%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM839+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 10:35:21 AM UTC 2026
% Result : Theorem 0.11s 0.24s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 104 ( 65 unt; 0 typ; 0 def)
% Number of atoms : 485 ( 187 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 718 ( 133 ~; 116 |; 0 &; 454 @)
% ( 6 <=>; 9 =>; 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 : 15 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 218 ( 0 ^; 215 !; 3 ?; 218 :)
% 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_SY32,type,
sK1_SY32: $i > $i > $i ).
thf(tp_v1,type,
v1: $i ).
thf(tp_vd328,type,
vd328: $i ).
thf(tp_vd329,type,
vd329: $i ).
thf(tp_vd330,type,
vd330: $i ).
thf(tp_vplus,type,
vplus: $i > $i > $i ).
thf(tp_vskolem2,type,
vskolem2: $i > $i ).
thf(tp_vsucc,type,
vsucc: $i > $i ).
thf(15,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(17,axiom,
! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
thf(18,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(20,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(21,axiom,
! [Vd208: $i,Vd209: $i] :
( ( greater @ Vd208 @ Vd209 )
=> ( less @ Vd209 @ Vd208 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
thf(22,axiom,
! [Vd226: $i,Vd227: $i] :
( ( less @ Vd226 @ Vd227 )
=> ( greater @ Vd227 @ Vd226 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
thf(23,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(30,axiom,
! [Vd295: $i,Vd296: $i] : ( greater @ ( vplus @ Vd295 @ Vd296 ) @ Vd295 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
thf(31,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(34,axiom,
greater @ ( vplus @ vd328 @ vd330 ) @ ( vplus @ vd329 @ vd330 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(antec(204), 331, 0)') ).
thf(35,conjecture,
greater @ vd328 @ vd329,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq(204), 332, 0)') ).
thf(36,negated_conjecture,
( ( greater @ vd328 @ vd329 )
= $false ),
inference(negate_conjecture,[status(cth)],[35]) ).
thf(37,plain,
( ( greater @ vd328 @ vd329 )
= $false ),
inference(unfold_def,[status(thm)],[36]) ).
thf(38,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(39,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(40,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ~ ( greater @ Vd203 @ Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(41,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 )
| ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(42,plain,
( ( ! [Vd208: $i,Vd209: $i] :
( ( greater @ Vd208 @ Vd209 )
=> ( less @ Vd209 @ Vd208 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(43,plain,
( ( ! [Vd226: $i,Vd227: $i] :
( ( less @ Vd226 @ Vd227 )
=> ( greater @ Vd227 @ Vd226 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(44,plain,
( ( ! [Vd244: $i,Vd245: $i] :
( ( geq @ Vd245 @ Vd244 )
<=> ( ( greater @ Vd245 @ Vd244 )
| ( Vd245 = Vd244 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(45,plain,
( ( ! [Vd295: $i,Vd296: $i] : ( greater @ ( vplus @ Vd295 @ Vd296 ) @ Vd295 ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(46,plain,
( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( greater @ Vd301 @ Vd302 )
=> ( greater @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(47,plain,
( ( greater @ ( vplus @ vd328 @ vd330 ) @ ( vplus @ vd329 @ vd330 ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(48,plain,
( ( ~ ( greater @ vd328 @ vd329 ) )
= $true ),
inference(polarity_switch,[status(thm)],[37]) ).
thf(49,plain,
( ( greater @ ( vplus @ vd328 @ vd330 ) @ ( vplus @ vd329 @ vd330 ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(50,plain,
( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
( ( greater @ Vd301 @ Vd302 )
=> ( greater @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(51,plain,
( ( ! [Vd295: $i,Vd296: $i] : ( greater @ ( vplus @ Vd295 @ Vd296 ) @ Vd295 ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(52,plain,
( ( ! [Vd244: $i,Vd245: $i] :
( ( geq @ Vd245 @ Vd244 )
<=> ( ( greater @ Vd245 @ Vd244 )
| ( Vd245 = Vd244 ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(53,plain,
( ( ! [Vd226: $i,Vd227: $i] :
( ( less @ Vd226 @ Vd227 )
=> ( greater @ Vd227 @ Vd226 ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(54,plain,
( ( ! [Vd208: $i,Vd209: $i] :
( ( greater @ Vd208 @ Vd209 )
=> ( less @ Vd209 @ Vd208 ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(55,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 )
| ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(56,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ~ ( greater @ Vd203 @ Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(57,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(58,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(59,plain,
( ( ~ ( greater @ vd328 @ vd329 ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(60,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( greater @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(61,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX0 @ SX1 )
| ( greater @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(62,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX0 @ SX1 )
| ( less @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(63,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)],[58]) ).
thf(64,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)],[52]) ).
thf(65,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( greater @ SX0 @ SX1 )
| ( greater @ ( vplus @ SX0 @ SX2 ) @ ( vplus @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(66,plain,
! [SV1: $i] :
( ( ! [SY20: $i] : ( greater @ ( vplus @ SV1 @ SY20 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(67,plain,
! [SV2: $i] :
( ( ! [SY21: $i] :
( ( SV2 = SY21 )
| ( greater @ SV2 @ SY21 )
| ( less @ SV2 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(68,plain,
! [SV3: $i] :
( ( ! [SY22: $i] :
( ~ ( greater @ SV3 @ SY22 )
| ~ ( less @ SV3 @ SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(69,plain,
( ( greater @ vd328 @ vd329 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(70,plain,
! [SV4: $i] :
( ( ! [SY23: $i] :
( ( SV4 != SY23 )
| ~ ( greater @ SV4 @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(71,plain,
! [SV5: $i] :
( ( ! [SY24: $i] :
( ~ ( less @ SV5 @ SY24 )
| ( greater @ SY24 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(72,plain,
! [SV6: $i] :
( ( ! [SY25: $i] :
( ~ ( greater @ SV6 @ SY25 )
| ( less @ SY25 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(73,plain,
! [SV7: $i] :
( ( ! [SY26: $i] :
~ ( ~ ( ~ ( greater @ SY26 @ SV7 )
| ~ ! [SY27: $i] :
( SY26
!= ( vplus @ SV7 @ SY27 ) ) )
| ~ ( ~ ~ ! [SY28: $i] :
( SY26
!= ( vplus @ SV7 @ SY28 ) )
| ( greater @ SY26 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(74,plain,
! [SV8: $i] :
( ( ! [SY29: $i] :
~ ( ~ ( ~ ( geq @ SY29 @ SV8 )
| ( greater @ SY29 @ SV8 )
| ( SY29 = SV8 ) )
| ~ ( ~ ( ( greater @ SY29 @ SV8 )
| ( SY29 = SV8 ) )
| ( geq @ SY29 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(75,plain,
! [SV9: $i] :
( ( ! [SY30: $i,SY31: $i] :
( ~ ( greater @ SV9 @ SY30 )
| ( greater @ ( vplus @ SV9 @ SY31 ) @ ( vplus @ SY30 @ SY31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(76,plain,
! [SV10: $i,SV1: $i] :
( ( greater @ ( vplus @ SV1 @ SV10 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(77,plain,
! [SV11: $i,SV2: $i] :
( ( ( SV2 = SV11 )
| ( greater @ SV2 @ SV11 )
| ( less @ SV2 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(78,plain,
! [SV12: $i,SV3: $i] :
( ( ~ ( greater @ SV3 @ SV12 )
| ~ ( less @ SV3 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(79,plain,
! [SV13: $i,SV4: $i] :
( ( ( SV4 != SV13 )
| ~ ( greater @ SV4 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(80,plain,
! [SV14: $i,SV5: $i] :
( ( ~ ( less @ SV5 @ SV14 )
| ( greater @ SV14 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(81,plain,
! [SV15: $i,SV6: $i] :
( ( ~ ( greater @ SV6 @ SV15 )
| ( less @ SV15 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(82,plain,
! [SV7: $i,SV16: $i] :
( ( ~ ( ~ ( ~ ( greater @ SV16 @ SV7 )
| ~ ! [SY32: $i] :
( SV16
!= ( vplus @ SV7 @ SY32 ) ) )
| ~ ( ~ ~ ! [SY33: $i] :
( SV16
!= ( vplus @ SV7 @ SY33 ) )
| ( greater @ SV16 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(83,plain,
! [SV8: $i,SV17: $i] :
( ( ~ ( ~ ( ~ ( geq @ SV17 @ SV8 )
| ( greater @ SV17 @ SV8 )
| ( SV17 = SV8 ) )
| ~ ( ~ ( ( greater @ SV17 @ SV8 )
| ( SV17 = SV8 ) )
| ( geq @ SV17 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(84,plain,
! [SV18: $i,SV9: $i] :
( ( ! [SY34: $i] :
( ~ ( greater @ SV9 @ SV18 )
| ( greater @ ( vplus @ SV9 @ SY34 ) @ ( vplus @ SV18 @ SY34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(85,plain,
! [SV11: $i,SV2: $i] :
( ( ( ( SV2 = SV11 )
| ( greater @ SV2 @ SV11 ) )
= $true )
| ( ( less @ SV2 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(86,plain,
! [SV12: $i,SV3: $i] :
( ( ( ~ ( greater @ SV3 @ SV12 ) )
= $true )
| ( ( ~ ( less @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(87,plain,
! [SV13: $i,SV4: $i] :
( ( ( SV4 != SV13 )
= $true )
| ( ( ~ ( greater @ SV4 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(88,plain,
! [SV14: $i,SV5: $i] :
( ( ( ~ ( less @ SV5 @ SV14 ) )
= $true )
| ( ( greater @ SV14 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(89,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ( greater @ SV6 @ SV15 ) )
= $true )
| ( ( less @ SV15 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(90,plain,
! [SV7: $i,SV16: $i] :
( ( ~ ( ~ ( greater @ SV16 @ SV7 )
| ~ ! [SY32: $i] :
( SV16
!= ( vplus @ SV7 @ SY32 ) ) )
| ~ ( ~ ~ ! [SY33: $i] :
( SV16
!= ( vplus @ SV7 @ SY33 ) )
| ( greater @ SV16 @ SV7 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(91,plain,
! [SV8: $i,SV17: $i] :
( ( ~ ( ~ ( geq @ SV17 @ SV8 )
| ( greater @ SV17 @ SV8 )
| ( SV17 = SV8 ) )
| ~ ( ~ ( ( greater @ SV17 @ SV8 )
| ( SV17 = SV8 ) )
| ( geq @ SV17 @ SV8 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(92,plain,
! [SV19: $i,SV18: $i,SV9: $i] :
( ( ~ ( greater @ SV9 @ SV18 )
| ( greater @ ( vplus @ SV9 @ SV19 ) @ ( vplus @ SV18 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(93,plain,
! [SV11: $i,SV2: $i] :
( ( ( SV2 = SV11 )
= $true )
| ( ( greater @ SV2 @ SV11 )
= $true )
| ( ( less @ SV2 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(94,plain,
! [SV12: $i,SV3: $i] :
( ( ( greater @ SV3 @ SV12 )
= $false )
| ( ( ~ ( less @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(95,plain,
! [SV13: $i,SV4: $i] :
( ( ( SV4 = SV13 )
= $false )
| ( ( ~ ( greater @ SV4 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(96,plain,
! [SV14: $i,SV5: $i] :
( ( ( less @ SV5 @ SV14 )
= $false )
| ( ( greater @ SV14 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(97,plain,
! [SV15: $i,SV6: $i] :
( ( ( greater @ SV6 @ SV15 )
= $false )
| ( ( less @ SV15 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(98,plain,
! [SV7: $i,SV16: $i] :
( ( ~ ( ~ ( greater @ SV16 @ SV7 )
| ~ ! [SY32: $i] :
( SV16
!= ( vplus @ SV7 @ SY32 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(99,plain,
! [SV7: $i,SV16: $i] :
( ( ~ ( ~ ~ ! [SY33: $i] :
( SV16
!= ( vplus @ SV7 @ SY33 ) )
| ( greater @ SV16 @ SV7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(100,plain,
! [SV8: $i,SV17: $i] :
( ( ~ ( ~ ( geq @ SV17 @ SV8 )
| ( greater @ SV17 @ SV8 )
| ( SV17 = SV8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(101,plain,
! [SV8: $i,SV17: $i] :
( ( ~ ( ~ ( ( greater @ SV17 @ SV8 )
| ( SV17 = SV8 ) )
| ( geq @ SV17 @ SV8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(102,plain,
! [SV19: $i,SV18: $i,SV9: $i] :
( ( ( ~ ( greater @ SV9 @ SV18 ) )
= $true )
| ( ( greater @ ( vplus @ SV9 @ SV19 ) @ ( vplus @ SV18 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(103,plain,
! [SV12: $i,SV3: $i] :
( ( ( less @ SV3 @ SV12 )
= $false )
| ( ( greater @ SV3 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(104,plain,
! [SV13: $i,SV4: $i] :
( ( ( greater @ SV4 @ SV13 )
= $false )
| ( ( SV4 = SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(105,plain,
! [SV7: $i,SV16: $i] :
( ( ~ ( greater @ SV16 @ SV7 )
| ~ ! [SY32: $i] :
( SV16
!= ( vplus @ SV7 @ SY32 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(106,plain,
! [SV7: $i,SV16: $i] :
( ( ~ ~ ! [SY33: $i] :
( SV16
!= ( vplus @ SV7 @ SY33 ) )
| ( greater @ SV16 @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(107,plain,
! [SV8: $i,SV17: $i] :
( ( ~ ( geq @ SV17 @ SV8 )
| ( greater @ SV17 @ SV8 )
| ( SV17 = SV8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(108,plain,
! [SV8: $i,SV17: $i] :
( ( ~ ( ( greater @ SV17 @ SV8 )
| ( SV17 = SV8 ) )
| ( geq @ SV17 @ SV8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(109,plain,
! [SV19: $i,SV18: $i,SV9: $i] :
( ( ( greater @ SV9 @ SV18 )
= $false )
| ( ( greater @ ( vplus @ SV9 @ SV19 ) @ ( vplus @ SV18 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(110,plain,
! [SV7: $i,SV16: $i] :
( ( ( ~ ( greater @ SV16 @ SV7 ) )
= $true )
| ( ( ~ ! [SY32: $i] :
( SV16
!= ( vplus @ SV7 @ SY32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(111,plain,
! [SV7: $i,SV16: $i] :
( ( ( ~ ~ ! [SY33: $i] :
( SV16
!= ( vplus @ SV7 @ SY33 ) ) )
= $true )
| ( ( greater @ SV16 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(112,plain,
! [SV8: $i,SV17: $i] :
( ( ( ~ ( geq @ SV17 @ SV8 ) )
= $true )
| ( ( ( greater @ SV17 @ SV8 )
| ( SV17 = SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(113,plain,
! [SV8: $i,SV17: $i] :
( ( ( ~ ( ( greater @ SV17 @ SV8 )
| ( SV17 = SV8 ) ) )
= $true )
| ( ( geq @ SV17 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(114,plain,
! [SV7: $i,SV16: $i] :
( ( ( greater @ SV16 @ SV7 )
= $false )
| ( ( ~ ! [SY32: $i] :
( SV16
!= ( vplus @ SV7 @ SY32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(115,plain,
! [SV7: $i,SV16: $i] :
( ( ( ~ ! [SY33: $i] :
( SV16
!= ( vplus @ SV7 @ SY33 ) ) )
= $false )
| ( ( greater @ SV16 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(116,plain,
! [SV8: $i,SV17: $i] :
( ( ( geq @ SV17 @ SV8 )
= $false )
| ( ( ( greater @ SV17 @ SV8 )
| ( SV17 = SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(117,plain,
! [SV8: $i,SV17: $i] :
( ( ( ( greater @ SV17 @ SV8 )
| ( SV17 = SV8 ) )
= $false )
| ( ( geq @ SV17 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(118,plain,
! [SV7: $i,SV16: $i] :
( ( ( ! [SY32: $i] :
( SV16
!= ( vplus @ SV7 @ SY32 ) ) )
= $false )
| ( ( greater @ SV16 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(119,plain,
! [SV7: $i,SV16: $i] :
( ( ( ! [SY33: $i] :
( SV16
!= ( vplus @ SV7 @ SY33 ) ) )
= $true )
| ( ( greater @ SV16 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(120,plain,
! [SV8: $i,SV17: $i] :
( ( ( greater @ SV17 @ SV8 )
= $true )
| ( ( SV17 = SV8 )
= $true )
| ( ( geq @ SV17 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(121,plain,
! [SV8: $i,SV17: $i] :
( ( ( greater @ SV17 @ SV8 )
= $false )
| ( ( geq @ SV17 @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(122,plain,
! [SV8: $i,SV17: $i] :
( ( ( SV17 = SV8 )
= $false )
| ( ( geq @ SV17 @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(123,plain,
! [SV7: $i,SV16: $i] :
( ( ( SV16
!= ( vplus @ SV7 @ ( sK1_SY32 @ SV7 @ SV16 ) ) )
= $false )
| ( ( greater @ SV16 @ SV7 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[118]) ).
thf(124,plain,
! [SV20: $i,SV7: $i,SV16: $i] :
( ( ( SV16
!= ( vplus @ SV7 @ SV20 ) )
= $true )
| ( ( greater @ SV16 @ SV7 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(125,plain,
! [SV7: $i,SV16: $i] :
( ( ( SV16
= ( vplus @ SV7 @ ( sK1_SY32 @ SV7 @ SV16 ) ) )
= $true )
| ( ( greater @ SV16 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(126,plain,
! [SV20: $i,SV7: $i,SV16: $i] :
( ( ( SV16
= ( vplus @ SV7 @ SV20 ) )
= $false )
| ( ( greater @ SV16 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(127,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[49,126,125,122,121,120,109,104,103,97,96,93,76,69]) ).
thf(128,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM839+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.17 % Computer : n014.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Oct 6 13:40:11 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.24
% 0.11/0.24 No.of.Axioms: 10
% 0.11/0.24
% 0.11/0.24 Length.of.Defs: 0
% 0.11/0.24
% 0.11/0.24 Contains.Choice.Funs: false
% 0.11/0.24 ..
% 0.11/0.24
% 0.11/0.24 ********************************
% 0.11/0.24 * All subproblems solved! *
% 0.11/0.24 ********************************
% 0.11/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:10,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:127,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.24
% 0.11/0.24 %**** Beginning of derivation protocol ****
% 0.11/0.24 % SZS output start CNFRefutation
% See solution above
% 0.11/0.24
% 0.11/0.24 %**** End of derivation protocol ****
% 0.11/0.24 %**** no. of clauses in derivation: 104 ****
% 0.11/0.24 %**** clause counter: 127 ****
% 0.11/0.24
% 0.11/0.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:10,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:127,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------