TSTP Solution File: NUM837+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM837+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 : n016.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 11:55:52 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 46
% Syntax : Number of formulae : 313 ( 211 unt; 15 typ; 0 def)
% Number of atoms : 1308 ( 674 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1851 ( 330 ~; 298 |; 16 &;1183 @)
% ( 8 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 698 ( 0 ^ 678 !; 20 ?; 698 :)
% 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_vd268,type,
vd268: $i ).
thf(tp_vd269,type,
vd269: $i ).
thf(tp_vd271,type,
vd271: $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,
less @ vd268 @ vd269,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(170), 270, 0)') ).
thf(30,axiom,
less @ vd269 @ vd271,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(170), 272, 0)') ).
thf(31,conjecture,
? [Vd273: $i] :
( vd269
= ( vplus @ vd268 @ Vd273 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qe(171)') ).
thf(32,negated_conjecture,
( ( ? [Vd273: $i] :
( vd269
= ( vplus @ vd268 @ Vd273 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[31]) ).
thf(33,plain,
( ( ? [Vd273: $i] :
( vd269
= ( vplus @ vd268 @ Vd273 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[32]) ).
thf(34,plain,
( ( ! [Vd1: $i] :
( ( vsucc @ Vd1 )
!= v1 ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(35,plain,
( ( ! [Vd3: $i,Vd4: $i] :
( ( ( vsucc @ Vd3 )
= ( vsucc @ Vd4 ) )
=> ( Vd3 = Vd4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(36,plain,
( ( ! [Vd7: $i,Vd8: $i] :
( ( Vd7 != Vd8 )
=> ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(37,plain,
( ( ! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(38,plain,
( ( ! [Vd24: $i] :
( ( Vd24 != v1 )
=> ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(39,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(40,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(41,plain,
( ( ! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(42,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(43,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(44,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(45,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 != Vd105 )
=> ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(46,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(47,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(48,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(49,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(50,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(51,plain,
( ( ! [Vd198: $i,Vd199: $i] :
( ( less @ Vd199 @ Vd198 )
<=> ? [Vd201: $i] :
( Vd198
= ( vplus @ Vd199 @ Vd201 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(52,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(53,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ~ ( greater @ Vd203 @ Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(54,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(55,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 )
| ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(56,plain,
( ( ! [Vd208: $i,Vd209: $i] :
( ( greater @ Vd208 @ Vd209 )
=> ( less @ Vd209 @ Vd208 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(57,plain,
( ( ! [Vd226: $i,Vd227: $i] :
( ( less @ Vd226 @ Vd227 )
=> ( greater @ Vd227 @ Vd226 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(58,plain,
( ( ! [Vd244: $i,Vd245: $i] :
( ( geq @ Vd245 @ Vd244 )
<=> ( ( greater @ Vd245 @ Vd244 )
| ( Vd245 = Vd244 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(59,plain,
( ( ! [Vd249: $i,Vd250: $i] :
( ( leq @ Vd250 @ Vd249 )
<=> ( ( less @ Vd250 @ Vd249 )
| ( Vd250 = Vd249 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(60,plain,
( ( ! [Vd254: $i,Vd255: $i] :
( ( geq @ Vd254 @ Vd255 )
=> ( leq @ Vd255 @ Vd254 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(61,plain,
( ( ! [Vd258: $i,Vd259: $i] :
( ( leq @ Vd258 @ Vd259 )
=> ( geq @ Vd259 @ Vd258 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(62,plain,
( ( less @ vd268 @ vd269 )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(63,plain,
( ( less @ vd269 @ vd271 )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(64,plain,
( ( ~ ? [Vd273: $i] :
( vd269
= ( vplus @ vd268 @ Vd273 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[33]) ).
thf(65,plain,
( ( ! [Vd273: $i] :
( vd269
!= ( vplus @ vd268 @ Vd273 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(66,plain,
( ( ! [Vd1: $i] :
( ( vsucc @ Vd1 )
!= v1 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(67,plain,
( ( ! [Vd3: $i,Vd4: $i] :
( ( ( vsucc @ Vd3 )
!= ( vsucc @ Vd4 ) )
| ( Vd3 = Vd4 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(68,plain,
( ( ! [Vd7: $i,Vd8: $i] :
( ( Vd7 = Vd8 )
| ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(69,plain,
( ( ! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(70,plain,
( ( ! [Vd24: $i] :
( ( Vd24 = v1 )
| ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(71,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)],[39]) ).
thf(72,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(73,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 = Vd105 )
| ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(74,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ! [Vd123: $i] :
( Vd120
!= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(75,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ! [Vd123: $i] :
( Vd120
!= ( vplus @ Vd121 @ Vd123 ) )
| ! [Vd125: $i] :
( Vd121
!= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(76,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ! [Vd125: $i] :
( Vd121
!= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(77,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)],[49]) ).
thf(78,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)],[50]) ).
thf(79,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)],[51]) ).
thf(80,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(81,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(82,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( less @ Vd203 @ Vd204 )
| ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(83,plain,
( ( ! [Vd208: $i,Vd209: $i] :
( ~ ( greater @ Vd208 @ Vd209 )
| ( less @ Vd209 @ Vd208 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(84,plain,
( ( ! [Vd226: $i,Vd227: $i] :
( ~ ( less @ Vd226 @ Vd227 )
| ( greater @ Vd227 @ Vd226 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(85,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)],[58]) ).
thf(86,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)],[59]) ).
thf(87,plain,
( ( ! [Vd254: $i,Vd255: $i] :
( ~ ( geq @ Vd254 @ Vd255 )
| ( leq @ Vd255 @ Vd254 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(88,plain,
( ( ! [Vd258: $i,Vd259: $i] :
( ~ ( leq @ Vd258 @ Vd259 )
| ( geq @ Vd259 @ Vd258 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(89,plain,
( ( less @ vd269 @ vd271 )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(90,plain,
( ( less @ vd268 @ vd269 )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(91,plain,
( ( ! [Vd258: $i,Vd259: $i] :
( ~ ( leq @ Vd258 @ Vd259 )
| ( geq @ Vd259 @ Vd258 ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(92,plain,
( ( ! [Vd254: $i,Vd255: $i] :
( ~ ( geq @ Vd254 @ Vd255 )
| ( leq @ Vd255 @ Vd254 ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(93,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)],[86]) ).
thf(94,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)],[85]) ).
thf(95,plain,
( ( ! [Vd226: $i,Vd227: $i] :
( ~ ( less @ Vd226 @ Vd227 )
| ( greater @ Vd227 @ Vd226 ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(96,plain,
( ( ! [Vd208: $i,Vd209: $i] :
( ~ ( greater @ Vd208 @ Vd209 )
| ( less @ Vd209 @ Vd208 ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(97,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( less @ Vd203 @ Vd204 )
| ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(98,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(99,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ~ ( greater @ Vd203 @ Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(100,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(101,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)],[79]) ).
thf(102,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)],[78]) ).
thf(103,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)],[77]) ).
thf(104,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ! [Vd125: $i] :
( Vd121
!= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(105,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ! [Vd123: $i] :
( Vd120
!= ( vplus @ Vd121 @ Vd123 ) )
| ! [Vd125: $i] :
( Vd121
!= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(106,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ! [Vd123: $i] :
( Vd120
!= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(107,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 = Vd105 )
| ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(108,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(109,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(110,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(111,plain,
( ( ! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(112,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(113,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)],[71]) ).
thf(114,plain,
( ( ! [Vd24: $i] :
( ( Vd24 = v1 )
| ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(115,plain,
( ( ! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(116,plain,
( ( ! [Vd7: $i,Vd8: $i] :
( ( Vd7 = Vd8 )
| ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(117,plain,
( ( ! [Vd3: $i,Vd4: $i] :
( ( ( vsucc @ Vd3 )
!= ( vsucc @ Vd4 ) )
| ( Vd3 = Vd4 ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(118,plain,
( ( ! [Vd1: $i] :
( ( vsucc @ Vd1 )
!= v1 ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(119,plain,
( ( ! [Vd273: $i] :
( vd269
!= ( vplus @ vd268 @ Vd273 ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(120,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)],[93]) ).
thf(121,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)],[113]) ).
thf(122,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)],[94]) ).
thf(123,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)],[101]) ).
thf(124,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)],[102]) ).
thf(125,plain,
! [SV1: $i] :
( ( ! [SY63: $i] :
( ~ ( leq @ SV1 @ SY63 )
| ( geq @ SY63 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(126,plain,
! [SV2: $i] :
( ( ! [SY64: $i] :
( ~ ( geq @ SV2 @ SY64 )
| ( leq @ SY64 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(127,plain,
! [SV3: $i] :
( ( ! [SY65: $i] :
( ~ ( less @ SV3 @ SY65 )
| ( greater @ SY65 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(128,plain,
! [SV4: $i] :
( ( ! [SY66: $i] :
( ~ ( greater @ SV4 @ SY66 )
| ( less @ SY66 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(129,plain,
! [SV5: $i] :
( ( ! [SY67: $i] :
( ( less @ SV5 @ SY67 )
| ( SV5 = SY67 )
| ( greater @ SV5 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(130,plain,
! [SV6: $i] :
( ( ! [SY68: $i] :
( ( SV6 != SY68 )
| ~ ( less @ SV6 @ SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(131,plain,
! [SV7: $i] :
( ( ! [SY69: $i] :
( ~ ( greater @ SV7 @ SY69 )
| ~ ( less @ SV7 @ SY69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(132,plain,
! [SV8: $i] :
( ( ! [SY70: $i] :
( ( SV8 != SY70 )
| ~ ( greater @ SV8 @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(133,plain,
! [SV9: $i] :
( ( ! [SY71: $i] :
( ( SY71
= ( vplus @ SV9 @ ( sK2_Vd125 @ SY71 @ SV9 ) ) )
| ( SV9 = SY71 )
| ( SV9
= ( vplus @ SY71 @ ( sK1_Vd123 @ SY71 @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(134,plain,
! [SV10: $i] :
( ( ! [SY72: $i] :
( ( SV10 != SY72 )
| ! [SY73: $i] :
( SY72
!= ( vplus @ SV10 @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(135,plain,
! [SV11: $i] :
( ( ! [SY74: $i] :
( ! [SY75: $i] :
( SV11
!= ( vplus @ SY74 @ SY75 ) )
| ! [SY76: $i] :
( SY74
!= ( vplus @ SV11 @ SY76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(136,plain,
! [SV12: $i] :
( ( ! [SY77: $i] :
( ( SV12 != SY77 )
| ! [SY78: $i] :
( SV12
!= ( vplus @ SY77 @ SY78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(137,plain,
! [SV13: $i] :
( ( ! [SY79: $i] :
( ( SV13 = SY79 )
| ! [SY80: $i] :
( ( vplus @ SY80 @ SV13 )
!= ( vplus @ SY80 @ SY79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(138,plain,
! [SV14: $i] :
( ( ! [SY81: $i] :
( SY81
!= ( vplus @ SV14 @ SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(139,plain,
! [SV15: $i] :
( ( ! [SY82: $i] :
( ( vplus @ SY82 @ SV15 )
= ( vplus @ SV15 @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(140,plain,
! [SV16: $i] :
( ( ! [SY83: $i] :
( ( vplus @ ( vsucc @ SV16 ) @ SY83 )
= ( vsucc @ ( vplus @ SV16 @ SY83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(141,plain,
! [SV17: $i] :
( ( ( vplus @ v1 @ SV17 )
= ( vsucc @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(142,plain,
! [SV18: $i] :
( ( ! [SY84: $i,SY85: $i] :
( ( vplus @ ( vplus @ SV18 @ SY84 ) @ SY85 )
= ( vplus @ SV18 @ ( vplus @ SY84 @ SY85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(143,plain,
! [SV19: $i] :
( ( ( SV19 = v1 )
| ( SV19
= ( vsucc @ ( vskolem2 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(144,plain,
! [SV20: $i] :
( ( ( ( vsucc @ SV20 )
!= SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(145,plain,
! [SV21: $i] :
( ( ! [SY86: $i] :
( ( SV21 = SY86 )
| ( ( vsucc @ SV21 )
!= ( vsucc @ SY86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(146,plain,
! [SV22: $i] :
( ( ! [SY87: $i] :
( ( ( vsucc @ SV22 )
!= ( vsucc @ SY87 ) )
| ( SV22 = SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(147,plain,
! [SV23: $i] :
( ( ( ( vsucc @ SV23 )
!= v1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(148,plain,
! [SV24: $i] :
( ( ( vd269
!= ( vplus @ vd268 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(149,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)],[120]) ).
thf(150,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)],[121]) ).
thf(151,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)],[122]) ).
thf(152,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)],[123]) ).
thf(153,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)],[124]) ).
thf(154,plain,
! [SV25: $i,SV1: $i] :
( ( ~ ( leq @ SV1 @ SV25 )
| ( geq @ SV25 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(155,plain,
! [SV26: $i,SV2: $i] :
( ( ~ ( geq @ SV2 @ SV26 )
| ( leq @ SV26 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(156,plain,
! [SV27: $i,SV3: $i] :
( ( ~ ( less @ SV3 @ SV27 )
| ( greater @ SV27 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(157,plain,
! [SV28: $i,SV4: $i] :
( ( ~ ( greater @ SV4 @ SV28 )
| ( less @ SV28 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(158,plain,
! [SV29: $i,SV5: $i] :
( ( ( less @ SV5 @ SV29 )
| ( SV5 = SV29 )
| ( greater @ SV5 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(159,plain,
! [SV30: $i,SV6: $i] :
( ( ( SV6 != SV30 )
| ~ ( less @ SV6 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(160,plain,
! [SV31: $i,SV7: $i] :
( ( ~ ( greater @ SV7 @ SV31 )
| ~ ( less @ SV7 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(161,plain,
! [SV32: $i,SV8: $i] :
( ( ( SV8 != SV32 )
| ~ ( greater @ SV8 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(162,plain,
! [SV9: $i,SV33: $i] :
( ( ( SV33
= ( vplus @ SV9 @ ( sK2_Vd125 @ SV33 @ SV9 ) ) )
| ( SV9 = SV33 )
| ( SV9
= ( vplus @ SV33 @ ( sK1_Vd123 @ SV33 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(163,plain,
! [SV34: $i,SV10: $i] :
( ( ( SV10 != SV34 )
| ! [SY88: $i] :
( SV34
!= ( vplus @ SV10 @ SY88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(164,plain,
! [SV35: $i,SV11: $i] :
( ( ! [SY89: $i] :
( SV11
!= ( vplus @ SV35 @ SY89 ) )
| ! [SY90: $i] :
( SV35
!= ( vplus @ SV11 @ SY90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(165,plain,
! [SV36: $i,SV12: $i] :
( ( ( SV12 != SV36 )
| ! [SY91: $i] :
( SV12
!= ( vplus @ SV36 @ SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(166,plain,
! [SV37: $i,SV13: $i] :
( ( ( SV13 = SV37 )
| ! [SY92: $i] :
( ( vplus @ SY92 @ SV13 )
!= ( vplus @ SY92 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(167,plain,
! [SV14: $i,SV38: $i] :
( ( ( SV38
!= ( vplus @ SV14 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(168,plain,
! [SV15: $i,SV39: $i] :
( ( ( vplus @ SV39 @ SV15 )
= ( vplus @ SV15 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(169,plain,
! [SV40: $i,SV16: $i] :
( ( ( vplus @ ( vsucc @ SV16 ) @ SV40 )
= ( vsucc @ ( vplus @ SV16 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(170,plain,
! [SV41: $i,SV18: $i] :
( ( ! [SY93: $i] :
( ( vplus @ ( vplus @ SV18 @ SV41 ) @ SY93 )
= ( vplus @ SV18 @ ( vplus @ SV41 @ SY93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(171,plain,
! [SV19: $i] :
( ( ( SV19 = v1 )
= $true )
| ( ( SV19
= ( vsucc @ ( vskolem2 @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(172,plain,
! [SV20: $i] :
( ( ( vsucc @ SV20 )
= SV20 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(173,plain,
! [SV42: $i,SV21: $i] :
( ( ( SV21 = SV42 )
| ( ( vsucc @ SV21 )
!= ( vsucc @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(174,plain,
! [SV43: $i,SV22: $i] :
( ( ( ( vsucc @ SV22 )
!= ( vsucc @ SV43 ) )
| ( SV22 = SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(175,plain,
! [SV23: $i] :
( ( ( vsucc @ SV23 )
= v1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(176,plain,
! [SV24: $i] :
( ( vd269
= ( vplus @ vd268 @ SV24 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(177,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX1 @ SX0 )
| ( SX1 = SX0 )
| ( less @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(178,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)],[149]) ).
thf(179,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(180,plain,
( ( ~ ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(181,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( geq @ SX1 @ SX0 )
| ( SX1 = SX0 )
| ( greater @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(182,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)],[151]) ).
thf(183,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( less @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(184,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( SX0
= ( vplus @ SX1 @ ( sK4_Vd201 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(185,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( greater @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(186,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( SX1
= ( vplus @ SX0 @ ( sK3_Vd196 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(187,plain,
! [SV25: $i,SV1: $i] :
( ( ( ~ ( leq @ SV1 @ SV25 ) )
= $true )
| ( ( geq @ SV25 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(188,plain,
! [SV26: $i,SV2: $i] :
( ( ( ~ ( geq @ SV2 @ SV26 ) )
= $true )
| ( ( leq @ SV26 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(189,plain,
! [SV27: $i,SV3: $i] :
( ( ( ~ ( less @ SV3 @ SV27 ) )
= $true )
| ( ( greater @ SV27 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(190,plain,
! [SV28: $i,SV4: $i] :
( ( ( ~ ( greater @ SV4 @ SV28 ) )
= $true )
| ( ( less @ SV28 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(191,plain,
! [SV29: $i,SV5: $i] :
( ( ( less @ SV5 @ SV29 )
= $true )
| ( ( ( SV5 = SV29 )
| ( greater @ SV5 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(192,plain,
! [SV30: $i,SV6: $i] :
( ( ( ( SV6 != SV30 ) )
= $true )
| ( ( ~ ( less @ SV6 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(193,plain,
! [SV31: $i,SV7: $i] :
( ( ( ~ ( greater @ SV7 @ SV31 ) )
= $true )
| ( ( ~ ( less @ SV7 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(194,plain,
! [SV32: $i,SV8: $i] :
( ( ( ( SV8 != SV32 ) )
= $true )
| ( ( ~ ( greater @ SV8 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(195,plain,
! [SV9: $i,SV33: $i] :
( ( ( SV33
= ( vplus @ SV9 @ ( sK2_Vd125 @ SV33 @ SV9 ) ) )
= $true )
| ( ( ( SV9 = SV33 )
| ( SV9
= ( vplus @ SV33 @ ( sK1_Vd123 @ SV33 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(196,plain,
! [SV34: $i,SV10: $i] :
( ( ( ( SV10 != SV34 ) )
= $true )
| ( ( ! [SY88: $i] :
( SV34
!= ( vplus @ SV10 @ SY88 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(197,plain,
! [SV35: $i,SV11: $i] :
( ( ( ! [SY89: $i] :
( SV11
!= ( vplus @ SV35 @ SY89 ) ) )
= $true )
| ( ( ! [SY90: $i] :
( SV35
!= ( vplus @ SV11 @ SY90 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(198,plain,
! [SV36: $i,SV12: $i] :
( ( ( ( SV12 != SV36 ) )
= $true )
| ( ( ! [SY91: $i] :
( SV12
!= ( vplus @ SV36 @ SY91 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(199,plain,
! [SV37: $i,SV13: $i] :
( ( ( SV13 = SV37 )
= $true )
| ( ( ! [SY92: $i] :
( ( vplus @ SY92 @ SV13 )
!= ( vplus @ SY92 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(200,plain,
! [SV14: $i,SV38: $i] :
( ( SV38
= ( vplus @ SV14 @ SV38 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(201,plain,
! [SV44: $i,SV41: $i,SV18: $i] :
( ( ( vplus @ ( vplus @ SV18 @ SV41 ) @ SV44 )
= ( vplus @ SV18 @ ( vplus @ SV41 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(202,plain,
! [SV42: $i,SV21: $i] :
( ( ( SV21 = SV42 )
= $true )
| ( ( ( ( vsucc @ SV21 )
!= ( vsucc @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(203,plain,
! [SV43: $i,SV22: $i] :
( ( ( ( ( vsucc @ SV22 )
!= ( vsucc @ SV43 ) ) )
= $true )
| ( ( SV22 = SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(204,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX1 @ SX0 )
| ( SX1 = SX0 )
| ( less @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(205,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)],[178]) ).
thf(206,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(207,plain,
( ( ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(208,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( geq @ SX1 @ SX0 )
| ( SX1 = SX0 )
| ( greater @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(209,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)],[182]) ).
thf(210,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( less @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(211,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( SX0
= ( vplus @ SX1 @ ( sK4_Vd201 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(212,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( greater @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(213,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( SX1
= ( vplus @ SX0 @ ( sK3_Vd196 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(214,plain,
! [SV25: $i,SV1: $i] :
( ( ( leq @ SV1 @ SV25 )
= $false )
| ( ( geq @ SV25 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(215,plain,
! [SV26: $i,SV2: $i] :
( ( ( geq @ SV2 @ SV26 )
= $false )
| ( ( leq @ SV26 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(216,plain,
! [SV27: $i,SV3: $i] :
( ( ( less @ SV3 @ SV27 )
= $false )
| ( ( greater @ SV27 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(217,plain,
! [SV28: $i,SV4: $i] :
( ( ( greater @ SV4 @ SV28 )
= $false )
| ( ( less @ SV28 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(218,plain,
! [SV29: $i,SV5: $i] :
( ( ( SV5 = SV29 )
= $true )
| ( ( greater @ SV5 @ SV29 )
= $true )
| ( ( less @ SV5 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(219,plain,
! [SV30: $i,SV6: $i] :
( ( ( SV6 = SV30 )
= $false )
| ( ( ~ ( less @ SV6 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(220,plain,
! [SV31: $i,SV7: $i] :
( ( ( greater @ SV7 @ SV31 )
= $false )
| ( ( ~ ( less @ SV7 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(221,plain,
! [SV32: $i,SV8: $i] :
( ( ( SV8 = SV32 )
= $false )
| ( ( ~ ( greater @ SV8 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(222,plain,
! [SV33: $i,SV9: $i] :
( ( ( SV9 = SV33 )
= $true )
| ( ( SV9
= ( vplus @ SV33 @ ( sK1_Vd123 @ SV33 @ SV9 ) ) )
= $true )
| ( ( SV33
= ( vplus @ SV9 @ ( sK2_Vd125 @ SV33 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(223,plain,
! [SV34: $i,SV10: $i] :
( ( ( SV10 = SV34 )
= $false )
| ( ( ! [SY88: $i] :
( SV34
!= ( vplus @ SV10 @ SY88 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(224,plain,
! [SV45: $i,SV35: $i,SV11: $i] :
( ( ( ( SV11
!= ( vplus @ SV35 @ SV45 ) ) )
= $true )
| ( ( ! [SY90: $i] :
( SV35
!= ( vplus @ SV11 @ SY90 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(225,plain,
! [SV36: $i,SV12: $i] :
( ( ( SV12 = SV36 )
= $false )
| ( ( ! [SY91: $i] :
( SV12
!= ( vplus @ SV36 @ SY91 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(226,plain,
! [SV37: $i,SV13: $i,SV46: $i] :
( ( ( ( ( vplus @ SV46 @ SV13 )
!= ( vplus @ SV46 @ SV37 ) ) )
= $true )
| ( ( SV13 = SV37 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(227,plain,
! [SV42: $i,SV21: $i] :
( ( ( ( vsucc @ SV21 )
= ( vsucc @ SV42 ) )
= $false )
| ( ( SV21 = SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(228,plain,
! [SV43: $i,SV22: $i] :
( ( ( ( vsucc @ SV22 )
= ( vsucc @ SV43 ) )
= $false )
| ( ( SV22 = SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(229,plain,
! [SV47: $i] :
( ( ! [SY94: $i] :
( ~ ( leq @ SY94 @ SV47 )
| ( SY94 = SV47 )
| ( less @ SY94 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(230,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)],[205]) ).
thf(231,plain,
! [SV48: $i] :
( ( ! [SY95: $i] :
( ( vplus @ SV48 @ ( vsucc @ SY95 ) )
= ( vsucc @ ( vplus @ SV48 @ SY95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(232,plain,
! [SV49: $i] :
( ( ( vplus @ SV49 @ v1 )
= ( vsucc @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(233,plain,
! [SV50: $i] :
( ( ! [SY96: $i] :
( ~ ( geq @ SY96 @ SV50 )
| ( SY96 = SV50 )
| ( greater @ SY96 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(234,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)],[209]) ).
thf(235,plain,
! [SV51: $i] :
( ( ! [SY97: $i] :
( ! [SY98: $i] :
( SV51
!= ( vplus @ SY97 @ SY98 ) )
| ( less @ SY97 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(236,plain,
! [SV52: $i] :
( ( ! [SY99: $i] :
( ~ ( less @ SY99 @ SV52 )
| ( SV52
= ( vplus @ SY99 @ ( sK4_Vd201 @ SY99 @ SV52 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(237,plain,
! [SV53: $i] :
( ( ! [SY100: $i] :
( ! [SY101: $i] :
( SY100
!= ( vplus @ SV53 @ SY101 ) )
| ( greater @ SY100 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(238,plain,
! [SV54: $i] :
( ( ! [SY102: $i] :
( ~ ( greater @ SY102 @ SV54 )
| ( SY102
= ( vplus @ SV54 @ ( sK3_Vd196 @ SY102 @ SV54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(239,plain,
! [SV30: $i,SV6: $i] :
( ( ( less @ SV6 @ SV30 )
= $false )
| ( ( SV6 = SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(240,plain,
! [SV31: $i,SV7: $i] :
( ( ( less @ SV7 @ SV31 )
= $false )
| ( ( greater @ SV7 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(241,plain,
! [SV32: $i,SV8: $i] :
( ( ( greater @ SV8 @ SV32 )
= $false )
| ( ( SV8 = SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(242,plain,
! [SV55: $i,SV10: $i,SV34: $i] :
( ( ( ( SV34
!= ( vplus @ SV10 @ SV55 ) ) )
= $true )
| ( ( SV10 = SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(243,plain,
! [SV45: $i,SV35: $i,SV11: $i] :
( ( ( SV11
= ( vplus @ SV35 @ SV45 ) )
= $false )
| ( ( ! [SY90: $i] :
( SV35
!= ( vplus @ SV11 @ SY90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(244,plain,
! [SV56: $i,SV36: $i,SV12: $i] :
( ( ( ( SV12
!= ( vplus @ SV36 @ SV56 ) ) )
= $true )
| ( ( SV12 = SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(245,plain,
! [SV37: $i,SV13: $i,SV46: $i] :
( ( ( ( vplus @ SV46 @ SV13 )
= ( vplus @ SV46 @ SV37 ) )
= $false )
| ( ( SV13 = SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(246,plain,
! [SV47: $i,SV57: $i] :
( ( ~ ( leq @ SV57 @ SV47 )
| ( SV57 = SV47 )
| ( less @ SV57 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(247,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( leq @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(248,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( leq @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(249,plain,
! [SV58: $i,SV48: $i] :
( ( ( vplus @ SV48 @ ( vsucc @ SV58 ) )
= ( vsucc @ ( vplus @ SV48 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(250,plain,
! [SV50: $i,SV59: $i] :
( ( ~ ( geq @ SV59 @ SV50 )
| ( SV59 = SV50 )
| ( greater @ SV59 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(251,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( geq @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(252,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( geq @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(253,plain,
! [SV60: $i,SV51: $i] :
( ( ! [SY103: $i] :
( SV51
!= ( vplus @ SV60 @ SY103 ) )
| ( less @ SV60 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(254,plain,
! [SV52: $i,SV61: $i] :
( ( ~ ( less @ SV61 @ SV52 )
| ( SV52
= ( vplus @ SV61 @ ( sK4_Vd201 @ SV61 @ SV52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(255,plain,
! [SV53: $i,SV62: $i] :
( ( ! [SY104: $i] :
( SV62
!= ( vplus @ SV53 @ SY104 ) )
| ( greater @ SV62 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(256,plain,
! [SV54: $i,SV63: $i] :
( ( ~ ( greater @ SV63 @ SV54 )
| ( SV63
= ( vplus @ SV54 @ ( sK3_Vd196 @ SV63 @ SV54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(257,plain,
! [SV55: $i,SV10: $i,SV34: $i] :
( ( ( SV34
= ( vplus @ SV10 @ SV55 ) )
= $false )
| ( ( SV10 = SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(258,plain,
! [SV45: $i,SV64: $i,SV11: $i,SV35: $i] :
( ( ( ( SV35
!= ( vplus @ SV11 @ SV64 ) ) )
= $true )
| ( ( SV11
= ( vplus @ SV35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(259,plain,
! [SV56: $i,SV36: $i,SV12: $i] :
( ( ( SV12
= ( vplus @ SV36 @ SV56 ) )
= $false )
| ( ( SV12 = SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(260,plain,
! [SV47: $i,SV57: $i] :
( ( ( ~ ( leq @ SV57 @ SV47 ) )
= $true )
| ( ( ( SV57 = SV47 )
| ( less @ SV57 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(261,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( leq @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(262,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( leq @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(263,plain,
! [SV50: $i,SV59: $i] :
( ( ( ~ ( geq @ SV59 @ SV50 ) )
= $true )
| ( ( ( SV59 = SV50 )
| ( greater @ SV59 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(264,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( geq @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(265,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( geq @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(266,plain,
! [SV60: $i,SV51: $i] :
( ( ( ! [SY103: $i] :
( SV51
!= ( vplus @ SV60 @ SY103 ) ) )
= $true )
| ( ( less @ SV60 @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(267,plain,
! [SV52: $i,SV61: $i] :
( ( ( ~ ( less @ SV61 @ SV52 ) )
= $true )
| ( ( SV52
= ( vplus @ SV61 @ ( sK4_Vd201 @ SV61 @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(268,plain,
! [SV53: $i,SV62: $i] :
( ( ( ! [SY104: $i] :
( SV62
!= ( vplus @ SV53 @ SY104 ) ) )
= $true )
| ( ( greater @ SV62 @ SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(269,plain,
! [SV54: $i,SV63: $i] :
( ( ( ~ ( greater @ SV63 @ SV54 ) )
= $true )
| ( ( SV63
= ( vplus @ SV54 @ ( sK3_Vd196 @ SV63 @ SV54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(270,plain,
! [SV45: $i,SV64: $i,SV11: $i,SV35: $i] :
( ( ( SV35
= ( vplus @ SV11 @ SV64 ) )
= $false )
| ( ( SV11
= ( vplus @ SV35 @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(271,plain,
! [SV47: $i,SV57: $i] :
( ( ( leq @ SV57 @ SV47 )
= $false )
| ( ( ( SV57 = SV47 )
| ( less @ SV57 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(272,plain,
! [SV65: $i] :
( ( ! [SY105: $i] :
( ( SY105 != SV65 )
| ( leq @ SY105 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(273,plain,
! [SV66: $i] :
( ( ! [SY106: $i] :
( ~ ( less @ SY106 @ SV66 )
| ( leq @ SY106 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(274,plain,
! [SV50: $i,SV59: $i] :
( ( ( geq @ SV59 @ SV50 )
= $false )
| ( ( ( SV59 = SV50 )
| ( greater @ SV59 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(275,plain,
! [SV67: $i] :
( ( ! [SY107: $i] :
( ( SY107 != SV67 )
| ( geq @ SY107 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(276,plain,
! [SV68: $i] :
( ( ! [SY108: $i] :
( ~ ( greater @ SY108 @ SV68 )
| ( geq @ SY108 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(277,plain,
! [SV69: $i,SV60: $i,SV51: $i] :
( ( ( ( SV51
!= ( vplus @ SV60 @ SV69 ) ) )
= $true )
| ( ( less @ SV60 @ SV51 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(278,plain,
! [SV52: $i,SV61: $i] :
( ( ( less @ SV61 @ SV52 )
= $false )
| ( ( SV52
= ( vplus @ SV61 @ ( sK4_Vd201 @ SV61 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(279,plain,
! [SV70: $i,SV53: $i,SV62: $i] :
( ( ( ( SV62
!= ( vplus @ SV53 @ SV70 ) ) )
= $true )
| ( ( greater @ SV62 @ SV53 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(280,plain,
! [SV54: $i,SV63: $i] :
( ( ( greater @ SV63 @ SV54 )
= $false )
| ( ( SV63
= ( vplus @ SV54 @ ( sK3_Vd196 @ SV63 @ SV54 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(281,plain,
! [SV47: $i,SV57: $i] :
( ( ( SV57 = SV47 )
= $true )
| ( ( less @ SV57 @ SV47 )
= $true )
| ( ( leq @ SV57 @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(282,plain,
! [SV65: $i,SV71: $i] :
( ( ( SV71 != SV65 )
| ( leq @ SV71 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(283,plain,
! [SV66: $i,SV72: $i] :
( ( ~ ( less @ SV72 @ SV66 )
| ( leq @ SV72 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(284,plain,
! [SV50: $i,SV59: $i] :
( ( ( SV59 = SV50 )
= $true )
| ( ( greater @ SV59 @ SV50 )
= $true )
| ( ( geq @ SV59 @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(285,plain,
! [SV67: $i,SV73: $i] :
( ( ( SV73 != SV67 )
| ( geq @ SV73 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(286,plain,
! [SV68: $i,SV74: $i] :
( ( ~ ( greater @ SV74 @ SV68 )
| ( geq @ SV74 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(287,plain,
! [SV69: $i,SV60: $i,SV51: $i] :
( ( ( SV51
= ( vplus @ SV60 @ SV69 ) )
= $false )
| ( ( less @ SV60 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(288,plain,
! [SV70: $i,SV53: $i,SV62: $i] :
( ( ( SV62
= ( vplus @ SV53 @ SV70 ) )
= $false )
| ( ( greater @ SV62 @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(289,plain,
! [SV65: $i,SV71: $i] :
( ( ( ( SV71 != SV65 ) )
= $true )
| ( ( leq @ SV71 @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(290,plain,
! [SV66: $i,SV72: $i] :
( ( ( ~ ( less @ SV72 @ SV66 ) )
= $true )
| ( ( leq @ SV72 @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(291,plain,
! [SV67: $i,SV73: $i] :
( ( ( ( SV73 != SV67 ) )
= $true )
| ( ( geq @ SV73 @ SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(292,plain,
! [SV68: $i,SV74: $i] :
( ( ( ~ ( greater @ SV74 @ SV68 ) )
= $true )
| ( ( geq @ SV74 @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(293,plain,
! [SV65: $i,SV71: $i] :
( ( ( SV71 = SV65 )
= $false )
| ( ( leq @ SV71 @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(294,plain,
! [SV66: $i,SV72: $i] :
( ( ( less @ SV72 @ SV66 )
= $false )
| ( ( leq @ SV72 @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(295,plain,
! [SV67: $i,SV73: $i] :
( ( ( SV73 = SV67 )
= $false )
| ( ( geq @ SV73 @ SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(296,plain,
! [SV68: $i,SV74: $i] :
( ( ( greater @ SV74 @ SV68 )
= $false )
| ( ( geq @ SV74 @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(297,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[89,296,295,294,293,288,287,284,281,280,278,270,259,257,249,245,241,240,239,232,228,227,222,218,217,216,215,214,201,200,176,175,172,171,169,168,141,90]) ).
thf(298,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM837+1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n016.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 15:33:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 30
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.36 .
% 0.13/0.37 (rf:0,axioms:30,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:32,loop_count:0,foatp_calls:0,translation:fof_full)................
% 0.20/0.51
% 0.20/0.51 ********************************
% 0.20/0.51 * All subproblems solved! *
% 0.20/0.51 ********************************
% 0.20/0.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:30,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:297,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.38/0.54
% 0.38/0.54 %**** Beginning of derivation protocol ****
% 0.38/0.54 % SZS output start CNFRefutation
% See solution above
% 0.38/0.54
% 0.38/0.54 %**** End of derivation protocol ****
% 0.38/0.54 %**** no. of clauses in derivation: 298 ****
% 0.38/0.54 %**** clause counter: 297 ****
% 0.38/0.54
% 0.38/0.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:30,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:297,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------