ) > nat ).
thf(func_def_114,type,
sK40: ( nat > $o ) > nat ).
thf(func_def_115,type,
sK41: nat > ( nat > $o ) > nat ).
thf(func_def_116,type,
sK42: ( nat > $o ) > nat > nat ).
thf(func_def_117,type,
sK43: ( nat > nat > $o ) > nat ).
thf(func_def_118,type,
sK44: ( nat > nat > $o ) > nat ).
thf(func_def_119,type,
sK45: ( nat > nat > $o ) > nat ).
thf(func_def_120,type,
sK46: ( nat > nat > $o ) > nat ).
thf(func_def_121,type,
sK47: ( nat > nat > $o ) > nat ).
thf(func_def_122,type,
sK48: ( nat > nat > $o ) > nat ).
thf(func_def_123,type,
sK49: ( nat > nat > $o ) > nat ).
thf(func_def_124,type,
sK50: ( nat > nat > $o ) > nat ).
thf(func_def_125,type,
sK51: ( nat > nat > $o ) > nat ).
thf(func_def_126,type,
sK52: ( nat > $o ) > nat > nat ).
thf(func_def_127,type,
sK53: ( nat > $o ) > nat > nat > nat ).
thf(func_def_128,type,
sK54: ( nat > $o ) > nat > nat > nat ).
thf(func_def_129,type,
sK55:
!>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).
thf(func_def_130,type,
sK56:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).
thf(func_def_131,type,
sK57:
!>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).
thf(func_def_132,type,
sK58: ( nat > a ) > ( nat > a ) > nat > nat ).
thf(func_def_133,type,
sK59: ( nat > a ) > ( nat > a ) > nat > nat ).
thf(func_def_134,type,
sK60:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( X3 > set(X3) > carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X2))) > carrier_ext(X3,aGroup_ext(X3,module_ext(X3,X0,X1))) > nat ) ).
thf(func_def_135,type,
sK61:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( X3 > set(X3) > carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X2))) > carrier_ext(X3,aGroup_ext(X3,module_ext(X3,X0,X1))) > nat > X3 ) ).
thf(func_def_136,type,
sK62:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( X3 > set(X3) > carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X2))) > carrier_ext(X3,aGroup_ext(X3,module_ext(X3,X0,X1))) > nat > X0 ) ).
thf(func_def_137,type,
sK63:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( X3 > set(X0) > carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X2))) > carrier_ext(X3,aGroup_ext(X3,module_ext(X3,X0,X1))) > nat ) ).
thf(func_def_138,type,
sK64:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( X3 > set(X0) > carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X2))) > carrier_ext(X3,aGroup_ext(X3,module_ext(X3,X0,X1))) > nat > X0 ) ).
thf(func_def_139,type,
sK65:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( X3 > set(X0) > carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X2))) > carrier_ext(X3,aGroup_ext(X3,module_ext(X3,X0,X1))) > nat > X3 ) ).
thf(func_def_140,type,
sK66:
!>[X0: $tType] : ( ( nat > X0 ) > ( nat > X0 ) > nat > nat ) ).
thf(func_def_141,type,
sK67:
!>[X0: $tType] : ( ( nat > X0 ) > ( nat > X0 ) > nat > nat ) ).
thf(func_def_143,type,
sK69: nat > nat > nat ).
thf(func_def_144,type,
sK70: nat > nat > nat ).
thf(func_def_145,type,
sK71: ( nat > $o ) > nat > nat ).
thf(func_def_146,type,
sK72: ( nat > $o ) > nat > nat ).
thf(func_def_147,type,
sK73: ( nat > $o ) > nat > nat ).
thf(func_def_148,type,
sK74: ( nat > $o ) > nat > nat ).
thf(func_def_149,type,
sK75:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_150,type,
sK76: ( nat > $o ) > nat > nat ).
thf(func_def_151,type,
sK77: ( nat > $o ) > nat > nat ).
thf(func_def_152,type,
sK78: ( nat > $o ) > nat > nat ).
thf(func_def_153,type,
sK79: ( nat > $o ) > nat > nat ).
thf(func_def_154,type,
sK80:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_155,type,
sK81:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_156,type,
sK82: nat > nat ).
thf(f12221,plain,
$false,
inference(avatar_sat_refutation,[],[f10182,f11320,f12126,f12216]) ).
thf(f12216,plain,
spl68_98,
inference(avatar_contradiction_clause,[],[f12215]) ).
thf(f12215,plain,
( $false
| spl68_98 ),
inference(trivial_inequality_removal,[],[f12214]) ).
thf(f12214,plain,
( ( $true = $false )
| spl68_98 ),
inference(forward_demodulation,[],[f12213,f12146]) ).
thf(f12146,plain,
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),m2) )
| spl68_98 ),
inference(trivial_inequality_removal,[],[f12145]) ).
thf(f12145,plain,
( ( $true != $true )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),m2) )
| spl68_98 ),
inference(superposition,[],[f10177,f289]) ).
thf(f289,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f10177,plain,
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),m2) )
| spl68_98 ),
inference(avatar_component_clause,[],[f10175]) ).
thf(f10175,plain,
( spl68_98
<=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),m2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl68_98])]) ).
thf(f12213,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),m2),
inference(forward_demodulation,[],[f11281,f12203]) ).
thf(f12203,plain,
m2 = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat)))),
inference(trivial_inequality_removal,[],[f12180]) ).
thf(f12180,plain,
( ( $true != $true )
| ( m2 = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat)))) ) ),
inference(superposition,[],[f1287,f1234]) ).
thf(f1234,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),m2) = $true,
inference(cnf_transformation,[],[f299]) ).
thf(f299,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),m2) = $true,
inference(fool_elimination,[],[f298]) ).
thf(f298,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),m2),
inference(rectify,[],[f281]) ).
thf(f281,axiom,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),m2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_16) ).
thf(f1287,plain,
! [X0: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) )
| ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,suc,zero_zero(nat)))) = X0 ) ),
inference(cnf_transformation,[],[f871]) ).
thf(f871,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,suc,zero_zero(nat)))) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) ) ),
inference(ennf_transformation,[],[f379]) ).
thf(f379,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) )
=> ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,suc,zero_zero(nat)))) = X0 ) ),
inference(fool_elimination,[],[f378]) ).
thf(f378,plain,
! [X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)
=> ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,suc,zero_zero(nat)))) = X0 ) ),
inference(rectify,[],[f27]) ).
thf(f27,axiom,
! [X19: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X19)
=> ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X19),vAPP(nat,nat,suc,zero_zero(nat)))) = X19 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_Suc__pred) ).
thf(f11281,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat))))),
inference(trivial_inequality_removal,[],[f11278]) ).
thf(f11278,plain,
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat))))) ) ),
inference(superposition,[],[f1401,f1237]) ).
thf(f1237,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat)))) = $true,
inference(cnf_transformation,[],[f305]) ).
thf(f305,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat)))) = $true,
inference(fool_elimination,[],[f304]) ).
thf(f304,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat)))),
inference(rectify,[],[f284]) ).
thf(f284,axiom,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_19) ).
thf(f1401,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,suc,X1)) ) ),
inference(cnf_transformation,[],[f938]) ).
thf(f938,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,suc,X1)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
inference(ennf_transformation,[],[f547]) ).
thf(f547,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,suc,X1)) ) ),
inference(fool_elimination,[],[f546]) ).
thf(f546,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,suc,X1)) ),
inference(rectify,[],[f93]) ).
thf(f93,axiom,
! [X26: nat,X19: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X26),X19)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X26),vAPP(nat,nat,suc,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_le__SucI) ).
thf(f12126,plain,
~ spl68_102,
inference(avatar_contradiction_clause,[],[f12125]) ).
thf(f12125,plain,
( $false
| ~ spl68_102 ),
inference(subsumption_resolution,[],[f12124,f1253]) ).
thf(f1253,plain,
! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 ),
inference(cnf_transformation,[],[f796]) ).
thf(f796,plain,
! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 ),
inference(rectify,[],[f72]) ).
thf(f72,axiom,
! [X19: nat] : ( vAPP(nat,nat,suc,X19) != X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_n__not__Suc__n) ).
thf(f12124,plain,
( ( xa = vAPP(nat,nat,suc,xa) )
| ~ spl68_102 ),
inference(forward_demodulation,[],[f12123,f11515]) ).
thf(f11515,plain,
( ( xa = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),xa),vAPP(nat,nat,suc,zero_zero(nat))) )
| ~ spl68_102 ),
inference(forward_demodulation,[],[f11514,f10251]) ).
thf(f10251,plain,
( ( m2 = xa )
| ~ spl68_102 ),
inference(avatar_component_clause,[],[f10249]) ).
thf(f10249,plain,
( spl68_102
<=> ( m2 = xa ) ),
introduced(avatar_definition,[new_symbols(naming,[spl68_102])]) ).
thf(f11514,plain,
( ( xa = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat))) )
| ~ spl68_102 ),
inference(subsumption_resolution,[],[f11513,f1430]) ).
thf(f1430,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X0) ),
inference(cnf_transformation,[],[f599]) ).
thf(f599,plain,
! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X0) ),
inference(fool_elimination,[],[f598]) ).
thf(f598,plain,
! [X0: nat,X1: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X0),
inference(rectify,[],[f146]) ).
thf(f146,axiom,
! [X26: nat,X19: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X26),X19)),X26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_diff__le__self) ).
thf(f11513,plain,
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),xa),vAPP(nat,nat,suc,zero_zero(nat)))),xa) )
| ( xa = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat))) )
| ~ spl68_102 ),
inference(forward_demodulation,[],[f11283,f10251]) ).
thf(f11283,plain,
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat)))),xa) )
| ( xa = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat))) ) ),
inference(trivial_inequality_removal,[],[f11276]) ).
thf(f11276,plain,
( ( $true != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat)))),xa) )
| ( xa = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat))) ) ),
inference(superposition,[],[f1399,f1237]) ).
thf(f1399,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f936]) ).
thf(f936,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
inference(flattening,[],[f935]) ).
thf(f935,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
inference(ennf_transformation,[],[f543]) ).
thf(f543,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f542]) ).
thf(f542,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f70]) ).
thf(f70,axiom,
! [X26: nat,X19: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X26),X19)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X19),X26)
=> ( X19 = X26 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_le__antisym) ).
thf(f12123,plain,
( ( xa = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),xa),vAPP(nat,nat,suc,zero_zero(nat)))) )
| ~ spl68_102 ),
inference(trivial_inequality_removal,[],[f12105]) ).
thf(f12105,plain,
( ( $true != $true )
| ( xa = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),xa),vAPP(nat,nat,suc,zero_zero(nat)))) )
| ~ spl68_102 ),
inference(superposition,[],[f1287,f11324]) ).
thf(f11324,plain,
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),xa) )
| ~ spl68_102 ),
inference(backward_demodulation,[],[f1234,f10251]) ).
thf(f11320,plain,
( spl68_102
| ~ spl68_99 ),
inference(avatar_split_clause,[],[f11319,f10179,f10249]) ).
thf(f10179,plain,
( spl68_99
<=> ! [X0: nat] :
( ( h2 != vAPP(nat,a,g,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),m2) )
| ( xa = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl68_99])]) ).
thf(f11319,plain,
( ( m2 = xa )
| ~ spl68_99 ),
inference(subsumption_resolution,[],[f11318,f1575]) ).
thf(f1575,plain,
! [X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X1) ),
inference(equality_resolution,[],[f1354]) ).
thf(f1354,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f895]) ).
thf(f895,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
| ( ( X0 != X1 )
& ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ) ),
inference(ennf_transformation,[],[f483]) ).
thf(f483,plain,
! [X0: nat,X1: nat] :
( ( ( X0 = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
inference(fool_elimination,[],[f482]) ).
thf(f482,plain,
! [X0: nat,X1: nat] :
( ( ( X0 = X1 )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ),
inference(rectify,[],[f115]) ).
thf(f115,axiom,
! [X26: nat,X19: nat] :
( ( ( X19 = X26 )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X26),X19) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X26),X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_less__or__eq__imp__le) ).
thf(f11318,plain,
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),m2),m2) )
| ( m2 = xa )
| ~ spl68_99 ),
inference(trivial_inequality_removal,[],[f11317]) ).
thf(f11317,plain,
( ( h2 != h2 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),m2),m2) )
| ( m2 = xa )
| ~ spl68_99 ),
inference(superposition,[],[f10180,f1229]) ).
thf(f1229,plain,
h2 = vAPP(nat,a,g,m2),
inference(cnf_transformation,[],[f268]) ).
thf(f268,axiom,
h2 = vAPP(nat,a,g,m2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(f10180,plain,
( ! [X0: nat] :
( ( h2 != vAPP(nat,a,g,X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),m2) )
| ( xa = X0 ) )
| ~ spl68_99 ),
inference(avatar_component_clause,[],[f10179]) ).
thf(f10182,plain,
( ~ spl68_98
| spl68_99 ),
inference(avatar_split_clause,[],[f10160,f10179,f10175]) ).
thf(f10160,plain,
! [X0: nat] :
( ( h2 != vAPP(nat,a,g,X0) )
| ( xa = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),m2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),m2) ) ),
inference(superposition,[],[f1233,f1816]) ).
thf(f1816,plain,
h2 = vAPP(nat,a,g,xa),
inference(subsumption_resolution,[],[f1231,f1228]) ).
thf(f1228,plain,
vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(nat,a,g,xa)),h1) != $true,
inference(cnf_transformation,[],[f794]) ).
thf(f794,plain,
vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(nat,a,g,xa)),h1) != $true,
inference(flattening,[],[f291]) ).
thf(f291,plain,
vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(nat,a,g,xa)),h1) != $true,
inference(fool_elimination,[],[f290]) ).
thf(f290,plain,
~ vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(nat,a,g,xa)),h1),
inference(rectify,[],[f287]) ).
thf(f287,negated_conjecture,
~ vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(nat,a,g,xa)),h1),
inference(negated_conjecture,[],[f286]) ).
thf(f286,conjecture,
vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(nat,a,g,xa)),h1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_21) ).
thf(f1231,plain,
( ( vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(nat,a,g,xa)),h1) = $true )
| ( h2 = vAPP(nat,a,g,xa) ) ),
inference(cnf_transformation,[],[f293]) ).
thf(f293,plain,
( ( vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(nat,a,g,xa)),h1) = $true )
| ( h2 = vAPP(nat,a,g,xa) ) ),
inference(fool_elimination,[],[f292]) ).
thf(f292,plain,
( vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(nat,a,g,xa)),h1)
| ( h2 = vAPP(nat,a,g,xa) ) ),
inference(rectify,[],[f285]) ).
thf(f285,axiom,
( vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(nat,a,g,xa)),h1)
| ( h2 = vAPP(nat,a,g,xa) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_20) ).
thf(f1233,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,a,g,X0) != vAPP(nat,a,g,X1) )
| ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),m2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),m2) ) ),
inference(cnf_transformation,[],[f850]) ).
thf(f850,plain,
! [X0: nat] :
( ! [X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,a,g,X0) != vAPP(nat,a,g,X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),m2) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),m2) ) ),
inference(flattening,[],[f849]) ).
thf(f849,plain,
! [X0: nat] :
( ! [X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,a,g,X0) != vAPP(nat,a,g,X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),m2) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),m2) ) ),
inference(ennf_transformation,[],[f297]) ).
thf(f297,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),m2) )
=> ! [X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),m2) )
=> ( ( vAPP(nat,a,g,X0) = vAPP(nat,a,g,X1) )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[],[f296]) ).
thf(f296,plain,
! [X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),m2)
=> ! [X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),m2)
=> ( ( vAPP(nat,a,g,X0) = vAPP(nat,a,g,X1) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f266]) ).
thf(f266,axiom,
! [X79: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X79),m2)
=> ! [X48: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X48),m2)
=> ( ( vAPP(nat,a,g,X79) = vAPP(nat,a,g,X48) )
=> ( X48 = X79 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : ITP026^2 : TPTP v8.2.0. Released v7.5.0.
% 0.02/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat May 18 18:34:52 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % (764)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.39 % (767)WARNING: value z3 for option sas not known
% 0.18/0.39 % (769)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)
% 0.18/0.39 % (771)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)
% 0.18/0.39 % (774)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)
% 0.18/0.39 % (767)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)
% 0.18/0.39 % (765)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.18/0.39 % (768)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.18/0.39 % (766)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.18/0.44 % (774)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.18/0.44 % Exception at run slice level
% 0.18/0.44 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.45 % Exception at run slice level
% 0.18/0.45 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.45 % Exception at run slice level
% 0.18/0.45 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.46 % (775)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.18/0.46 % (776)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)
% 0.18/0.46 % (777)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)
% 0.18/0.51 % (776)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.18/0.51 % (775)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.18/0.52 % Exception at run slice level
% 0.18/0.52 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.54 % (778)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)
% 6.64/1.31 % (777)First to succeed.
% 6.64/1.31 % (777)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-764"
% 6.64/1.32 % (777)Refutation found. Thanks to Tanya!
% 6.64/1.32 % SZS status Theorem for theBenchmark
% 6.64/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 6.64/1.32 % (777)------------------------------
% 6.64/1.32 % (777)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 6.64/1.32 % (777)Termination reason: Refutation
% 6.64/1.32
% 6.64/1.32 % (777)Memory used [KB]: 4385
% 6.64/1.32 % (777)Time elapsed: 0.849 s
% 6.64/1.32 % (777)Instructions burned: 1518 (million)
% 6.64/1.32 % (764)Success in time 0.956 s
%------------------------------------------------------------------------------