%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM853+1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 10:35:25 AM UTC 2026
% Result : Theorem 0.54s 0.27s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 164 ( 96 unt; 0 typ; 0 def)
% Number of atoms : 835 ( 275 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 1514 ( 243 ~; 206 |; 9 &;1026 @)
% ( 6 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 424 ( 0 ^; 421 !; 3 ?; 424 :)
% 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_SY59,type,
sK1_SY59: $i > $i > $i ).
thf(tp_v1,type,
v1: $i ).
thf(tp_vd486,type,
vd486: $i ).
thf(tp_vd487,type,
vd487: $i ).
thf(tp_vd488,type,
vd488: $i ).
thf(tp_vmul,type,
vmul: $i > $i > $i ).
thf(tp_vplus,type,
vplus: $i > $i > $i ).
thf(tp_vskolem2,type,
vskolem2: $i > $i ).
thf(tp_vsucc,type,
vsucc: $i > $i ).
thf(17,axiom,
! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
thf(19,axiom,
! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
thf(20,axiom,
! [Vd203: $i,Vd204: $i] :
( ~ ( greater @ Vd203 @ Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
thf(22,axiom,
! [Vd203: $i,Vd204: $i] :
( ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 )
| ( less @ Vd203 @ Vd204 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
thf(23,axiom,
! [Vd208: $i,Vd209: $i] :
( ( greater @ Vd208 @ Vd209 )
=> ( less @ Vd209 @ Vd208 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
thf(24,axiom,
! [Vd226: $i,Vd227: $i] :
( ( less @ Vd226 @ Vd227 )
=> ( greater @ Vd227 @ Vd226 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
thf(25,axiom,
! [Vd244: $i,Vd245: $i] :
( ( geq @ Vd245 @ Vd244 )
<=> ( ( greater @ Vd245 @ Vd244 )
| ( Vd245 = Vd244 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
thf(32,axiom,
! [Vd295: $i,Vd296: $i] : ( greater @ ( vplus @ Vd295 @ Vd296 ) @ Vd295 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
thf(33,axiom,
! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( greater @ Vd301 @ Vd302 )
=> ( greater @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).
thf(36,axiom,
! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( greater @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
=> ( greater @ Vd328 @ Vd329 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 2)') ).
thf(39,axiom,
! [Vd337: $i,Vd338: $i,Vd340: $i,Vd341: $i] :
( ( ( greater @ Vd340 @ Vd341 )
& ( greater @ Vd337 @ Vd338 ) )
=> ( greater @ ( vplus @ Vd337 @ Vd340 ) @ ( vplus @ Vd338 @ Vd341 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(209, 0), 0)') ).
thf(40,axiom,
! [Vd353: $i,Vd354: $i,Vd355: $i,Vd356: $i] :
( ( ( ( greater @ Vd355 @ Vd356 )
& ( geq @ Vd353 @ Vd354 ) )
| ( ( geq @ Vd355 @ Vd356 )
& ( greater @ Vd353 @ Vd354 ) ) )
=> ( greater @ ( vplus @ Vd353 @ Vd355 ) @ ( vplus @ Vd354 @ Vd356 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(216), 0), 0)') ).
thf(43,axiom,
! [Vd375: $i,Vd376: $i] :
( ( greater @ Vd375 @ Vd376 )
=> ( geq @ Vd375 @ ( vplus @ Vd376 @ v1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(234, 0), 0)') ).
thf(51,axiom,
! [Vd456: $i,Vd457: $i,Vd458: $i] :
( ( greater @ Vd457 @ Vd458 )
=> ( greater @ ( vmul @ Vd457 @ Vd456 ) @ ( vmul @ Vd458 @ Vd456 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(299, 0), 2)') ).
thf(54,axiom,
greater @ ( vmul @ vd486 @ vd487 ) @ ( vmul @ vd488 @ vd487 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(antec(307), 489, 0)') ).
thf(55,conjecture,
greater @ vd486 @ vd488,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq(307), 490, 0)') ).
thf(56,negated_conjecture,
( ( greater @ vd486 @ vd488 )
= $false ),
inference(negate_conjecture,[status(cth)],[55]) ).
thf(57,plain,
( ( greater @ vd486 @ vd488 )
= $false ),
inference(unfold_def,[status(thm)],[56]) ).
thf(58,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(59,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(60,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ~ ( greater @ Vd203 @ Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(61,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 )
| ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(62,plain,
( ( ! [Vd208: $i,Vd209: $i] :
( ( greater @ Vd208 @ Vd209 )
=> ( less @ Vd209 @ Vd208 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(63,plain,
( ( ! [Vd226: $i,Vd227: $i] :
( ( less @ Vd226 @ Vd227 )
=> ( greater @ Vd227 @ Vd226 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(64,plain,
( ( ! [Vd244: $i,Vd245: $i] :
( ( geq @ Vd245 @ Vd244 )
<=> ( ( greater @ Vd245 @ Vd244 )
| ( Vd245 = Vd244 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(65,plain,
( ( ! [Vd295: $i,Vd296: $i] : ( greater @ ( vplus @ Vd295 @ Vd296 ) @ Vd295 ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(66,plain,
( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( greater @ Vd301 @ Vd302 )
=> ( greater @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(67,plain,
( ( ! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( greater @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
=> ( greater @ Vd328 @ Vd329 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(68,plain,
( ( ! [Vd337: $i,Vd338: $i,Vd340: $i,Vd341: $i] :
( ( ( greater @ Vd340 @ Vd341 )
& ( greater @ Vd337 @ Vd338 ) )
=> ( greater @ ( vplus @ Vd337 @ Vd340 ) @ ( vplus @ Vd338 @ Vd341 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(69,plain,
( ( ! [Vd353: $i,Vd354: $i,Vd355: $i,Vd356: $i] :
( ( ( ( greater @ Vd355 @ Vd356 )
& ( geq @ Vd353 @ Vd354 ) )
| ( ( geq @ Vd355 @ Vd356 )
& ( greater @ Vd353 @ Vd354 ) ) )
=> ( greater @ ( vplus @ Vd353 @ Vd355 ) @ ( vplus @ Vd354 @ Vd356 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(70,plain,
( ( ! [Vd375: $i,Vd376: $i] :
( ( greater @ Vd375 @ Vd376 )
=> ( geq @ Vd375 @ ( vplus @ Vd376 @ v1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(71,plain,
( ( ! [Vd456: $i,Vd457: $i,Vd458: $i] :
( ( greater @ Vd457 @ Vd458 )
=> ( greater @ ( vmul @ Vd457 @ Vd456 ) @ ( vmul @ Vd458 @ Vd456 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(72,plain,
( ( greater @ ( vmul @ vd486 @ vd487 ) @ ( vmul @ vd488 @ vd487 ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(73,plain,
( ( ~ ( greater @ vd486 @ vd488 ) )
= $true ),
inference(polarity_switch,[status(thm)],[57]) ).
thf(74,plain,
( ( greater @ ( vmul @ vd486 @ vd487 ) @ ( vmul @ vd488 @ vd487 ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(75,plain,
( ( ! [Vd456: $i,Vd457: $i,Vd458: $i] :
( ( greater @ Vd457 @ Vd458 )
=> ( greater @ ( vmul @ Vd457 @ Vd456 ) @ ( vmul @ Vd458 @ Vd456 ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(76,plain,
( ( ! [Vd375: $i,Vd376: $i] :
( ( greater @ Vd375 @ Vd376 )
=> ( geq @ Vd375 @ ( vplus @ Vd376 @ v1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(77,plain,
( ( ! [Vd353: $i,Vd354: $i,Vd355: $i,Vd356: $i] :
( ( ( ( greater @ Vd355 @ Vd356 )
& ( geq @ Vd353 @ Vd354 ) )
| ( ( geq @ Vd355 @ Vd356 )
& ( greater @ Vd353 @ Vd354 ) ) )
=> ( greater @ ( vplus @ Vd353 @ Vd355 ) @ ( vplus @ Vd354 @ Vd356 ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(78,plain,
( ( ! [Vd337: $i,Vd338: $i,Vd340: $i,Vd341: $i] :
( ( ( greater @ Vd340 @ Vd341 )
& ( greater @ Vd337 @ Vd338 ) )
=> ( greater @ ( vplus @ Vd337 @ Vd340 ) @ ( vplus @ Vd338 @ Vd341 ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(79,plain,
( ( ! [Vd328: $i,Vd329: $i,Vd330: $i] :
( ( greater @ ( vplus @ Vd328 @ Vd330 ) @ ( vplus @ Vd329 @ Vd330 ) )
=> ( greater @ Vd328 @ Vd329 ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(80,plain,
( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( greater @ Vd301 @ Vd302 )
=> ( greater @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(81,plain,
( ( ! [Vd295: $i,Vd296: $i] : ( greater @ ( vplus @ Vd295 @ Vd296 ) @ Vd295 ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(82,plain,
( ( ! [Vd244: $i,Vd245: $i] :
( ( geq @ Vd245 @ Vd244 )
<=> ( ( greater @ Vd245 @ Vd244 )
| ( Vd245 = Vd244 ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(83,plain,
( ( ! [Vd226: $i,Vd227: $i] :
( ( less @ Vd226 @ Vd227 )
=> ( greater @ Vd227 @ Vd226 ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(84,plain,
( ( ! [Vd208: $i,Vd209: $i] :
( ( greater @ Vd208 @ Vd209 )
=> ( less @ Vd209 @ Vd208 ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(85,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 )
| ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(86,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ~ ( greater @ Vd203 @ Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(87,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(88,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(89,plain,
( ( ~ ( greater @ vd486 @ vd488 ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(90,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)],[88]) ).
thf(91,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX0 @ SX1 )
| ( greater @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(92,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( greater @ SX1 @ SX2 )
| ( greater @ ( vmul @ SX1 @ SX0 ) @ ( vmul @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(93,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX0 @ SX1 )
| ( less @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(94,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( greater @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(95,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX0 @ SX1 )
| ( geq @ SX0 @ ( vplus @ SX1 @ v1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(96,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ~ ( ~ ( greater @ SX2 @ SX3 )
| ~ ( geq @ SX0 @ SX1 ) )
| ~ ( ~ ( geq @ SX2 @ SX3 )
| ~ ( greater @ SX0 @ SX1 ) ) )
| ( greater @ ( vplus @ SX0 @ SX2 ) @ ( vplus @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(97,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( greater @ SX2 @ SX3 )
| ~ ( greater @ SX0 @ SX1 ) )
| ( greater @ ( vplus @ SX0 @ SX2 ) @ ( vplus @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(98,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( greater @ ( vplus @ SX0 @ SX2 ) @ ( vplus @ SX1 @ SX2 ) )
| ( greater @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(99,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( geq @ SX1 @ SX0 )
| ( greater @ SX1 @ SX0 )
| ( SX1 = SX0 ) )
| ~ ( ~ ( ( greater @ SX1 @ SX0 )
| ( SX1 = SX0 ) )
| ( geq @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(100,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( greater @ SX0 @ SX1 )
| ( greater @ ( vplus @ SX0 @ SX2 ) @ ( vplus @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(101,plain,
! [SV1: $i] :
( ( ! [SY36: $i] : ( greater @ ( vplus @ SV1 @ SY36 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(102,plain,
! [SV2: $i] :
( ( ! [SY37: $i] :
( ( SV2 = SY37 )
| ( greater @ SV2 @ SY37 )
| ( less @ SV2 @ SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(103,plain,
! [SV3: $i] :
( ( ! [SY38: $i] :
( ~ ( greater @ SV3 @ SY38 )
| ~ ( less @ SV3 @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(104,plain,
( ( greater @ vd486 @ vd488 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(105,plain,
! [SV4: $i] :
( ( ! [SY39: $i] :
~ ( ~ ( ~ ( greater @ SY39 @ SV4 )
| ~ ! [SY40: $i] :
( SY39
!= ( vplus @ SV4 @ SY40 ) ) )
| ~ ( ~ ~ ! [SY41: $i] :
( SY39
!= ( vplus @ SV4 @ SY41 ) )
| ( greater @ SY39 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(106,plain,
! [SV5: $i] :
( ( ! [SY42: $i] :
( ~ ( less @ SV5 @ SY42 )
| ( greater @ SY42 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(107,plain,
! [SV6: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ~ ( greater @ SY43 @ SY44 )
| ( greater @ ( vmul @ SY43 @ SV6 ) @ ( vmul @ SY44 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(108,plain,
! [SV7: $i] :
( ( ! [SY45: $i] :
( ~ ( greater @ SV7 @ SY45 )
| ( less @ SY45 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(109,plain,
! [SV8: $i] :
( ( ! [SY46: $i] :
( ( SV8 != SY46 )
| ~ ( greater @ SV8 @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(110,plain,
! [SV9: $i] :
( ( ! [SY47: $i] :
( ~ ( greater @ SV9 @ SY47 )
| ( geq @ SV9 @ ( vplus @ SY47 @ v1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(111,plain,
! [SV10: $i] :
( ( ! [SY48: $i,SY49: $i,SY50: $i] :
( ~ ( ~ ( ~ ( greater @ SY49 @ SY50 )
| ~ ( geq @ SV10 @ SY48 ) )
| ~ ( ~ ( geq @ SY49 @ SY50 )
| ~ ( greater @ SV10 @ SY48 ) ) )
| ( greater @ ( vplus @ SV10 @ SY49 ) @ ( vplus @ SY48 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(112,plain,
! [SV11: $i] :
( ( ! [SY51: $i,SY52: $i,SY53: $i] :
( ~ ~ ( ~ ( greater @ SY52 @ SY53 )
| ~ ( greater @ SV11 @ SY51 ) )
| ( greater @ ( vplus @ SV11 @ SY52 ) @ ( vplus @ SY51 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(113,plain,
! [SV12: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ~ ( greater @ ( vplus @ SV12 @ SY55 ) @ ( vplus @ SY54 @ SY55 ) )
| ( greater @ SV12 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(114,plain,
! [SV13: $i] :
( ( ! [SY56: $i] :
~ ( ~ ( ~ ( geq @ SY56 @ SV13 )
| ( greater @ SY56 @ SV13 )
| ( SY56 = SV13 ) )
| ~ ( ~ ( ( greater @ SY56 @ SV13 )
| ( SY56 = SV13 ) )
| ( geq @ SY56 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(115,plain,
! [SV14: $i] :
( ( ! [SY57: $i,SY58: $i] :
( ~ ( greater @ SV14 @ SY57 )
| ( greater @ ( vplus @ SV14 @ SY58 ) @ ( vplus @ SY57 @ SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(116,plain,
! [SV15: $i,SV1: $i] :
( ( greater @ ( vplus @ SV1 @ SV15 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(117,plain,
! [SV16: $i,SV2: $i] :
( ( ( SV2 = SV16 )
| ( greater @ SV2 @ SV16 )
| ( less @ SV2 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(118,plain,
! [SV17: $i,SV3: $i] :
( ( ~ ( greater @ SV3 @ SV17 )
| ~ ( less @ SV3 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(119,plain,
! [SV4: $i,SV18: $i] :
( ( ~ ( ~ ( ~ ( greater @ SV18 @ SV4 )
| ~ ! [SY59: $i] :
( SV18
!= ( vplus @ SV4 @ SY59 ) ) )
| ~ ( ~ ~ ! [SY60: $i] :
( SV18
!= ( vplus @ SV4 @ SY60 ) )
| ( greater @ SV18 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(120,plain,
! [SV19: $i,SV5: $i] :
( ( ~ ( less @ SV5 @ SV19 )
| ( greater @ SV19 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(121,plain,
! [SV6: $i,SV20: $i] :
( ( ! [SY61: $i] :
( ~ ( greater @ SV20 @ SY61 )
| ( greater @ ( vmul @ SV20 @ SV6 ) @ ( vmul @ SY61 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(122,plain,
! [SV21: $i,SV7: $i] :
( ( ~ ( greater @ SV7 @ SV21 )
| ( less @ SV21 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(123,plain,
! [SV22: $i,SV8: $i] :
( ( ( SV8 != SV22 )
| ~ ( greater @ SV8 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(124,plain,
! [SV23: $i,SV9: $i] :
( ( ~ ( greater @ SV9 @ SV23 )
| ( geq @ SV9 @ ( vplus @ SV23 @ v1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(125,plain,
! [SV24: $i,SV10: $i] :
( ( ! [SY62: $i,SY63: $i] :
( ~ ( ~ ( ~ ( greater @ SY62 @ SY63 )
| ~ ( geq @ SV10 @ SV24 ) )
| ~ ( ~ ( geq @ SY62 @ SY63 )
| ~ ( greater @ SV10 @ SV24 ) ) )
| ( greater @ ( vplus @ SV10 @ SY62 ) @ ( vplus @ SV24 @ SY63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(126,plain,
! [SV25: $i,SV11: $i] :
( ( ! [SY64: $i,SY65: $i] :
( ~ ~ ( ~ ( greater @ SY64 @ SY65 )
| ~ ( greater @ SV11 @ SV25 ) )
| ( greater @ ( vplus @ SV11 @ SY64 ) @ ( vplus @ SV25 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(127,plain,
! [SV26: $i,SV12: $i] :
( ( ! [SY66: $i] :
( ~ ( greater @ ( vplus @ SV12 @ SY66 ) @ ( vplus @ SV26 @ SY66 ) )
| ( greater @ SV12 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(128,plain,
! [SV13: $i,SV27: $i] :
( ( ~ ( ~ ( ~ ( geq @ SV27 @ SV13 )
| ( greater @ SV27 @ SV13 )
| ( SV27 = SV13 ) )
| ~ ( ~ ( ( greater @ SV27 @ SV13 )
| ( SV27 = SV13 ) )
| ( geq @ SV27 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(129,plain,
! [SV28: $i,SV14: $i] :
( ( ! [SY67: $i] :
( ~ ( greater @ SV14 @ SV28 )
| ( greater @ ( vplus @ SV14 @ SY67 ) @ ( vplus @ SV28 @ SY67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(130,plain,
! [SV16: $i,SV2: $i] :
( ( ( ( SV2 = SV16 )
| ( greater @ SV2 @ SV16 ) )
= $true )
| ( ( less @ SV2 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(131,plain,
! [SV17: $i,SV3: $i] :
( ( ( ~ ( greater @ SV3 @ SV17 ) )
= $true )
| ( ( ~ ( less @ SV3 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(132,plain,
! [SV4: $i,SV18: $i] :
( ( ~ ( ~ ( greater @ SV18 @ SV4 )
| ~ ! [SY59: $i] :
( SV18
!= ( vplus @ SV4 @ SY59 ) ) )
| ~ ( ~ ~ ! [SY60: $i] :
( SV18
!= ( vplus @ SV4 @ SY60 ) )
| ( greater @ SV18 @ SV4 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(133,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ( less @ SV5 @ SV19 ) )
= $true )
| ( ( greater @ SV19 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(134,plain,
! [SV6: $i,SV29: $i,SV20: $i] :
( ( ~ ( greater @ SV20 @ SV29 )
| ( greater @ ( vmul @ SV20 @ SV6 ) @ ( vmul @ SV29 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(135,plain,
! [SV21: $i,SV7: $i] :
( ( ( ~ ( greater @ SV7 @ SV21 ) )
= $true )
| ( ( less @ SV21 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(136,plain,
! [SV22: $i,SV8: $i] :
( ( ( SV8 != SV22 )
= $true )
| ( ( ~ ( greater @ SV8 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(137,plain,
! [SV23: $i,SV9: $i] :
( ( ( ~ ( greater @ SV9 @ SV23 ) )
= $true )
| ( ( geq @ SV9 @ ( vplus @ SV23 @ v1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(138,plain,
! [SV24: $i,SV10: $i,SV30: $i] :
( ( ! [SY68: $i] :
( ~ ( ~ ( ~ ( greater @ SV30 @ SY68 )
| ~ ( geq @ SV10 @ SV24 ) )
| ~ ( ~ ( geq @ SV30 @ SY68 )
| ~ ( greater @ SV10 @ SV24 ) ) )
| ( greater @ ( vplus @ SV10 @ SV30 ) @ ( vplus @ SV24 @ SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(139,plain,
! [SV25: $i,SV11: $i,SV31: $i] :
( ( ! [SY69: $i] :
( ~ ~ ( ~ ( greater @ SV31 @ SY69 )
| ~ ( greater @ SV11 @ SV25 ) )
| ( greater @ ( vplus @ SV11 @ SV31 ) @ ( vplus @ SV25 @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(140,plain,
! [SV26: $i,SV32: $i,SV12: $i] :
( ( ~ ( greater @ ( vplus @ SV12 @ SV32 ) @ ( vplus @ SV26 @ SV32 ) )
| ( greater @ SV12 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(141,plain,
! [SV13: $i,SV27: $i] :
( ( ~ ( ~ ( geq @ SV27 @ SV13 )
| ( greater @ SV27 @ SV13 )
| ( SV27 = SV13 ) )
| ~ ( ~ ( ( greater @ SV27 @ SV13 )
| ( SV27 = SV13 ) )
| ( geq @ SV27 @ SV13 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(142,plain,
! [SV33: $i,SV28: $i,SV14: $i] :
( ( ~ ( greater @ SV14 @ SV28 )
| ( greater @ ( vplus @ SV14 @ SV33 ) @ ( vplus @ SV28 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(143,plain,
! [SV16: $i,SV2: $i] :
( ( ( SV2 = SV16 )
= $true )
| ( ( greater @ SV2 @ SV16 )
= $true )
| ( ( less @ SV2 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(144,plain,
! [SV17: $i,SV3: $i] :
( ( ( greater @ SV3 @ SV17 )
= $false )
| ( ( ~ ( less @ SV3 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(145,plain,
! [SV4: $i,SV18: $i] :
( ( ~ ( ~ ( greater @ SV18 @ SV4 )
| ~ ! [SY59: $i] :
( SV18
!= ( vplus @ SV4 @ SY59 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(146,plain,
! [SV4: $i,SV18: $i] :
( ( ~ ( ~ ~ ! [SY60: $i] :
( SV18
!= ( vplus @ SV4 @ SY60 ) )
| ( greater @ SV18 @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(147,plain,
! [SV19: $i,SV5: $i] :
( ( ( less @ SV5 @ SV19 )
= $false )
| ( ( greater @ SV19 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(148,plain,
! [SV6: $i,SV29: $i,SV20: $i] :
( ( ( ~ ( greater @ SV20 @ SV29 ) )
= $true )
| ( ( greater @ ( vmul @ SV20 @ SV6 ) @ ( vmul @ SV29 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(149,plain,
! [SV21: $i,SV7: $i] :
( ( ( greater @ SV7 @ SV21 )
= $false )
| ( ( less @ SV21 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(150,plain,
! [SV22: $i,SV8: $i] :
( ( ( SV8 = SV22 )
= $false )
| ( ( ~ ( greater @ SV8 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(151,plain,
! [SV23: $i,SV9: $i] :
( ( ( greater @ SV9 @ SV23 )
= $false )
| ( ( geq @ SV9 @ ( vplus @ SV23 @ v1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(152,plain,
! [SV24: $i,SV10: $i,SV34: $i,SV30: $i] :
( ( ~ ( ~ ( ~ ( greater @ SV30 @ SV34 )
| ~ ( geq @ SV10 @ SV24 ) )
| ~ ( ~ ( geq @ SV30 @ SV34 )
| ~ ( greater @ SV10 @ SV24 ) ) )
| ( greater @ ( vplus @ SV10 @ SV30 ) @ ( vplus @ SV24 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(153,plain,
! [SV25: $i,SV11: $i,SV35: $i,SV31: $i] :
( ( ~ ~ ( ~ ( greater @ SV31 @ SV35 )
| ~ ( greater @ SV11 @ SV25 ) )
| ( greater @ ( vplus @ SV11 @ SV31 ) @ ( vplus @ SV25 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(154,plain,
! [SV26: $i,SV32: $i,SV12: $i] :
( ( ( ~ ( greater @ ( vplus @ SV12 @ SV32 ) @ ( vplus @ SV26 @ SV32 ) ) )
= $true )
| ( ( greater @ SV12 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(155,plain,
! [SV13: $i,SV27: $i] :
( ( ~ ( ~ ( geq @ SV27 @ SV13 )
| ( greater @ SV27 @ SV13 )
| ( SV27 = SV13 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(156,plain,
! [SV13: $i,SV27: $i] :
( ( ~ ( ~ ( ( greater @ SV27 @ SV13 )
| ( SV27 = SV13 ) )
| ( geq @ SV27 @ SV13 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(157,plain,
! [SV33: $i,SV28: $i,SV14: $i] :
( ( ( ~ ( greater @ SV14 @ SV28 ) )
= $true )
| ( ( greater @ ( vplus @ SV14 @ SV33 ) @ ( vplus @ SV28 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(158,plain,
! [SV17: $i,SV3: $i] :
( ( ( less @ SV3 @ SV17 )
= $false )
| ( ( greater @ SV3 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(159,plain,
! [SV4: $i,SV18: $i] :
( ( ~ ( greater @ SV18 @ SV4 )
| ~ ! [SY59: $i] :
( SV18
!= ( vplus @ SV4 @ SY59 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(160,plain,
! [SV4: $i,SV18: $i] :
( ( ~ ~ ! [SY60: $i] :
( SV18
!= ( vplus @ SV4 @ SY60 ) )
| ( greater @ SV18 @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(161,plain,
! [SV6: $i,SV29: $i,SV20: $i] :
( ( ( greater @ SV20 @ SV29 )
= $false )
| ( ( greater @ ( vmul @ SV20 @ SV6 ) @ ( vmul @ SV29 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(162,plain,
! [SV22: $i,SV8: $i] :
( ( ( greater @ SV8 @ SV22 )
= $false )
| ( ( SV8 = SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(163,plain,
! [SV24: $i,SV10: $i,SV34: $i,SV30: $i] :
( ( ( ~ ( ~ ( ~ ( greater @ SV30 @ SV34 )
| ~ ( geq @ SV10 @ SV24 ) )
| ~ ( ~ ( geq @ SV30 @ SV34 )
| ~ ( greater @ SV10 @ SV24 ) ) ) )
= $true )
| ( ( greater @ ( vplus @ SV10 @ SV30 ) @ ( vplus @ SV24 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(164,plain,
! [SV25: $i,SV11: $i,SV35: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( greater @ SV31 @ SV35 )
| ~ ( greater @ SV11 @ SV25 ) ) )
= $true )
| ( ( greater @ ( vplus @ SV11 @ SV31 ) @ ( vplus @ SV25 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(165,plain,
! [SV26: $i,SV32: $i,SV12: $i] :
( ( ( greater @ ( vplus @ SV12 @ SV32 ) @ ( vplus @ SV26 @ SV32 ) )
= $false )
| ( ( greater @ SV12 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(166,plain,
! [SV13: $i,SV27: $i] :
( ( ~ ( geq @ SV27 @ SV13 )
| ( greater @ SV27 @ SV13 )
| ( SV27 = SV13 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(167,plain,
! [SV13: $i,SV27: $i] :
( ( ~ ( ( greater @ SV27 @ SV13 )
| ( SV27 = SV13 ) )
| ( geq @ SV27 @ SV13 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(168,plain,
! [SV33: $i,SV28: $i,SV14: $i] :
( ( ( greater @ SV14 @ SV28 )
= $false )
| ( ( greater @ ( vplus @ SV14 @ SV33 ) @ ( vplus @ SV28 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(169,plain,
! [SV4: $i,SV18: $i] :
( ( ( ~ ( greater @ SV18 @ SV4 ) )
= $true )
| ( ( ~ ! [SY59: $i] :
( SV18
!= ( vplus @ SV4 @ SY59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(170,plain,
! [SV4: $i,SV18: $i] :
( ( ( ~ ~ ! [SY60: $i] :
( SV18
!= ( vplus @ SV4 @ SY60 ) ) )
= $true )
| ( ( greater @ SV18 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(171,plain,
! [SV24: $i,SV10: $i,SV34: $i,SV30: $i] :
( ( ( ~ ( ~ ( greater @ SV30 @ SV34 )
| ~ ( geq @ SV10 @ SV24 ) )
| ~ ( ~ ( geq @ SV30 @ SV34 )
| ~ ( greater @ SV10 @ SV24 ) ) )
= $false )
| ( ( greater @ ( vplus @ SV10 @ SV30 ) @ ( vplus @ SV24 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(172,plain,
! [SV25: $i,SV11: $i,SV35: $i,SV31: $i] :
( ( ( ~ ( ~ ( greater @ SV31 @ SV35 )
| ~ ( greater @ SV11 @ SV25 ) ) )
= $false )
| ( ( greater @ ( vplus @ SV11 @ SV31 ) @ ( vplus @ SV25 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(173,plain,
! [SV13: $i,SV27: $i] :
( ( ( ~ ( geq @ SV27 @ SV13 ) )
= $true )
| ( ( ( greater @ SV27 @ SV13 )
| ( SV27 = SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(174,plain,
! [SV13: $i,SV27: $i] :
( ( ( ~ ( ( greater @ SV27 @ SV13 )
| ( SV27 = SV13 ) ) )
= $true )
| ( ( geq @ SV27 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(175,plain,
! [SV4: $i,SV18: $i] :
( ( ( greater @ SV18 @ SV4 )
= $false )
| ( ( ~ ! [SY59: $i] :
( SV18
!= ( vplus @ SV4 @ SY59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(176,plain,
! [SV4: $i,SV18: $i] :
( ( ( ~ ! [SY60: $i] :
( SV18
!= ( vplus @ SV4 @ SY60 ) ) )
= $false )
| ( ( greater @ SV18 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(177,plain,
! [SV24: $i,SV10: $i,SV34: $i,SV30: $i] :
( ( ( ~ ( ~ ( greater @ SV30 @ SV34 )
| ~ ( geq @ SV10 @ SV24 ) ) )
= $false )
| ( ( greater @ ( vplus @ SV10 @ SV30 ) @ ( vplus @ SV24 @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(178,plain,
! [SV24: $i,SV10: $i,SV34: $i,SV30: $i] :
( ( ( ~ ( ~ ( geq @ SV30 @ SV34 )
| ~ ( greater @ SV10 @ SV24 ) ) )
= $false )
| ( ( greater @ ( vplus @ SV10 @ SV30 ) @ ( vplus @ SV24 @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(179,plain,
! [SV25: $i,SV11: $i,SV35: $i,SV31: $i] :
( ( ( ~ ( greater @ SV31 @ SV35 )
| ~ ( greater @ SV11 @ SV25 ) )
= $true )
| ( ( greater @ ( vplus @ SV11 @ SV31 ) @ ( vplus @ SV25 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(180,plain,
! [SV13: $i,SV27: $i] :
( ( ( geq @ SV27 @ SV13 )
= $false )
| ( ( ( greater @ SV27 @ SV13 )
| ( SV27 = SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(181,plain,
! [SV13: $i,SV27: $i] :
( ( ( ( greater @ SV27 @ SV13 )
| ( SV27 = SV13 ) )
= $false )
| ( ( geq @ SV27 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(182,plain,
! [SV4: $i,SV18: $i] :
( ( ( ! [SY59: $i] :
( SV18
!= ( vplus @ SV4 @ SY59 ) ) )
= $false )
| ( ( greater @ SV18 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(183,plain,
! [SV4: $i,SV18: $i] :
( ( ( ! [SY60: $i] :
( SV18
!= ( vplus @ SV4 @ SY60 ) ) )
= $true )
| ( ( greater @ SV18 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(184,plain,
! [SV24: $i,SV10: $i,SV34: $i,SV30: $i] :
( ( ( ~ ( greater @ SV30 @ SV34 )
| ~ ( geq @ SV10 @ SV24 ) )
= $true )
| ( ( greater @ ( vplus @ SV10 @ SV30 ) @ ( vplus @ SV24 @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(185,plain,
! [SV24: $i,SV10: $i,SV34: $i,SV30: $i] :
( ( ( ~ ( geq @ SV30 @ SV34 )
| ~ ( greater @ SV10 @ SV24 ) )
= $true )
| ( ( greater @ ( vplus @ SV10 @ SV30 ) @ ( vplus @ SV24 @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(186,plain,
! [SV25: $i,SV11: $i,SV35: $i,SV31: $i] :
( ( ( ~ ( greater @ SV31 @ SV35 ) )
= $true )
| ( ( ~ ( greater @ SV11 @ SV25 ) )
= $true )
| ( ( greater @ ( vplus @ SV11 @ SV31 ) @ ( vplus @ SV25 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(187,plain,
! [SV13: $i,SV27: $i] :
( ( ( greater @ SV27 @ SV13 )
= $true )
| ( ( SV27 = SV13 )
= $true )
| ( ( geq @ SV27 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(188,plain,
! [SV13: $i,SV27: $i] :
( ( ( greater @ SV27 @ SV13 )
= $false )
| ( ( geq @ SV27 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(189,plain,
! [SV13: $i,SV27: $i] :
( ( ( SV27 = SV13 )
= $false )
| ( ( geq @ SV27 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(190,plain,
! [SV4: $i,SV18: $i] :
( ( ( SV18
!= ( vplus @ SV4 @ ( sK1_SY59 @ SV4 @ SV18 ) ) )
= $false )
| ( ( greater @ SV18 @ SV4 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[182]) ).
thf(191,plain,
! [SV36: $i,SV4: $i,SV18: $i] :
( ( ( SV18
!= ( vplus @ SV4 @ SV36 ) )
= $true )
| ( ( greater @ SV18 @ SV4 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(192,plain,
! [SV24: $i,SV10: $i,SV34: $i,SV30: $i] :
( ( ( ~ ( greater @ SV30 @ SV34 ) )
= $true )
| ( ( ~ ( geq @ SV10 @ SV24 ) )
= $true )
| ( ( greater @ ( vplus @ SV10 @ SV30 ) @ ( vplus @ SV24 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(193,plain,
! [SV24: $i,SV10: $i,SV34: $i,SV30: $i] :
( ( ( ~ ( geq @ SV30 @ SV34 ) )
= $true )
| ( ( ~ ( greater @ SV10 @ SV24 ) )
= $true )
| ( ( greater @ ( vplus @ SV10 @ SV30 ) @ ( vplus @ SV24 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(194,plain,
! [SV25: $i,SV11: $i,SV35: $i,SV31: $i] :
( ( ( greater @ SV31 @ SV35 )
= $false )
| ( ( ~ ( greater @ SV11 @ SV25 ) )
= $true )
| ( ( greater @ ( vplus @ SV11 @ SV31 ) @ ( vplus @ SV25 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(195,plain,
! [SV4: $i,SV18: $i] :
( ( ( SV18
= ( vplus @ SV4 @ ( sK1_SY59 @ SV4 @ SV18 ) ) )
= $true )
| ( ( greater @ SV18 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(196,plain,
! [SV36: $i,SV4: $i,SV18: $i] :
( ( ( SV18
= ( vplus @ SV4 @ SV36 ) )
= $false )
| ( ( greater @ SV18 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(197,plain,
! [SV24: $i,SV10: $i,SV34: $i,SV30: $i] :
( ( ( greater @ SV30 @ SV34 )
= $false )
| ( ( ~ ( geq @ SV10 @ SV24 ) )
= $true )
| ( ( greater @ ( vplus @ SV10 @ SV30 ) @ ( vplus @ SV24 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(198,plain,
! [SV24: $i,SV10: $i,SV34: $i,SV30: $i] :
( ( ( geq @ SV30 @ SV34 )
= $false )
| ( ( ~ ( greater @ SV10 @ SV24 ) )
= $true )
| ( ( greater @ ( vplus @ SV10 @ SV30 ) @ ( vplus @ SV24 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(199,plain,
! [SV35: $i,SV31: $i,SV25: $i,SV11: $i] :
( ( ( greater @ SV11 @ SV25 )
= $false )
| ( ( greater @ SV31 @ SV35 )
= $false )
| ( ( greater @ ( vplus @ SV11 @ SV31 ) @ ( vplus @ SV25 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(200,plain,
! [SV34: $i,SV30: $i,SV24: $i,SV10: $i] :
( ( ( geq @ SV10 @ SV24 )
= $false )
| ( ( greater @ SV30 @ SV34 )
= $false )
| ( ( greater @ ( vplus @ SV10 @ SV30 ) @ ( vplus @ SV24 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(201,plain,
! [SV34: $i,SV30: $i,SV24: $i,SV10: $i] :
( ( ( greater @ SV10 @ SV24 )
= $false )
| ( ( geq @ SV30 @ SV34 )
= $false )
| ( ( greater @ ( vplus @ SV10 @ SV30 ) @ ( vplus @ SV24 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(202,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[74,201,200,199,196,195,189,188,187,168,165,162,161,158,151,149,147,143,116,104]) ).
thf(203,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[202]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM853+1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n013.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 13:41:51 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.54/0.27
% 0.54/0.27 No.of.Axioms: 15
% 0.54/0.27
% 0.54/0.27 Length.of.Defs: 0
% 0.54/0.27
% 0.54/0.27 Contains.Choice.Funs: false
% 0.54/0.27 .....
% 0.54/0.27
% 0.54/0.27 ********************************
% 0.54/0.27 * All subproblems solved! *
% 0.54/0.27 ********************************
% 0.54/0.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:15,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:202,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.54/0.27
% 0.54/0.27 %**** Beginning of derivation protocol ****
% 0.54/0.27 % SZS output start CNFRefutation
% See solution above
% 0.54/0.27
% 0.54/0.27 %**** End of derivation protocol ****
% 0.54/0.27 %**** no. of clauses in derivation: 164 ****
% 0.54/0.27 %**** clause counter: 202 ****
% 0.54/0.27
% 0.54/0.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:15,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:202,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------