%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM837+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 : n016.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 0.09s 0.22s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 162 ( 100 unt; 0 typ; 0 def)
% Number of atoms : 717 ( 453 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1124 ( 314 ~; 131 |; 3 &; 667 @)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 430 ( 0 ^; 401 !; 29 ?; 430 :)
% 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_SY66,type,
sK1_SY66: $i > $i > $i ).
thf(tp_sK2_SY61,type,
sK2_SY61: $i > $i > $i ).
thf(tp_sK3_SY67,type,
sK3_SY67: $i > $i > $i ).
thf(tp_sK4_SY70,type,
sK4_SY70: $i > $i > $i ).
thf(tp_v1,type,
v1: $i ).
thf(tp_vd268,type,
vd268: $i ).
thf(tp_vd269,type,
vd269: $i ).
thf(tp_vd271,type,
vd271: $i ).
thf(tp_vplus,type,
vplus: $i > $i > $i ).
thf(tp_vskolem2,type,
vskolem2: $i > $i ).
thf(tp_vsucc,type,
vsucc: $i > $i ).
thf(6,axiom,
! [Vd42: $i,Vd43: $i] :
( ( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
thf(7,axiom,
! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
thf(8,axiom,
! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(9,axiom,
! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
thf(10,axiom,
! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(11,axiom,
! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
thf(12,axiom,
! [Vd104: $i,Vd105: $i] :
( ( Vd104 != Vd105 )
=> ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
thf(13,axiom,
! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
thf(14,axiom,
! [Vd120: $i,Vd121: $i] :
( ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
thf(15,axiom,
! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
thf(16,axiom,
! [Vd120: $i,Vd121: $i] :
( ( Vd120 = Vd121 )
| ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
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(18,axiom,
! [Vd198: $i,Vd199: $i] :
( ( less @ Vd199 @ Vd198 )
<=> ? [Vd201: $i] :
( Vd198
= ( vplus @ Vd199 @ Vd201 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
thf(29,axiom,
less @ vd268 @ vd269,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(170), 270, 0)') ).
thf(30,axiom,
less @ vd269 @ vd271,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct2(170), 272, 0)') ).
thf(31,conjecture,
? [Vd273: $i] :
( vd269
= ( vplus @ vd268 @ Vd273 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(171)') ).
thf(32,negated_conjecture,
( ( ? [Vd273: $i] :
( vd269
= ( vplus @ vd268 @ Vd273 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[31]) ).
thf(33,plain,
( ( ? [Vd273: $i] :
( vd269
= ( vplus @ vd268 @ Vd273 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[32]) ).
thf(34,plain,
( ( ! [Vd42: $i,Vd43: $i] :
( ( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(35,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(36,plain,
( ( ! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(37,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(38,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(39,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(40,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 != Vd105 )
=> ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(41,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(42,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(43,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(44,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)],[16]) ).
thf(45,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(46,plain,
( ( ! [Vd198: $i,Vd199: $i] :
( ( less @ Vd199 @ Vd198 )
<=> ? [Vd201: $i] :
( Vd198
= ( vplus @ Vd199 @ Vd201 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(47,plain,
( ( less @ vd268 @ vd269 )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(48,plain,
( ( less @ vd269 @ vd271 )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(49,plain,
( ( ~ ? [Vd273: $i] :
( vd269
= ( vplus @ vd268 @ Vd273 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[33]) ).
thf(50,plain,
( ( less @ vd269 @ vd271 )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(51,plain,
( ( less @ vd268 @ vd269 )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(52,plain,
( ( ! [Vd198: $i,Vd199: $i] :
( ( less @ Vd199 @ Vd198 )
<=> ? [Vd201: $i] :
( Vd198
= ( vplus @ Vd199 @ Vd201 ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(53,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(54,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 = Vd121 )
| ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(55,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(56,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(57,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(58,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 != Vd105 )
=> ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(59,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(60,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(61,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(62,plain,
( ( ! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(63,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(64,plain,
( ( ! [Vd42: $i,Vd43: $i] :
( ( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(65,plain,
( ( ~ ? [Vd273: $i] :
( vd269
= ( vplus @ vd268 @ Vd273 ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(66,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
!= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) )
| ( ( vplus @ SX0 @ v1 )
!= ( vsucc @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(67,plain,
( ( ~ ~ ! [SX0: $i] :
( vd269
!= ( vplus @ vd268 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(68,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)],[53]) ).
thf(69,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ( SX0 != SX1 ) )
| ! [SX2: $i] :
( ( vplus @ SX2 @ SX0 )
!= ( vplus @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(70,plain,
( ( ! [SX0: $i,SX1: $i] :
( SX1
!= ( vplus @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(71,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(72,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(73,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)],[54]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ~ ~ ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(75,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)],[52]) ).
thf(76,plain,
! [SV1: $i] :
( ( ! [SY36: $i] :
( ( vplus @ SY36 @ SV1 )
= ( vplus @ SV1 @ SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(77,plain,
! [SV2: $i] :
( ( ! [SY37: $i] :
( ( vplus @ ( vsucc @ SV2 ) @ SY37 )
= ( vsucc @ ( vplus @ SV2 @ SY37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(78,plain,
! [SV3: $i] :
( ( ( vplus @ v1 @ SV3 )
= ( vsucc @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(79,plain,
! [SV4: $i] :
( ( ! [SY38: $i,SY39: $i] :
( ( vplus @ ( vplus @ SV4 @ SY38 ) @ SY39 )
= ( vplus @ SV4 @ ( vplus @ SY38 @ SY39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(80,plain,
! [SV5: $i] :
( ( ! [SY40: $i] :
~ ( ( ( vplus @ SV5 @ ( vsucc @ SY40 ) )
!= ( vsucc @ ( vplus @ SV5 @ SY40 ) ) )
| ( ( vplus @ SV5 @ v1 )
!= ( vsucc @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(81,plain,
( ( ~ ! [SX0: $i] :
( vd269
!= ( vplus @ vd268 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(82,plain,
! [SV6: $i] :
( ( ! [SY41: $i] :
~ ( ~ ( ~ ( greater @ SY41 @ SV6 )
| ~ ! [SY42: $i] :
( SY41
!= ( vplus @ SV6 @ SY42 ) ) )
| ~ ( ~ ~ ! [SY43: $i] :
( SY41
!= ( vplus @ SV6 @ SY43 ) )
| ( greater @ SY41 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(83,plain,
! [SV7: $i] :
( ( ! [SY44: $i] :
( ~ ( ( SV7 != SY44 ) )
| ! [SY45: $i] :
( ( vplus @ SY45 @ SV7 )
!= ( vplus @ SY45 @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(84,plain,
! [SV8: $i] :
( ( ! [SY46: $i] :
( SY46
!= ( vplus @ SV8 @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(85,plain,
! [SV9: $i] :
( ( ! [SY47: $i] :
( ( SV9 != SY47 )
| ~ ~ ! [SY48: $i] :
( SY47
!= ( vplus @ SV9 @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(86,plain,
! [SV10: $i] :
( ( ! [SY49: $i] :
( ( SV10 != SY49 )
| ~ ~ ! [SY50: $i] :
( SV10
!= ( vplus @ SY49 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(87,plain,
! [SV11: $i] :
( ( ! [SY51: $i] :
( ( SV11 = SY51 )
| ~ ! [SY52: $i] :
( SV11
!= ( vplus @ SY51 @ SY52 ) )
| ~ ! [SY53: $i] :
( SY51
!= ( vplus @ SV11 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(88,plain,
! [SV12: $i] :
( ( ! [SY54: $i] :
( ~ ~ ! [SY55: $i] :
( SV12
!= ( vplus @ SY54 @ SY55 ) )
| ~ ~ ! [SY56: $i] :
( SY54
!= ( vplus @ SV12 @ SY56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(89,plain,
! [SV13: $i] :
( ( ! [SY57: $i] :
~ ( ~ ( ~ ( less @ SY57 @ SV13 )
| ~ ! [SY58: $i] :
( SV13
!= ( vplus @ SY57 @ SY58 ) ) )
| ~ ( ~ ~ ! [SY59: $i] :
( SV13
!= ( vplus @ SY57 @ SY59 ) )
| ( less @ SY57 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(90,plain,
! [SV1: $i,SV14: $i] :
( ( ( vplus @ SV14 @ SV1 )
= ( vplus @ SV1 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(91,plain,
! [SV15: $i,SV2: $i] :
( ( ( vplus @ ( vsucc @ SV2 ) @ SV15 )
= ( vsucc @ ( vplus @ SV2 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(92,plain,
! [SV16: $i,SV4: $i] :
( ( ! [SY60: $i] :
( ( vplus @ ( vplus @ SV4 @ SV16 ) @ SY60 )
= ( vplus @ SV4 @ ( vplus @ SV16 @ SY60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(93,plain,
! [SV17: $i,SV5: $i] :
( ( ~ ( ( ( vplus @ SV5 @ ( vsucc @ SV17 ) )
!= ( vsucc @ ( vplus @ SV5 @ SV17 ) ) )
| ( ( vplus @ SV5 @ v1 )
!= ( vsucc @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(94,plain,
( ( ! [SX0: $i] :
( vd269
!= ( vplus @ vd268 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(95,plain,
! [SV6: $i,SV18: $i] :
( ( ~ ( ~ ( ~ ( greater @ SV18 @ SV6 )
| ~ ! [SY61: $i] :
( SV18
!= ( vplus @ SV6 @ SY61 ) ) )
| ~ ( ~ ~ ! [SY62: $i] :
( SV18
!= ( vplus @ SV6 @ SY62 ) )
| ( greater @ SV18 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(96,plain,
! [SV19: $i,SV7: $i] :
( ( ~ ( ( SV7 != SV19 ) )
| ! [SY63: $i] :
( ( vplus @ SY63 @ SV7 )
!= ( vplus @ SY63 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(97,plain,
! [SV8: $i,SV20: $i] :
( ( SV20
!= ( vplus @ SV8 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(98,plain,
! [SV21: $i,SV9: $i] :
( ( ( SV9 != SV21 )
| ~ ~ ! [SY64: $i] :
( SV21
!= ( vplus @ SV9 @ SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(99,plain,
! [SV22: $i,SV10: $i] :
( ( ( SV10 != SV22 )
| ~ ~ ! [SY65: $i] :
( SV10
!= ( vplus @ SV22 @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(100,plain,
! [SV23: $i,SV11: $i] :
( ( ( SV11 = SV23 )
| ~ ! [SY66: $i] :
( SV11
!= ( vplus @ SV23 @ SY66 ) )
| ~ ! [SY67: $i] :
( SV23
!= ( vplus @ SV11 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(101,plain,
! [SV24: $i,SV12: $i] :
( ( ~ ~ ! [SY68: $i] :
( SV12
!= ( vplus @ SV24 @ SY68 ) )
| ~ ~ ! [SY69: $i] :
( SV24
!= ( vplus @ SV12 @ SY69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(102,plain,
! [SV13: $i,SV25: $i] :
( ( ~ ( ~ ( ~ ( less @ SV25 @ SV13 )
| ~ ! [SY70: $i] :
( SV13
!= ( vplus @ SV25 @ SY70 ) ) )
| ~ ( ~ ~ ! [SY71: $i] :
( SV13
!= ( vplus @ SV25 @ SY71 ) )
| ( less @ SV25 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(103,plain,
! [SV26: $i,SV16: $i,SV4: $i] :
( ( ( vplus @ ( vplus @ SV4 @ SV16 ) @ SV26 )
= ( vplus @ SV4 @ ( vplus @ SV16 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(104,plain,
! [SV17: $i,SV5: $i] :
( ( ( ( vplus @ SV5 @ ( vsucc @ SV17 ) )
!= ( vsucc @ ( vplus @ SV5 @ SV17 ) ) )
| ( ( vplus @ SV5 @ v1 )
!= ( vsucc @ SV5 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(105,plain,
! [SV27: $i] :
( ( vd269
!= ( vplus @ vd268 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(106,plain,
! [SV6: $i,SV18: $i] :
( ( ~ ( ~ ( greater @ SV18 @ SV6 )
| ~ ! [SY61: $i] :
( SV18
!= ( vplus @ SV6 @ SY61 ) ) )
| ~ ( ~ ~ ! [SY62: $i] :
( SV18
!= ( vplus @ SV6 @ SY62 ) )
| ( greater @ SV18 @ SV6 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(107,plain,
! [SV19: $i,SV7: $i] :
( ( ( ~ ( ( SV7 != SV19 ) ) )
= $true )
| ( ( ! [SY63: $i] :
( ( vplus @ SY63 @ SV7 )
!= ( vplus @ SY63 @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(108,plain,
! [SV8: $i,SV20: $i] :
( ( SV20
= ( vplus @ SV8 @ SV20 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(109,plain,
! [SV21: $i,SV9: $i] :
( ( ( SV9 != SV21 )
= $true )
| ( ( ~ ~ ! [SY64: $i] :
( SV21
!= ( vplus @ SV9 @ SY64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(110,plain,
! [SV22: $i,SV10: $i] :
( ( ( SV10 != SV22 )
= $true )
| ( ( ~ ~ ! [SY65: $i] :
( SV10
!= ( vplus @ SV22 @ SY65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(111,plain,
! [SV23: $i,SV11: $i] :
( ( ( ( SV11 = SV23 )
| ~ ! [SY66: $i] :
( SV11
!= ( vplus @ SV23 @ SY66 ) ) )
= $true )
| ( ( ~ ! [SY67: $i] :
( SV23
!= ( vplus @ SV11 @ SY67 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(112,plain,
! [SV24: $i,SV12: $i] :
( ( ( ~ ~ ! [SY68: $i] :
( SV12
!= ( vplus @ SV24 @ SY68 ) ) )
= $true )
| ( ( ~ ~ ! [SY69: $i] :
( SV24
!= ( vplus @ SV12 @ SY69 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(113,plain,
! [SV13: $i,SV25: $i] :
( ( ~ ( ~ ( less @ SV25 @ SV13 )
| ~ ! [SY70: $i] :
( SV13
!= ( vplus @ SV25 @ SY70 ) ) )
| ~ ( ~ ~ ! [SY71: $i] :
( SV13
!= ( vplus @ SV25 @ SY71 ) )
| ( less @ SV25 @ SV13 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(114,plain,
! [SV17: $i,SV5: $i] :
( ( ( vplus @ SV5 @ ( vsucc @ SV17 ) )
!= ( vsucc @ ( vplus @ SV5 @ SV17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[104]) ).
thf(115,plain,
! [SV5: $i] :
( ( ( vplus @ SV5 @ v1 )
!= ( vsucc @ SV5 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[104]) ).
thf(116,plain,
! [SV27: $i] :
( ( vd269
= ( vplus @ vd268 @ SV27 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(117,plain,
! [SV6: $i,SV18: $i] :
( ( ~ ( ~ ( greater @ SV18 @ SV6 )
| ~ ! [SY61: $i] :
( SV18
!= ( vplus @ SV6 @ SY61 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(118,plain,
! [SV6: $i,SV18: $i] :
( ( ~ ( ~ ~ ! [SY62: $i] :
( SV18
!= ( vplus @ SV6 @ SY62 ) )
| ( greater @ SV18 @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(119,plain,
! [SV19: $i,SV7: $i] :
( ( ( SV7 != SV19 )
= $false )
| ( ( ! [SY63: $i] :
( ( vplus @ SY63 @ SV7 )
!= ( vplus @ SY63 @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(120,plain,
! [SV21: $i,SV9: $i] :
( ( ( SV9 = SV21 )
= $false )
| ( ( ~ ~ ! [SY64: $i] :
( SV21
!= ( vplus @ SV9 @ SY64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(121,plain,
! [SV22: $i,SV10: $i] :
( ( ( SV10 = SV22 )
= $false )
| ( ( ~ ~ ! [SY65: $i] :
( SV10
!= ( vplus @ SV22 @ SY65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(122,plain,
! [SV23: $i,SV11: $i] :
( ( ( SV11 = SV23 )
= $true )
| ( ( ~ ! [SY66: $i] :
( SV11
!= ( vplus @ SV23 @ SY66 ) ) )
= $true )
| ( ( ~ ! [SY67: $i] :
( SV23
!= ( vplus @ SV11 @ SY67 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(123,plain,
! [SV24: $i,SV12: $i] :
( ( ( ~ ! [SY68: $i] :
( SV12
!= ( vplus @ SV24 @ SY68 ) ) )
= $false )
| ( ( ~ ~ ! [SY69: $i] :
( SV24
!= ( vplus @ SV12 @ SY69 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(124,plain,
! [SV13: $i,SV25: $i] :
( ( ~ ( ~ ( less @ SV25 @ SV13 )
| ~ ! [SY70: $i] :
( SV13
!= ( vplus @ SV25 @ SY70 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(125,plain,
! [SV25: $i,SV13: $i] :
( ( ~ ( ~ ~ ! [SY71: $i] :
( SV13
!= ( vplus @ SV25 @ SY71 ) )
| ( less @ SV25 @ SV13 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(126,plain,
! [SV17: $i,SV5: $i] :
( ( ( vplus @ SV5 @ ( vsucc @ SV17 ) )
= ( vsucc @ ( vplus @ SV5 @ SV17 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(127,plain,
! [SV5: $i] :
( ( ( vplus @ SV5 @ v1 )
= ( vsucc @ SV5 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(128,plain,
! [SV6: $i,SV18: $i] :
( ( ~ ( greater @ SV18 @ SV6 )
| ~ ! [SY61: $i] :
( SV18
!= ( vplus @ SV6 @ SY61 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(129,plain,
! [SV6: $i,SV18: $i] :
( ( ~ ~ ! [SY62: $i] :
( SV18
!= ( vplus @ SV6 @ SY62 ) )
| ( greater @ SV18 @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(130,plain,
! [SV19: $i,SV7: $i] :
( ( ( SV7 = SV19 )
= $true )
| ( ( ! [SY63: $i] :
( ( vplus @ SY63 @ SV7 )
!= ( vplus @ SY63 @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(131,plain,
! [SV9: $i,SV21: $i] :
( ( ( ~ ! [SY64: $i] :
( SV21
!= ( vplus @ SV9 @ SY64 ) ) )
= $false )
| ( ( SV9 = SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(132,plain,
! [SV22: $i,SV10: $i] :
( ( ( ~ ! [SY65: $i] :
( SV10
!= ( vplus @ SV22 @ SY65 ) ) )
= $false )
| ( ( SV10 = SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(133,plain,
! [SV23: $i,SV11: $i] :
( ( ( ! [SY66: $i] :
( SV11
!= ( vplus @ SV23 @ SY66 ) ) )
= $false )
| ( ( SV11 = SV23 )
= $true )
| ( ( ~ ! [SY67: $i] :
( SV23
!= ( vplus @ SV11 @ SY67 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(134,plain,
! [SV24: $i,SV12: $i] :
( ( ( ! [SY68: $i] :
( SV12
!= ( vplus @ SV24 @ SY68 ) ) )
= $true )
| ( ( ~ ~ ! [SY69: $i] :
( SV24
!= ( vplus @ SV12 @ SY69 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(135,plain,
! [SV13: $i,SV25: $i] :
( ( ~ ( less @ SV25 @ SV13 )
| ~ ! [SY70: $i] :
( SV13
!= ( vplus @ SV25 @ SY70 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(136,plain,
! [SV25: $i,SV13: $i] :
( ( ~ ~ ! [SY71: $i] :
( SV13
!= ( vplus @ SV25 @ SY71 ) )
| ( less @ SV25 @ SV13 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(137,plain,
! [SV6: $i,SV18: $i] :
( ( ( ~ ( greater @ SV18 @ SV6 ) )
= $true )
| ( ( ~ ! [SY61: $i] :
( SV18
!= ( vplus @ SV6 @ SY61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(138,plain,
! [SV6: $i,SV18: $i] :
( ( ( ~ ~ ! [SY62: $i] :
( SV18
!= ( vplus @ SV6 @ SY62 ) ) )
= $true )
| ( ( greater @ SV18 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(139,plain,
! [SV19: $i,SV7: $i,SV28: $i] :
( ( ( ( vplus @ SV28 @ SV7 )
!= ( vplus @ SV28 @ SV19 ) )
= $true )
| ( ( SV7 = SV19 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(140,plain,
! [SV9: $i,SV21: $i] :
( ( ( ! [SY64: $i] :
( SV21
!= ( vplus @ SV9 @ SY64 ) ) )
= $true )
| ( ( SV9 = SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(141,plain,
! [SV22: $i,SV10: $i] :
( ( ( ! [SY65: $i] :
( SV10
!= ( vplus @ SV22 @ SY65 ) ) )
= $true )
| ( ( SV10 = SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(142,plain,
! [SV23: $i,SV11: $i] :
( ( ( SV11
!= ( vplus @ SV23 @ ( sK1_SY66 @ SV23 @ SV11 ) ) )
= $false )
| ( ( SV11 = SV23 )
= $true )
| ( ( ~ ! [SY67: $i] :
( SV23
!= ( vplus @ SV11 @ SY67 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[133]) ).
thf(143,plain,
! [SV29: $i,SV24: $i,SV12: $i] :
( ( ( SV12
!= ( vplus @ SV24 @ SV29 ) )
= $true )
| ( ( ~ ~ ! [SY69: $i] :
( SV24
!= ( vplus @ SV12 @ SY69 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(144,plain,
! [SV13: $i,SV25: $i] :
( ( ( ~ ( less @ SV25 @ SV13 ) )
= $true )
| ( ( ~ ! [SY70: $i] :
( SV13
!= ( vplus @ SV25 @ SY70 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(145,plain,
! [SV25: $i,SV13: $i] :
( ( ( ~ ~ ! [SY71: $i] :
( SV13
!= ( vplus @ SV25 @ SY71 ) ) )
= $true )
| ( ( less @ SV25 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(146,plain,
! [SV6: $i,SV18: $i] :
( ( ( greater @ SV18 @ SV6 )
= $false )
| ( ( ~ ! [SY61: $i] :
( SV18
!= ( vplus @ SV6 @ SY61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(147,plain,
! [SV6: $i,SV18: $i] :
( ( ( ~ ! [SY62: $i] :
( SV18
!= ( vplus @ SV6 @ SY62 ) ) )
= $false )
| ( ( greater @ SV18 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(148,plain,
! [SV19: $i,SV7: $i,SV28: $i] :
( ( ( ( vplus @ SV28 @ SV7 )
= ( vplus @ SV28 @ SV19 ) )
= $false )
| ( ( SV7 = SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(149,plain,
! [SV30: $i,SV9: $i,SV21: $i] :
( ( ( SV21
!= ( vplus @ SV9 @ SV30 ) )
= $true )
| ( ( SV9 = SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(150,plain,
! [SV31: $i,SV22: $i,SV10: $i] :
( ( ( SV10
!= ( vplus @ SV22 @ SV31 ) )
= $true )
| ( ( SV10 = SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(151,plain,
! [SV23: $i,SV11: $i] :
( ( ( SV11
= ( vplus @ SV23 @ ( sK1_SY66 @ SV23 @ SV11 ) ) )
= $true )
| ( ( SV11 = SV23 )
= $true )
| ( ( ~ ! [SY67: $i] :
( SV23
!= ( vplus @ SV11 @ SY67 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(152,plain,
! [SV29: $i,SV24: $i,SV12: $i] :
( ( ( SV12
= ( vplus @ SV24 @ SV29 ) )
= $false )
| ( ( ~ ~ ! [SY69: $i] :
( SV24
!= ( vplus @ SV12 @ SY69 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(153,plain,
! [SV13: $i,SV25: $i] :
( ( ( less @ SV25 @ SV13 )
= $false )
| ( ( ~ ! [SY70: $i] :
( SV13
!= ( vplus @ SV25 @ SY70 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(154,plain,
! [SV25: $i,SV13: $i] :
( ( ( ~ ! [SY71: $i] :
( SV13
!= ( vplus @ SV25 @ SY71 ) ) )
= $false )
| ( ( less @ SV25 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(155,plain,
! [SV6: $i,SV18: $i] :
( ( ( ! [SY61: $i] :
( SV18
!= ( vplus @ SV6 @ SY61 ) ) )
= $false )
| ( ( greater @ SV18 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(156,plain,
! [SV6: $i,SV18: $i] :
( ( ( ! [SY62: $i] :
( SV18
!= ( vplus @ SV6 @ SY62 ) ) )
= $true )
| ( ( greater @ SV18 @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(157,plain,
! [SV30: $i,SV9: $i,SV21: $i] :
( ( ( SV21
= ( vplus @ SV9 @ SV30 ) )
= $false )
| ( ( SV9 = SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(158,plain,
! [SV31: $i,SV22: $i,SV10: $i] :
( ( ( SV10
= ( vplus @ SV22 @ SV31 ) )
= $false )
| ( ( SV10 = SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(159,plain,
! [SV11: $i,SV23: $i] :
( ( ( ! [SY67: $i] :
( SV23
!= ( vplus @ SV11 @ SY67 ) ) )
= $false )
| ( ( SV11 = SV23 )
= $true )
| ( ( SV11
= ( vplus @ SV23 @ ( sK1_SY66 @ SV23 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(160,plain,
! [SV29: $i,SV12: $i,SV24: $i] :
( ( ( ~ ! [SY69: $i] :
( SV24
!= ( vplus @ SV12 @ SY69 ) ) )
= $false )
| ( ( SV12
= ( vplus @ SV24 @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(161,plain,
! [SV25: $i,SV13: $i] :
( ( ( ! [SY70: $i] :
( SV13
!= ( vplus @ SV25 @ SY70 ) ) )
= $false )
| ( ( less @ SV25 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(162,plain,
! [SV25: $i,SV13: $i] :
( ( ( ! [SY71: $i] :
( SV13
!= ( vplus @ SV25 @ SY71 ) ) )
= $true )
| ( ( less @ SV25 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(163,plain,
! [SV6: $i,SV18: $i] :
( ( ( SV18
!= ( vplus @ SV6 @ ( sK2_SY61 @ SV6 @ SV18 ) ) )
= $false )
| ( ( greater @ SV18 @ SV6 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[155]) ).
thf(164,plain,
! [SV32: $i,SV6: $i,SV18: $i] :
( ( ( SV18
!= ( vplus @ SV6 @ SV32 ) )
= $true )
| ( ( greater @ SV18 @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(165,plain,
! [SV11: $i,SV23: $i] :
( ( ( SV23
!= ( vplus @ SV11 @ ( sK3_SY67 @ SV11 @ SV23 ) ) )
= $false )
| ( ( SV11 = SV23 )
= $true )
| ( ( SV11
= ( vplus @ SV23 @ ( sK1_SY66 @ SV23 @ SV11 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[159]) ).
thf(166,plain,
! [SV29: $i,SV12: $i,SV24: $i] :
( ( ( ! [SY69: $i] :
( SV24
!= ( vplus @ SV12 @ SY69 ) ) )
= $true )
| ( ( SV12
= ( vplus @ SV24 @ SV29 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(167,plain,
! [SV25: $i,SV13: $i] :
( ( ( SV13
!= ( vplus @ SV25 @ ( sK4_SY70 @ SV25 @ SV13 ) ) )
= $false )
| ( ( less @ SV25 @ SV13 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[161]) ).
thf(168,plain,
! [SV33: $i,SV25: $i,SV13: $i] :
( ( ( SV13
!= ( vplus @ SV25 @ SV33 ) )
= $true )
| ( ( less @ SV25 @ SV13 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(169,plain,
! [SV6: $i,SV18: $i] :
( ( ( SV18
= ( vplus @ SV6 @ ( sK2_SY61 @ SV6 @ SV18 ) ) )
= $true )
| ( ( greater @ SV18 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(170,plain,
! [SV32: $i,SV6: $i,SV18: $i] :
( ( ( SV18
= ( vplus @ SV6 @ SV32 ) )
= $false )
| ( ( greater @ SV18 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(171,plain,
! [SV11: $i,SV23: $i] :
( ( ( SV23
= ( vplus @ SV11 @ ( sK3_SY67 @ SV11 @ SV23 ) ) )
= $true )
| ( ( SV11 = SV23 )
= $true )
| ( ( SV11
= ( vplus @ SV23 @ ( sK1_SY66 @ SV23 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(172,plain,
! [SV29: $i,SV34: $i,SV12: $i,SV24: $i] :
( ( ( SV24
!= ( vplus @ SV12 @ SV34 ) )
= $true )
| ( ( SV12
= ( vplus @ SV24 @ SV29 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(173,plain,
! [SV25: $i,SV13: $i] :
( ( ( SV13
= ( vplus @ SV25 @ ( sK4_SY70 @ SV25 @ SV13 ) ) )
= $true )
| ( ( less @ SV25 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(174,plain,
! [SV33: $i,SV25: $i,SV13: $i] :
( ( ( SV13
= ( vplus @ SV25 @ SV33 ) )
= $false )
| ( ( less @ SV25 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(175,plain,
! [SV29: $i,SV34: $i,SV12: $i,SV24: $i] :
( ( ( SV24
= ( vplus @ SV12 @ SV34 ) )
= $false )
| ( ( SV12
= ( vplus @ SV24 @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(176,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[50,175,174,173,171,170,169,158,157,148,127,126,116,108,103,91,90,78,51]) ).
thf(177,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM837+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
% 0.09/0.16 % Computer : n016.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Oct 6 13:45:29 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.22
% 0.09/0.22 No.of.Axioms: 15
% 0.09/0.22
% 0.09/0.22 Length.of.Defs: 0
% 0.09/0.22
% 0.09/0.22 Contains.Choice.Funs: false
% 0.09/0.22 ....
% 0.09/0.22
% 0.09/0.22 ********************************
% 0.09/0.22 * All subproblems solved! *
% 0.09/0.22 ********************************
% 0.09/0.22 % 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:176,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.22
% 0.09/0.22 %**** Beginning of derivation protocol ****
% 0.09/0.22 % SZS output start CNFRefutation
% See solution above
% 0.09/0.22
% 0.09/0.22 %**** End of derivation protocol ****
% 0.09/0.22 %**** no. of clauses in derivation: 162 ****
% 0.09/0.22 %**** clause counter: 176 ****
% 0.09/0.22
% 0.09/0.22 % 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:176,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------