%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM838+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:35:20 AM UTC 2026
% Result : Theorem 0.46s 0.31s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 27
% Syntax : Number of formulae : 257 ( 155 unt; 0 typ; 0 def)
% Number of atoms : 1155 ( 583 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 2112 ( 352 ~; 220 |; 0 &;1498 @)
% ( 6 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 699 ( 0 ^; 675 !; 24 ?; 699 :)
% Comments :
%------------------------------------------------------------------------------
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_SY131,type,
sK1_SY131: $i > $i > $i ).
thf(tp_sK2_SY124,type,
sK2_SY124: $i > $i > $i ).
thf(tp_sK3_SY128,type,
sK3_SY128: $i > $i > $i ).
thf(tp_sK4_SY132,type,
sK4_SY132: $i > $i > $i ).
thf(tp_v1,type,
v1: $i ).
thf(tp_vd301,type,
vd301: $i ).
thf(tp_vd302,type,
vd302: $i ).
thf(tp_vd303,type,
vd303: $i ).
thf(tp_vplus,type,
vplus: $i > $i > $i ).
thf(tp_vskolem7,type,
vskolem7: $i > $i > $i ).
thf(tp_vsucc,type,
vsucc: $i > $i ).
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,
! [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(4,axiom,
! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(5,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(6,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(7,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(8,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(9,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(10,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(11,axiom,
! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
thf(12,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(14,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(15,axiom,
! [Vd208: $i,Vd209: $i] :
( ( greater @ Vd208 @ Vd209 )
=> ( less @ Vd209 @ Vd208 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
thf(16,axiom,
! [Vd226: $i,Vd227: $i] :
( ( less @ Vd226 @ Vd227 )
=> ( greater @ Vd227 @ Vd226 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
thf(18,axiom,
! [Vd295: $i,Vd296: $i] : ( greater @ ( vplus @ Vd295 @ Vd296 ) @ Vd295 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
thf(19,axiom,
! [Vd310: $i,Vd311: $i,Vd312: $i] :
( ( greater @ Vd311 @ Vd312 )
=> ( Vd311
= ( vplus @ Vd312 @ ( vskolem7 @ Vd311 @ Vd312 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 9)') ).
thf(20,axiom,
! [Vd310: $i,Vd311: $i,Vd312: $i] :
( ( greater @ Vd311 @ Vd312 )
=> ( ( vplus @ Vd311 @ Vd310 )
= ( vplus @ ( vplus @ Vd312 @ ( vskolem7 @ Vd311 @ Vd312 ) ) @ Vd310 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 8)') ).
thf(21,axiom,
! [Vd310: $i,Vd311: $i,Vd312: $i] :
( ( greater @ Vd311 @ Vd312 )
=> ( ( vplus @ ( vplus @ Vd312 @ ( vskolem7 @ Vd311 @ Vd312 ) ) @ Vd310 )
= ( vplus @ ( vplus @ ( vskolem7 @ Vd311 @ Vd312 ) @ Vd312 ) @ Vd310 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 7)') ).
thf(22,axiom,
! [Vd310: $i,Vd311: $i,Vd312: $i] :
( ( greater @ Vd311 @ Vd312 )
=> ( ( vplus @ ( vplus @ ( vskolem7 @ Vd311 @ Vd312 ) @ Vd312 ) @ Vd310 )
= ( vplus @ ( vskolem7 @ Vd311 @ Vd312 ) @ ( vplus @ Vd312 @ Vd310 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 6)') ).
thf(23,axiom,
! [Vd310: $i,Vd311: $i,Vd312: $i] :
( ( greater @ Vd311 @ Vd312 )
=> ( ( vplus @ ( vskolem7 @ Vd311 @ Vd312 ) @ ( vplus @ Vd312 @ Vd310 ) )
= ( vplus @ ( vplus @ Vd312 @ Vd310 ) @ ( vskolem7 @ Vd311 @ Vd312 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 5)') ).
thf(24,axiom,
! [Vd310: $i,Vd311: $i,Vd312: $i] :
( ( greater @ Vd311 @ Vd312 )
=> ( greater @ ( vplus @ Vd311 @ Vd310 ) @ ( vplus @ Vd312 @ Vd310 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 4)') ).
thf(25,axiom,
! [Vd310: $i,Vd318: $i,Vd319: $i] :
( ( Vd318 = Vd319 )
=> ( ( vplus @ Vd318 @ Vd310 )
= ( vplus @ Vd319 @ Vd310 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 3)') ).
thf(26,axiom,
! [Vd310: $i,Vd322: $i,Vd323: $i] :
( ( less @ Vd322 @ Vd323 )
=> ( greater @ Vd323 @ Vd322 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 2)') ).
thf(27,axiom,
! [Vd310: $i,Vd322: $i,Vd323: $i] :
( ( less @ Vd322 @ Vd323 )
=> ( greater @ ( vplus @ Vd323 @ Vd310 ) @ ( vplus @ Vd322 @ Vd310 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 1)') ).
thf(28,axiom,
! [Vd310: $i,Vd322: $i,Vd323: $i] :
( ( less @ Vd322 @ Vd323 )
=> ( less @ ( vplus @ Vd322 @ Vd310 ) @ ( vplus @ Vd323 @ Vd310 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 0)') ).
thf(29,axiom,
greater @ vd301 @ vd302,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(antec(195), 304, 0)') ).
thf(30,conjecture,
greater @ ( vplus @ vd301 @ vd303 ) @ ( vplus @ vd302 @ vd303 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq(195), 305, 0)') ).
thf(31,negated_conjecture,
( ( greater @ ( vplus @ vd301 @ vd303 ) @ ( vplus @ vd302 @ vd303 ) )
= $false ),
inference(negate_conjecture,[status(cth)],[30]) ).
thf(32,plain,
( ( greater @ ( vplus @ vd301 @ vd303 ) @ ( vplus @ vd302 @ vd303 ) )
= $false ),
inference(unfold_def,[status(thm)],[31]) ).
thf(33,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(34,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(35,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(36,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(37,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(38,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(39,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)],[8]) ).
thf(40,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(41,plain,
( ( ! [Vd198: $i,Vd199: $i] :
( ( less @ Vd199 @ Vd198 )
<=> ? [Vd201: $i] :
( Vd198
= ( vplus @ Vd199 @ Vd201 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(42,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(43,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ~ ( greater @ Vd203 @ Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(44,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 )
| ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(45,plain,
( ( ! [Vd208: $i,Vd209: $i] :
( ( greater @ Vd208 @ Vd209 )
=> ( less @ Vd209 @ Vd208 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(46,plain,
( ( ! [Vd226: $i,Vd227: $i] :
( ( less @ Vd226 @ Vd227 )
=> ( greater @ Vd227 @ Vd226 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(47,plain,
( ( ! [Vd295: $i,Vd296: $i] : ( greater @ ( vplus @ Vd295 @ Vd296 ) @ Vd295 ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(48,plain,
( ( ! [Vd310: $i,Vd311: $i,Vd312: $i] :
( ( greater @ Vd311 @ Vd312 )
=> ( Vd311
= ( vplus @ Vd312 @ ( vskolem7 @ Vd311 @ Vd312 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(49,plain,
( ( ! [Vd310: $i,Vd311: $i,Vd312: $i] :
( ( greater @ Vd311 @ Vd312 )
=> ( ( vplus @ Vd311 @ Vd310 )
= ( vplus @ ( vplus @ Vd312 @ ( vskolem7 @ Vd311 @ Vd312 ) ) @ Vd310 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(50,plain,
( ( ! [Vd310: $i,Vd311: $i,Vd312: $i] :
( ( greater @ Vd311 @ Vd312 )
=> ( ( vplus @ ( vplus @ Vd312 @ ( vskolem7 @ Vd311 @ Vd312 ) ) @ Vd310 )
= ( vplus @ ( vplus @ ( vskolem7 @ Vd311 @ Vd312 ) @ Vd312 ) @ Vd310 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(51,plain,
( ( ! [Vd310: $i,Vd311: $i,Vd312: $i] :
( ( greater @ Vd311 @ Vd312 )
=> ( ( vplus @ ( vplus @ ( vskolem7 @ Vd311 @ Vd312 ) @ Vd312 ) @ Vd310 )
= ( vplus @ ( vskolem7 @ Vd311 @ Vd312 ) @ ( vplus @ Vd312 @ Vd310 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(52,plain,
( ( ! [Vd310: $i,Vd311: $i,Vd312: $i] :
( ( greater @ Vd311 @ Vd312 )
=> ( ( vplus @ ( vskolem7 @ Vd311 @ Vd312 ) @ ( vplus @ Vd312 @ Vd310 ) )
= ( vplus @ ( vplus @ Vd312 @ Vd310 ) @ ( vskolem7 @ Vd311 @ Vd312 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(53,plain,
( ( ! [Vd310: $i,Vd311: $i,Vd312: $i] :
( ( greater @ Vd311 @ Vd312 )
=> ( greater @ ( vplus @ Vd311 @ Vd310 ) @ ( vplus @ Vd312 @ Vd310 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(54,plain,
( ( ! [Vd310: $i,Vd318: $i,Vd319: $i] :
( ( Vd318 = Vd319 )
=> ( ( vplus @ Vd318 @ Vd310 )
= ( vplus @ Vd319 @ Vd310 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(55,plain,
( ( ! [Vd310: $i,Vd322: $i,Vd323: $i] :
( ( less @ Vd322 @ Vd323 )
=> ( greater @ Vd323 @ Vd322 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(56,plain,
( ( ! [Vd310: $i,Vd322: $i,Vd323: $i] :
( ( less @ Vd322 @ Vd323 )
=> ( greater @ ( vplus @ Vd323 @ Vd310 ) @ ( vplus @ Vd322 @ Vd310 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(57,plain,
( ( ! [Vd310: $i,Vd322: $i,Vd323: $i] :
( ( less @ Vd322 @ Vd323 )
=> ( less @ ( vplus @ Vd322 @ Vd310 ) @ ( vplus @ Vd323 @ Vd310 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(58,plain,
( ( greater @ vd301 @ vd302 )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(59,plain,
( ( ~ ( greater @ ( vplus @ vd301 @ vd303 ) @ ( vplus @ vd302 @ vd303 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[32]) ).
thf(60,plain,
( ( greater @ vd301 @ vd302 )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(61,plain,
( ( ! [Vd310: $i,Vd322: $i,Vd323: $i] :
( ( less @ Vd322 @ Vd323 )
=> ( less @ ( vplus @ Vd322 @ Vd310 ) @ ( vplus @ Vd323 @ Vd310 ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(62,plain,
( ( ! [Vd310: $i,Vd322: $i,Vd323: $i] :
( ( less @ Vd322 @ Vd323 )
=> ( greater @ ( vplus @ Vd323 @ Vd310 ) @ ( vplus @ Vd322 @ Vd310 ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(63,plain,
( ( ! [Vd310: $i,Vd322: $i,Vd323: $i] :
( ( less @ Vd322 @ Vd323 )
=> ( greater @ Vd323 @ Vd322 ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(64,plain,
( ( ! [Vd310: $i,Vd318: $i,Vd319: $i] :
( ( Vd318 = Vd319 )
=> ( ( vplus @ Vd318 @ Vd310 )
= ( vplus @ Vd319 @ Vd310 ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(65,plain,
( ( ! [Vd310: $i,Vd311: $i,Vd312: $i] :
( ( greater @ Vd311 @ Vd312 )
=> ( greater @ ( vplus @ Vd311 @ Vd310 ) @ ( vplus @ Vd312 @ Vd310 ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(66,plain,
( ( ! [Vd310: $i,Vd311: $i,Vd312: $i] :
( ( greater @ Vd311 @ Vd312 )
=> ( ( vplus @ ( vskolem7 @ Vd311 @ Vd312 ) @ ( vplus @ Vd312 @ Vd310 ) )
= ( vplus @ ( vplus @ Vd312 @ Vd310 ) @ ( vskolem7 @ Vd311 @ Vd312 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(67,plain,
( ( ! [Vd310: $i,Vd311: $i,Vd312: $i] :
( ( greater @ Vd311 @ Vd312 )
=> ( ( vplus @ ( vplus @ ( vskolem7 @ Vd311 @ Vd312 ) @ Vd312 ) @ Vd310 )
= ( vplus @ ( vskolem7 @ Vd311 @ Vd312 ) @ ( vplus @ Vd312 @ Vd310 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(68,plain,
( ( ! [Vd310: $i,Vd311: $i,Vd312: $i] :
( ( greater @ Vd311 @ Vd312 )
=> ( ( vplus @ ( vplus @ Vd312 @ ( vskolem7 @ Vd311 @ Vd312 ) ) @ Vd310 )
= ( vplus @ ( vplus @ ( vskolem7 @ Vd311 @ Vd312 ) @ Vd312 ) @ Vd310 ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(69,plain,
( ( ! [Vd310: $i,Vd311: $i,Vd312: $i] :
( ( greater @ Vd311 @ Vd312 )
=> ( ( vplus @ Vd311 @ Vd310 )
= ( vplus @ ( vplus @ Vd312 @ ( vskolem7 @ Vd311 @ Vd312 ) ) @ Vd310 ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(70,plain,
( ( ! [Vd310: $i,Vd311: $i,Vd312: $i] :
( ( greater @ Vd311 @ Vd312 )
=> ( Vd311
= ( vplus @ Vd312 @ ( vskolem7 @ Vd311 @ Vd312 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(71,plain,
( ( ! [Vd295: $i,Vd296: $i] : ( greater @ ( vplus @ Vd295 @ Vd296 ) @ Vd295 ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(72,plain,
( ( ! [Vd226: $i,Vd227: $i] :
( ( less @ Vd226 @ Vd227 )
=> ( greater @ Vd227 @ Vd226 ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(73,plain,
( ( ! [Vd208: $i,Vd209: $i] :
( ( greater @ Vd208 @ Vd209 )
=> ( less @ Vd209 @ Vd208 ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(74,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 )
| ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(75,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ~ ( greater @ Vd203 @ Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(76,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(77,plain,
( ( ! [Vd198: $i,Vd199: $i] :
( ( less @ Vd199 @ Vd198 )
<=> ? [Vd201: $i] :
( Vd198
= ( vplus @ Vd199 @ Vd201 ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(78,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(79,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 = Vd121 )
| ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(80,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(81,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(82,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(83,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(84,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(85,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(86,plain,
( ( ~ ( greater @ ( vplus @ vd301 @ vd303 ) @ ( vplus @ vd302 @ vd303 ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(87,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( greater @ SX1 @ SX2 )
| ( ( vplus @ ( vskolem7 @ SX1 @ SX2 ) @ ( vplus @ SX2 @ SX0 ) )
= ( vplus @ ( vplus @ SX2 @ SX0 ) @ ( vskolem7 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(88,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX1 != SX2 )
| ( ( vplus @ SX1 @ SX0 )
= ( vplus @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(89,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX0 @ SX1 )
| ( greater @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(90,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX0 @ SX1 )
| ( less @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(91,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( greater @ SX1 @ SX2 )
| ( greater @ ( vplus @ SX1 @ SX0 ) @ ( vplus @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(92,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( less @ SX1 @ SX2 )
| ( less @ ( vplus @ SX1 @ SX0 ) @ ( vplus @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(93,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( greater @ SX1 @ SX2 )
| ( ( vplus @ ( vplus @ ( vskolem7 @ SX1 @ SX2 ) @ SX2 ) @ SX0 )
= ( vplus @ ( vskolem7 @ SX1 @ SX2 ) @ ( vplus @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(94,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( less @ SX1 @ SX2 )
| ( greater @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(95,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( greater @ SX1 @ SX2 )
| ( ( vplus @ ( vplus @ SX2 @ ( vskolem7 @ SX1 @ SX2 ) ) @ SX0 )
= ( vplus @ ( vplus @ ( vskolem7 @ SX1 @ SX2 ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(96,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( greater @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(97,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( greater @ SX1 @ SX2 )
| ( SX1
= ( vplus @ SX2 @ ( vskolem7 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(98,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( less @ SX1 @ SX0 )
| ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( less @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(99,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ~ ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(100,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( greater @ SX1 @ SX0 )
| ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( greater @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(101,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( greater @ SX1 @ SX2 )
| ( ( vplus @ SX1 @ SX0 )
= ( vplus @ ( vplus @ SX2 @ ( vskolem7 @ SX1 @ SX2 ) ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(102,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(103,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(104,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( less @ SX1 @ SX2 )
| ( greater @ ( vplus @ SX2 @ SX0 ) @ ( vplus @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(105,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(106,plain,
! [SV1: $i] :
( ( ! [SY69: $i] : ( greater @ ( vplus @ SV1 @ SY69 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(107,plain,
! [SV2: $i] :
( ( ! [SY70: $i] :
( ( SV2 = SY70 )
| ( greater @ SV2 @ SY70 )
| ( less @ SV2 @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(108,plain,
! [SV3: $i] :
( ( ! [SY71: $i] :
( ~ ( greater @ SV3 @ SY71 )
| ~ ( less @ SV3 @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(109,plain,
! [SV4: $i] :
( ( ! [SY72: $i] :
( ( vplus @ SY72 @ SV4 )
= ( vplus @ SV4 @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(110,plain,
! [SV5: $i] :
( ( ! [SY73: $i] :
( ( vplus @ ( vsucc @ SV5 ) @ SY73 )
= ( vsucc @ ( vplus @ SV5 @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(111,plain,
! [SV6: $i] :
( ( ! [SY74: $i,SY75: $i] :
( ( vplus @ ( vplus @ SV6 @ SY74 ) @ SY75 )
= ( vplus @ SV6 @ ( vplus @ SY74 @ SY75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(112,plain,
( ( greater @ ( vplus @ vd301 @ vd303 ) @ ( vplus @ vd302 @ vd303 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(113,plain,
! [SV7: $i] :
( ( ! [SY76: $i,SY77: $i] :
( ~ ( greater @ SY76 @ SY77 )
| ( ( vplus @ ( vskolem7 @ SY76 @ SY77 ) @ ( vplus @ SY77 @ SV7 ) )
= ( vplus @ ( vplus @ SY77 @ SV7 ) @ ( vskolem7 @ SY76 @ SY77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(114,plain,
! [SV8: $i] :
( ( ! [SY78: $i,SY79: $i] :
( ( SY78 != SY79 )
| ( ( vplus @ SY78 @ SV8 )
= ( vplus @ SY79 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(115,plain,
! [SV9: $i] :
( ( ! [SY80: $i] :
( ~ ( less @ SV9 @ SY80 )
| ( greater @ SY80 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(116,plain,
! [SV10: $i] :
( ( ! [SY81: $i] :
( ~ ( greater @ SV10 @ SY81 )
| ( less @ SY81 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(117,plain,
! [SV11: $i] :
( ( ! [SY82: $i,SY83: $i] :
( ~ ( greater @ SY82 @ SY83 )
| ( greater @ ( vplus @ SY82 @ SV11 ) @ ( vplus @ SY83 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(118,plain,
! [SV12: $i] :
( ( ! [SY84: $i,SY85: $i] :
( ~ ( less @ SY84 @ SY85 )
| ( less @ ( vplus @ SY84 @ SV12 ) @ ( vplus @ SY85 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(119,plain,
! [SV13: $i] :
( ( ! [SY86: $i,SY87: $i] :
( ~ ( greater @ SY86 @ SY87 )
| ( ( vplus @ ( vplus @ ( vskolem7 @ SY86 @ SY87 ) @ SY87 ) @ SV13 )
= ( vplus @ ( vskolem7 @ SY86 @ SY87 ) @ ( vplus @ SY87 @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(120,plain,
( ( ! [SX1: $i,SX2: $i] :
( ~ ( less @ SX1 @ SX2 )
| ( greater @ SX2 @ SX1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(121,plain,
! [SV15: $i] :
( ( ! [SY90: $i,SY91: $i] :
( ~ ( greater @ SY90 @ SY91 )
| ( ( vplus @ ( vplus @ SY91 @ ( vskolem7 @ SY90 @ SY91 ) ) @ SV15 )
= ( vplus @ ( vplus @ ( vskolem7 @ SY90 @ SY91 ) @ SY91 ) @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(122,plain,
! [SV16: $i] :
( ( ! [SY92: $i] :
( ( SV16 != SY92 )
| ~ ( greater @ SV16 @ SY92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(123,plain,
( ( ! [SX1: $i,SX2: $i] :
( ~ ( greater @ SX1 @ SX2 )
| ( SX1
= ( vplus @ SX2 @ ( vskolem7 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(124,plain,
! [SV18: $i] :
( ( ! [SY95: $i] :
~ ( ~ ( ~ ( less @ SY95 @ SV18 )
| ~ ! [SY96: $i] :
( SV18
!= ( vplus @ SY95 @ SY96 ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
( SV18
!= ( vplus @ SY95 @ SY97 ) )
| ( less @ SY95 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(125,plain,
! [SV19: $i] :
( ( ! [SY98: $i] :
( ~ ~ ! [SY99: $i] :
( SV19
!= ( vplus @ SY98 @ SY99 ) )
| ~ ~ ! [SY100: $i] :
( SY98
!= ( vplus @ SV19 @ SY100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(126,plain,
! [SV20: $i] :
( ( ! [SY101: $i] :
~ ( ~ ( ~ ( greater @ SY101 @ SV20 )
| ~ ! [SY102: $i] :
( SY101
!= ( vplus @ SV20 @ SY102 ) ) )
| ~ ( ~ ~ ! [SY103: $i] :
( SY101
!= ( vplus @ SV20 @ SY103 ) )
| ( greater @ SY101 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(127,plain,
! [SV21: $i] :
( ( ! [SY104: $i,SY105: $i] :
( ~ ( greater @ SY104 @ SY105 )
| ( ( vplus @ SY104 @ SV21 )
= ( vplus @ ( vplus @ SY105 @ ( vskolem7 @ SY104 @ SY105 ) ) @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(128,plain,
! [SV22: $i] :
( ( ! [SY106: $i] :
( ( SV22 = SY106 )
| ~ ! [SY107: $i] :
( SV22
!= ( vplus @ SY106 @ SY107 ) )
| ~ ! [SY108: $i] :
( SY106
!= ( vplus @ SV22 @ SY108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(129,plain,
! [SV23: $i] :
( ( ! [SY109: $i] :
( ( SV23 != SY109 )
| ~ ~ ! [SY110: $i] :
( SV23
!= ( vplus @ SY109 @ SY110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(130,plain,
! [SV24: $i] :
( ( ! [SY111: $i,SY112: $i] :
( ~ ( less @ SY111 @ SY112 )
| ( greater @ ( vplus @ SY112 @ SV24 ) @ ( vplus @ SY111 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(131,plain,
! [SV25: $i] :
( ( ! [SY113: $i] :
( ( SV25 != SY113 )
| ~ ~ ! [SY114: $i] :
( SY113
!= ( vplus @ SV25 @ SY114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(132,plain,
! [SV26: $i,SV1: $i] :
( ( greater @ ( vplus @ SV1 @ SV26 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(133,plain,
! [SV27: $i,SV2: $i] :
( ( ( SV2 = SV27 )
| ( greater @ SV2 @ SV27 )
| ( less @ SV2 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(134,plain,
! [SV28: $i,SV3: $i] :
( ( ~ ( greater @ SV3 @ SV28 )
| ~ ( less @ SV3 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(135,plain,
! [SV4: $i,SV29: $i] :
( ( ( vplus @ SV29 @ SV4 )
= ( vplus @ SV4 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(136,plain,
! [SV30: $i,SV5: $i] :
( ( ( vplus @ ( vsucc @ SV5 ) @ SV30 )
= ( vsucc @ ( vplus @ SV5 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(137,plain,
! [SV31: $i,SV6: $i] :
( ( ! [SY115: $i] :
( ( vplus @ ( vplus @ SV6 @ SV31 ) @ SY115 )
= ( vplus @ SV6 @ ( vplus @ SV31 @ SY115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(138,plain,
! [SV7: $i,SV32: $i] :
( ( ! [SY116: $i] :
( ~ ( greater @ SV32 @ SY116 )
| ( ( vplus @ ( vskolem7 @ SV32 @ SY116 ) @ ( vplus @ SY116 @ SV7 ) )
= ( vplus @ ( vplus @ SY116 @ SV7 ) @ ( vskolem7 @ SV32 @ SY116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(139,plain,
! [SV8: $i,SV33: $i] :
( ( ! [SY117: $i] :
( ( SV33 != SY117 )
| ( ( vplus @ SV33 @ SV8 )
= ( vplus @ SY117 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(140,plain,
! [SV34: $i,SV9: $i] :
( ( ~ ( less @ SV9 @ SV34 )
| ( greater @ SV34 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(141,plain,
! [SV35: $i,SV10: $i] :
( ( ~ ( greater @ SV10 @ SV35 )
| ( less @ SV35 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(142,plain,
! [SV11: $i,SV36: $i] :
( ( ! [SY118: $i] :
( ~ ( greater @ SV36 @ SY118 )
| ( greater @ ( vplus @ SV36 @ SV11 ) @ ( vplus @ SY118 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(143,plain,
! [SV12: $i,SV37: $i] :
( ( ! [SY119: $i] :
( ~ ( less @ SV37 @ SY119 )
| ( less @ ( vplus @ SV37 @ SV12 ) @ ( vplus @ SY119 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(144,plain,
! [SV13: $i,SV38: $i] :
( ( ! [SY120: $i] :
( ~ ( greater @ SV38 @ SY120 )
| ( ( vplus @ ( vplus @ ( vskolem7 @ SV38 @ SY120 ) @ SY120 ) @ SV13 )
= ( vplus @ ( vskolem7 @ SV38 @ SY120 ) @ ( vplus @ SY120 @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(145,plain,
! [SV39: $i] :
( ( ! [SY121: $i] :
( ~ ( less @ SV39 @ SY121 )
| ( greater @ SY121 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(146,plain,
! [SV15: $i,SV40: $i] :
( ( ! [SY122: $i] :
( ~ ( greater @ SV40 @ SY122 )
| ( ( vplus @ ( vplus @ SY122 @ ( vskolem7 @ SV40 @ SY122 ) ) @ SV15 )
= ( vplus @ ( vplus @ ( vskolem7 @ SV40 @ SY122 ) @ SY122 ) @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(147,plain,
! [SV41: $i,SV16: $i] :
( ( ( SV16 != SV41 )
| ~ ( greater @ SV16 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(148,plain,
! [SV42: $i] :
( ( ! [SY123: $i] :
( ~ ( greater @ SV42 @ SY123 )
| ( SV42
= ( vplus @ SY123 @ ( vskolem7 @ SV42 @ SY123 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(149,plain,
! [SV18: $i,SV43: $i] :
( ( ~ ( ~ ( ~ ( less @ SV43 @ SV18 )
| ~ ! [SY124: $i] :
( SV18
!= ( vplus @ SV43 @ SY124 ) ) )
| ~ ( ~ ~ ! [SY125: $i] :
( SV18
!= ( vplus @ SV43 @ SY125 ) )
| ( less @ SV43 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(150,plain,
! [SV44: $i,SV19: $i] :
( ( ~ ~ ! [SY126: $i] :
( SV19
!= ( vplus @ SV44 @ SY126 ) )
| ~ ~ ! [SY127: $i] :
( SV44
!= ( vplus @ SV19 @ SY127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(151,plain,
! [SV20: $i,SV45: $i] :
( ( ~ ( ~ ( ~ ( greater @ SV45 @ SV20 )
| ~ ! [SY128: $i] :
( SV45
!= ( vplus @ SV20 @ SY128 ) ) )
| ~ ( ~ ~ ! [SY129: $i] :
( SV45
!= ( vplus @ SV20 @ SY129 ) )
| ( greater @ SV45 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(152,plain,
! [SV21: $i,SV46: $i] :
( ( ! [SY130: $i] :
( ~ ( greater @ SV46 @ SY130 )
| ( ( vplus @ SV46 @ SV21 )
= ( vplus @ ( vplus @ SY130 @ ( vskolem7 @ SV46 @ SY130 ) ) @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(153,plain,
! [SV47: $i,SV22: $i] :
( ( ( SV22 = SV47 )
| ~ ! [SY131: $i] :
( SV22
!= ( vplus @ SV47 @ SY131 ) )
| ~ ! [SY132: $i] :
( SV47
!= ( vplus @ SV22 @ SY132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(154,plain,
! [SV48: $i,SV23: $i] :
( ( ( SV23 != SV48 )
| ~ ~ ! [SY133: $i] :
( SV23
!= ( vplus @ SV48 @ SY133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(155,plain,
! [SV24: $i,SV49: $i] :
( ( ! [SY134: $i] :
( ~ ( less @ SV49 @ SY134 )
| ( greater @ ( vplus @ SY134 @ SV24 ) @ ( vplus @ SV49 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(156,plain,
! [SV50: $i,SV25: $i] :
( ( ( SV25 != SV50 )
| ~ ~ ! [SY135: $i] :
( SV50
!= ( vplus @ SV25 @ SY135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(157,plain,
! [SV27: $i,SV2: $i] :
( ( ( ( SV2 = SV27 )
| ( greater @ SV2 @ SV27 ) )
= $true )
| ( ( less @ SV2 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(158,plain,
! [SV28: $i,SV3: $i] :
( ( ( ~ ( greater @ SV3 @ SV28 ) )
= $true )
| ( ( ~ ( less @ SV3 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(159,plain,
! [SV51: $i,SV31: $i,SV6: $i] :
( ( ( vplus @ ( vplus @ SV6 @ SV31 ) @ SV51 )
= ( vplus @ SV6 @ ( vplus @ SV31 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(160,plain,
! [SV7: $i,SV52: $i,SV32: $i] :
( ( ~ ( greater @ SV32 @ SV52 )
| ( ( vplus @ ( vskolem7 @ SV32 @ SV52 ) @ ( vplus @ SV52 @ SV7 ) )
= ( vplus @ ( vplus @ SV52 @ SV7 ) @ ( vskolem7 @ SV32 @ SV52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(161,plain,
! [SV8: $i,SV53: $i,SV33: $i] :
( ( ( SV33 != SV53 )
| ( ( vplus @ SV33 @ SV8 )
= ( vplus @ SV53 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(162,plain,
! [SV34: $i,SV9: $i] :
( ( ( ~ ( less @ SV9 @ SV34 ) )
= $true )
| ( ( greater @ SV34 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(163,plain,
! [SV35: $i,SV10: $i] :
( ( ( ~ ( greater @ SV10 @ SV35 ) )
= $true )
| ( ( less @ SV35 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(164,plain,
! [SV11: $i,SV54: $i,SV36: $i] :
( ( ~ ( greater @ SV36 @ SV54 )
| ( greater @ ( vplus @ SV36 @ SV11 ) @ ( vplus @ SV54 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(165,plain,
! [SV12: $i,SV55: $i,SV37: $i] :
( ( ~ ( less @ SV37 @ SV55 )
| ( less @ ( vplus @ SV37 @ SV12 ) @ ( vplus @ SV55 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(166,plain,
! [SV13: $i,SV56: $i,SV38: $i] :
( ( ~ ( greater @ SV38 @ SV56 )
| ( ( vplus @ ( vplus @ ( vskolem7 @ SV38 @ SV56 ) @ SV56 ) @ SV13 )
= ( vplus @ ( vskolem7 @ SV38 @ SV56 ) @ ( vplus @ SV56 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(167,plain,
! [SV57: $i,SV39: $i] :
( ( ~ ( less @ SV39 @ SV57 )
| ( greater @ SV57 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(168,plain,
! [SV15: $i,SV58: $i,SV40: $i] :
( ( ~ ( greater @ SV40 @ SV58 )
| ( ( vplus @ ( vplus @ SV58 @ ( vskolem7 @ SV40 @ SV58 ) ) @ SV15 )
= ( vplus @ ( vplus @ ( vskolem7 @ SV40 @ SV58 ) @ SV58 ) @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(169,plain,
! [SV41: $i,SV16: $i] :
( ( ( SV16 != SV41 )
= $true )
| ( ( ~ ( greater @ SV16 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(170,plain,
! [SV59: $i,SV42: $i] :
( ( ~ ( greater @ SV42 @ SV59 )
| ( SV42
= ( vplus @ SV59 @ ( vskolem7 @ SV42 @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(171,plain,
! [SV18: $i,SV43: $i] :
( ( ~ ( ~ ( less @ SV43 @ SV18 )
| ~ ! [SY124: $i] :
( SV18
!= ( vplus @ SV43 @ SY124 ) ) )
| ~ ( ~ ~ ! [SY125: $i] :
( SV18
!= ( vplus @ SV43 @ SY125 ) )
| ( less @ SV43 @ SV18 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(172,plain,
! [SV44: $i,SV19: $i] :
( ( ( ~ ~ ! [SY126: $i] :
( SV19
!= ( vplus @ SV44 @ SY126 ) ) )
= $true )
| ( ( ~ ~ ! [SY127: $i] :
( SV44
!= ( vplus @ SV19 @ SY127 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(173,plain,
! [SV20: $i,SV45: $i] :
( ( ~ ( ~ ( greater @ SV45 @ SV20 )
| ~ ! [SY128: $i] :
( SV45
!= ( vplus @ SV20 @ SY128 ) ) )
| ~ ( ~ ~ ! [SY129: $i] :
( SV45
!= ( vplus @ SV20 @ SY129 ) )
| ( greater @ SV45 @ SV20 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(174,plain,
! [SV21: $i,SV60: $i,SV46: $i] :
( ( ~ ( greater @ SV46 @ SV60 )
| ( ( vplus @ SV46 @ SV21 )
= ( vplus @ ( vplus @ SV60 @ ( vskolem7 @ SV46 @ SV60 ) ) @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(175,plain,
! [SV47: $i,SV22: $i] :
( ( ( ( SV22 = SV47 )
| ~ ! [SY131: $i] :
( SV22
!= ( vplus @ SV47 @ SY131 ) ) )
= $true )
| ( ( ~ ! [SY132: $i] :
( SV47
!= ( vplus @ SV22 @ SY132 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(176,plain,
! [SV48: $i,SV23: $i] :
( ( ( SV23 != SV48 )
= $true )
| ( ( ~ ~ ! [SY133: $i] :
( SV23
!= ( vplus @ SV48 @ SY133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(177,plain,
! [SV24: $i,SV61: $i,SV49: $i] :
( ( ~ ( less @ SV49 @ SV61 )
| ( greater @ ( vplus @ SV61 @ SV24 ) @ ( vplus @ SV49 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(178,plain,
! [SV50: $i,SV25: $i] :
( ( ( SV25 != SV50 )
= $true )
| ( ( ~ ~ ! [SY135: $i] :
( SV50
!= ( vplus @ SV25 @ SY135 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(179,plain,
! [SV27: $i,SV2: $i] :
( ( ( SV2 = SV27 )
= $true )
| ( ( greater @ SV2 @ SV27 )
= $true )
| ( ( less @ SV2 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(180,plain,
! [SV28: $i,SV3: $i] :
( ( ( greater @ SV3 @ SV28 )
= $false )
| ( ( ~ ( less @ SV3 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(181,plain,
! [SV7: $i,SV52: $i,SV32: $i] :
( ( ( ~ ( greater @ SV32 @ SV52 ) )
= $true )
| ( ( ( vplus @ ( vskolem7 @ SV32 @ SV52 ) @ ( vplus @ SV52 @ SV7 ) )
= ( vplus @ ( vplus @ SV52 @ SV7 ) @ ( vskolem7 @ SV32 @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(182,plain,
! [SV8: $i,SV53: $i,SV33: $i] :
( ( ( SV33 != SV53 )
= $true )
| ( ( ( vplus @ SV33 @ SV8 )
= ( vplus @ SV53 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(183,plain,
! [SV34: $i,SV9: $i] :
( ( ( less @ SV9 @ SV34 )
= $false )
| ( ( greater @ SV34 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(184,plain,
! [SV35: $i,SV10: $i] :
( ( ( greater @ SV10 @ SV35 )
= $false )
| ( ( less @ SV35 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(185,plain,
! [SV11: $i,SV54: $i,SV36: $i] :
( ( ( ~ ( greater @ SV36 @ SV54 ) )
= $true )
| ( ( greater @ ( vplus @ SV36 @ SV11 ) @ ( vplus @ SV54 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(186,plain,
! [SV12: $i,SV55: $i,SV37: $i] :
( ( ( ~ ( less @ SV37 @ SV55 ) )
= $true )
| ( ( less @ ( vplus @ SV37 @ SV12 ) @ ( vplus @ SV55 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(187,plain,
! [SV13: $i,SV56: $i,SV38: $i] :
( ( ( ~ ( greater @ SV38 @ SV56 ) )
= $true )
| ( ( ( vplus @ ( vplus @ ( vskolem7 @ SV38 @ SV56 ) @ SV56 ) @ SV13 )
= ( vplus @ ( vskolem7 @ SV38 @ SV56 ) @ ( vplus @ SV56 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(188,plain,
! [SV57: $i,SV39: $i] :
( ( ( ~ ( less @ SV39 @ SV57 ) )
= $true )
| ( ( greater @ SV57 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(189,plain,
! [SV15: $i,SV58: $i,SV40: $i] :
( ( ( ~ ( greater @ SV40 @ SV58 ) )
= $true )
| ( ( ( vplus @ ( vplus @ SV58 @ ( vskolem7 @ SV40 @ SV58 ) ) @ SV15 )
= ( vplus @ ( vplus @ ( vskolem7 @ SV40 @ SV58 ) @ SV58 ) @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(190,plain,
! [SV41: $i,SV16: $i] :
( ( ( SV16 = SV41 )
= $false )
| ( ( ~ ( greater @ SV16 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(191,plain,
! [SV59: $i,SV42: $i] :
( ( ( ~ ( greater @ SV42 @ SV59 ) )
= $true )
| ( ( SV42
= ( vplus @ SV59 @ ( vskolem7 @ SV42 @ SV59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(192,plain,
! [SV18: $i,SV43: $i] :
( ( ~ ( ~ ( less @ SV43 @ SV18 )
| ~ ! [SY124: $i] :
( SV18
!= ( vplus @ SV43 @ SY124 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(193,plain,
! [SV43: $i,SV18: $i] :
( ( ~ ( ~ ~ ! [SY125: $i] :
( SV18
!= ( vplus @ SV43 @ SY125 ) )
| ( less @ SV43 @ SV18 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(194,plain,
! [SV44: $i,SV19: $i] :
( ( ( ~ ! [SY126: $i] :
( SV19
!= ( vplus @ SV44 @ SY126 ) ) )
= $false )
| ( ( ~ ~ ! [SY127: $i] :
( SV44
!= ( vplus @ SV19 @ SY127 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(195,plain,
! [SV20: $i,SV45: $i] :
( ( ~ ( ~ ( greater @ SV45 @ SV20 )
| ~ ! [SY128: $i] :
( SV45
!= ( vplus @ SV20 @ SY128 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(196,plain,
! [SV20: $i,SV45: $i] :
( ( ~ ( ~ ~ ! [SY129: $i] :
( SV45
!= ( vplus @ SV20 @ SY129 ) )
| ( greater @ SV45 @ SV20 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(197,plain,
! [SV21: $i,SV60: $i,SV46: $i] :
( ( ( ~ ( greater @ SV46 @ SV60 ) )
= $true )
| ( ( ( vplus @ SV46 @ SV21 )
= ( vplus @ ( vplus @ SV60 @ ( vskolem7 @ SV46 @ SV60 ) ) @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(198,plain,
! [SV47: $i,SV22: $i] :
( ( ( SV22 = SV47 )
= $true )
| ( ( ~ ! [SY131: $i] :
( SV22
!= ( vplus @ SV47 @ SY131 ) ) )
= $true )
| ( ( ~ ! [SY132: $i] :
( SV47
!= ( vplus @ SV22 @ SY132 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(199,plain,
! [SV48: $i,SV23: $i] :
( ( ( SV23 = SV48 )
= $false )
| ( ( ~ ~ ! [SY133: $i] :
( SV23
!= ( vplus @ SV48 @ SY133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(200,plain,
! [SV24: $i,SV61: $i,SV49: $i] :
( ( ( ~ ( less @ SV49 @ SV61 ) )
= $true )
| ( ( greater @ ( vplus @ SV61 @ SV24 ) @ ( vplus @ SV49 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(201,plain,
! [SV50: $i,SV25: $i] :
( ( ( SV25 = SV50 )
= $false )
| ( ( ~ ~ ! [SY135: $i] :
( SV50
!= ( vplus @ SV25 @ SY135 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(202,plain,
! [SV28: $i,SV3: $i] :
( ( ( less @ SV3 @ SV28 )
= $false )
| ( ( greater @ SV3 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(203,plain,
! [SV7: $i,SV52: $i,SV32: $i] :
( ( ( greater @ SV32 @ SV52 )
= $false )
| ( ( ( vplus @ ( vskolem7 @ SV32 @ SV52 ) @ ( vplus @ SV52 @ SV7 ) )
= ( vplus @ ( vplus @ SV52 @ SV7 ) @ ( vskolem7 @ SV32 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(204,plain,
! [SV8: $i,SV53: $i,SV33: $i] :
( ( ( SV33 = SV53 )
= $false )
| ( ( ( vplus @ SV33 @ SV8 )
= ( vplus @ SV53 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(205,plain,
! [SV11: $i,SV54: $i,SV36: $i] :
( ( ( greater @ SV36 @ SV54 )
= $false )
| ( ( greater @ ( vplus @ SV36 @ SV11 ) @ ( vplus @ SV54 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(206,plain,
! [SV12: $i,SV55: $i,SV37: $i] :
( ( ( less @ SV37 @ SV55 )
= $false )
| ( ( less @ ( vplus @ SV37 @ SV12 ) @ ( vplus @ SV55 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(207,plain,
! [SV13: $i,SV56: $i,SV38: $i] :
( ( ( greater @ SV38 @ SV56 )
= $false )
| ( ( ( vplus @ ( vplus @ ( vskolem7 @ SV38 @ SV56 ) @ SV56 ) @ SV13 )
= ( vplus @ ( vskolem7 @ SV38 @ SV56 ) @ ( vplus @ SV56 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(208,plain,
! [SV57: $i,SV39: $i] :
( ( ( less @ SV39 @ SV57 )
= $false )
| ( ( greater @ SV57 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(209,plain,
! [SV15: $i,SV58: $i,SV40: $i] :
( ( ( greater @ SV40 @ SV58 )
= $false )
| ( ( ( vplus @ ( vplus @ SV58 @ ( vskolem7 @ SV40 @ SV58 ) ) @ SV15 )
= ( vplus @ ( vplus @ ( vskolem7 @ SV40 @ SV58 ) @ SV58 ) @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(210,plain,
! [SV41: $i,SV16: $i] :
( ( ( greater @ SV16 @ SV41 )
= $false )
| ( ( SV16 = SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(211,plain,
! [SV59: $i,SV42: $i] :
( ( ( greater @ SV42 @ SV59 )
= $false )
| ( ( SV42
= ( vplus @ SV59 @ ( vskolem7 @ SV42 @ SV59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(212,plain,
! [SV18: $i,SV43: $i] :
( ( ~ ( less @ SV43 @ SV18 )
| ~ ! [SY124: $i] :
( SV18
!= ( vplus @ SV43 @ SY124 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[192]) ).
thf(213,plain,
! [SV43: $i,SV18: $i] :
( ( ~ ~ ! [SY125: $i] :
( SV18
!= ( vplus @ SV43 @ SY125 ) )
| ( less @ SV43 @ SV18 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(214,plain,
! [SV44: $i,SV19: $i] :
( ( ( ! [SY126: $i] :
( SV19
!= ( vplus @ SV44 @ SY126 ) ) )
= $true )
| ( ( ~ ~ ! [SY127: $i] :
( SV44
!= ( vplus @ SV19 @ SY127 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(215,plain,
! [SV20: $i,SV45: $i] :
( ( ~ ( greater @ SV45 @ SV20 )
| ~ ! [SY128: $i] :
( SV45
!= ( vplus @ SV20 @ SY128 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(216,plain,
! [SV20: $i,SV45: $i] :
( ( ~ ~ ! [SY129: $i] :
( SV45
!= ( vplus @ SV20 @ SY129 ) )
| ( greater @ SV45 @ SV20 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(217,plain,
! [SV21: $i,SV60: $i,SV46: $i] :
( ( ( greater @ SV46 @ SV60 )
= $false )
| ( ( ( vplus @ SV46 @ SV21 )
= ( vplus @ ( vplus @ SV60 @ ( vskolem7 @ SV46 @ SV60 ) ) @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(218,plain,
! [SV47: $i,SV22: $i] :
( ( ( ! [SY131: $i] :
( SV22
!= ( vplus @ SV47 @ SY131 ) ) )
= $false )
| ( ( SV22 = SV47 )
= $true )
| ( ( ~ ! [SY132: $i] :
( SV47
!= ( vplus @ SV22 @ SY132 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(219,plain,
! [SV48: $i,SV23: $i] :
( ( ( ~ ! [SY133: $i] :
( SV23
!= ( vplus @ SV48 @ SY133 ) ) )
= $false )
| ( ( SV23 = SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(220,plain,
! [SV24: $i,SV61: $i,SV49: $i] :
( ( ( less @ SV49 @ SV61 )
= $false )
| ( ( greater @ ( vplus @ SV61 @ SV24 ) @ ( vplus @ SV49 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(221,plain,
! [SV25: $i,SV50: $i] :
( ( ( ~ ! [SY135: $i] :
( SV50
!= ( vplus @ SV25 @ SY135 ) ) )
= $false )
| ( ( SV25 = SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(222,plain,
! [SV18: $i,SV43: $i] :
( ( ( ~ ( less @ SV43 @ SV18 ) )
= $true )
| ( ( ~ ! [SY124: $i] :
( SV18
!= ( vplus @ SV43 @ SY124 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(223,plain,
! [SV43: $i,SV18: $i] :
( ( ( ~ ~ ! [SY125: $i] :
( SV18
!= ( vplus @ SV43 @ SY125 ) ) )
= $true )
| ( ( less @ SV43 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(224,plain,
! [SV62: $i,SV44: $i,SV19: $i] :
( ( ( SV19
!= ( vplus @ SV44 @ SV62 ) )
= $true )
| ( ( ~ ~ ! [SY127: $i] :
( SV44
!= ( vplus @ SV19 @ SY127 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(225,plain,
! [SV20: $i,SV45: $i] :
( ( ( ~ ( greater @ SV45 @ SV20 ) )
= $true )
| ( ( ~ ! [SY128: $i] :
( SV45
!= ( vplus @ SV20 @ SY128 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(226,plain,
! [SV20: $i,SV45: $i] :
( ( ( ~ ~ ! [SY129: $i] :
( SV45
!= ( vplus @ SV20 @ SY129 ) ) )
= $true )
| ( ( greater @ SV45 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(227,plain,
! [SV47: $i,SV22: $i] :
( ( ( SV22
!= ( vplus @ SV47 @ ( sK1_SY131 @ SV47 @ SV22 ) ) )
= $false )
| ( ( SV22 = SV47 )
= $true )
| ( ( ~ ! [SY132: $i] :
( SV47
!= ( vplus @ SV22 @ SY132 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[218]) ).
thf(228,plain,
! [SV48: $i,SV23: $i] :
( ( ( ! [SY133: $i] :
( SV23
!= ( vplus @ SV48 @ SY133 ) ) )
= $true )
| ( ( SV23 = SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(229,plain,
! [SV25: $i,SV50: $i] :
( ( ( ! [SY135: $i] :
( SV50
!= ( vplus @ SV25 @ SY135 ) ) )
= $true )
| ( ( SV25 = SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(230,plain,
! [SV18: $i,SV43: $i] :
( ( ( less @ SV43 @ SV18 )
= $false )
| ( ( ~ ! [SY124: $i] :
( SV18
!= ( vplus @ SV43 @ SY124 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(231,plain,
! [SV43: $i,SV18: $i] :
( ( ( ~ ! [SY125: $i] :
( SV18
!= ( vplus @ SV43 @ SY125 ) ) )
= $false )
| ( ( less @ SV43 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(232,plain,
! [SV62: $i,SV44: $i,SV19: $i] :
( ( ( SV19
= ( vplus @ SV44 @ SV62 ) )
= $false )
| ( ( ~ ~ ! [SY127: $i] :
( SV44
!= ( vplus @ SV19 @ SY127 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(233,plain,
! [SV20: $i,SV45: $i] :
( ( ( greater @ SV45 @ SV20 )
= $false )
| ( ( ~ ! [SY128: $i] :
( SV45
!= ( vplus @ SV20 @ SY128 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(234,plain,
! [SV20: $i,SV45: $i] :
( ( ( ~ ! [SY129: $i] :
( SV45
!= ( vplus @ SV20 @ SY129 ) ) )
= $false )
| ( ( greater @ SV45 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(235,plain,
! [SV47: $i,SV22: $i] :
( ( ( SV22
= ( vplus @ SV47 @ ( sK1_SY131 @ SV47 @ SV22 ) ) )
= $true )
| ( ( SV22 = SV47 )
= $true )
| ( ( ~ ! [SY132: $i] :
( SV47
!= ( vplus @ SV22 @ SY132 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(236,plain,
! [SV63: $i,SV48: $i,SV23: $i] :
( ( ( SV23
!= ( vplus @ SV48 @ SV63 ) )
= $true )
| ( ( SV23 = SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(237,plain,
! [SV64: $i,SV25: $i,SV50: $i] :
( ( ( SV50
!= ( vplus @ SV25 @ SV64 ) )
= $true )
| ( ( SV25 = SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(238,plain,
! [SV43: $i,SV18: $i] :
( ( ( ! [SY124: $i] :
( SV18
!= ( vplus @ SV43 @ SY124 ) ) )
= $false )
| ( ( less @ SV43 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(239,plain,
! [SV43: $i,SV18: $i] :
( ( ( ! [SY125: $i] :
( SV18
!= ( vplus @ SV43 @ SY125 ) ) )
= $true )
| ( ( less @ SV43 @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(240,plain,
! [SV62: $i,SV19: $i,SV44: $i] :
( ( ( ~ ! [SY127: $i] :
( SV44
!= ( vplus @ SV19 @ SY127 ) ) )
= $false )
| ( ( SV19
= ( vplus @ SV44 @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(241,plain,
! [SV20: $i,SV45: $i] :
( ( ( ! [SY128: $i] :
( SV45
!= ( vplus @ SV20 @ SY128 ) ) )
= $false )
| ( ( greater @ SV45 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(242,plain,
! [SV20: $i,SV45: $i] :
( ( ( ! [SY129: $i] :
( SV45
!= ( vplus @ SV20 @ SY129 ) ) )
= $true )
| ( ( greater @ SV45 @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(243,plain,
! [SV22: $i,SV47: $i] :
( ( ( ! [SY132: $i] :
( SV47
!= ( vplus @ SV22 @ SY132 ) ) )
= $false )
| ( ( SV22 = SV47 )
= $true )
| ( ( SV22
= ( vplus @ SV47 @ ( sK1_SY131 @ SV47 @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(244,plain,
! [SV63: $i,SV48: $i,SV23: $i] :
( ( ( SV23
= ( vplus @ SV48 @ SV63 ) )
= $false )
| ( ( SV23 = SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(245,plain,
! [SV64: $i,SV25: $i,SV50: $i] :
( ( ( SV50
= ( vplus @ SV25 @ SV64 ) )
= $false )
| ( ( SV25 = SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(246,plain,
! [SV43: $i,SV18: $i] :
( ( ( SV18
!= ( vplus @ SV43 @ ( sK2_SY124 @ SV43 @ SV18 ) ) )
= $false )
| ( ( less @ SV43 @ SV18 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[238]) ).
thf(247,plain,
! [SV65: $i,SV43: $i,SV18: $i] :
( ( ( SV18
!= ( vplus @ SV43 @ SV65 ) )
= $true )
| ( ( less @ SV43 @ SV18 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(248,plain,
! [SV62: $i,SV19: $i,SV44: $i] :
( ( ( ! [SY127: $i] :
( SV44
!= ( vplus @ SV19 @ SY127 ) ) )
= $true )
| ( ( SV19
= ( vplus @ SV44 @ SV62 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(249,plain,
! [SV20: $i,SV45: $i] :
( ( ( SV45
!= ( vplus @ SV20 @ ( sK3_SY128 @ SV20 @ SV45 ) ) )
= $false )
| ( ( greater @ SV45 @ SV20 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[241]) ).
thf(250,plain,
! [SV66: $i,SV20: $i,SV45: $i] :
( ( ( SV45
!= ( vplus @ SV20 @ SV66 ) )
= $true )
| ( ( greater @ SV45 @ SV20 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(251,plain,
! [SV22: $i,SV47: $i] :
( ( ( SV47
!= ( vplus @ SV22 @ ( sK4_SY132 @ SV22 @ SV47 ) ) )
= $false )
| ( ( SV22 = SV47 )
= $true )
| ( ( SV22
= ( vplus @ SV47 @ ( sK1_SY131 @ SV47 @ SV22 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[243]) ).
thf(252,plain,
! [SV43: $i,SV18: $i] :
( ( ( SV18
= ( vplus @ SV43 @ ( sK2_SY124 @ SV43 @ SV18 ) ) )
= $true )
| ( ( less @ SV43 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(253,plain,
! [SV65: $i,SV43: $i,SV18: $i] :
( ( ( SV18
= ( vplus @ SV43 @ SV65 ) )
= $false )
| ( ( less @ SV43 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(254,plain,
! [SV62: $i,SV67: $i,SV19: $i,SV44: $i] :
( ( ( SV44
!= ( vplus @ SV19 @ SV67 ) )
= $true )
| ( ( SV19
= ( vplus @ SV44 @ SV62 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(255,plain,
! [SV20: $i,SV45: $i] :
( ( ( SV45
= ( vplus @ SV20 @ ( sK3_SY128 @ SV20 @ SV45 ) ) )
= $true )
| ( ( greater @ SV45 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(256,plain,
! [SV66: $i,SV20: $i,SV45: $i] :
( ( ( SV45
= ( vplus @ SV20 @ SV66 ) )
= $false )
| ( ( greater @ SV45 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(257,plain,
! [SV22: $i,SV47: $i] :
( ( ( SV47
= ( vplus @ SV22 @ ( sK4_SY132 @ SV22 @ SV47 ) ) )
= $true )
| ( ( SV22 = SV47 )
= $true )
| ( ( SV22
= ( vplus @ SV47 @ ( sK1_SY131 @ SV47 @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(258,plain,
! [SV62: $i,SV67: $i,SV19: $i,SV44: $i] :
( ( ( SV44
= ( vplus @ SV19 @ SV67 ) )
= $false )
| ( ( SV19
= ( vplus @ SV44 @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(259,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[60,258,257,256,255,253,252,245,244,220,217,211,210,209,208,207,206,205,204,203,202,184,183,179,159,136,135,132,112]) ).
thf(260,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[259]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM838+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n007.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 13:38:30 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.31
% 0.46/0.31 No.of.Axioms: 26
% 0.46/0.31
% 0.46/0.31 Length.of.Defs: 0
% 0.46/0.31
% 0.46/0.31 Contains.Choice.Funs: false
% 0.46/0.31 ........
% 0.46/0.31
% 0.46/0.31 ********************************
% 0.46/0.31 * All subproblems solved! *
% 0.46/0.31 ********************************
% 0.46/0.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:26,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:259,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.46/0.31
% 0.46/0.31 %**** Beginning of derivation protocol ****
% 0.46/0.31 % SZS output start CNFRefutation
% See solution above
% 0.46/0.31
% 0.46/0.31 %**** End of derivation protocol ****
% 0.46/0.31 %**** no. of clauses in derivation: 257 ****
% 0.46/0.31 %**** clause counter: 259 ****
% 0.46/0.31
% 0.46/0.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:26,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:259,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------