%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM852+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 : n015.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 0.10s 0.27s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 100 ( 69 unt; 0 typ; 0 def)
% Number of atoms : 406 ( 185 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 643 ( 105 ~; 72 |; 0 &; 454 @)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 207 ( 0 ^; 204 !; 3 ?; 207 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_greater,type,
greater: $i > $i > $o ).
thf(tp_less,type,
less: $i > $i > $o ).
thf(tp_sK1_SY39,type,
sK1_SY39: $i > $i > $i ).
thf(tp_vd469,type,
vd469: $i ).
thf(tp_vd480,type,
vd480: $i ).
thf(tp_vd481,type,
vd481: $i ).
thf(tp_vmul,type,
vmul: $i > $i > $i ).
thf(tp_vplus,type,
vplus: $i > $i > $i ).
thf(tp_vskolem9,type,
vskolem9: $i > $i > $i ).
thf(tp_vsucc,type,
vsucc: $i > $i ).
thf(1,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(3,axiom,
! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
thf(4,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(6,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(7,axiom,
! [Vd208: $i,Vd209: $i] :
( ( greater @ Vd208 @ Vd209 )
=> ( less @ Vd209 @ Vd208 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
thf(8,axiom,
! [Vd226: $i,Vd227: $i] :
( ( less @ Vd226 @ Vd227 )
=> ( greater @ Vd227 @ Vd226 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
thf(10,axiom,
! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
thf(11,axiom,
! [Vd432: $i,Vd433: $i,Vd434: $i] :
( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
= ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
thf(12,axiom,
! [Vd444: $i,Vd445: $i,Vd446: $i] :
( ( vmul @ ( vmul @ Vd444 @ Vd445 ) @ Vd446 )
= ( vmul @ Vd444 @ ( vmul @ Vd445 @ Vd446 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(290, 0), 0)') ).
thf(17,axiom,
! [Vd476: $i,Vd477: $i] :
( ( Vd476 = Vd477 )
=> ( ( vmul @ Vd476 @ vd469 )
= ( vmul @ Vd477 @ vd469 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(303, 0), 0)') ).
thf(18,axiom,
less @ vd480 @ vd481,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(antec(304), 482, 0)') ).
thf(19,axiom,
greater @ vd481 @ vd480,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq(304)), 483, 0)') ).
thf(20,conjecture,
greater @ ( vmul @ vd481 @ vd469 ) @ ( vmul @ vd480 @ vd469 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)') ).
thf(21,negated_conjecture,
( ( greater @ ( vmul @ vd481 @ vd469 ) @ ( vmul @ vd480 @ vd469 ) )
= $false ),
inference(negate_conjecture,[status(cth)],[20]) ).
thf(22,plain,
( ( greater @ ( vmul @ vd481 @ vd469 ) @ ( vmul @ vd480 @ vd469 ) )
= $false ),
inference(unfold_def,[status(thm)],[21]) ).
thf(23,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(24,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(25,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ~ ( greater @ Vd203 @ Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(26,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 )
| ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(27,plain,
( ( ! [Vd208: $i,Vd209: $i] :
( ( greater @ Vd208 @ Vd209 )
=> ( less @ Vd209 @ Vd208 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(28,plain,
( ( ! [Vd226: $i,Vd227: $i] :
( ( less @ Vd226 @ Vd227 )
=> ( greater @ Vd227 @ Vd226 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(29,plain,
( ( ! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(30,plain,
( ( ! [Vd432: $i,Vd433: $i,Vd434: $i] :
( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
= ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(31,plain,
( ( ! [Vd444: $i,Vd445: $i,Vd446: $i] :
( ( vmul @ ( vmul @ Vd444 @ Vd445 ) @ Vd446 )
= ( vmul @ Vd444 @ ( vmul @ Vd445 @ Vd446 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(32,plain,
( ( ! [Vd476: $i,Vd477: $i] :
( ( Vd476 = Vd477 )
=> ( ( vmul @ Vd476 @ vd469 )
= ( vmul @ Vd477 @ vd469 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(33,plain,
( ( less @ vd480 @ vd481 )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(34,plain,
( ( greater @ vd481 @ vd480 )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(35,plain,
( ( ~ ( greater @ ( vmul @ vd481 @ vd469 ) @ ( vmul @ vd480 @ vd469 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(36,plain,
( ( greater @ vd481 @ vd480 )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(37,plain,
( ( less @ vd480 @ vd481 )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(38,plain,
( ( ! [Vd476: $i,Vd477: $i] :
( ( Vd476 = Vd477 )
=> ( ( vmul @ Vd476 @ vd469 )
= ( vmul @ Vd477 @ vd469 ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(39,plain,
( ( ! [Vd444: $i,Vd445: $i,Vd446: $i] :
( ( vmul @ ( vmul @ Vd444 @ Vd445 ) @ Vd446 )
= ( vmul @ Vd444 @ ( vmul @ Vd445 @ Vd446 ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(40,plain,
( ( ! [Vd432: $i,Vd433: $i,Vd434: $i] :
( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
= ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(41,plain,
( ( ! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(42,plain,
( ( ! [Vd226: $i,Vd227: $i] :
( ( less @ Vd226 @ Vd227 )
=> ( greater @ Vd227 @ Vd226 ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(43,plain,
( ( ! [Vd208: $i,Vd209: $i] :
( ( greater @ Vd208 @ Vd209 )
=> ( less @ Vd209 @ Vd208 ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(44,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 = Vd204 )
| ( greater @ Vd203 @ Vd204 )
| ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(45,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ~ ( greater @ Vd203 @ Vd204 )
| ~ ( less @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(46,plain,
( ( ! [Vd203: $i,Vd204: $i] :
( ( Vd203 != Vd204 )
| ~ ( greater @ Vd203 @ Vd204 ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(47,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(48,plain,
( ( ~ ( greater @ ( vmul @ vd481 @ vd469 ) @ ( vmul @ vd480 @ vd469 ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(49,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX0 @ SX1 )
| ( less @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(50,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( greater @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(51,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX0 @ SX1 )
| ( greater @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(52,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)],[47]) ).
thf(53,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( vmul @ SX0 @ vd469 )
= ( vmul @ SX1 @ vd469 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(54,plain,
! [SV1: $i] :
( ( ! [SY23: $i,SY24: $i] :
( ( vmul @ ( vmul @ SV1 @ SY23 ) @ SY24 )
= ( vmul @ SV1 @ ( vmul @ SY23 @ SY24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(55,plain,
! [SV2: $i] :
( ( ! [SY25: $i,SY26: $i] :
( ( vmul @ SV2 @ ( vplus @ SY25 @ SY26 ) )
= ( vplus @ ( vmul @ SV2 @ SY25 ) @ ( vmul @ SV2 @ SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(56,plain,
! [SV3: $i] :
( ( ! [SY27: $i] :
( ( vmul @ SV3 @ SY27 )
= ( vmul @ SY27 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(57,plain,
! [SV4: $i] :
( ( ! [SY28: $i] :
( ( SV4 = SY28 )
| ( greater @ SV4 @ SY28 )
| ( less @ SV4 @ SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(58,plain,
! [SV5: $i] :
( ( ! [SY29: $i] :
( ~ ( greater @ SV5 @ SY29 )
| ~ ( less @ SV5 @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(59,plain,
( ( greater @ ( vmul @ vd481 @ vd469 ) @ ( vmul @ vd480 @ vd469 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(60,plain,
! [SV6: $i] :
( ( ! [SY30: $i] :
( ~ ( greater @ SV6 @ SY30 )
| ( less @ SY30 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(61,plain,
! [SV7: $i] :
( ( ! [SY31: $i] :
( ( SV7 != SY31 )
| ~ ( greater @ SV7 @ SY31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(62,plain,
! [SV8: $i] :
( ( ! [SY32: $i] :
( ~ ( less @ SV8 @ SY32 )
| ( greater @ SY32 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(63,plain,
! [SV9: $i] :
( ( ! [SY33: $i] :
~ ( ~ ( ~ ( greater @ SY33 @ SV9 )
| ~ ! [SY34: $i] :
( SY33
!= ( vplus @ SV9 @ SY34 ) ) )
| ~ ( ~ ~ ! [SY35: $i] :
( SY33
!= ( vplus @ SV9 @ SY35 ) )
| ( greater @ SY33 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(64,plain,
! [SV10: $i] :
( ( ! [SY36: $i] :
( ( SV10 != SY36 )
| ( ( vmul @ SV10 @ vd469 )
= ( vmul @ SY36 @ vd469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(65,plain,
! [SV11: $i,SV1: $i] :
( ( ! [SY37: $i] :
( ( vmul @ ( vmul @ SV1 @ SV11 ) @ SY37 )
= ( vmul @ SV1 @ ( vmul @ SV11 @ SY37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(66,plain,
! [SV12: $i,SV2: $i] :
( ( ! [SY38: $i] :
( ( vmul @ SV2 @ ( vplus @ SV12 @ SY38 ) )
= ( vplus @ ( vmul @ SV2 @ SV12 ) @ ( vmul @ SV2 @ SY38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(67,plain,
! [SV13: $i,SV3: $i] :
( ( ( vmul @ SV3 @ SV13 )
= ( vmul @ SV13 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(68,plain,
! [SV14: $i,SV4: $i] :
( ( ( SV4 = SV14 )
| ( greater @ SV4 @ SV14 )
| ( less @ SV4 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(69,plain,
! [SV15: $i,SV5: $i] :
( ( ~ ( greater @ SV5 @ SV15 )
| ~ ( less @ SV5 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(70,plain,
! [SV16: $i,SV6: $i] :
( ( ~ ( greater @ SV6 @ SV16 )
| ( less @ SV16 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(71,plain,
! [SV17: $i,SV7: $i] :
( ( ( SV7 != SV17 )
| ~ ( greater @ SV7 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(72,plain,
! [SV18: $i,SV8: $i] :
( ( ~ ( less @ SV8 @ SV18 )
| ( greater @ SV18 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(73,plain,
! [SV9: $i,SV19: $i] :
( ( ~ ( ~ ( ~ ( greater @ SV19 @ SV9 )
| ~ ! [SY39: $i] :
( SV19
!= ( vplus @ SV9 @ SY39 ) ) )
| ~ ( ~ ~ ! [SY40: $i] :
( SV19
!= ( vplus @ SV9 @ SY40 ) )
| ( greater @ SV19 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(74,plain,
! [SV20: $i,SV10: $i] :
( ( ( SV10 != SV20 )
| ( ( vmul @ SV10 @ vd469 )
= ( vmul @ SV20 @ vd469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(75,plain,
! [SV21: $i,SV11: $i,SV1: $i] :
( ( ( vmul @ ( vmul @ SV1 @ SV11 ) @ SV21 )
= ( vmul @ SV1 @ ( vmul @ SV11 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(76,plain,
! [SV22: $i,SV12: $i,SV2: $i] :
( ( ( vmul @ SV2 @ ( vplus @ SV12 @ SV22 ) )
= ( vplus @ ( vmul @ SV2 @ SV12 ) @ ( vmul @ SV2 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(77,plain,
! [SV14: $i,SV4: $i] :
( ( ( ( SV4 = SV14 )
| ( greater @ SV4 @ SV14 ) )
= $true )
| ( ( less @ SV4 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(78,plain,
! [SV15: $i,SV5: $i] :
( ( ( ~ ( greater @ SV5 @ SV15 ) )
= $true )
| ( ( ~ ( less @ SV5 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(79,plain,
! [SV16: $i,SV6: $i] :
( ( ( ~ ( greater @ SV6 @ SV16 ) )
= $true )
| ( ( less @ SV16 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(80,plain,
! [SV17: $i,SV7: $i] :
( ( ( SV7 != SV17 )
= $true )
| ( ( ~ ( greater @ SV7 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(81,plain,
! [SV18: $i,SV8: $i] :
( ( ( ~ ( less @ SV8 @ SV18 ) )
= $true )
| ( ( greater @ SV18 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(82,plain,
! [SV9: $i,SV19: $i] :
( ( ~ ( ~ ( greater @ SV19 @ SV9 )
| ~ ! [SY39: $i] :
( SV19
!= ( vplus @ SV9 @ SY39 ) ) )
| ~ ( ~ ~ ! [SY40: $i] :
( SV19
!= ( vplus @ SV9 @ SY40 ) )
| ( greater @ SV19 @ SV9 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(83,plain,
! [SV20: $i,SV10: $i] :
( ( ( SV10 != SV20 )
= $true )
| ( ( ( vmul @ SV10 @ vd469 )
= ( vmul @ SV20 @ vd469 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(84,plain,
! [SV14: $i,SV4: $i] :
( ( ( SV4 = SV14 )
= $true )
| ( ( greater @ SV4 @ SV14 )
= $true )
| ( ( less @ SV4 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(85,plain,
! [SV15: $i,SV5: $i] :
( ( ( greater @ SV5 @ SV15 )
= $false )
| ( ( ~ ( less @ SV5 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(86,plain,
! [SV16: $i,SV6: $i] :
( ( ( greater @ SV6 @ SV16 )
= $false )
| ( ( less @ SV16 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(87,plain,
! [SV17: $i,SV7: $i] :
( ( ( SV7 = SV17 )
= $false )
| ( ( ~ ( greater @ SV7 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(88,plain,
! [SV18: $i,SV8: $i] :
( ( ( less @ SV8 @ SV18 )
= $false )
| ( ( greater @ SV18 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(89,plain,
! [SV9: $i,SV19: $i] :
( ( ~ ( ~ ( greater @ SV19 @ SV9 )
| ~ ! [SY39: $i] :
( SV19
!= ( vplus @ SV9 @ SY39 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(90,plain,
! [SV9: $i,SV19: $i] :
( ( ~ ( ~ ~ ! [SY40: $i] :
( SV19
!= ( vplus @ SV9 @ SY40 ) )
| ( greater @ SV19 @ SV9 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(91,plain,
! [SV20: $i,SV10: $i] :
( ( ( SV10 = SV20 )
= $false )
| ( ( ( vmul @ SV10 @ vd469 )
= ( vmul @ SV20 @ vd469 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(92,plain,
! [SV15: $i,SV5: $i] :
( ( ( less @ SV5 @ SV15 )
= $false )
| ( ( greater @ SV5 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(93,plain,
! [SV17: $i,SV7: $i] :
( ( ( greater @ SV7 @ SV17 )
= $false )
| ( ( SV7 = SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(94,plain,
! [SV9: $i,SV19: $i] :
( ( ~ ( greater @ SV19 @ SV9 )
| ~ ! [SY39: $i] :
( SV19
!= ( vplus @ SV9 @ SY39 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(95,plain,
! [SV9: $i,SV19: $i] :
( ( ~ ~ ! [SY40: $i] :
( SV19
!= ( vplus @ SV9 @ SY40 ) )
| ( greater @ SV19 @ SV9 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(96,plain,
! [SV9: $i,SV19: $i] :
( ( ( ~ ( greater @ SV19 @ SV9 ) )
= $true )
| ( ( ~ ! [SY39: $i] :
( SV19
!= ( vplus @ SV9 @ SY39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(97,plain,
! [SV9: $i,SV19: $i] :
( ( ( ~ ~ ! [SY40: $i] :
( SV19
!= ( vplus @ SV9 @ SY40 ) ) )
= $true )
| ( ( greater @ SV19 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(98,plain,
! [SV9: $i,SV19: $i] :
( ( ( greater @ SV19 @ SV9 )
= $false )
| ( ( ~ ! [SY39: $i] :
( SV19
!= ( vplus @ SV9 @ SY39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(99,plain,
! [SV9: $i,SV19: $i] :
( ( ( ~ ! [SY40: $i] :
( SV19
!= ( vplus @ SV9 @ SY40 ) ) )
= $false )
| ( ( greater @ SV19 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(100,plain,
! [SV9: $i,SV19: $i] :
( ( ( ! [SY39: $i] :
( SV19
!= ( vplus @ SV9 @ SY39 ) ) )
= $false )
| ( ( greater @ SV19 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(101,plain,
! [SV9: $i,SV19: $i] :
( ( ( ! [SY40: $i] :
( SV19
!= ( vplus @ SV9 @ SY40 ) ) )
= $true )
| ( ( greater @ SV19 @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(102,plain,
! [SV9: $i,SV19: $i] :
( ( ( SV19
!= ( vplus @ SV9 @ ( sK1_SY39 @ SV9 @ SV19 ) ) )
= $false )
| ( ( greater @ SV19 @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[100]) ).
thf(103,plain,
! [SV23: $i,SV9: $i,SV19: $i] :
( ( ( SV19
!= ( vplus @ SV9 @ SV23 ) )
= $true )
| ( ( greater @ SV19 @ SV9 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(104,plain,
! [SV9: $i,SV19: $i] :
( ( ( SV19
= ( vplus @ SV9 @ ( sK1_SY39 @ SV9 @ SV19 ) ) )
= $true )
| ( ( greater @ SV19 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(105,plain,
! [SV23: $i,SV9: $i,SV19: $i] :
( ( ( SV19
= ( vplus @ SV9 @ SV23 ) )
= $false )
| ( ( greater @ SV19 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(106,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[36,105,104,93,92,91,88,86,84,76,75,67,59,37]) ).
thf(107,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM852+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
% 0.10/0.16 % Computer : n015.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Oct 6 13:45:43 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.27
% 0.10/0.27 No.of.Axioms: 12
% 0.10/0.27
% 0.10/0.27 Length.of.Defs: 0
% 0.10/0.27
% 0.10/0.27 Contains.Choice.Funs: false
% 0.10/0.27 ..
% 0.10/0.27
% 0.10/0.27 ********************************
% 0.10/0.27 * All subproblems solved! *
% 0.10/0.27 ********************************
% 0.10/0.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:12,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:106,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.27
% 0.10/0.27 %**** Beginning of derivation protocol ****
% 0.10/0.27 % SZS output start CNFRefutation
% See solution above
% 0.10/0.27
% 0.10/0.27 %**** End of derivation protocol ****
% 0.10/0.27 %**** no. of clauses in derivation: 100 ****
% 0.10/0.27 %**** clause counter: 106 ****
% 0.10/0.27
% 0.10/0.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:12,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:106,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------