TSTP Solution File: NUM851+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM851+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n019.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 : 600s
% DateTime : Mon Jul 18 11:56:04 EDT 2022
% Result : Theorem 1.07s 1.32s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 71
% Syntax : Number of formulae : 527 ( 354 unt; 17 typ; 0 def)
% Number of atoms : 2357 (1026 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 4046 ( 561 ~; 549 |; 40 &;2844 @)
% ( 8 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 7 con; 0-2 aty)
% Number of variables : 1334 ( 0 ^1318 !; 16 ?;1334 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_geq,type,
geq: $i > $i > $o ).
thf(tp_greater,type,
greater: $i > $i > $o ).
thf(tp_leq,type,
leq: $i > $i > $o ).
thf(tp_less,type,
less: $i > $i > $o ).
thf(tp_sK1_Vd123,type,
sK1_Vd123: $i > $i > $i ).
thf(tp_sK2_Vd125,type,
sK2_Vd125: $i > $i > $i ).
thf(tp_sK3_Vd196,type,
sK3_Vd196: $i > $i > $i ).
thf(tp_sK4_Vd201,type,
sK4_Vd201: $i > $i > $i ).
thf(tp_v1,type,
v1: $i ).
thf(tp_vd469,type,
vd469: $i ).
thf(tp_vd470,type,
vd470: $i ).
thf(tp_vd471,type,
vd471: $i ).
thf(tp_vd473,type,
vd473: $i ).
thf(tp_vmul,type,
vmul: $i > $i > $i ).
thf(tp_vplus,type,
vplus: $i > $i > $i ).
thf(tp_vskolem2,type,
vskolem2: $i > $i ).
thf(tp_vsucc,type,
vsucc: $i > $i ).
thf(1,axiom,
! [Vd1: $i] :
( ( vsucc @ Vd1 )
!= v1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).
thf(2,axiom,
! [Vd3: $i,Vd4: $i] :
( ( ( vsucc @ Vd3 )
= ( vsucc @ Vd4 ) )
=> ( Vd3 = Vd4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(antec(axiom(3)), imp(antec(axiom(3))))') ).
thf(3,axiom,
! [Vd7: $i,Vd8: $i] :
( ( Vd7 != Vd8 )
=> ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
thf(4,axiom,
! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
thf(5,axiom,
! [Vd24: $i] :
( ( Vd24 != v1 )
=> ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
thf(6,axiom,
! [Vd42: $i,Vd43: $i] :
( ( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
thf(7,axiom,
! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
thf(8,axiom,
! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(9,axiom,
! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
thf(10,axiom,
! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(11,axiom,
! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
thf(12,axiom,
! [Vd104: $i,Vd105: $i] :
( ( Vd104 != Vd105 )
=> ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
thf(13,axiom,
! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
thf(14,axiom,
! [Vd120: $i,Vd121: $i] :
( ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
thf(15,axiom,
! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
thf(16,axiom,
! [Vd120: $i,Vd121: $i] :
( ( Vd120 = Vd121 )
| ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
thf(17,axiom,
! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
thf(18,axiom,
! [Vd198: $i,Vd199: $i] :
( ( less @ Vd199 @ Vd198 )
<=> ? [Vd201: $i] :
( Vd198
= ( vplus @ Vd199 @ Vd201 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
thf(19,axiom,
! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
thf(20,axiom,
! [Vd203: $i,Vd204: $i] :
( ~ ( greater @ Vd203 @ Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
thf(21,axiom,
! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
thf(22,axiom,
! [Vd203: $i,Vd204: $i] :
( ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 )
| ( less @ Vd203 @ Vd204 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
thf(23,axiom,
! [Vd208: $i,Vd209: $i] :
( ( greater @ Vd208 @ Vd209 )
=> ( less @ Vd209 @ Vd208 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
thf(24,axiom,
! [Vd226: $i,Vd227: $i] :
( ( less @ Vd226 @ Vd227 )
=> ( greater @ Vd227 @ Vd226 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
thf(25,axiom,
! [Vd244: $i,Vd245: $i] :
( ( geq @ Vd245 @ Vd244 )
<=> ( ( greater @ Vd245 @ Vd244 )
| ( Vd245 = Vd244 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
thf(26,axiom,
! [Vd249: $i,Vd250: $i] :
( ( leq @ Vd250 @ Vd249 )
<=> ( ( less @ Vd250 @ Vd249 )
| ( Vd250 = Vd249 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 17), 1)') ).
thf(27,axiom,
! [Vd254: $i,Vd255: $i] :
( ( geq @ Vd254 @ Vd255 )
=> ( leq @ Vd255 @ Vd254 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(158, 0), 0)') ).
thf(28,axiom,
! [Vd258: $i,Vd259: $i] :
( ( leq @ Vd258 @ Vd259 )
=> ( geq @ Vd259 @ Vd258 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(163, 0), 0)') ).
thf(29,axiom,
! [Vd262: $i,Vd263: $i,Vd265: $i] :
( ( ( less @ Vd263 @ Vd265 )
& ( less @ Vd262 @ Vd263 ) )
=> ( less @ Vd262 @ Vd265 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(168, 0), 0)') ).
thf(30,axiom,
! [Vd281: $i,Vd282: $i,Vd283: $i] :
( ( ( ( less @ Vd282 @ Vd283 )
& ( leq @ Vd281 @ Vd282 ) )
| ( ( leq @ Vd282 @ Vd283 )
& ( less @ Vd281 @ Vd282 ) ) )
=> ( less @ Vd281 @ Vd283 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(177), 0), 0)') ).
thf(31,axiom,
! [Vd289: $i,Vd290: $i,Vd292: $i] :
( ( ( leq @ Vd290 @ Vd292 )
& ( leq @ Vd289 @ Vd290 ) )
=> ( leq @ Vd289 @ Vd292 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(184, 0), 0)') ).
thf(32,axiom,
! [Vd295: $i,Vd296: $i] : ( greater @ ( vplus @ Vd295 @ Vd296 ) @ Vd295 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
thf(33,axiom,
! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( greater @ Vd301 @ Vd302 )
=> ( greater @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).
thf(34,axiom,
! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( Vd301 = Vd302 )
=> ( ( vplus @ Vd301 @ Vd303 )
= ( vplus @ Vd302 @ Vd303 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 1)') ).
thf(35,axiom,
! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( less @ Vd301 @ Vd302 )
=> ( less @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 0)') ).
thf(36,axiom,
! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( greater @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
=> ( greater @ Vd328 @ Vd329 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 2)') ).
thf(37,axiom,
! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( ( vplus @ Vd328 @ Vd330 )
= ( vplus @ Vd329 @ Vd330 ) )
=> ( Vd328 = Vd329 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 1)') ).
thf(38,axiom,
! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( less @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
=> ( less @ Vd328 @ Vd329 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 0)') ).
thf(39,axiom,
! [Vd337: $i,Vd338: $i,Vd340: $i,Vd341: $i] :
( ( ( greater @ Vd340 @ Vd341 )
& ( greater @ Vd337 @ Vd338 ) )
=> ( greater @ ( vplus @ Vd337 @ Vd340 ) @ ( vplus @ Vd338 @ Vd341 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(209, 0), 0)') ).
thf(40,axiom,
! [Vd353: $i,Vd354: $i,Vd355: $i,Vd356: $i] :
( ( ( ( greater @ Vd355 @ Vd356 )
& ( geq @ Vd353 @ Vd354 ) )
| ( ( geq @ Vd355 @ Vd356 )
& ( greater @ Vd353 @ Vd354 ) ) )
=> ( greater @ ( vplus @ Vd353 @ Vd355 ) @ ( vplus @ Vd354 @ Vd356 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(216), 0), 0)') ).
thf(41,axiom,
! [Vd362: $i,Vd363: $i,Vd365: $i,Vd366: $i] :
( ( ( geq @ Vd365 @ Vd366 )
& ( geq @ Vd362 @ Vd363 ) )
=> ( geq @ ( vplus @ Vd362 @ Vd365 ) @ ( vplus @ Vd363 @ Vd366 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(223, 0), 0)') ).
thf(42,axiom,
! [Vd369: $i] : ( geq @ Vd369 @ v1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(228, 0), 0)') ).
thf(43,axiom,
! [Vd375: $i,Vd376: $i] :
( ( greater @ Vd375 @ Vd376 )
=> ( geq @ Vd375 @ ( vplus @ Vd376 @ v1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(234, 0), 0)') ).
thf(44,axiom,
! [Vd386: $i,Vd387: $i] :
( ( less @ Vd386 @ ( vplus @ Vd387 @ v1 ) )
=> ( leq @ Vd386 @ Vd387 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(241, 0), 0)') ).
thf(45,axiom,
! [Vd396: $i,Vd397: $i] :
( ( ( vmul @ Vd396 @ ( vsucc @ Vd397 ) )
= ( vplus @ ( vmul @ Vd396 @ Vd397 ) @ Vd396 ) )
& ( ( vmul @ Vd396 @ v1 )
= Vd396 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
thf(46,axiom,
! [Vd400: $i] :
( ( vmul @ v1 @ Vd400 )
= Vd400 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
thf(47,axiom,
! [Vd408: $i,Vd409: $i] :
( ( vmul @ ( vsucc @ Vd408 ) @ Vd409 )
= ( vplus @ ( vmul @ Vd408 @ Vd409 ) @ Vd409 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).
thf(48,axiom,
! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
thf(49,axiom,
! [Vd432: $i,Vd433: $i,Vd434: $i] :
( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
= ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
thf(50,axiom,
! [Vd444: $i,Vd445: $i,Vd446: $i] :
( ( vmul @ ( vmul @ Vd444 @ Vd445 ) @ Vd446 )
= ( vmul @ Vd444 @ ( vmul @ Vd445 @ Vd446 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(290, 0), 0)') ).
thf(51,axiom,
greater @ vd470 @ vd471,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(antec(302), 472, 0)') ).
thf(52,axiom,
( vd470
= ( vplus @ vd471 @ vd473 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq(302)), 474, 0)') ).
thf(53,axiom,
( ( vmul @ vd470 @ vd469 )
= ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct2(conseq(302)), 475, 0)') ).
thf(54,conjecture,
( ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 )
= ( vplus @ ( vmul @ vd471 @ vd469 ) @ ( vmul @ vd473 @ vd469 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct2(conseq(302)), 475, 1)') ).
thf(55,negated_conjecture,
( ( ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 )
= ( vplus @ ( vmul @ vd471 @ vd469 ) @ ( vmul @ vd473 @ vd469 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[54]) ).
thf(56,plain,
( ( ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 )
= ( vplus @ ( vmul @ vd471 @ vd469 ) @ ( vmul @ vd473 @ vd469 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[55]) ).
thf(57,plain,
( ( ! [Vd1: $i] :
( ( vsucc @ Vd1 )
!= v1 ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(58,plain,
( ( ! [Vd3: $i,Vd4: $i] :
( ( ( vsucc @ Vd3 )
= ( vsucc @ Vd4 ) )
=> ( Vd3 = Vd4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(59,plain,
( ( ! [Vd7: $i,Vd8: $i] :
( ( Vd7 != Vd8 )
=> ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(60,plain,
( ( ! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(61,plain,
( ( ! [Vd24: $i] :
( ( Vd24 != v1 )
=> ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(62,plain,
( ( ! [Vd42: $i,Vd43: $i] :
( ( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(63,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(64,plain,
( ( ! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(65,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(66,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(67,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(68,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 != Vd105 )
=> ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(69,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(70,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(71,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(72,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 = Vd121 )
| ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(73,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(74,plain,
( ( ! [Vd198: $i,Vd199: $i] :
( ( less @ Vd199 @ Vd198 )
<=> ? [Vd201: $i] :
( Vd198
= ( vplus @ Vd199 @ Vd201 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(75,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(76,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ~ ( greater @ Vd203 @ Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(77,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(78,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 )
| ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(79,plain,
( ( ! [Vd208: $i,Vd209: $i] :
( ( greater @ Vd208 @ Vd209 )
=> ( less @ Vd209 @ Vd208 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(80,plain,
( ( ! [Vd226: $i,Vd227: $i] :
( ( less @ Vd226 @ Vd227 )
=> ( greater @ Vd227 @ Vd226 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(81,plain,
( ( ! [Vd244: $i,Vd245: $i] :
( ( geq @ Vd245 @ Vd244 )
<=> ( ( greater @ Vd245 @ Vd244 )
| ( Vd245 = Vd244 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(82,plain,
( ( ! [Vd249: $i,Vd250: $i] :
( ( leq @ Vd250 @ Vd249 )
<=> ( ( less @ Vd250 @ Vd249 )
| ( Vd250 = Vd249 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(83,plain,
( ( ! [Vd254: $i,Vd255: $i] :
( ( geq @ Vd254 @ Vd255 )
=> ( leq @ Vd255 @ Vd254 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(84,plain,
( ( ! [Vd258: $i,Vd259: $i] :
( ( leq @ Vd258 @ Vd259 )
=> ( geq @ Vd259 @ Vd258 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(85,plain,
( ( ! [Vd262: $i,Vd263: $i,Vd265: $i] :
( ( ( less @ Vd263 @ Vd265 )
& ( less @ Vd262 @ Vd263 ) )
=> ( less @ Vd262 @ Vd265 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(86,plain,
( ( ! [Vd281: $i,Vd282: $i,Vd283: $i] :
( ( ( ( less @ Vd282 @ Vd283 )
& ( leq @ Vd281 @ Vd282 ) )
| ( ( leq @ Vd282 @ Vd283 )
& ( less @ Vd281 @ Vd282 ) ) )
=> ( less @ Vd281 @ Vd283 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(87,plain,
( ( ! [Vd289: $i,Vd290: $i,Vd292: $i] :
( ( ( leq @ Vd290 @ Vd292 )
& ( leq @ Vd289 @ Vd290 ) )
=> ( leq @ Vd289 @ Vd292 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(88,plain,
( ( ! [Vd295: $i,Vd296: $i] : ( greater @ ( vplus @ Vd295 @ Vd296 ) @ Vd295 ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(89,plain,
( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( greater @ Vd301 @ Vd302 )
=> ( greater @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(90,plain,
( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( Vd301 = Vd302 )
=> ( ( vplus @ Vd301 @ Vd303 )
= ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(91,plain,
( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( less @ Vd301 @ Vd302 )
=> ( less @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(92,plain,
( ( ! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( greater @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
=> ( greater @ Vd328 @ Vd329 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(93,plain,
( ( ! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( ( vplus @ Vd328 @ Vd330 )
= ( vplus @ Vd329 @ Vd330 ) )
=> ( Vd328 = Vd329 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(94,plain,
( ( ! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( less @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
=> ( less @ Vd328 @ Vd329 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(95,plain,
( ( ! [Vd337: $i,Vd338: $i,Vd340: $i,Vd341: $i] :
( ( ( greater @ Vd340 @ Vd341 )
& ( greater @ Vd337 @ Vd338 ) )
=> ( greater @ ( vplus @ Vd337 @ Vd340 ) @ ( vplus @ Vd338 @ Vd341 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(96,plain,
( ( ! [Vd353: $i,Vd354: $i,Vd355: $i,Vd356: $i] :
( ( ( ( greater @ Vd355 @ Vd356 )
& ( geq @ Vd353 @ Vd354 ) )
| ( ( geq @ Vd355 @ Vd356 )
& ( greater @ Vd353 @ Vd354 ) ) )
=> ( greater @ ( vplus @ Vd353 @ Vd355 ) @ ( vplus @ Vd354 @ Vd356 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(97,plain,
( ( ! [Vd362: $i,Vd363: $i,Vd365: $i,Vd366: $i] :
( ( ( geq @ Vd365 @ Vd366 )
& ( geq @ Vd362 @ Vd363 ) )
=> ( geq @ ( vplus @ Vd362 @ Vd365 ) @ ( vplus @ Vd363 @ Vd366 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(98,plain,
( ( ! [Vd369: $i] : ( geq @ Vd369 @ v1 ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(99,plain,
( ( ! [Vd375: $i,Vd376: $i] :
( ( greater @ Vd375 @ Vd376 )
=> ( geq @ Vd375 @ ( vplus @ Vd376 @ v1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(100,plain,
( ( ! [Vd386: $i,Vd387: $i] :
( ( less @ Vd386 @ ( vplus @ Vd387 @ v1 ) )
=> ( leq @ Vd386 @ Vd387 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(101,plain,
( ( ! [Vd396: $i,Vd397: $i] :
( ( ( vmul @ Vd396 @ ( vsucc @ Vd397 ) )
= ( vplus @ ( vmul @ Vd396 @ Vd397 ) @ Vd396 ) )
& ( ( vmul @ Vd396 @ v1 )
= Vd396 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(102,plain,
( ( ! [Vd400: $i] :
( ( vmul @ v1 @ Vd400 )
= Vd400 ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(103,plain,
( ( ! [Vd408: $i,Vd409: $i] :
( ( vmul @ ( vsucc @ Vd408 ) @ Vd409 )
= ( vplus @ ( vmul @ Vd408 @ Vd409 ) @ Vd409 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(104,plain,
( ( ! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(105,plain,
( ( ! [Vd432: $i,Vd433: $i,Vd434: $i] :
( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
= ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(106,plain,
( ( ! [Vd444: $i,Vd445: $i,Vd446: $i] :
( ( vmul @ ( vmul @ Vd444 @ Vd445 ) @ Vd446 )
= ( vmul @ Vd444 @ ( vmul @ Vd445 @ Vd446 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(107,plain,
( ( greater @ vd470 @ vd471 )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(108,plain,
( ( vd470
= ( vplus @ vd471 @ vd473 ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(109,plain,
( ( ( vmul @ vd470 @ vd469 )
= ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(110,plain,
( ( ( ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 )
!= ( vplus @ ( vmul @ vd471 @ vd469 ) @ ( vmul @ vd473 @ vd469 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[56]) ).
thf(111,plain,
( ( ! [Vd1: $i] :
( ( vsucc @ Vd1 )
!= v1 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(112,plain,
( ( ! [Vd3: $i,Vd4: $i] :
( ( ( vsucc @ Vd3 )
!= ( vsucc @ Vd4 ) )
| ( Vd3 = Vd4 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(113,plain,
( ( ! [Vd7: $i,Vd8: $i] :
( ( Vd7 = Vd8 )
| ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(114,plain,
( ( ! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(115,plain,
( ( ! [Vd24: $i] :
( ( Vd24 = v1 )
| ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(116,plain,
( ( ! [Vd42: $i,Vd43: $i] :
( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ! [Vd42: $i] :
( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(117,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(118,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 = Vd105 )
| ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(119,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ! [Vd123: $i] :
( Vd120
!= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(120,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ! [Vd123: $i] :
( Vd120
!= ( vplus @ Vd121 @ Vd123 ) )
| ! [Vd125: $i] :
( Vd121
!= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(121,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ! [Vd125: $i] :
( Vd121
!= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[71]) ).
thf(122,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd121
= ( vplus @ Vd120 @ ( sK2_Vd125 @ Vd121 @ Vd120 ) ) )
| ( Vd120 = Vd121 )
| ( Vd120
= ( vplus @ Vd121 @ ( sK1_Vd123 @ Vd121 @ Vd120 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[72]) ).
thf(123,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ! [Vd196: $i] :
( Vd194
!= ( vplus @ Vd193 @ Vd196 ) )
| ( greater @ Vd194 @ Vd193 ) )
& ! [Vd193: $i,Vd194: $i] :
( ~ ( greater @ Vd194 @ Vd193 )
| ( Vd194
= ( vplus @ Vd193 @ ( sK3_Vd196 @ Vd194 @ Vd193 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(124,plain,
( ( ! [Vd198: $i,Vd199: $i] :
( ! [Vd201: $i] :
( Vd198
!= ( vplus @ Vd199 @ Vd201 ) )
| ( less @ Vd199 @ Vd198 ) )
& ! [Vd198: $i,Vd199: $i] :
( ~ ( less @ Vd199 @ Vd198 )
| ( Vd198
= ( vplus @ Vd199 @ ( sK4_Vd201 @ Vd199 @ Vd198 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(125,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[75]) ).
thf(126,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[77]) ).
thf(127,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( less @ Vd203 @ Vd204 )
| ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[78]) ).
thf(128,plain,
( ( ! [Vd208: $i,Vd209: $i] :
( ~ ( greater @ Vd208 @ Vd209 )
| ( less @ Vd209 @ Vd208 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[79]) ).
thf(129,plain,
( ( ! [Vd226: $i,Vd227: $i] :
( ~ ( less @ Vd226 @ Vd227 )
| ( greater @ Vd227 @ Vd226 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(130,plain,
( ( ! [Vd244: $i,Vd245: $i] :
( ~ ( geq @ Vd245 @ Vd244 )
| ( Vd245 = Vd244 )
| ( greater @ Vd245 @ Vd244 ) )
& ! [Vd244: $i,Vd245: $i] :
( ( Vd245 != Vd244 )
| ( geq @ Vd245 @ Vd244 ) )
& ! [Vd244: $i,Vd245: $i] :
( ~ ( greater @ Vd245 @ Vd244 )
| ( geq @ Vd245 @ Vd244 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(131,plain,
( ( ! [Vd249: $i,Vd250: $i] :
( ~ ( leq @ Vd250 @ Vd249 )
| ( Vd250 = Vd249 )
| ( less @ Vd250 @ Vd249 ) )
& ! [Vd249: $i,Vd250: $i] :
( ( Vd250 != Vd249 )
| ( leq @ Vd250 @ Vd249 ) )
& ! [Vd249: $i,Vd250: $i] :
( ~ ( less @ Vd250 @ Vd249 )
| ( leq @ Vd250 @ Vd249 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[82]) ).
thf(132,plain,
( ( ! [Vd254: $i,Vd255: $i] :
( ~ ( geq @ Vd254 @ Vd255 )
| ( leq @ Vd255 @ Vd254 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[83]) ).
thf(133,plain,
( ( ! [Vd258: $i,Vd259: $i] :
( ~ ( leq @ Vd258 @ Vd259 )
| ( geq @ Vd259 @ Vd258 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[84]) ).
thf(134,plain,
( ( ! [Vd262: $i,Vd263: $i,Vd265: $i] :
( ~ ( less @ Vd263 @ Vd265 )
| ~ ( less @ Vd262 @ Vd263 )
| ( less @ Vd262 @ Vd265 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(135,plain,
( ( ! [Vd281: $i] :
( ! [Vd282: $i,Vd283: $i] :
( ~ ( leq @ Vd281 @ Vd282 )
| ~ ( less @ Vd282 @ Vd283 )
| ( less @ Vd281 @ Vd283 ) )
& ! [Vd282: $i,Vd283: $i] :
( ~ ( leq @ Vd282 @ Vd283 )
| ~ ( less @ Vd281 @ Vd282 )
| ( less @ Vd281 @ Vd283 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[86]) ).
thf(136,plain,
( ( ! [Vd289: $i,Vd290: $i,Vd292: $i] :
( ~ ( leq @ Vd290 @ Vd292 )
| ~ ( leq @ Vd289 @ Vd290 )
| ( leq @ Vd289 @ Vd292 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(137,plain,
( ( ! [Vd301: $i,Vd302: $i] :
( ~ ( greater @ Vd301 @ Vd302 )
| ! [Vd303: $i] : ( greater @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[89]) ).
thf(138,plain,
( ( ! [Vd301: $i,Vd302: $i] :
( ( Vd301 != Vd302 )
| ! [Vd303: $i] :
( ( vplus @ Vd301 @ Vd303 )
= ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[90]) ).
thf(139,plain,
( ( ! [Vd301: $i,Vd302: $i] :
( ~ ( less @ Vd301 @ Vd302 )
| ! [Vd303: $i] : ( less @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[91]) ).
thf(140,plain,
( ( ! [Vd328: $i,Vd329: $i] :
( ! [Vd330: $i] :
~ ( greater @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
| ( greater @ Vd328 @ Vd329 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[92]) ).
thf(141,plain,
( ( ! [Vd328: $i,Vd329: $i] :
( ! [Vd330: $i] :
( ( vplus @ Vd328 @ Vd330 )
!= ( vplus @ Vd329 @ Vd330 ) )
| ( Vd328 = Vd329 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[93]) ).
thf(142,plain,
( ( ! [Vd328: $i,Vd329: $i] :
( ! [Vd330: $i] :
~ ( less @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
| ( less @ Vd328 @ Vd329 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[94]) ).
thf(143,plain,
( ( ! [Vd337: $i,Vd338: $i,Vd340: $i,Vd341: $i] :
( ~ ( greater @ Vd340 @ Vd341 )
| ~ ( greater @ Vd337 @ Vd338 )
| ( greater @ ( vplus @ Vd337 @ Vd340 ) @ ( vplus @ Vd338 @ Vd341 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[95]) ).
thf(144,plain,
( ( ! [Vd353: $i,Vd354: $i] :
( ! [Vd355: $i,Vd356: $i] :
( ~ ( geq @ Vd353 @ Vd354 )
| ~ ( greater @ Vd355 @ Vd356 )
| ( greater @ ( vplus @ Vd353 @ Vd355 ) @ ( vplus @ Vd354 @ Vd356 ) ) )
& ! [Vd355: $i,Vd356: $i] :
( ~ ( geq @ Vd355 @ Vd356 )
| ~ ( greater @ Vd353 @ Vd354 )
| ( greater @ ( vplus @ Vd353 @ Vd355 ) @ ( vplus @ Vd354 @ Vd356 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[96]) ).
thf(145,plain,
( ( ! [Vd362: $i,Vd363: $i,Vd365: $i,Vd366: $i] :
( ~ ( geq @ Vd365 @ Vd366 )
| ~ ( geq @ Vd362 @ Vd363 )
| ( geq @ ( vplus @ Vd362 @ Vd365 ) @ ( vplus @ Vd363 @ Vd366 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[97]) ).
thf(146,plain,
( ( ! [Vd375: $i,Vd376: $i] :
( ~ ( greater @ Vd375 @ Vd376 )
| ( geq @ Vd375 @ ( vplus @ Vd376 @ v1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[99]) ).
thf(147,plain,
( ( ! [Vd386: $i,Vd387: $i] :
( ~ ( less @ Vd386 @ ( vplus @ Vd387 @ v1 ) )
| ( leq @ Vd386 @ Vd387 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[100]) ).
thf(148,plain,
( ( ! [Vd396: $i,Vd397: $i] :
( ( vmul @ Vd396 @ ( vsucc @ Vd397 ) )
= ( vplus @ ( vmul @ Vd396 @ Vd397 ) @ Vd396 ) )
& ! [Vd396: $i] :
( ( vmul @ Vd396 @ v1 )
= Vd396 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[101]) ).
thf(149,plain,
( ( ( vmul @ vd470 @ vd469 )
= ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(150,plain,
( ( vd470
= ( vplus @ vd471 @ vd473 ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(151,plain,
( ( greater @ vd470 @ vd471 )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(152,plain,
( ( ! [Vd444: $i,Vd445: $i,Vd446: $i] :
( ( vmul @ ( vmul @ Vd444 @ Vd445 ) @ Vd446 )
= ( vmul @ Vd444 @ ( vmul @ Vd445 @ Vd446 ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(153,plain,
( ( ! [Vd432: $i,Vd433: $i,Vd434: $i] :
( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
= ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(154,plain,
( ( ! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(155,plain,
( ( ! [Vd408: $i,Vd409: $i] :
( ( vmul @ ( vsucc @ Vd408 ) @ Vd409 )
= ( vplus @ ( vmul @ Vd408 @ Vd409 ) @ Vd409 ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(156,plain,
( ( ! [Vd400: $i] :
( ( vmul @ v1 @ Vd400 )
= Vd400 ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(157,plain,
( ( ! [Vd396: $i,Vd397: $i] :
( ( vmul @ Vd396 @ ( vsucc @ Vd397 ) )
= ( vplus @ ( vmul @ Vd396 @ Vd397 ) @ Vd396 ) )
& ! [Vd396: $i] :
( ( vmul @ Vd396 @ v1 )
= Vd396 ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(158,plain,
( ( ! [Vd386: $i,Vd387: $i] :
( ~ ( less @ Vd386 @ ( vplus @ Vd387 @ v1 ) )
| ( leq @ Vd386 @ Vd387 ) ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(159,plain,
( ( ! [Vd375: $i,Vd376: $i] :
( ~ ( greater @ Vd375 @ Vd376 )
| ( geq @ Vd375 @ ( vplus @ Vd376 @ v1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(160,plain,
( ( ! [Vd369: $i] : ( geq @ Vd369 @ v1 ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(161,plain,
( ( ! [Vd362: $i,Vd363: $i,Vd365: $i,Vd366: $i] :
( ~ ( geq @ Vd365 @ Vd366 )
| ~ ( geq @ Vd362 @ Vd363 )
| ( geq @ ( vplus @ Vd362 @ Vd365 ) @ ( vplus @ Vd363 @ Vd366 ) ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(162,plain,
( ( ! [Vd353: $i,Vd354: $i] :
( ! [Vd355: $i,Vd356: $i] :
( ~ ( geq @ Vd353 @ Vd354 )
| ~ ( greater @ Vd355 @ Vd356 )
| ( greater @ ( vplus @ Vd353 @ Vd355 ) @ ( vplus @ Vd354 @ Vd356 ) ) )
& ! [Vd355: $i,Vd356: $i] :
( ~ ( geq @ Vd355 @ Vd356 )
| ~ ( greater @ Vd353 @ Vd354 )
| ( greater @ ( vplus @ Vd353 @ Vd355 ) @ ( vplus @ Vd354 @ Vd356 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(163,plain,
( ( ! [Vd337: $i,Vd338: $i,Vd340: $i,Vd341: $i] :
( ~ ( greater @ Vd340 @ Vd341 )
| ~ ( greater @ Vd337 @ Vd338 )
| ( greater @ ( vplus @ Vd337 @ Vd340 ) @ ( vplus @ Vd338 @ Vd341 ) ) ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(164,plain,
( ( ! [Vd328: $i,Vd329: $i] :
( ! [Vd330: $i] :
~ ( less @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
| ( less @ Vd328 @ Vd329 ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(165,plain,
( ( ! [Vd328: $i,Vd329: $i] :
( ! [Vd330: $i] :
( ( vplus @ Vd328 @ Vd330 )
!= ( vplus @ Vd329 @ Vd330 ) )
| ( Vd328 = Vd329 ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(166,plain,
( ( ! [Vd328: $i,Vd329: $i] :
( ! [Vd330: $i] :
~ ( greater @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
| ( greater @ Vd328 @ Vd329 ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(167,plain,
( ( ! [Vd301: $i,Vd302: $i] :
( ~ ( less @ Vd301 @ Vd302 )
| ! [Vd303: $i] : ( less @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(168,plain,
( ( ! [Vd301: $i,Vd302: $i] :
( ( Vd301 != Vd302 )
| ! [Vd303: $i] :
( ( vplus @ Vd301 @ Vd303 )
= ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(169,plain,
( ( ! [Vd301: $i,Vd302: $i] :
( ~ ( greater @ Vd301 @ Vd302 )
| ! [Vd303: $i] : ( greater @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(170,plain,
( ( ! [Vd295: $i,Vd296: $i] : ( greater @ ( vplus @ Vd295 @ Vd296 ) @ Vd295 ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(171,plain,
( ( ! [Vd289: $i,Vd290: $i,Vd292: $i] :
( ~ ( leq @ Vd290 @ Vd292 )
| ~ ( leq @ Vd289 @ Vd290 )
| ( leq @ Vd289 @ Vd292 ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(172,plain,
( ( ! [Vd281: $i] :
( ! [Vd282: $i,Vd283: $i] :
( ~ ( leq @ Vd281 @ Vd282 )
| ~ ( less @ Vd282 @ Vd283 )
| ( less @ Vd281 @ Vd283 ) )
& ! [Vd282: $i,Vd283: $i] :
( ~ ( leq @ Vd282 @ Vd283 )
| ~ ( less @ Vd281 @ Vd282 )
| ( less @ Vd281 @ Vd283 ) ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(173,plain,
( ( ! [Vd262: $i,Vd263: $i,Vd265: $i] :
( ~ ( less @ Vd263 @ Vd265 )
| ~ ( less @ Vd262 @ Vd263 )
| ( less @ Vd262 @ Vd265 ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(174,plain,
( ( ! [Vd258: $i,Vd259: $i] :
( ~ ( leq @ Vd258 @ Vd259 )
| ( geq @ Vd259 @ Vd258 ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(175,plain,
( ( ! [Vd254: $i,Vd255: $i] :
( ~ ( geq @ Vd254 @ Vd255 )
| ( leq @ Vd255 @ Vd254 ) ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(176,plain,
( ( ! [Vd249: $i,Vd250: $i] :
( ~ ( leq @ Vd250 @ Vd249 )
| ( Vd250 = Vd249 )
| ( less @ Vd250 @ Vd249 ) )
& ! [Vd249: $i,Vd250: $i] :
( ( Vd250 != Vd249 )
| ( leq @ Vd250 @ Vd249 ) )
& ! [Vd249: $i,Vd250: $i] :
( ~ ( less @ Vd250 @ Vd249 )
| ( leq @ Vd250 @ Vd249 ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(177,plain,
( ( ! [Vd244: $i,Vd245: $i] :
( ~ ( geq @ Vd245 @ Vd244 )
| ( Vd245 = Vd244 )
| ( greater @ Vd245 @ Vd244 ) )
& ! [Vd244: $i,Vd245: $i] :
( ( Vd245 != Vd244 )
| ( geq @ Vd245 @ Vd244 ) )
& ! [Vd244: $i,Vd245: $i] :
( ~ ( greater @ Vd245 @ Vd244 )
| ( geq @ Vd245 @ Vd244 ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(178,plain,
( ( ! [Vd226: $i,Vd227: $i] :
( ~ ( less @ Vd226 @ Vd227 )
| ( greater @ Vd227 @ Vd226 ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(179,plain,
( ( ! [Vd208: $i,Vd209: $i] :
( ~ ( greater @ Vd208 @ Vd209 )
| ( less @ Vd209 @ Vd208 ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(180,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( less @ Vd203 @ Vd204 )
| ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(181,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(182,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ~ ( greater @ Vd203 @ Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(183,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(184,plain,
( ( ! [Vd198: $i,Vd199: $i] :
( ! [Vd201: $i] :
( Vd198
!= ( vplus @ Vd199 @ Vd201 ) )
| ( less @ Vd199 @ Vd198 ) )
& ! [Vd198: $i,Vd199: $i] :
( ~ ( less @ Vd199 @ Vd198 )
| ( Vd198
= ( vplus @ Vd199 @ ( sK4_Vd201 @ Vd199 @ Vd198 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(185,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ! [Vd196: $i] :
( Vd194
!= ( vplus @ Vd193 @ Vd196 ) )
| ( greater @ Vd194 @ Vd193 ) )
& ! [Vd193: $i,Vd194: $i] :
( ~ ( greater @ Vd194 @ Vd193 )
| ( Vd194
= ( vplus @ Vd193 @ ( sK3_Vd196 @ Vd194 @ Vd193 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(186,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd121
= ( vplus @ Vd120 @ ( sK2_Vd125 @ Vd121 @ Vd120 ) ) )
| ( Vd120 = Vd121 )
| ( Vd120
= ( vplus @ Vd121 @ ( sK1_Vd123 @ Vd121 @ Vd120 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(187,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ! [Vd125: $i] :
( Vd121
!= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(188,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ! [Vd123: $i] :
( Vd120
!= ( vplus @ Vd121 @ Vd123 ) )
| ! [Vd125: $i] :
( Vd121
!= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(189,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ! [Vd123: $i] :
( Vd120
!= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(190,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 = Vd105 )
| ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(191,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(192,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(193,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(194,plain,
( ( ! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(195,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(196,plain,
( ( ! [Vd42: $i,Vd43: $i] :
( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ! [Vd42: $i] :
( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(197,plain,
( ( ! [Vd24: $i] :
( ( Vd24 = v1 )
| ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(198,plain,
( ( ! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(199,plain,
( ( ! [Vd7: $i,Vd8: $i] :
( ( Vd7 = Vd8 )
| ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(200,plain,
( ( ! [Vd3: $i,Vd4: $i] :
( ( ( vsucc @ Vd3 )
!= ( vsucc @ Vd4 ) )
| ( Vd3 = Vd4 ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(201,plain,
( ( ! [Vd1: $i] :
( ( vsucc @ Vd1 )
!= v1 ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(202,plain,
( ( ( ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 )
!= ( vplus @ ( vmul @ vd471 @ vd469 ) @ ( vmul @ vd473 @ vd469 ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(203,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( geq @ SX1 @ SX0 )
| ( SX1 = SX0 )
| ( greater @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( geq @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( geq @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(204,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(205,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( greater @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( SX1
= ( vplus @ SX0 @ ( sK3_Vd196 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(206,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( geq @ SX0 @ SX1 )
| ~ ( greater @ SX2 @ SX3 )
| ( greater @ ( vplus @ SX0 @ SX2 ) @ ( vplus @ SX1 @ SX3 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( geq @ SX2 @ SX3 )
| ~ ( greater @ SX0 @ SX1 )
| ( greater @ ( vplus @ SX0 @ SX2 ) @ ( vplus @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(207,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( less @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( SX0
= ( vplus @ SX1 @ ( sK4_Vd201 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(208,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( vmul @ SX0 @ ( vsucc @ SX1 ) )
= ( vplus @ ( vmul @ SX0 @ SX1 ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ( vmul @ SX0 @ v1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(209,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ~ ( less @ SX1 @ SX2 )
| ( less @ SX0 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( leq @ SX1 @ SX2 )
| ~ ( less @ SX0 @ SX1 )
| ( less @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(210,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX1 @ SX0 )
| ( SX1 = SX0 )
| ( less @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( leq @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( leq @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(211,plain,
! [SV1: $i] :
( ( ! [SY121: $i,SY122: $i] :
( ( vmul @ ( vmul @ SV1 @ SY121 ) @ SY122 )
= ( vmul @ SV1 @ ( vmul @ SY121 @ SY122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(212,plain,
! [SV2: $i] :
( ( ! [SY123: $i,SY124: $i] :
( ( vmul @ SV2 @ ( vplus @ SY123 @ SY124 ) )
= ( vplus @ ( vmul @ SV2 @ SY123 ) @ ( vmul @ SV2 @ SY124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(213,plain,
! [SV3: $i] :
( ( ! [SY125: $i] :
( ( vmul @ SV3 @ SY125 )
= ( vmul @ SY125 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(214,plain,
! [SV4: $i] :
( ( ! [SY126: $i] :
( ( vmul @ ( vsucc @ SV4 ) @ SY126 )
= ( vplus @ ( vmul @ SV4 @ SY126 ) @ SY126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(215,plain,
! [SV5: $i] :
( ( ( vmul @ v1 @ SV5 )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(216,plain,
! [SV6: $i] :
( ( ! [SY127: $i] :
( ~ ( less @ SV6 @ ( vplus @ SY127 @ v1 ) )
| ( leq @ SV6 @ SY127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(217,plain,
! [SV7: $i] :
( ( ! [SY128: $i] :
( ~ ( greater @ SV7 @ SY128 )
| ( geq @ SV7 @ ( vplus @ SY128 @ v1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(218,plain,
! [SV8: $i] :
( ( geq @ SV8 @ v1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(219,plain,
! [SV9: $i] :
( ( ! [SY129: $i,SY130: $i,SY131: $i] :
( ~ ( geq @ SY130 @ SY131 )
| ~ ( geq @ SV9 @ SY129 )
| ( geq @ ( vplus @ SV9 @ SY130 ) @ ( vplus @ SY129 @ SY131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(220,plain,
! [SV10: $i] :
( ( ! [SY132: $i,SY133: $i,SY134: $i] :
( ~ ( greater @ SY133 @ SY134 )
| ~ ( greater @ SV10 @ SY132 )
| ( greater @ ( vplus @ SV10 @ SY133 ) @ ( vplus @ SY132 @ SY134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(221,plain,
! [SV11: $i] :
( ( ! [SY135: $i] :
( ! [SY136: $i] :
~ ( less @ ( vplus @ SV11 @ SY136 ) @ ( vplus @ SY135 @ SY136 ) )
| ( less @ SV11 @ SY135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(222,plain,
! [SV12: $i] :
( ( ! [SY137: $i] :
( ! [SY138: $i] :
( ( vplus @ SV12 @ SY138 )
!= ( vplus @ SY137 @ SY138 ) )
| ( SV12 = SY137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(223,plain,
! [SV13: $i] :
( ( ! [SY139: $i] :
( ! [SY140: $i] :
~ ( greater @ ( vplus @ SV13 @ SY140 ) @ ( vplus @ SY139 @ SY140 ) )
| ( greater @ SV13 @ SY139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(224,plain,
! [SV14: $i] :
( ( ! [SY141: $i] :
( ~ ( less @ SV14 @ SY141 )
| ! [SY142: $i] : ( less @ ( vplus @ SV14 @ SY142 ) @ ( vplus @ SY141 @ SY142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(225,plain,
! [SV15: $i] :
( ( ! [SY143: $i] :
( ( SV15 != SY143 )
| ! [SY144: $i] :
( ( vplus @ SV15 @ SY144 )
= ( vplus @ SY143 @ SY144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(226,plain,
! [SV16: $i] :
( ( ! [SY145: $i] :
( ~ ( greater @ SV16 @ SY145 )
| ! [SY146: $i] : ( greater @ ( vplus @ SV16 @ SY146 ) @ ( vplus @ SY145 @ SY146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(227,plain,
! [SV17: $i] :
( ( ! [SY147: $i] : ( greater @ ( vplus @ SV17 @ SY147 ) @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(228,plain,
! [SV18: $i] :
( ( ! [SY148: $i,SY149: $i] :
( ~ ( leq @ SY148 @ SY149 )
| ~ ( leq @ SV18 @ SY148 )
| ( leq @ SV18 @ SY149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(229,plain,
! [SV19: $i] :
( ( ! [SY150: $i,SY151: $i] :
( ~ ( less @ SY150 @ SY151 )
| ~ ( less @ SV19 @ SY150 )
| ( less @ SV19 @ SY151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(230,plain,
! [SV20: $i] :
( ( ! [SY152: $i] :
( ~ ( leq @ SV20 @ SY152 )
| ( geq @ SY152 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(231,plain,
! [SV21: $i] :
( ( ! [SY153: $i] :
( ~ ( geq @ SV21 @ SY153 )
| ( leq @ SY153 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(232,plain,
! [SV22: $i] :
( ( ! [SY154: $i] :
( ~ ( less @ SV22 @ SY154 )
| ( greater @ SY154 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(233,plain,
! [SV23: $i] :
( ( ! [SY155: $i] :
( ~ ( greater @ SV23 @ SY155 )
| ( less @ SY155 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(234,plain,
! [SV24: $i] :
( ( ! [SY156: $i] :
( ( less @ SV24 @ SY156 )
| ( SV24 = SY156 )
| ( greater @ SV24 @ SY156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(235,plain,
! [SV25: $i] :
( ( ! [SY157: $i] :
( ( SV25 != SY157 )
| ~ ( less @ SV25 @ SY157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(236,plain,
! [SV26: $i] :
( ( ! [SY158: $i] :
( ~ ( greater @ SV26 @ SY158 )
| ~ ( less @ SV26 @ SY158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(237,plain,
! [SV27: $i] :
( ( ! [SY159: $i] :
( ( SV27 != SY159 )
| ~ ( greater @ SV27 @ SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(238,plain,
! [SV28: $i] :
( ( ! [SY160: $i] :
( ( SY160
= ( vplus @ SV28 @ ( sK2_Vd125 @ SY160 @ SV28 ) ) )
| ( SV28 = SY160 )
| ( SV28
= ( vplus @ SY160 @ ( sK1_Vd123 @ SY160 @ SV28 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(239,plain,
! [SV29: $i] :
( ( ! [SY161: $i] :
( ( SV29 != SY161 )
| ! [SY162: $i] :
( SY161
!= ( vplus @ SV29 @ SY162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(240,plain,
! [SV30: $i] :
( ( ! [SY163: $i] :
( ! [SY164: $i] :
( SV30
!= ( vplus @ SY163 @ SY164 ) )
| ! [SY165: $i] :
( SY163
!= ( vplus @ SV30 @ SY165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(241,plain,
! [SV31: $i] :
( ( ! [SY166: $i] :
( ( SV31 != SY166 )
| ! [SY167: $i] :
( SV31
!= ( vplus @ SY166 @ SY167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(242,plain,
! [SV32: $i] :
( ( ! [SY168: $i] :
( ( SV32 = SY168 )
| ! [SY169: $i] :
( ( vplus @ SY169 @ SV32 )
!= ( vplus @ SY169 @ SY168 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(243,plain,
! [SV33: $i] :
( ( ! [SY170: $i] :
( SY170
!= ( vplus @ SV33 @ SY170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(244,plain,
! [SV34: $i] :
( ( ! [SY171: $i] :
( ( vplus @ SY171 @ SV34 )
= ( vplus @ SV34 @ SY171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(245,plain,
! [SV35: $i] :
( ( ! [SY172: $i] :
( ( vplus @ ( vsucc @ SV35 ) @ SY172 )
= ( vsucc @ ( vplus @ SV35 @ SY172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(246,plain,
! [SV36: $i] :
( ( ( vplus @ v1 @ SV36 )
= ( vsucc @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(247,plain,
! [SV37: $i] :
( ( ! [SY173: $i,SY174: $i] :
( ( vplus @ ( vplus @ SV37 @ SY173 ) @ SY174 )
= ( vplus @ SV37 @ ( vplus @ SY173 @ SY174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(248,plain,
! [SV38: $i] :
( ( ( SV38 = v1 )
| ( SV38
= ( vsucc @ ( vskolem2 @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(249,plain,
! [SV39: $i] :
( ( ( ( vsucc @ SV39 )
!= SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(250,plain,
! [SV40: $i] :
( ( ! [SY175: $i] :
( ( SV40 = SY175 )
| ( ( vsucc @ SV40 )
!= ( vsucc @ SY175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(251,plain,
! [SV41: $i] :
( ( ! [SY176: $i] :
( ( ( vsucc @ SV41 )
!= ( vsucc @ SY176 ) )
| ( SV41 = SY176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(252,plain,
! [SV42: $i] :
( ( ( ( vsucc @ SV42 )
!= v1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(253,plain,
( ( ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 )
= ( vplus @ ( vmul @ vd471 @ vd469 ) @ ( vmul @ vd473 @ vd469 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(254,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( geq @ SX1 @ SX0 )
| ( SX1 = SX0 )
| ( greater @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( geq @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( geq @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(255,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(256,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( greater @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( SX1
= ( vplus @ SX0 @ ( sK3_Vd196 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(257,plain,
! [SV43: $i] :
( ( ! [SY177: $i] :
~ ( ~ ! [SY178: $i,SY179: $i] :
( ~ ( geq @ SV43 @ SY177 )
| ~ ( greater @ SY178 @ SY179 )
| ( greater @ ( vplus @ SV43 @ SY178 ) @ ( vplus @ SY177 @ SY179 ) ) )
| ~ ! [SY180: $i,SY181: $i] :
( ~ ( geq @ SY180 @ SY181 )
| ~ ( greater @ SV43 @ SY177 )
| ( greater @ ( vplus @ SV43 @ SY180 ) @ ( vplus @ SY177 @ SY181 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(258,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( less @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( SX0
= ( vplus @ SX1 @ ( sK4_Vd201 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(259,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( vmul @ SX0 @ ( vsucc @ SX1 ) )
= ( vplus @ ( vmul @ SX0 @ SX1 ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ( vmul @ SX0 @ v1 )
= SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(260,plain,
! [SV44: $i] :
( ( ~ ( ~ ! [SY182: $i,SY183: $i] :
( ~ ( leq @ SV44 @ SY182 )
| ~ ( less @ SY182 @ SY183 )
| ( less @ SV44 @ SY183 ) )
| ~ ! [SY184: $i,SY185: $i] :
( ~ ( leq @ SY184 @ SY185 )
| ~ ( less @ SV44 @ SY184 )
| ( less @ SV44 @ SY185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(261,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX1 @ SX0 )
| ( SX1 = SX0 )
| ( less @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( leq @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( leq @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(262,plain,
! [SV45: $i,SV1: $i] :
( ( ! [SY186: $i] :
( ( vmul @ ( vmul @ SV1 @ SV45 ) @ SY186 )
= ( vmul @ SV1 @ ( vmul @ SV45 @ SY186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(263,plain,
! [SV46: $i,SV2: $i] :
( ( ! [SY187: $i] :
( ( vmul @ SV2 @ ( vplus @ SV46 @ SY187 ) )
= ( vplus @ ( vmul @ SV2 @ SV46 ) @ ( vmul @ SV2 @ SY187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(264,plain,
! [SV47: $i,SV3: $i] :
( ( ( vmul @ SV3 @ SV47 )
= ( vmul @ SV47 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(265,plain,
! [SV48: $i,SV4: $i] :
( ( ( vmul @ ( vsucc @ SV4 ) @ SV48 )
= ( vplus @ ( vmul @ SV4 @ SV48 ) @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(266,plain,
! [SV49: $i,SV6: $i] :
( ( ~ ( less @ SV6 @ ( vplus @ SV49 @ v1 ) )
| ( leq @ SV6 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(267,plain,
! [SV50: $i,SV7: $i] :
( ( ~ ( greater @ SV7 @ SV50 )
| ( geq @ SV7 @ ( vplus @ SV50 @ v1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(268,plain,
! [SV51: $i,SV9: $i] :
( ( ! [SY188: $i,SY189: $i] :
( ~ ( geq @ SY188 @ SY189 )
| ~ ( geq @ SV9 @ SV51 )
| ( geq @ ( vplus @ SV9 @ SY188 ) @ ( vplus @ SV51 @ SY189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(269,plain,
! [SV52: $i,SV10: $i] :
( ( ! [SY190: $i,SY191: $i] :
( ~ ( greater @ SY190 @ SY191 )
| ~ ( greater @ SV10 @ SV52 )
| ( greater @ ( vplus @ SV10 @ SY190 ) @ ( vplus @ SV52 @ SY191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(270,plain,
! [SV53: $i,SV11: $i] :
( ( ! [SY192: $i] :
~ ( less @ ( vplus @ SV11 @ SY192 ) @ ( vplus @ SV53 @ SY192 ) )
| ( less @ SV11 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(271,plain,
! [SV54: $i,SV12: $i] :
( ( ! [SY193: $i] :
( ( vplus @ SV12 @ SY193 )
!= ( vplus @ SV54 @ SY193 ) )
| ( SV12 = SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(272,plain,
! [SV55: $i,SV13: $i] :
( ( ! [SY194: $i] :
~ ( greater @ ( vplus @ SV13 @ SY194 ) @ ( vplus @ SV55 @ SY194 ) )
| ( greater @ SV13 @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(273,plain,
! [SV56: $i,SV14: $i] :
( ( ~ ( less @ SV14 @ SV56 )
| ! [SY195: $i] : ( less @ ( vplus @ SV14 @ SY195 ) @ ( vplus @ SV56 @ SY195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(274,plain,
! [SV57: $i,SV15: $i] :
( ( ( SV15 != SV57 )
| ! [SY196: $i] :
( ( vplus @ SV15 @ SY196 )
= ( vplus @ SV57 @ SY196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(275,plain,
! [SV58: $i,SV16: $i] :
( ( ~ ( greater @ SV16 @ SV58 )
| ! [SY197: $i] : ( greater @ ( vplus @ SV16 @ SY197 ) @ ( vplus @ SV58 @ SY197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(276,plain,
! [SV59: $i,SV17: $i] :
( ( greater @ ( vplus @ SV17 @ SV59 ) @ SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(277,plain,
! [SV18: $i,SV60: $i] :
( ( ! [SY198: $i] :
( ~ ( leq @ SV60 @ SY198 )
| ~ ( leq @ SV18 @ SV60 )
| ( leq @ SV18 @ SY198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(278,plain,
! [SV19: $i,SV61: $i] :
( ( ! [SY199: $i] :
( ~ ( less @ SV61 @ SY199 )
| ~ ( less @ SV19 @ SV61 )
| ( less @ SV19 @ SY199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(279,plain,
! [SV62: $i,SV20: $i] :
( ( ~ ( leq @ SV20 @ SV62 )
| ( geq @ SV62 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(280,plain,
! [SV63: $i,SV21: $i] :
( ( ~ ( geq @ SV21 @ SV63 )
| ( leq @ SV63 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(281,plain,
! [SV64: $i,SV22: $i] :
( ( ~ ( less @ SV22 @ SV64 )
| ( greater @ SV64 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(282,plain,
! [SV65: $i,SV23: $i] :
( ( ~ ( greater @ SV23 @ SV65 )
| ( less @ SV65 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(283,plain,
! [SV66: $i,SV24: $i] :
( ( ( less @ SV24 @ SV66 )
| ( SV24 = SV66 )
| ( greater @ SV24 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(284,plain,
! [SV67: $i,SV25: $i] :
( ( ( SV25 != SV67 )
| ~ ( less @ SV25 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(285,plain,
! [SV68: $i,SV26: $i] :
( ( ~ ( greater @ SV26 @ SV68 )
| ~ ( less @ SV26 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(286,plain,
! [SV69: $i,SV27: $i] :
( ( ( SV27 != SV69 )
| ~ ( greater @ SV27 @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(287,plain,
! [SV28: $i,SV70: $i] :
( ( ( SV70
= ( vplus @ SV28 @ ( sK2_Vd125 @ SV70 @ SV28 ) ) )
| ( SV28 = SV70 )
| ( SV28
= ( vplus @ SV70 @ ( sK1_Vd123 @ SV70 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(288,plain,
! [SV71: $i,SV29: $i] :
( ( ( SV29 != SV71 )
| ! [SY200: $i] :
( SV71
!= ( vplus @ SV29 @ SY200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(289,plain,
! [SV72: $i,SV30: $i] :
( ( ! [SY201: $i] :
( SV30
!= ( vplus @ SV72 @ SY201 ) )
| ! [SY202: $i] :
( SV72
!= ( vplus @ SV30 @ SY202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(290,plain,
! [SV73: $i,SV31: $i] :
( ( ( SV31 != SV73 )
| ! [SY203: $i] :
( SV31
!= ( vplus @ SV73 @ SY203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(291,plain,
! [SV74: $i,SV32: $i] :
( ( ( SV32 = SV74 )
| ! [SY204: $i] :
( ( vplus @ SY204 @ SV32 )
!= ( vplus @ SY204 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(292,plain,
! [SV33: $i,SV75: $i] :
( ( ( SV75
!= ( vplus @ SV33 @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(293,plain,
! [SV34: $i,SV76: $i] :
( ( ( vplus @ SV76 @ SV34 )
= ( vplus @ SV34 @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(294,plain,
! [SV77: $i,SV35: $i] :
( ( ( vplus @ ( vsucc @ SV35 ) @ SV77 )
= ( vsucc @ ( vplus @ SV35 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(295,plain,
! [SV78: $i,SV37: $i] :
( ( ! [SY205: $i] :
( ( vplus @ ( vplus @ SV37 @ SV78 ) @ SY205 )
= ( vplus @ SV37 @ ( vplus @ SV78 @ SY205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(296,plain,
! [SV38: $i] :
( ( ( SV38 = v1 )
= $true )
| ( ( SV38
= ( vsucc @ ( vskolem2 @ SV38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(297,plain,
! [SV39: $i] :
( ( ( vsucc @ SV39 )
= SV39 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(298,plain,
! [SV79: $i,SV40: $i] :
( ( ( SV40 = SV79 )
| ( ( vsucc @ SV40 )
!= ( vsucc @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(299,plain,
! [SV80: $i,SV41: $i] :
( ( ( ( vsucc @ SV41 )
!= ( vsucc @ SV80 ) )
| ( SV41 = SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(300,plain,
! [SV42: $i] :
( ( ( vsucc @ SV42 )
= v1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(301,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( geq @ SX1 @ SX0 )
| ( SX1 = SX0 )
| ( greater @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[254]) ).
thf(302,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( geq @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( geq @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[254]) ).
thf(303,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(304,plain,
( ( ~ ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(305,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( greater @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(306,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( SX1
= ( vplus @ SX0 @ ( sK3_Vd196 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(307,plain,
! [SV81: $i,SV43: $i] :
( ( ~ ( ~ ! [SY206: $i,SY207: $i] :
( ~ ( geq @ SV43 @ SV81 )
| ~ ( greater @ SY206 @ SY207 )
| ( greater @ ( vplus @ SV43 @ SY206 ) @ ( vplus @ SV81 @ SY207 ) ) )
| ~ ! [SY208: $i,SY209: $i] :
( ~ ( geq @ SY208 @ SY209 )
| ~ ( greater @ SV43 @ SV81 )
| ( greater @ ( vplus @ SV43 @ SY208 ) @ ( vplus @ SV81 @ SY209 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(308,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( less @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(309,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( SX0
= ( vplus @ SX1 @ ( sK4_Vd201 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(310,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( vmul @ SX0 @ ( vsucc @ SX1 ) )
= ( vplus @ ( vmul @ SX0 @ SX1 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[259]) ).
thf(311,plain,
( ( ~ ! [SX0: $i] :
( ( vmul @ SX0 @ v1 )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[259]) ).
thf(312,plain,
! [SV44: $i] :
( ( ~ ! [SY182: $i,SY183: $i] :
( ~ ( leq @ SV44 @ SY182 )
| ~ ( less @ SY182 @ SY183 )
| ( less @ SV44 @ SY183 ) )
| ~ ! [SY184: $i,SY185: $i] :
( ~ ( leq @ SY184 @ SY185 )
| ~ ( less @ SV44 @ SY184 )
| ( less @ SV44 @ SY185 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(313,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX1 @ SX0 )
| ( SX1 = SX0 )
| ( less @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[261]) ).
thf(314,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( leq @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( leq @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[261]) ).
thf(315,plain,
! [SV82: $i,SV45: $i,SV1: $i] :
( ( ( vmul @ ( vmul @ SV1 @ SV45 ) @ SV82 )
= ( vmul @ SV1 @ ( vmul @ SV45 @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(316,plain,
! [SV83: $i,SV46: $i,SV2: $i] :
( ( ( vmul @ SV2 @ ( vplus @ SV46 @ SV83 ) )
= ( vplus @ ( vmul @ SV2 @ SV46 ) @ ( vmul @ SV2 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(317,plain,
! [SV49: $i,SV6: $i] :
( ( ( ~ ( less @ SV6 @ ( vplus @ SV49 @ v1 ) ) )
= $true )
| ( ( leq @ SV6 @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(318,plain,
! [SV50: $i,SV7: $i] :
( ( ( ~ ( greater @ SV7 @ SV50 ) )
= $true )
| ( ( geq @ SV7 @ ( vplus @ SV50 @ v1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(319,plain,
! [SV51: $i,SV9: $i,SV84: $i] :
( ( ! [SY210: $i] :
( ~ ( geq @ SV84 @ SY210 )
| ~ ( geq @ SV9 @ SV51 )
| ( geq @ ( vplus @ SV9 @ SV84 ) @ ( vplus @ SV51 @ SY210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(320,plain,
! [SV52: $i,SV10: $i,SV85: $i] :
( ( ! [SY211: $i] :
( ~ ( greater @ SV85 @ SY211 )
| ~ ( greater @ SV10 @ SV52 )
| ( greater @ ( vplus @ SV10 @ SV85 ) @ ( vplus @ SV52 @ SY211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(321,plain,
! [SV53: $i,SV11: $i] :
( ( ( ! [SY192: $i] :
~ ( less @ ( vplus @ SV11 @ SY192 ) @ ( vplus @ SV53 @ SY192 ) ) )
= $true )
| ( ( less @ SV11 @ SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(322,plain,
! [SV54: $i,SV12: $i] :
( ( ( ! [SY193: $i] :
( ( vplus @ SV12 @ SY193 )
!= ( vplus @ SV54 @ SY193 ) ) )
= $true )
| ( ( SV12 = SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(323,plain,
! [SV55: $i,SV13: $i] :
( ( ( ! [SY194: $i] :
~ ( greater @ ( vplus @ SV13 @ SY194 ) @ ( vplus @ SV55 @ SY194 ) ) )
= $true )
| ( ( greater @ SV13 @ SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(324,plain,
! [SV56: $i,SV14: $i] :
( ( ( ~ ( less @ SV14 @ SV56 ) )
= $true )
| ( ( ! [SY195: $i] : ( less @ ( vplus @ SV14 @ SY195 ) @ ( vplus @ SV56 @ SY195 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(325,plain,
! [SV57: $i,SV15: $i] :
( ( ( ( SV15 != SV57 ) )
= $true )
| ( ( ! [SY196: $i] :
( ( vplus @ SV15 @ SY196 )
= ( vplus @ SV57 @ SY196 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(326,plain,
! [SV58: $i,SV16: $i] :
( ( ( ~ ( greater @ SV16 @ SV58 ) )
= $true )
| ( ( ! [SY197: $i] : ( greater @ ( vplus @ SV16 @ SY197 ) @ ( vplus @ SV58 @ SY197 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(327,plain,
! [SV18: $i,SV86: $i,SV60: $i] :
( ( ~ ( leq @ SV60 @ SV86 )
| ~ ( leq @ SV18 @ SV60 )
| ( leq @ SV18 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(328,plain,
! [SV19: $i,SV87: $i,SV61: $i] :
( ( ~ ( less @ SV61 @ SV87 )
| ~ ( less @ SV19 @ SV61 )
| ( less @ SV19 @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(329,plain,
! [SV62: $i,SV20: $i] :
( ( ( ~ ( leq @ SV20 @ SV62 ) )
= $true )
| ( ( geq @ SV62 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(330,plain,
! [SV63: $i,SV21: $i] :
( ( ( ~ ( geq @ SV21 @ SV63 ) )
= $true )
| ( ( leq @ SV63 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(331,plain,
! [SV64: $i,SV22: $i] :
( ( ( ~ ( less @ SV22 @ SV64 ) )
= $true )
| ( ( greater @ SV64 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(332,plain,
! [SV65: $i,SV23: $i] :
( ( ( ~ ( greater @ SV23 @ SV65 ) )
= $true )
| ( ( less @ SV65 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(333,plain,
! [SV66: $i,SV24: $i] :
( ( ( less @ SV24 @ SV66 )
= $true )
| ( ( ( SV24 = SV66 )
| ( greater @ SV24 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(334,plain,
! [SV67: $i,SV25: $i] :
( ( ( ( SV25 != SV67 ) )
= $true )
| ( ( ~ ( less @ SV25 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(335,plain,
! [SV68: $i,SV26: $i] :
( ( ( ~ ( greater @ SV26 @ SV68 ) )
= $true )
| ( ( ~ ( less @ SV26 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(336,plain,
! [SV69: $i,SV27: $i] :
( ( ( ( SV27 != SV69 ) )
= $true )
| ( ( ~ ( greater @ SV27 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(337,plain,
! [SV28: $i,SV70: $i] :
( ( ( SV70
= ( vplus @ SV28 @ ( sK2_Vd125 @ SV70 @ SV28 ) ) )
= $true )
| ( ( ( SV28 = SV70 )
| ( SV28
= ( vplus @ SV70 @ ( sK1_Vd123 @ SV70 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(338,plain,
! [SV71: $i,SV29: $i] :
( ( ( ( SV29 != SV71 ) )
= $true )
| ( ( ! [SY200: $i] :
( SV71
!= ( vplus @ SV29 @ SY200 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(339,plain,
! [SV72: $i,SV30: $i] :
( ( ( ! [SY201: $i] :
( SV30
!= ( vplus @ SV72 @ SY201 ) ) )
= $true )
| ( ( ! [SY202: $i] :
( SV72
!= ( vplus @ SV30 @ SY202 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(340,plain,
! [SV73: $i,SV31: $i] :
( ( ( ( SV31 != SV73 ) )
= $true )
| ( ( ! [SY203: $i] :
( SV31
!= ( vplus @ SV73 @ SY203 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(341,plain,
! [SV74: $i,SV32: $i] :
( ( ( SV32 = SV74 )
= $true )
| ( ( ! [SY204: $i] :
( ( vplus @ SY204 @ SV32 )
!= ( vplus @ SY204 @ SV74 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(342,plain,
! [SV33: $i,SV75: $i] :
( ( SV75
= ( vplus @ SV33 @ SV75 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(343,plain,
! [SV88: $i,SV78: $i,SV37: $i] :
( ( ( vplus @ ( vplus @ SV37 @ SV78 ) @ SV88 )
= ( vplus @ SV37 @ ( vplus @ SV78 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(344,plain,
! [SV79: $i,SV40: $i] :
( ( ( SV40 = SV79 )
= $true )
| ( ( ( ( vsucc @ SV40 )
!= ( vsucc @ SV79 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(345,plain,
! [SV80: $i,SV41: $i] :
( ( ( ( ( vsucc @ SV41 )
!= ( vsucc @ SV80 ) ) )
= $true )
| ( ( SV41 = SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(346,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( geq @ SX1 @ SX0 )
| ( SX1 = SX0 )
| ( greater @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(347,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( geq @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( geq @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(348,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[303]) ).
thf(349,plain,
( ( ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(350,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( greater @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(351,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( SX1
= ( vplus @ SX0 @ ( sK3_Vd196 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(352,plain,
! [SV81: $i,SV43: $i] :
( ( ~ ! [SY206: $i,SY207: $i] :
( ~ ( geq @ SV43 @ SV81 )
| ~ ( greater @ SY206 @ SY207 )
| ( greater @ ( vplus @ SV43 @ SY206 ) @ ( vplus @ SV81 @ SY207 ) ) )
| ~ ! [SY208: $i,SY209: $i] :
( ~ ( geq @ SY208 @ SY209 )
| ~ ( greater @ SV43 @ SV81 )
| ( greater @ ( vplus @ SV43 @ SY208 ) @ ( vplus @ SV81 @ SY209 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(353,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( less @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(354,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( SX0
= ( vplus @ SX1 @ ( sK4_Vd201 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(355,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( vmul @ SX0 @ ( vsucc @ SX1 ) )
= ( vplus @ ( vmul @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(356,plain,
( ( ! [SX0: $i] :
( ( vmul @ SX0 @ v1 )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(357,plain,
! [SV44: $i] :
( ( ~ ! [SY182: $i,SY183: $i] :
( ~ ( leq @ SV44 @ SY182 )
| ~ ( less @ SY182 @ SY183 )
| ( less @ SV44 @ SY183 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(358,plain,
! [SV44: $i] :
( ( ~ ! [SY184: $i,SY185: $i] :
( ~ ( leq @ SY184 @ SY185 )
| ~ ( less @ SV44 @ SY184 )
| ( less @ SV44 @ SY185 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(359,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX1 @ SX0 )
| ( SX1 = SX0 )
| ( less @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(360,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( leq @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( leq @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(361,plain,
! [SV49: $i,SV6: $i] :
( ( ( less @ SV6 @ ( vplus @ SV49 @ v1 ) )
= $false )
| ( ( leq @ SV6 @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(362,plain,
! [SV50: $i,SV7: $i] :
( ( ( greater @ SV7 @ SV50 )
= $false )
| ( ( geq @ SV7 @ ( vplus @ SV50 @ v1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(363,plain,
! [SV51: $i,SV9: $i,SV89: $i,SV84: $i] :
( ( ~ ( geq @ SV84 @ SV89 )
| ~ ( geq @ SV9 @ SV51 )
| ( geq @ ( vplus @ SV9 @ SV84 ) @ ( vplus @ SV51 @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(364,plain,
! [SV52: $i,SV10: $i,SV90: $i,SV85: $i] :
( ( ~ ( greater @ SV85 @ SV90 )
| ~ ( greater @ SV10 @ SV52 )
| ( greater @ ( vplus @ SV10 @ SV85 ) @ ( vplus @ SV52 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(365,plain,
! [SV53: $i,SV91: $i,SV11: $i] :
( ( ( ~ ( less @ ( vplus @ SV11 @ SV91 ) @ ( vplus @ SV53 @ SV91 ) ) )
= $true )
| ( ( less @ SV11 @ SV53 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(366,plain,
! [SV54: $i,SV92: $i,SV12: $i] :
( ( ( ( ( vplus @ SV12 @ SV92 )
!= ( vplus @ SV54 @ SV92 ) ) )
= $true )
| ( ( SV12 = SV54 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(367,plain,
! [SV55: $i,SV93: $i,SV13: $i] :
( ( ( ~ ( greater @ ( vplus @ SV13 @ SV93 ) @ ( vplus @ SV55 @ SV93 ) ) )
= $true )
| ( ( greater @ SV13 @ SV55 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(368,plain,
! [SV56: $i,SV14: $i] :
( ( ( less @ SV14 @ SV56 )
= $false )
| ( ( ! [SY195: $i] : ( less @ ( vplus @ SV14 @ SY195 ) @ ( vplus @ SV56 @ SY195 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(369,plain,
! [SV57: $i,SV15: $i] :
( ( ( SV15 = SV57 )
= $false )
| ( ( ! [SY196: $i] :
( ( vplus @ SV15 @ SY196 )
= ( vplus @ SV57 @ SY196 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(370,plain,
! [SV58: $i,SV16: $i] :
( ( ( greater @ SV16 @ SV58 )
= $false )
| ( ( ! [SY197: $i] : ( greater @ ( vplus @ SV16 @ SY197 ) @ ( vplus @ SV58 @ SY197 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(371,plain,
! [SV18: $i,SV86: $i,SV60: $i] :
( ( ( ~ ( leq @ SV60 @ SV86 )
| ~ ( leq @ SV18 @ SV60 ) )
= $true )
| ( ( leq @ SV18 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(372,plain,
! [SV19: $i,SV87: $i,SV61: $i] :
( ( ( ~ ( less @ SV61 @ SV87 )
| ~ ( less @ SV19 @ SV61 ) )
= $true )
| ( ( less @ SV19 @ SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(373,plain,
! [SV62: $i,SV20: $i] :
( ( ( leq @ SV20 @ SV62 )
= $false )
| ( ( geq @ SV62 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(374,plain,
! [SV63: $i,SV21: $i] :
( ( ( geq @ SV21 @ SV63 )
= $false )
| ( ( leq @ SV63 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(375,plain,
! [SV64: $i,SV22: $i] :
( ( ( less @ SV22 @ SV64 )
= $false )
| ( ( greater @ SV64 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(376,plain,
! [SV65: $i,SV23: $i] :
( ( ( greater @ SV23 @ SV65 )
= $false )
| ( ( less @ SV65 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(377,plain,
! [SV66: $i,SV24: $i] :
( ( ( SV24 = SV66 )
= $true )
| ( ( greater @ SV24 @ SV66 )
= $true )
| ( ( less @ SV24 @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(378,plain,
! [SV67: $i,SV25: $i] :
( ( ( SV25 = SV67 )
= $false )
| ( ( ~ ( less @ SV25 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(379,plain,
! [SV68: $i,SV26: $i] :
( ( ( greater @ SV26 @ SV68 )
= $false )
| ( ( ~ ( less @ SV26 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(380,plain,
! [SV69: $i,SV27: $i] :
( ( ( SV27 = SV69 )
= $false )
| ( ( ~ ( greater @ SV27 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(381,plain,
! [SV70: $i,SV28: $i] :
( ( ( SV28 = SV70 )
= $true )
| ( ( SV28
= ( vplus @ SV70 @ ( sK1_Vd123 @ SV70 @ SV28 ) ) )
= $true )
| ( ( SV70
= ( vplus @ SV28 @ ( sK2_Vd125 @ SV70 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(382,plain,
! [SV71: $i,SV29: $i] :
( ( ( SV29 = SV71 )
= $false )
| ( ( ! [SY200: $i] :
( SV71
!= ( vplus @ SV29 @ SY200 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(383,plain,
! [SV94: $i,SV72: $i,SV30: $i] :
( ( ( ( SV30
!= ( vplus @ SV72 @ SV94 ) ) )
= $true )
| ( ( ! [SY202: $i] :
( SV72
!= ( vplus @ SV30 @ SY202 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(384,plain,
! [SV73: $i,SV31: $i] :
( ( ( SV31 = SV73 )
= $false )
| ( ( ! [SY203: $i] :
( SV31
!= ( vplus @ SV73 @ SY203 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(385,plain,
! [SV74: $i,SV32: $i,SV95: $i] :
( ( ( ( ( vplus @ SV95 @ SV32 )
!= ( vplus @ SV95 @ SV74 ) ) )
= $true )
| ( ( SV32 = SV74 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(386,plain,
! [SV79: $i,SV40: $i] :
( ( ( ( vsucc @ SV40 )
= ( vsucc @ SV79 ) )
= $false )
| ( ( SV40 = SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(387,plain,
! [SV80: $i,SV41: $i] :
( ( ( ( vsucc @ SV41 )
= ( vsucc @ SV80 ) )
= $false )
| ( ( SV41 = SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(388,plain,
! [SV96: $i] :
( ( ! [SY212: $i] :
( ~ ( geq @ SY212 @ SV96 )
| ( SY212 = SV96 )
| ( greater @ SY212 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(389,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( geq @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( geq @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(390,plain,
! [SV97: $i] :
( ( ! [SY213: $i] :
( ( vplus @ SV97 @ ( vsucc @ SY213 ) )
= ( vsucc @ ( vplus @ SV97 @ SY213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(391,plain,
! [SV98: $i] :
( ( ( vplus @ SV98 @ v1 )
= ( vsucc @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(392,plain,
! [SV99: $i] :
( ( ! [SY214: $i] :
( ! [SY215: $i] :
( SY214
!= ( vplus @ SV99 @ SY215 ) )
| ( greater @ SY214 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(393,plain,
! [SV100: $i] :
( ( ! [SY216: $i] :
( ~ ( greater @ SY216 @ SV100 )
| ( SY216
= ( vplus @ SV100 @ ( sK3_Vd196 @ SY216 @ SV100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(394,plain,
! [SV81: $i,SV43: $i] :
( ( ~ ! [SY206: $i,SY207: $i] :
( ~ ( geq @ SV43 @ SV81 )
| ~ ( greater @ SY206 @ SY207 )
| ( greater @ ( vplus @ SV43 @ SY206 ) @ ( vplus @ SV81 @ SY207 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[352]) ).
thf(395,plain,
! [SV81: $i,SV43: $i] :
( ( ~ ! [SY208: $i,SY209: $i] :
( ~ ( geq @ SY208 @ SY209 )
| ~ ( greater @ SV43 @ SV81 )
| ( greater @ ( vplus @ SV43 @ SY208 ) @ ( vplus @ SV81 @ SY209 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[352]) ).
thf(396,plain,
! [SV101: $i] :
( ( ! [SY217: $i] :
( ! [SY218: $i] :
( SV101
!= ( vplus @ SY217 @ SY218 ) )
| ( less @ SY217 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(397,plain,
! [SV102: $i] :
( ( ! [SY219: $i] :
( ~ ( less @ SY219 @ SV102 )
| ( SV102
= ( vplus @ SY219 @ ( sK4_Vd201 @ SY219 @ SV102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(398,plain,
! [SV103: $i] :
( ( ! [SY220: $i] :
( ( vmul @ SV103 @ ( vsucc @ SY220 ) )
= ( vplus @ ( vmul @ SV103 @ SY220 ) @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(399,plain,
! [SV104: $i] :
( ( ( vmul @ SV104 @ v1 )
= SV104 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(400,plain,
! [SV44: $i] :
( ( ! [SY182: $i,SY183: $i] :
( ~ ( leq @ SV44 @ SY182 )
| ~ ( less @ SY182 @ SY183 )
| ( less @ SV44 @ SY183 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[357]) ).
thf(401,plain,
! [SV44: $i] :
( ( ! [SY184: $i,SY185: $i] :
( ~ ( leq @ SY184 @ SY185 )
| ~ ( less @ SV44 @ SY184 )
| ( less @ SV44 @ SY185 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(402,plain,
! [SV105: $i] :
( ( ! [SY221: $i] :
( ~ ( leq @ SY221 @ SV105 )
| ( SY221 = SV105 )
| ( less @ SY221 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(403,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( leq @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( leq @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(404,plain,
! [SV51: $i,SV9: $i,SV89: $i,SV84: $i] :
( ( ( ~ ( geq @ SV84 @ SV89 )
| ~ ( geq @ SV9 @ SV51 ) )
= $true )
| ( ( geq @ ( vplus @ SV9 @ SV84 ) @ ( vplus @ SV51 @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[363]) ).
thf(405,plain,
! [SV52: $i,SV10: $i,SV90: $i,SV85: $i] :
( ( ( ~ ( greater @ SV85 @ SV90 )
| ~ ( greater @ SV10 @ SV52 ) )
= $true )
| ( ( greater @ ( vplus @ SV10 @ SV85 ) @ ( vplus @ SV52 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(406,plain,
! [SV53: $i,SV91: $i,SV11: $i] :
( ( ( less @ ( vplus @ SV11 @ SV91 ) @ ( vplus @ SV53 @ SV91 ) )
= $false )
| ( ( less @ SV11 @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(407,plain,
! [SV54: $i,SV92: $i,SV12: $i] :
( ( ( ( vplus @ SV12 @ SV92 )
= ( vplus @ SV54 @ SV92 ) )
= $false )
| ( ( SV12 = SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(408,plain,
! [SV55: $i,SV93: $i,SV13: $i] :
( ( ( greater @ ( vplus @ SV13 @ SV93 ) @ ( vplus @ SV55 @ SV93 ) )
= $false )
| ( ( greater @ SV13 @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(409,plain,
! [SV56: $i,SV106: $i,SV14: $i] :
( ( ( less @ ( vplus @ SV14 @ SV106 ) @ ( vplus @ SV56 @ SV106 ) )
= $true )
| ( ( less @ SV14 @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(410,plain,
! [SV57: $i,SV107: $i,SV15: $i] :
( ( ( ( vplus @ SV15 @ SV107 )
= ( vplus @ SV57 @ SV107 ) )
= $true )
| ( ( SV15 = SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(411,plain,
! [SV58: $i,SV108: $i,SV16: $i] :
( ( ( greater @ ( vplus @ SV16 @ SV108 ) @ ( vplus @ SV58 @ SV108 ) )
= $true )
| ( ( greater @ SV16 @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(412,plain,
! [SV18: $i,SV86: $i,SV60: $i] :
( ( ( ~ ( leq @ SV60 @ SV86 ) )
= $true )
| ( ( ~ ( leq @ SV18 @ SV60 ) )
= $true )
| ( ( leq @ SV18 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(413,plain,
! [SV19: $i,SV87: $i,SV61: $i] :
( ( ( ~ ( less @ SV61 @ SV87 ) )
= $true )
| ( ( ~ ( less @ SV19 @ SV61 ) )
= $true )
| ( ( less @ SV19 @ SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(414,plain,
! [SV67: $i,SV25: $i] :
( ( ( less @ SV25 @ SV67 )
= $false )
| ( ( SV25 = SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(415,plain,
! [SV68: $i,SV26: $i] :
( ( ( less @ SV26 @ SV68 )
= $false )
| ( ( greater @ SV26 @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(416,plain,
! [SV69: $i,SV27: $i] :
( ( ( greater @ SV27 @ SV69 )
= $false )
| ( ( SV27 = SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(417,plain,
! [SV109: $i,SV29: $i,SV71: $i] :
( ( ( ( SV71
!= ( vplus @ SV29 @ SV109 ) ) )
= $true )
| ( ( SV29 = SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(418,plain,
! [SV94: $i,SV72: $i,SV30: $i] :
( ( ( SV30
= ( vplus @ SV72 @ SV94 ) )
= $false )
| ( ( ! [SY202: $i] :
( SV72
!= ( vplus @ SV30 @ SY202 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(419,plain,
! [SV110: $i,SV73: $i,SV31: $i] :
( ( ( ( SV31
!= ( vplus @ SV73 @ SV110 ) ) )
= $true )
| ( ( SV31 = SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(420,plain,
! [SV74: $i,SV32: $i,SV95: $i] :
( ( ( ( vplus @ SV95 @ SV32 )
= ( vplus @ SV95 @ SV74 ) )
= $false )
| ( ( SV32 = SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(421,plain,
! [SV96: $i,SV111: $i] :
( ( ~ ( geq @ SV111 @ SV96 )
| ( SV111 = SV96 )
| ( greater @ SV111 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(422,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( geq @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(423,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( geq @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(424,plain,
! [SV112: $i,SV97: $i] :
( ( ( vplus @ SV97 @ ( vsucc @ SV112 ) )
= ( vsucc @ ( vplus @ SV97 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(425,plain,
! [SV99: $i,SV113: $i] :
( ( ! [SY222: $i] :
( SV113
!= ( vplus @ SV99 @ SY222 ) )
| ( greater @ SV113 @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(426,plain,
! [SV100: $i,SV114: $i] :
( ( ~ ( greater @ SV114 @ SV100 )
| ( SV114
= ( vplus @ SV100 @ ( sK3_Vd196 @ SV114 @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(427,plain,
! [SV81: $i,SV43: $i] :
( ( ! [SY206: $i,SY207: $i] :
( ~ ( geq @ SV43 @ SV81 )
| ~ ( greater @ SY206 @ SY207 )
| ( greater @ ( vplus @ SV43 @ SY206 ) @ ( vplus @ SV81 @ SY207 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[394]) ).
thf(428,plain,
! [SV81: $i,SV43: $i] :
( ( ! [SY208: $i,SY209: $i] :
( ~ ( geq @ SY208 @ SY209 )
| ~ ( greater @ SV43 @ SV81 )
| ( greater @ ( vplus @ SV43 @ SY208 ) @ ( vplus @ SV81 @ SY209 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(429,plain,
! [SV115: $i,SV101: $i] :
( ( ! [SY223: $i] :
( SV101
!= ( vplus @ SV115 @ SY223 ) )
| ( less @ SV115 @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(430,plain,
! [SV102: $i,SV116: $i] :
( ( ~ ( less @ SV116 @ SV102 )
| ( SV102
= ( vplus @ SV116 @ ( sK4_Vd201 @ SV116 @ SV102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(431,plain,
! [SV117: $i,SV103: $i] :
( ( ( vmul @ SV103 @ ( vsucc @ SV117 ) )
= ( vplus @ ( vmul @ SV103 @ SV117 ) @ SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(432,plain,
! [SV118: $i,SV44: $i] :
( ( ! [SY224: $i] :
( ~ ( leq @ SV44 @ SV118 )
| ~ ( less @ SV118 @ SY224 )
| ( less @ SV44 @ SY224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(433,plain,
! [SV44: $i,SV119: $i] :
( ( ! [SY225: $i] :
( ~ ( leq @ SV119 @ SY225 )
| ~ ( less @ SV44 @ SV119 )
| ( less @ SV44 @ SY225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(434,plain,
! [SV105: $i,SV120: $i] :
( ( ~ ( leq @ SV120 @ SV105 )
| ( SV120 = SV105 )
| ( less @ SV120 @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(435,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( leq @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(436,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( leq @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(437,plain,
! [SV51: $i,SV9: $i,SV89: $i,SV84: $i] :
( ( ( ~ ( geq @ SV84 @ SV89 ) )
= $true )
| ( ( ~ ( geq @ SV9 @ SV51 ) )
= $true )
| ( ( geq @ ( vplus @ SV9 @ SV84 ) @ ( vplus @ SV51 @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(438,plain,
! [SV52: $i,SV10: $i,SV90: $i,SV85: $i] :
( ( ( ~ ( greater @ SV85 @ SV90 ) )
= $true )
| ( ( ~ ( greater @ SV10 @ SV52 ) )
= $true )
| ( ( greater @ ( vplus @ SV10 @ SV85 ) @ ( vplus @ SV52 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(439,plain,
! [SV18: $i,SV86: $i,SV60: $i] :
( ( ( leq @ SV60 @ SV86 )
= $false )
| ( ( ~ ( leq @ SV18 @ SV60 ) )
= $true )
| ( ( leq @ SV18 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(440,plain,
! [SV19: $i,SV87: $i,SV61: $i] :
( ( ( less @ SV61 @ SV87 )
= $false )
| ( ( ~ ( less @ SV19 @ SV61 ) )
= $true )
| ( ( less @ SV19 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(441,plain,
! [SV109: $i,SV29: $i,SV71: $i] :
( ( ( SV71
= ( vplus @ SV29 @ SV109 ) )
= $false )
| ( ( SV29 = SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(442,plain,
! [SV94: $i,SV121: $i,SV30: $i,SV72: $i] :
( ( ( ( SV72
!= ( vplus @ SV30 @ SV121 ) ) )
= $true )
| ( ( SV30
= ( vplus @ SV72 @ SV94 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(443,plain,
! [SV110: $i,SV73: $i,SV31: $i] :
( ( ( SV31
= ( vplus @ SV73 @ SV110 ) )
= $false )
| ( ( SV31 = SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(444,plain,
! [SV96: $i,SV111: $i] :
( ( ( ~ ( geq @ SV111 @ SV96 ) )
= $true )
| ( ( ( SV111 = SV96 )
| ( greater @ SV111 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(445,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( geq @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[422]) ).
thf(446,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( geq @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[423]) ).
thf(447,plain,
! [SV99: $i,SV113: $i] :
( ( ( ! [SY222: $i] :
( SV113
!= ( vplus @ SV99 @ SY222 ) ) )
= $true )
| ( ( greater @ SV113 @ SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(448,plain,
! [SV100: $i,SV114: $i] :
( ( ( ~ ( greater @ SV114 @ SV100 ) )
= $true )
| ( ( SV114
= ( vplus @ SV100 @ ( sK3_Vd196 @ SV114 @ SV100 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(449,plain,
! [SV122: $i,SV81: $i,SV43: $i] :
( ( ! [SY226: $i] :
( ~ ( geq @ SV43 @ SV81 )
| ~ ( greater @ SV122 @ SY226 )
| ( greater @ ( vplus @ SV43 @ SV122 ) @ ( vplus @ SV81 @ SY226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(450,plain,
! [SV81: $i,SV43: $i,SV123: $i] :
( ( ! [SY227: $i] :
( ~ ( geq @ SV123 @ SY227 )
| ~ ( greater @ SV43 @ SV81 )
| ( greater @ ( vplus @ SV43 @ SV123 ) @ ( vplus @ SV81 @ SY227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(451,plain,
! [SV115: $i,SV101: $i] :
( ( ( ! [SY223: $i] :
( SV101
!= ( vplus @ SV115 @ SY223 ) ) )
= $true )
| ( ( less @ SV115 @ SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(452,plain,
! [SV102: $i,SV116: $i] :
( ( ( ~ ( less @ SV116 @ SV102 ) )
= $true )
| ( ( SV102
= ( vplus @ SV116 @ ( sK4_Vd201 @ SV116 @ SV102 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(453,plain,
! [SV124: $i,SV118: $i,SV44: $i] :
( ( ~ ( leq @ SV44 @ SV118 )
| ~ ( less @ SV118 @ SV124 )
| ( less @ SV44 @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(454,plain,
! [SV44: $i,SV125: $i,SV119: $i] :
( ( ~ ( leq @ SV119 @ SV125 )
| ~ ( less @ SV44 @ SV119 )
| ( less @ SV44 @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(455,plain,
! [SV105: $i,SV120: $i] :
( ( ( ~ ( leq @ SV120 @ SV105 ) )
= $true )
| ( ( ( SV120 = SV105 )
| ( less @ SV120 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(456,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( leq @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(457,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( leq @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[436]) ).
thf(458,plain,
! [SV51: $i,SV9: $i,SV89: $i,SV84: $i] :
( ( ( geq @ SV84 @ SV89 )
= $false )
| ( ( ~ ( geq @ SV9 @ SV51 ) )
= $true )
| ( ( geq @ ( vplus @ SV9 @ SV84 ) @ ( vplus @ SV51 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(459,plain,
! [SV52: $i,SV10: $i,SV90: $i,SV85: $i] :
( ( ( greater @ SV85 @ SV90 )
= $false )
| ( ( ~ ( greater @ SV10 @ SV52 ) )
= $true )
| ( ( greater @ ( vplus @ SV10 @ SV85 ) @ ( vplus @ SV52 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(460,plain,
! [SV86: $i,SV60: $i,SV18: $i] :
( ( ( leq @ SV18 @ SV60 )
= $false )
| ( ( leq @ SV60 @ SV86 )
= $false )
| ( ( leq @ SV18 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(461,plain,
! [SV87: $i,SV61: $i,SV19: $i] :
( ( ( less @ SV19 @ SV61 )
= $false )
| ( ( less @ SV61 @ SV87 )
= $false )
| ( ( less @ SV19 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(462,plain,
! [SV94: $i,SV121: $i,SV30: $i,SV72: $i] :
( ( ( SV72
= ( vplus @ SV30 @ SV121 ) )
= $false )
| ( ( SV30
= ( vplus @ SV72 @ SV94 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(463,plain,
! [SV96: $i,SV111: $i] :
( ( ( geq @ SV111 @ SV96 )
= $false )
| ( ( ( SV111 = SV96 )
| ( greater @ SV111 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(464,plain,
! [SV126: $i] :
( ( ! [SY228: $i] :
( ( SY228 != SV126 )
| ( geq @ SY228 @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(465,plain,
! [SV127: $i] :
( ( ! [SY229: $i] :
( ~ ( greater @ SY229 @ SV127 )
| ( geq @ SY229 @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(466,plain,
! [SV128: $i,SV99: $i,SV113: $i] :
( ( ( ( SV113
!= ( vplus @ SV99 @ SV128 ) ) )
= $true )
| ( ( greater @ SV113 @ SV99 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(467,plain,
! [SV100: $i,SV114: $i] :
( ( ( greater @ SV114 @ SV100 )
= $false )
| ( ( SV114
= ( vplus @ SV100 @ ( sK3_Vd196 @ SV114 @ SV100 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(468,plain,
! [SV129: $i,SV122: $i,SV81: $i,SV43: $i] :
( ( ~ ( geq @ SV43 @ SV81 )
| ~ ( greater @ SV122 @ SV129 )
| ( greater @ ( vplus @ SV43 @ SV122 ) @ ( vplus @ SV81 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(469,plain,
! [SV81: $i,SV43: $i,SV130: $i,SV123: $i] :
( ( ~ ( geq @ SV123 @ SV130 )
| ~ ( greater @ SV43 @ SV81 )
| ( greater @ ( vplus @ SV43 @ SV123 ) @ ( vplus @ SV81 @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(470,plain,
! [SV131: $i,SV115: $i,SV101: $i] :
( ( ( ( SV101
!= ( vplus @ SV115 @ SV131 ) ) )
= $true )
| ( ( less @ SV115 @ SV101 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(471,plain,
! [SV102: $i,SV116: $i] :
( ( ( less @ SV116 @ SV102 )
= $false )
| ( ( SV102
= ( vplus @ SV116 @ ( sK4_Vd201 @ SV116 @ SV102 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(472,plain,
! [SV124: $i,SV118: $i,SV44: $i] :
( ( ( ~ ( leq @ SV44 @ SV118 )
| ~ ( less @ SV118 @ SV124 ) )
= $true )
| ( ( less @ SV44 @ SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(473,plain,
! [SV44: $i,SV125: $i,SV119: $i] :
( ( ( ~ ( leq @ SV119 @ SV125 )
| ~ ( less @ SV44 @ SV119 ) )
= $true )
| ( ( less @ SV44 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(474,plain,
! [SV105: $i,SV120: $i] :
( ( ( leq @ SV120 @ SV105 )
= $false )
| ( ( ( SV120 = SV105 )
| ( less @ SV120 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(475,plain,
! [SV132: $i] :
( ( ! [SY230: $i] :
( ( SY230 != SV132 )
| ( leq @ SY230 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(476,plain,
! [SV133: $i] :
( ( ! [SY231: $i] :
( ~ ( less @ SY231 @ SV133 )
| ( leq @ SY231 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(477,plain,
! [SV89: $i,SV84: $i,SV51: $i,SV9: $i] :
( ( ( geq @ SV9 @ SV51 )
= $false )
| ( ( geq @ SV84 @ SV89 )
= $false )
| ( ( geq @ ( vplus @ SV9 @ SV84 ) @ ( vplus @ SV51 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(478,plain,
! [SV90: $i,SV85: $i,SV52: $i,SV10: $i] :
( ( ( greater @ SV10 @ SV52 )
= $false )
| ( ( greater @ SV85 @ SV90 )
= $false )
| ( ( greater @ ( vplus @ SV10 @ SV85 ) @ ( vplus @ SV52 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(479,plain,
! [SV96: $i,SV111: $i] :
( ( ( SV111 = SV96 )
= $true )
| ( ( greater @ SV111 @ SV96 )
= $true )
| ( ( geq @ SV111 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(480,plain,
! [SV126: $i,SV134: $i] :
( ( ( SV134 != SV126 )
| ( geq @ SV134 @ SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(481,plain,
! [SV127: $i,SV135: $i] :
( ( ~ ( greater @ SV135 @ SV127 )
| ( geq @ SV135 @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(482,plain,
! [SV128: $i,SV99: $i,SV113: $i] :
( ( ( SV113
= ( vplus @ SV99 @ SV128 ) )
= $false )
| ( ( greater @ SV113 @ SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(483,plain,
! [SV129: $i,SV122: $i,SV81: $i,SV43: $i] :
( ( ( ~ ( geq @ SV43 @ SV81 )
| ~ ( greater @ SV122 @ SV129 ) )
= $true )
| ( ( greater @ ( vplus @ SV43 @ SV122 ) @ ( vplus @ SV81 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(484,plain,
! [SV81: $i,SV43: $i,SV130: $i,SV123: $i] :
( ( ( ~ ( geq @ SV123 @ SV130 )
| ~ ( greater @ SV43 @ SV81 ) )
= $true )
| ( ( greater @ ( vplus @ SV43 @ SV123 ) @ ( vplus @ SV81 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[469]) ).
thf(485,plain,
! [SV131: $i,SV115: $i,SV101: $i] :
( ( ( SV101
= ( vplus @ SV115 @ SV131 ) )
= $false )
| ( ( less @ SV115 @ SV101 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(486,plain,
! [SV124: $i,SV118: $i,SV44: $i] :
( ( ( ~ ( leq @ SV44 @ SV118 ) )
= $true )
| ( ( ~ ( less @ SV118 @ SV124 ) )
= $true )
| ( ( less @ SV44 @ SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(487,plain,
! [SV44: $i,SV125: $i,SV119: $i] :
( ( ( ~ ( leq @ SV119 @ SV125 ) )
= $true )
| ( ( ~ ( less @ SV44 @ SV119 ) )
= $true )
| ( ( less @ SV44 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(488,plain,
! [SV105: $i,SV120: $i] :
( ( ( SV120 = SV105 )
= $true )
| ( ( less @ SV120 @ SV105 )
= $true )
| ( ( leq @ SV120 @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(489,plain,
! [SV132: $i,SV136: $i] :
( ( ( SV136 != SV132 )
| ( leq @ SV136 @ SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(490,plain,
! [SV133: $i,SV137: $i] :
( ( ~ ( less @ SV137 @ SV133 )
| ( leq @ SV137 @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(491,plain,
! [SV126: $i,SV134: $i] :
( ( ( ( SV134 != SV126 ) )
= $true )
| ( ( geq @ SV134 @ SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[480]) ).
thf(492,plain,
! [SV127: $i,SV135: $i] :
( ( ( ~ ( greater @ SV135 @ SV127 ) )
= $true )
| ( ( geq @ SV135 @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(493,plain,
! [SV129: $i,SV122: $i,SV81: $i,SV43: $i] :
( ( ( ~ ( geq @ SV43 @ SV81 ) )
= $true )
| ( ( ~ ( greater @ SV122 @ SV129 ) )
= $true )
| ( ( greater @ ( vplus @ SV43 @ SV122 ) @ ( vplus @ SV81 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[483]) ).
thf(494,plain,
! [SV81: $i,SV43: $i,SV130: $i,SV123: $i] :
( ( ( ~ ( geq @ SV123 @ SV130 ) )
= $true )
| ( ( ~ ( greater @ SV43 @ SV81 ) )
= $true )
| ( ( greater @ ( vplus @ SV43 @ SV123 ) @ ( vplus @ SV81 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(495,plain,
! [SV124: $i,SV118: $i,SV44: $i] :
( ( ( leq @ SV44 @ SV118 )
= $false )
| ( ( ~ ( less @ SV118 @ SV124 ) )
= $true )
| ( ( less @ SV44 @ SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(496,plain,
! [SV44: $i,SV125: $i,SV119: $i] :
( ( ( leq @ SV119 @ SV125 )
= $false )
| ( ( ~ ( less @ SV44 @ SV119 ) )
= $true )
| ( ( less @ SV44 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(497,plain,
! [SV132: $i,SV136: $i] :
( ( ( ( SV136 != SV132 ) )
= $true )
| ( ( leq @ SV136 @ SV132 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(498,plain,
! [SV133: $i,SV137: $i] :
( ( ( ~ ( less @ SV137 @ SV133 ) )
= $true )
| ( ( leq @ SV137 @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(499,plain,
! [SV126: $i,SV134: $i] :
( ( ( SV134 = SV126 )
= $false )
| ( ( geq @ SV134 @ SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(500,plain,
! [SV127: $i,SV135: $i] :
( ( ( greater @ SV135 @ SV127 )
= $false )
| ( ( geq @ SV135 @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(501,plain,
! [SV129: $i,SV122: $i,SV81: $i,SV43: $i] :
( ( ( geq @ SV43 @ SV81 )
= $false )
| ( ( ~ ( greater @ SV122 @ SV129 ) )
= $true )
| ( ( greater @ ( vplus @ SV43 @ SV122 ) @ ( vplus @ SV81 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(502,plain,
! [SV81: $i,SV43: $i,SV130: $i,SV123: $i] :
( ( ( geq @ SV123 @ SV130 )
= $false )
| ( ( ~ ( greater @ SV43 @ SV81 ) )
= $true )
| ( ( greater @ ( vplus @ SV43 @ SV123 ) @ ( vplus @ SV81 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(503,plain,
! [SV44: $i,SV124: $i,SV118: $i] :
( ( ( less @ SV118 @ SV124 )
= $false )
| ( ( leq @ SV44 @ SV118 )
= $false )
| ( ( less @ SV44 @ SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(504,plain,
! [SV125: $i,SV119: $i,SV44: $i] :
( ( ( less @ SV44 @ SV119 )
= $false )
| ( ( leq @ SV119 @ SV125 )
= $false )
| ( ( less @ SV44 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(505,plain,
! [SV132: $i,SV136: $i] :
( ( ( SV136 = SV132 )
= $false )
| ( ( leq @ SV136 @ SV132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(506,plain,
! [SV133: $i,SV137: $i] :
( ( ( less @ SV137 @ SV133 )
= $false )
| ( ( leq @ SV137 @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(507,plain,
! [SV81: $i,SV43: $i,SV129: $i,SV122: $i] :
( ( ( greater @ SV122 @ SV129 )
= $false )
| ( ( geq @ SV43 @ SV81 )
= $false )
| ( ( greater @ ( vplus @ SV43 @ SV122 ) @ ( vplus @ SV81 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(508,plain,
! [SV130: $i,SV123: $i,SV81: $i,SV43: $i] :
( ( ( greater @ SV43 @ SV81 )
= $false )
| ( ( geq @ SV123 @ SV130 )
= $false )
| ( ( greater @ ( vplus @ SV43 @ SV123 ) @ ( vplus @ SV81 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(509,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[149,508,507,506,505,504,503,500,499,488,485,482,479,478,477,471,467,462,461,460,443,441,431,424,420,416,415,414,411,410,409,408,407,406,399,391,387,386,381,377,376,375,374,373,362,361,343,342,316,315,300,297,296,294,293,276,265,264,253,246,218,215,151,150]) ).
thf(510,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[509]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM851+1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jul 7 20:45:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.37 .
% 0.13/0.38
% 0.13/0.38 No.of.Axioms: 53
% 0.13/0.38
% 0.13/0.38 Length.of.Defs: 0
% 0.13/0.38
% 0.13/0.38 Contains.Choice.Funs: false
% 0.13/0.39 .
% 0.13/0.41 (rf:0,axioms:53,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:55,loop_count:0,foatp_calls:0,translation:fof_full).............................
% 1.07/1.32
% 1.07/1.32 ********************************
% 1.07/1.32 * All subproblems solved! *
% 1.07/1.32 ********************************
% 1.07/1.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:53,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:509,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.24/1.45
% 1.24/1.45 %**** Beginning of derivation protocol ****
% 1.24/1.45 % SZS output start CNFRefutation
% See solution above
% 1.24/1.45
% 1.24/1.45 %**** End of derivation protocol ****
% 1.24/1.45 %**** no. of clauses in derivation: 510 ****
% 1.24/1.45 %**** clause counter: 509 ****
% 1.24/1.45
% 1.24/1.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:53,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:509,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------