TSTP Solution File: NUM837+2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM837+2 : 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 : n011.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 0.21s 0.49s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 36
% Syntax : Number of formulae : 257 ( 164 unt; 14 typ; 0 def)
% Number of atoms : 1129 ( 546 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1665 ( 298 ~; 282 |; 16 &;1051 @)
% ( 8 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 610 ( 0 ^ 590 !; 20 ?; 610 :)
% 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_vsucc,type,
vsucc: $i > $i ).
thf(1,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(2,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(3,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(4,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(5,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(6,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(7,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(8,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(9,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(10,axiom,
! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
thf(11,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(12,axiom,
! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
thf(13,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(14,axiom,
! [Vd208: $i,Vd209: $i] :
( ( greater @ Vd208 @ Vd209 )
=> ( less @ Vd209 @ Vd208 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
thf(15,axiom,
! [Vd226: $i,Vd227: $i] :
( ( less @ Vd226 @ Vd227 )
=> ( greater @ Vd227 @ Vd226 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
thf(16,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(17,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(18,axiom,
! [Vd254: $i,Vd255: $i] :
( ( geq @ Vd254 @ Vd255 )
=> ( leq @ Vd255 @ Vd254 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(158, 0), 0)') ).
thf(19,axiom,
! [Vd258: $i,Vd259: $i] :
( ( leq @ Vd258 @ Vd259 )
=> ( geq @ Vd259 @ Vd258 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(163, 0), 0)') ).
thf(20,axiom,
less @ vd268 @ vd269,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(170), 270, 0)') ).
thf(21,axiom,
less @ vd269 @ vd271,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','(conjunct2(170),272,0)') ).
thf(22,conjecture,
? [Vd273: $i] :
( vd269
= ( vplus @ vd268 @ Vd273 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qe(171)') ).
thf(23,negated_conjecture,
( ( ? [Vd273: $i] :
( vd269
= ( vplus @ vd268 @ Vd273 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[22]) ).
thf(24,plain,
( ( ? [Vd273: $i] :
( vd269
= ( vplus @ vd268 @ Vd273 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[23]) ).
thf(25,plain,
( ( ! [Vd42: $i,Vd43: $i] :
( ( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(26,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(27,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 != Vd105 )
=> ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(28,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(29,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(30,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(31,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)],[7]) ).
thf(32,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(33,plain,
( ( ! [Vd198: $i,Vd199: $i] :
( ( less @ Vd199 @ Vd198 )
<=> ? [Vd201: $i] :
( Vd198
= ( vplus @ Vd199 @ Vd201 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(34,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(35,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ~ ( greater @ Vd203 @ Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(36,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(37,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 )
| ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(38,plain,
( ( ! [Vd208: $i,Vd209: $i] :
( ( greater @ Vd208 @ Vd209 )
=> ( less @ Vd209 @ Vd208 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(39,plain,
( ( ! [Vd226: $i,Vd227: $i] :
( ( less @ Vd226 @ Vd227 )
=> ( greater @ Vd227 @ Vd226 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(40,plain,
( ( ! [Vd244: $i,Vd245: $i] :
( ( geq @ Vd245 @ Vd244 )
<=> ( ( greater @ Vd245 @ Vd244 )
| ( Vd245 = Vd244 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(41,plain,
( ( ! [Vd249: $i,Vd250: $i] :
( ( leq @ Vd250 @ Vd249 )
<=> ( ( less @ Vd250 @ Vd249 )
| ( Vd250 = Vd249 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(42,plain,
( ( ! [Vd254: $i,Vd255: $i] :
( ( geq @ Vd254 @ Vd255 )
=> ( leq @ Vd255 @ Vd254 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(43,plain,
( ( ! [Vd258: $i,Vd259: $i] :
( ( leq @ Vd258 @ Vd259 )
=> ( geq @ Vd259 @ Vd258 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(44,plain,
( ( less @ vd268 @ vd269 )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(45,plain,
( ( less @ vd269 @ vd271 )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(46,plain,
( ( ~ ? [Vd273: $i] :
( vd269
= ( vplus @ vd268 @ Vd273 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[24]) ).
thf(47,plain,
( ( ! [Vd273: $i] :
( vd269
!= ( vplus @ vd268 @ Vd273 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(48,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)],[25]) ).
thf(49,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 = Vd105 )
| ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(50,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ! [Vd123: $i] :
( Vd120
!= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(51,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ! [Vd123: $i] :
( Vd120
!= ( vplus @ Vd121 @ Vd123 ) )
| ! [Vd125: $i] :
( Vd121
!= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(52,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ! [Vd125: $i] :
( Vd121
!= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(53,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)],[31]) ).
thf(54,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)],[32]) ).
thf(55,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)],[33]) ).
thf(56,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(57,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(58,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( less @ Vd203 @ Vd204 )
| ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(59,plain,
( ( ! [Vd208: $i,Vd209: $i] :
( ~ ( greater @ Vd208 @ Vd209 )
| ( less @ Vd209 @ Vd208 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(60,plain,
( ( ! [Vd226: $i,Vd227: $i] :
( ~ ( less @ Vd226 @ Vd227 )
| ( greater @ Vd227 @ Vd226 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(61,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)],[40]) ).
thf(62,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)],[41]) ).
thf(63,plain,
( ( ! [Vd254: $i,Vd255: $i] :
( ~ ( geq @ Vd254 @ Vd255 )
| ( leq @ Vd255 @ Vd254 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(64,plain,
( ( ! [Vd258: $i,Vd259: $i] :
( ~ ( leq @ Vd258 @ Vd259 )
| ( geq @ Vd259 @ Vd258 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(65,plain,
( ( less @ vd269 @ vd271 )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(66,plain,
( ( less @ vd268 @ vd269 )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(67,plain,
( ( ! [Vd258: $i,Vd259: $i] :
( ~ ( leq @ Vd258 @ Vd259 )
| ( geq @ Vd259 @ Vd258 ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(68,plain,
( ( ! [Vd254: $i,Vd255: $i] :
( ~ ( geq @ Vd254 @ Vd255 )
| ( leq @ Vd255 @ Vd254 ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(69,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)],[62]) ).
thf(70,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)],[61]) ).
thf(71,plain,
( ( ! [Vd226: $i,Vd227: $i] :
( ~ ( less @ Vd226 @ Vd227 )
| ( greater @ Vd227 @ Vd226 ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(72,plain,
( ( ! [Vd208: $i,Vd209: $i] :
( ~ ( greater @ Vd208 @ Vd209 )
| ( less @ Vd209 @ Vd208 ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(73,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( less @ Vd203 @ Vd204 )
| ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(74,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(75,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ~ ( greater @ Vd203 @ Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(76,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(77,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)],[55]) ).
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(copy,[status(thm)],[54]) ).
thf(79,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)],[53]) ).
thf(80,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ! [Vd125: $i] :
( Vd121
!= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(81,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ! [Vd123: $i] :
( Vd120
!= ( vplus @ Vd121 @ Vd123 ) )
| ! [Vd125: $i] :
( Vd121
!= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(82,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ! [Vd123: $i] :
( Vd120
!= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(83,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 = Vd105 )
| ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(84,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(85,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)],[48]) ).
thf(86,plain,
( ( ! [Vd273: $i] :
( vd269
!= ( vplus @ vd268 @ Vd273 ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(87,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)],[85]) ).
thf(88,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)],[70]) ).
thf(89,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)],[77]) ).
thf(90,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)],[78]) ).
thf(91,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)],[69]) ).
thf(92,plain,
! [SV1: $i] :
( ( ! [SY49: $i] :
( ~ ( leq @ SV1 @ SY49 )
| ( geq @ SY49 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(93,plain,
! [SV2: $i] :
( ( ! [SY50: $i] :
( ~ ( geq @ SV2 @ SY50 )
| ( leq @ SY50 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(94,plain,
! [SV3: $i] :
( ( ! [SY51: $i] :
( ~ ( less @ SV3 @ SY51 )
| ( greater @ SY51 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(95,plain,
! [SV4: $i] :
( ( ! [SY52: $i] :
( ~ ( greater @ SV4 @ SY52 )
| ( less @ SY52 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(96,plain,
! [SV5: $i] :
( ( ! [SY53: $i] :
( ( less @ SV5 @ SY53 )
| ( SV5 = SY53 )
| ( greater @ SV5 @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(97,plain,
! [SV6: $i] :
( ( ! [SY54: $i] :
( ( SV6 != SY54 )
| ~ ( less @ SV6 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(98,plain,
! [SV7: $i] :
( ( ! [SY55: $i] :
( ~ ( greater @ SV7 @ SY55 )
| ~ ( less @ SV7 @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(99,plain,
! [SV8: $i] :
( ( ! [SY56: $i] :
( ( SV8 != SY56 )
| ~ ( greater @ SV8 @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(100,plain,
! [SV9: $i] :
( ( ! [SY57: $i] :
( ( SY57
= ( vplus @ SV9 @ ( sK2_Vd125 @ SY57 @ SV9 ) ) )
| ( SV9 = SY57 )
| ( SV9
= ( vplus @ SY57 @ ( sK1_Vd123 @ SY57 @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(101,plain,
! [SV10: $i] :
( ( ! [SY58: $i] :
( ( SV10 != SY58 )
| ! [SY59: $i] :
( SY58
!= ( vplus @ SV10 @ SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(102,plain,
! [SV11: $i] :
( ( ! [SY60: $i] :
( ! [SY61: $i] :
( SV11
!= ( vplus @ SY60 @ SY61 ) )
| ! [SY62: $i] :
( SY60
!= ( vplus @ SV11 @ SY62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(103,plain,
! [SV12: $i] :
( ( ! [SY63: $i] :
( ( SV12 != SY63 )
| ! [SY64: $i] :
( SV12
!= ( vplus @ SY63 @ SY64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(104,plain,
! [SV13: $i] :
( ( ! [SY65: $i] :
( ( SV13 = SY65 )
| ! [SY66: $i] :
( ( vplus @ SY66 @ SV13 )
!= ( vplus @ SY66 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(105,plain,
! [SV14: $i] :
( ( ! [SY67: $i,SY68: $i] :
( ( vplus @ ( vplus @ SV14 @ SY67 ) @ SY68 )
= ( vplus @ SV14 @ ( vplus @ SY67 @ SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(106,plain,
! [SV15: $i] :
( ( ( vd269
!= ( vplus @ vd268 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(107,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)],[87]) ).
thf(108,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)],[88]) ).
thf(109,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)],[89]) ).
thf(110,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)],[90]) ).
thf(111,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)],[91]) ).
thf(112,plain,
! [SV16: $i,SV1: $i] :
( ( ~ ( leq @ SV1 @ SV16 )
| ( geq @ SV16 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(113,plain,
! [SV17: $i,SV2: $i] :
( ( ~ ( geq @ SV2 @ SV17 )
| ( leq @ SV17 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(114,plain,
! [SV18: $i,SV3: $i] :
( ( ~ ( less @ SV3 @ SV18 )
| ( greater @ SV18 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(115,plain,
! [SV19: $i,SV4: $i] :
( ( ~ ( greater @ SV4 @ SV19 )
| ( less @ SV19 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(116,plain,
! [SV20: $i,SV5: $i] :
( ( ( less @ SV5 @ SV20 )
| ( SV5 = SV20 )
| ( greater @ SV5 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(117,plain,
! [SV21: $i,SV6: $i] :
( ( ( SV6 != SV21 )
| ~ ( less @ SV6 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(118,plain,
! [SV22: $i,SV7: $i] :
( ( ~ ( greater @ SV7 @ SV22 )
| ~ ( less @ SV7 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(119,plain,
! [SV23: $i,SV8: $i] :
( ( ( SV8 != SV23 )
| ~ ( greater @ SV8 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(120,plain,
! [SV9: $i,SV24: $i] :
( ( ( SV24
= ( vplus @ SV9 @ ( sK2_Vd125 @ SV24 @ SV9 ) ) )
| ( SV9 = SV24 )
| ( SV9
= ( vplus @ SV24 @ ( sK1_Vd123 @ SV24 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(121,plain,
! [SV25: $i,SV10: $i] :
( ( ( SV10 != SV25 )
| ! [SY69: $i] :
( SV25
!= ( vplus @ SV10 @ SY69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(122,plain,
! [SV26: $i,SV11: $i] :
( ( ! [SY70: $i] :
( SV11
!= ( vplus @ SV26 @ SY70 ) )
| ! [SY71: $i] :
( SV26
!= ( vplus @ SV11 @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(123,plain,
! [SV27: $i,SV12: $i] :
( ( ( SV12 != SV27 )
| ! [SY72: $i] :
( SV12
!= ( vplus @ SV27 @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(124,plain,
! [SV28: $i,SV13: $i] :
( ( ( SV13 = SV28 )
| ! [SY73: $i] :
( ( vplus @ SY73 @ SV13 )
!= ( vplus @ SY73 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(125,plain,
! [SV29: $i,SV14: $i] :
( ( ! [SY74: $i] :
( ( vplus @ ( vplus @ SV14 @ SV29 ) @ SY74 )
= ( vplus @ SV14 @ ( vplus @ SV29 @ SY74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(126,plain,
! [SV15: $i] :
( ( vd269
= ( vplus @ vd268 @ SV15 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(127,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(128,plain,
( ( ~ ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(129,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( geq @ SX1 @ SX0 )
| ( SX1 = SX0 )
| ( greater @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(130,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)],[108]) ).
thf(131,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( less @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(132,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( SX0
= ( vplus @ SX1 @ ( sK4_Vd201 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(133,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( greater @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(134,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( SX1
= ( vplus @ SX0 @ ( sK3_Vd196 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(135,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX1 @ SX0 )
| ( SX1 = SX0 )
| ( less @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(136,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)],[111]) ).
thf(137,plain,
! [SV16: $i,SV1: $i] :
( ( ( ~ ( leq @ SV1 @ SV16 ) )
= $true )
| ( ( geq @ SV16 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(138,plain,
! [SV17: $i,SV2: $i] :
( ( ( ~ ( geq @ SV2 @ SV17 ) )
= $true )
| ( ( leq @ SV17 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(139,plain,
! [SV18: $i,SV3: $i] :
( ( ( ~ ( less @ SV3 @ SV18 ) )
= $true )
| ( ( greater @ SV18 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(140,plain,
! [SV19: $i,SV4: $i] :
( ( ( ~ ( greater @ SV4 @ SV19 ) )
= $true )
| ( ( less @ SV19 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(141,plain,
! [SV20: $i,SV5: $i] :
( ( ( less @ SV5 @ SV20 )
= $true )
| ( ( ( SV5 = SV20 )
| ( greater @ SV5 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(142,plain,
! [SV21: $i,SV6: $i] :
( ( ( ( SV6 != SV21 ) )
= $true )
| ( ( ~ ( less @ SV6 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(143,plain,
! [SV22: $i,SV7: $i] :
( ( ( ~ ( greater @ SV7 @ SV22 ) )
= $true )
| ( ( ~ ( less @ SV7 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(144,plain,
! [SV23: $i,SV8: $i] :
( ( ( ( SV8 != SV23 ) )
= $true )
| ( ( ~ ( greater @ SV8 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(145,plain,
! [SV9: $i,SV24: $i] :
( ( ( SV24
= ( vplus @ SV9 @ ( sK2_Vd125 @ SV24 @ SV9 ) ) )
= $true )
| ( ( ( SV9 = SV24 )
| ( SV9
= ( vplus @ SV24 @ ( sK1_Vd123 @ SV24 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(146,plain,
! [SV25: $i,SV10: $i] :
( ( ( ( SV10 != SV25 ) )
= $true )
| ( ( ! [SY69: $i] :
( SV25
!= ( vplus @ SV10 @ SY69 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(147,plain,
! [SV26: $i,SV11: $i] :
( ( ( ! [SY70: $i] :
( SV11
!= ( vplus @ SV26 @ SY70 ) ) )
= $true )
| ( ( ! [SY71: $i] :
( SV26
!= ( vplus @ SV11 @ SY71 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(148,plain,
! [SV27: $i,SV12: $i] :
( ( ( ( SV12 != SV27 ) )
= $true )
| ( ( ! [SY72: $i] :
( SV12
!= ( vplus @ SV27 @ SY72 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(149,plain,
! [SV28: $i,SV13: $i] :
( ( ( SV13 = SV28 )
= $true )
| ( ( ! [SY73: $i] :
( ( vplus @ SY73 @ SV13 )
!= ( vplus @ SY73 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(150,plain,
! [SV30: $i,SV29: $i,SV14: $i] :
( ( ( vplus @ ( vplus @ SV14 @ SV29 ) @ SV30 )
= ( vplus @ SV14 @ ( vplus @ SV29 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(151,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(152,plain,
( ( ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(153,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( geq @ SX1 @ SX0 )
| ( SX1 = SX0 )
| ( greater @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(154,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)],[130]) ).
thf(155,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( less @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(156,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( SX0
= ( vplus @ SX1 @ ( sK4_Vd201 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(157,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( greater @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(158,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( SX1
= ( vplus @ SX0 @ ( sK3_Vd196 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(159,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX1 @ SX0 )
| ( SX1 = SX0 )
| ( less @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(160,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)],[136]) ).
thf(161,plain,
! [SV16: $i,SV1: $i] :
( ( ( leq @ SV1 @ SV16 )
= $false )
| ( ( geq @ SV16 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(162,plain,
! [SV17: $i,SV2: $i] :
( ( ( geq @ SV2 @ SV17 )
= $false )
| ( ( leq @ SV17 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(163,plain,
! [SV18: $i,SV3: $i] :
( ( ( less @ SV3 @ SV18 )
= $false )
| ( ( greater @ SV18 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(164,plain,
! [SV19: $i,SV4: $i] :
( ( ( greater @ SV4 @ SV19 )
= $false )
| ( ( less @ SV19 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(165,plain,
! [SV20: $i,SV5: $i] :
( ( ( SV5 = SV20 )
= $true )
| ( ( greater @ SV5 @ SV20 )
= $true )
| ( ( less @ SV5 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(166,plain,
! [SV21: $i,SV6: $i] :
( ( ( SV6 = SV21 )
= $false )
| ( ( ~ ( less @ SV6 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(167,plain,
! [SV22: $i,SV7: $i] :
( ( ( greater @ SV7 @ SV22 )
= $false )
| ( ( ~ ( less @ SV7 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(168,plain,
! [SV23: $i,SV8: $i] :
( ( ( SV8 = SV23 )
= $false )
| ( ( ~ ( greater @ SV8 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(169,plain,
! [SV24: $i,SV9: $i] :
( ( ( SV9 = SV24 )
= $true )
| ( ( SV9
= ( vplus @ SV24 @ ( sK1_Vd123 @ SV24 @ SV9 ) ) )
= $true )
| ( ( SV24
= ( vplus @ SV9 @ ( sK2_Vd125 @ SV24 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(170,plain,
! [SV25: $i,SV10: $i] :
( ( ( SV10 = SV25 )
= $false )
| ( ( ! [SY69: $i] :
( SV25
!= ( vplus @ SV10 @ SY69 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(171,plain,
! [SV31: $i,SV26: $i,SV11: $i] :
( ( ( ( SV11
!= ( vplus @ SV26 @ SV31 ) ) )
= $true )
| ( ( ! [SY71: $i] :
( SV26
!= ( vplus @ SV11 @ SY71 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(172,plain,
! [SV27: $i,SV12: $i] :
( ( ( SV12 = SV27 )
= $false )
| ( ( ! [SY72: $i] :
( SV12
!= ( vplus @ SV27 @ SY72 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(173,plain,
! [SV28: $i,SV13: $i,SV32: $i] :
( ( ( ( ( vplus @ SV32 @ SV13 )
!= ( vplus @ SV32 @ SV28 ) ) )
= $true )
| ( ( SV13 = SV28 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(174,plain,
! [SV33: $i] :
( ( ! [SY75: $i] :
( ( vplus @ SV33 @ ( vsucc @ SY75 ) )
= ( vsucc @ ( vplus @ SV33 @ SY75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(175,plain,
! [SV34: $i] :
( ( ( vplus @ SV34 @ v1 )
= ( vsucc @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(176,plain,
! [SV35: $i] :
( ( ! [SY76: $i] :
( ~ ( geq @ SY76 @ SV35 )
| ( SY76 = SV35 )
| ( greater @ SY76 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(177,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)],[154]) ).
thf(178,plain,
! [SV36: $i] :
( ( ! [SY77: $i] :
( ! [SY78: $i] :
( SV36
!= ( vplus @ SY77 @ SY78 ) )
| ( less @ SY77 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(179,plain,
! [SV37: $i] :
( ( ! [SY79: $i] :
( ~ ( less @ SY79 @ SV37 )
| ( SV37
= ( vplus @ SY79 @ ( sK4_Vd201 @ SY79 @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(180,plain,
! [SV38: $i] :
( ( ! [SY80: $i] :
( ! [SY81: $i] :
( SY80
!= ( vplus @ SV38 @ SY81 ) )
| ( greater @ SY80 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(181,plain,
! [SV39: $i] :
( ( ! [SY82: $i] :
( ~ ( greater @ SY82 @ SV39 )
| ( SY82
= ( vplus @ SV39 @ ( sK3_Vd196 @ SY82 @ SV39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(182,plain,
! [SV40: $i] :
( ( ! [SY83: $i] :
( ~ ( leq @ SY83 @ SV40 )
| ( SY83 = SV40 )
| ( less @ SY83 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(183,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)],[160]) ).
thf(184,plain,
! [SV21: $i,SV6: $i] :
( ( ( less @ SV6 @ SV21 )
= $false )
| ( ( SV6 = SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(185,plain,
! [SV22: $i,SV7: $i] :
( ( ( less @ SV7 @ SV22 )
= $false )
| ( ( greater @ SV7 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(186,plain,
! [SV23: $i,SV8: $i] :
( ( ( greater @ SV8 @ SV23 )
= $false )
| ( ( SV8 = SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(187,plain,
! [SV41: $i,SV10: $i,SV25: $i] :
( ( ( ( SV25
!= ( vplus @ SV10 @ SV41 ) ) )
= $true )
| ( ( SV10 = SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(188,plain,
! [SV31: $i,SV26: $i,SV11: $i] :
( ( ( SV11
= ( vplus @ SV26 @ SV31 ) )
= $false )
| ( ( ! [SY71: $i] :
( SV26
!= ( vplus @ SV11 @ SY71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(189,plain,
! [SV42: $i,SV27: $i,SV12: $i] :
( ( ( ( SV12
!= ( vplus @ SV27 @ SV42 ) ) )
= $true )
| ( ( SV12 = SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(190,plain,
! [SV28: $i,SV13: $i,SV32: $i] :
( ( ( ( vplus @ SV32 @ SV13 )
= ( vplus @ SV32 @ SV28 ) )
= $false )
| ( ( SV13 = SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(191,plain,
! [SV43: $i,SV33: $i] :
( ( ( vplus @ SV33 @ ( vsucc @ SV43 ) )
= ( vsucc @ ( vplus @ SV33 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(192,plain,
! [SV35: $i,SV44: $i] :
( ( ~ ( geq @ SV44 @ SV35 )
| ( SV44 = SV35 )
| ( greater @ SV44 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(193,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( geq @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(194,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( geq @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(195,plain,
! [SV45: $i,SV36: $i] :
( ( ! [SY84: $i] :
( SV36
!= ( vplus @ SV45 @ SY84 ) )
| ( less @ SV45 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(196,plain,
! [SV37: $i,SV46: $i] :
( ( ~ ( less @ SV46 @ SV37 )
| ( SV37
= ( vplus @ SV46 @ ( sK4_Vd201 @ SV46 @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(197,plain,
! [SV38: $i,SV47: $i] :
( ( ! [SY85: $i] :
( SV47
!= ( vplus @ SV38 @ SY85 ) )
| ( greater @ SV47 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(198,plain,
! [SV39: $i,SV48: $i] :
( ( ~ ( greater @ SV48 @ SV39 )
| ( SV48
= ( vplus @ SV39 @ ( sK3_Vd196 @ SV48 @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(199,plain,
! [SV40: $i,SV49: $i] :
( ( ~ ( leq @ SV49 @ SV40 )
| ( SV49 = SV40 )
| ( less @ SV49 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(200,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( leq @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(201,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( leq @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(202,plain,
! [SV41: $i,SV10: $i,SV25: $i] :
( ( ( SV25
= ( vplus @ SV10 @ SV41 ) )
= $false )
| ( ( SV10 = SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(203,plain,
! [SV31: $i,SV50: $i,SV11: $i,SV26: $i] :
( ( ( ( SV26
!= ( vplus @ SV11 @ SV50 ) ) )
= $true )
| ( ( SV11
= ( vplus @ SV26 @ SV31 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(204,plain,
! [SV42: $i,SV27: $i,SV12: $i] :
( ( ( SV12
= ( vplus @ SV27 @ SV42 ) )
= $false )
| ( ( SV12 = SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(205,plain,
! [SV35: $i,SV44: $i] :
( ( ( ~ ( geq @ SV44 @ SV35 ) )
= $true )
| ( ( ( SV44 = SV35 )
| ( greater @ SV44 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(206,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( geq @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(207,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( geq @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(208,plain,
! [SV45: $i,SV36: $i] :
( ( ( ! [SY84: $i] :
( SV36
!= ( vplus @ SV45 @ SY84 ) ) )
= $true )
| ( ( less @ SV45 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(209,plain,
! [SV37: $i,SV46: $i] :
( ( ( ~ ( less @ SV46 @ SV37 ) )
= $true )
| ( ( SV37
= ( vplus @ SV46 @ ( sK4_Vd201 @ SV46 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(210,plain,
! [SV38: $i,SV47: $i] :
( ( ( ! [SY85: $i] :
( SV47
!= ( vplus @ SV38 @ SY85 ) ) )
= $true )
| ( ( greater @ SV47 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(211,plain,
! [SV39: $i,SV48: $i] :
( ( ( ~ ( greater @ SV48 @ SV39 ) )
= $true )
| ( ( SV48
= ( vplus @ SV39 @ ( sK3_Vd196 @ SV48 @ SV39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(212,plain,
! [SV40: $i,SV49: $i] :
( ( ( ~ ( leq @ SV49 @ SV40 ) )
= $true )
| ( ( ( SV49 = SV40 )
| ( less @ SV49 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(213,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( leq @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(214,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( leq @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(215,plain,
! [SV31: $i,SV50: $i,SV11: $i,SV26: $i] :
( ( ( SV26
= ( vplus @ SV11 @ SV50 ) )
= $false )
| ( ( SV11
= ( vplus @ SV26 @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(216,plain,
! [SV35: $i,SV44: $i] :
( ( ( geq @ SV44 @ SV35 )
= $false )
| ( ( ( SV44 = SV35 )
| ( greater @ SV44 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(217,plain,
! [SV51: $i] :
( ( ! [SY86: $i] :
( ( SY86 != SV51 )
| ( geq @ SY86 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(218,plain,
! [SV52: $i] :
( ( ! [SY87: $i] :
( ~ ( greater @ SY87 @ SV52 )
| ( geq @ SY87 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(219,plain,
! [SV53: $i,SV45: $i,SV36: $i] :
( ( ( ( SV36
!= ( vplus @ SV45 @ SV53 ) ) )
= $true )
| ( ( less @ SV45 @ SV36 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(220,plain,
! [SV37: $i,SV46: $i] :
( ( ( less @ SV46 @ SV37 )
= $false )
| ( ( SV37
= ( vplus @ SV46 @ ( sK4_Vd201 @ SV46 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(221,plain,
! [SV54: $i,SV38: $i,SV47: $i] :
( ( ( ( SV47
!= ( vplus @ SV38 @ SV54 ) ) )
= $true )
| ( ( greater @ SV47 @ SV38 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(222,plain,
! [SV39: $i,SV48: $i] :
( ( ( greater @ SV48 @ SV39 )
= $false )
| ( ( SV48
= ( vplus @ SV39 @ ( sK3_Vd196 @ SV48 @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(223,plain,
! [SV40: $i,SV49: $i] :
( ( ( leq @ SV49 @ SV40 )
= $false )
| ( ( ( SV49 = SV40 )
| ( less @ SV49 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(224,plain,
! [SV55: $i] :
( ( ! [SY88: $i] :
( ( SY88 != SV55 )
| ( leq @ SY88 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(225,plain,
! [SV56: $i] :
( ( ! [SY89: $i] :
( ~ ( less @ SY89 @ SV56 )
| ( leq @ SY89 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(226,plain,
! [SV35: $i,SV44: $i] :
( ( ( SV44 = SV35 )
= $true )
| ( ( greater @ SV44 @ SV35 )
= $true )
| ( ( geq @ SV44 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(227,plain,
! [SV51: $i,SV57: $i] :
( ( ( SV57 != SV51 )
| ( geq @ SV57 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(228,plain,
! [SV52: $i,SV58: $i] :
( ( ~ ( greater @ SV58 @ SV52 )
| ( geq @ SV58 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(229,plain,
! [SV53: $i,SV45: $i,SV36: $i] :
( ( ( SV36
= ( vplus @ SV45 @ SV53 ) )
= $false )
| ( ( less @ SV45 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(230,plain,
! [SV54: $i,SV38: $i,SV47: $i] :
( ( ( SV47
= ( vplus @ SV38 @ SV54 ) )
= $false )
| ( ( greater @ SV47 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(231,plain,
! [SV40: $i,SV49: $i] :
( ( ( SV49 = SV40 )
= $true )
| ( ( less @ SV49 @ SV40 )
= $true )
| ( ( leq @ SV49 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(232,plain,
! [SV55: $i,SV59: $i] :
( ( ( SV59 != SV55 )
| ( leq @ SV59 @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(233,plain,
! [SV56: $i,SV60: $i] :
( ( ~ ( less @ SV60 @ SV56 )
| ( leq @ SV60 @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(234,plain,
! [SV51: $i,SV57: $i] :
( ( ( ( SV57 != SV51 ) )
= $true )
| ( ( geq @ SV57 @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(235,plain,
! [SV52: $i,SV58: $i] :
( ( ( ~ ( greater @ SV58 @ SV52 ) )
= $true )
| ( ( geq @ SV58 @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(236,plain,
! [SV55: $i,SV59: $i] :
( ( ( ( SV59 != SV55 ) )
= $true )
| ( ( leq @ SV59 @ SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(237,plain,
! [SV56: $i,SV60: $i] :
( ( ( ~ ( less @ SV60 @ SV56 ) )
= $true )
| ( ( leq @ SV60 @ SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(238,plain,
! [SV51: $i,SV57: $i] :
( ( ( SV57 = SV51 )
= $false )
| ( ( geq @ SV57 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(239,plain,
! [SV52: $i,SV58: $i] :
( ( ( greater @ SV58 @ SV52 )
= $false )
| ( ( geq @ SV58 @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(240,plain,
! [SV55: $i,SV59: $i] :
( ( ( SV59 = SV55 )
= $false )
| ( ( leq @ SV59 @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(241,plain,
! [SV56: $i,SV60: $i] :
( ( ( less @ SV60 @ SV56 )
= $false )
| ( ( leq @ SV60 @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(242,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[65,241,240,239,238,231,230,229,226,222,220,215,204,202,191,190,186,185,184,175,169,165,164,163,162,161,150,126,66]) ).
thf(243,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[242]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM837+2 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Wed Jul 6 13:15:08 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36
% 0.14/0.36 No.of.Axioms: 21
% 0.14/0.36
% 0.14/0.36 Length.of.Defs: 0
% 0.14/0.36
% 0.14/0.36 Contains.Choice.Funs: false
% 0.14/0.37 .
% 0.14/0.37 (rf:0,axioms:21,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:23,loop_count:0,foatp_calls:0,translation:fof_full).............
% 0.21/0.49
% 0.21/0.49 ********************************
% 0.21/0.49 * All subproblems solved! *
% 0.21/0.49 ********************************
% 0.21/0.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:21,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:242,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.50
% 0.21/0.50 %**** Beginning of derivation protocol ****
% 0.21/0.50 % SZS output start CNFRefutation
% See solution above
% 0.21/0.50
% 0.21/0.50 %**** End of derivation protocol ****
% 0.21/0.50 %**** no. of clauses in derivation: 243 ****
% 0.21/0.50 %**** clause counter: 242 ****
% 0.21/0.50
% 0.21/0.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:21,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:242,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------