%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM836+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 0.54s 0.31s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 181 ( 132 unt; 0 typ; 0 def)
% Number of atoms : 728 ( 456 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1052 ( 178 ~; 131 |; 10 &; 721 @)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 402 ( 0 ^; 386 !; 16 ?; 402 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_greater,type,
greater: $i > $i > $o ).
thf(tp_less,type,
less: $i > $i > $o ).
thf(tp_sK1_Vd123,type,
sK1_Vd123: $i > $i > $i ).
thf(tp_sK2_Vd125,type,
sK2_Vd125: $i > $i > $i ).
thf(tp_sK3_Vd196,type,
sK3_Vd196: $i > $i > $i ).
thf(tp_sK4_Vd201,type,
sK4_Vd201: $i > $i > $i ).
thf(tp_v1,type,
v1: $i ).
thf(tp_vd203,type,
vd203: $i ).
thf(tp_vd204,type,
vd204: $i ).
thf(tp_vplus,type,
vplus: $i > $i > $i ).
thf(tp_vskolem2,type,
vskolem2: $i > $i ).
thf(tp_vsucc,type,
vsucc: $i > $i ).
thf(1,axiom,
! [Vd1: $i] :
( ( vsucc @ Vd1 )
!= v1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).
thf(2,axiom,
! [Vd3: $i,Vd4: $i] :
( ( ( vsucc @ Vd3 )
= ( vsucc @ Vd4 ) )
=> ( Vd3 = Vd4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(antec(axiom(3)), imp(antec(axiom(3))))') ).
thf(3,axiom,
! [Vd7: $i,Vd8: $i] :
( ( Vd7 != Vd8 )
=> ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
thf(4,axiom,
! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
thf(5,axiom,
! [Vd24: $i] :
( ( Vd24 != v1 )
=> ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
thf(6,axiom,
! [Vd42: $i,Vd43: $i] :
( ( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
thf(8,axiom,
! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
thf(10,axiom,
! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(11,axiom,
! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
thf(19,axiom,
( ( vd203 != vd204 )
| ~ ( greater @ vd203 @ vd204 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dis(ex(cond(conseq(131), 0), 0))') ).
thf(20,conjecture,
( ~ ( greater @ vd203 @ vd204 )
| ~ ( less @ vd203 @ vd204 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dis(ex(cond(conseq(131), 0), 1))') ).
thf(21,negated_conjecture,
( ( ~ ( greater @ vd203 @ vd204 )
| ~ ( less @ vd203 @ vd204 ) )
= $false ),
inference(negate_conjecture,[status(cth)],[20]) ).
thf(22,plain,
( ( ~ ( greater @ vd203 @ vd204 )
| ~ ( less @ vd203 @ vd204 ) )
= $false ),
inference(unfold_def,[status(thm)],[21]) ).
thf(23,plain,
( ( ! [Vd1: $i] :
( ( vsucc @ Vd1 )
!= v1 ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(24,plain,
( ( ! [Vd3: $i,Vd4: $i] :
( ( ( vsucc @ Vd3 )
= ( vsucc @ Vd4 ) )
=> ( Vd3 = Vd4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(25,plain,
( ( ! [Vd7: $i,Vd8: $i] :
( ( Vd7 != Vd8 )
=> ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(26,plain,
( ( ! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(27,plain,
( ( ! [Vd24: $i] :
( ( Vd24 != v1 )
=> ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(28,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(29,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(30,plain,
( ( ! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(31,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(32,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(33,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(34,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 != Vd105 )
=> ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(35,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(36,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(37,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(38,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(39,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(40,plain,
( ( ! [Vd198: $i,Vd199: $i] :
( ( less @ Vd199 @ Vd198 )
<=> ? [Vd201: $i] :
( Vd198
= ( vplus @ Vd199 @ Vd201 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(41,plain,
( ( ( vd203 != vd204 )
| ~ ( greater @ vd203 @ vd204 ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(42,plain,
( ( ~ ( ~ ( greater @ vd203 @ vd204 )
| ~ ( less @ vd203 @ vd204 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(43,plain,
( ( ( greater @ vd203 @ vd204 )
& ( less @ vd203 @ vd204 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(44,plain,
( ( ! [Vd1: $i] :
( ( vsucc @ Vd1 )
!= v1 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(45,plain,
( ( ! [Vd3: $i,Vd4: $i] :
( ( ( vsucc @ Vd3 )
!= ( vsucc @ Vd4 ) )
| ( Vd3 = Vd4 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(46,plain,
( ( ! [Vd7: $i,Vd8: $i] :
( ( Vd7 = Vd8 )
| ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(47,plain,
( ( ! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(48,plain,
( ( ! [Vd24: $i] :
( ( Vd24 = v1 )
| ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(49,plain,
( ( ! [Vd42: $i,Vd43: $i] :
( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ! [Vd42: $i] :
( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(50,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(51,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 = Vd105 )
| ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(52,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ! [Vd123: $i] :
( Vd120
!= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(53,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ! [Vd123: $i] :
( Vd120
!= ( vplus @ Vd121 @ Vd123 ) )
| ! [Vd125: $i] :
( Vd121
!= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(54,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ! [Vd125: $i] :
( Vd121
!= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(55,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd121
= ( vplus @ Vd120 @ ( sK2_Vd125 @ Vd121 @ Vd120 ) ) )
| ( Vd120 = Vd121 )
| ( Vd120
= ( vplus @ Vd121 @ ( sK1_Vd123 @ Vd121 @ Vd120 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(56,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ! [Vd196: $i] :
( Vd194
!= ( vplus @ Vd193 @ Vd196 ) )
| ( greater @ Vd194 @ Vd193 ) )
& ! [Vd193: $i,Vd194: $i] :
( ~ ( greater @ Vd194 @ Vd193 )
| ( Vd194
= ( vplus @ Vd193 @ ( sK3_Vd196 @ Vd194 @ Vd193 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(57,plain,
( ( ! [Vd198: $i,Vd199: $i] :
( ! [Vd201: $i] :
( Vd198
!= ( vplus @ Vd199 @ Vd201 ) )
| ( less @ Vd199 @ Vd198 ) )
& ! [Vd198: $i,Vd199: $i] :
( ~ ( less @ Vd199 @ Vd198 )
| ( Vd198
= ( vplus @ Vd199 @ ( sK4_Vd201 @ Vd199 @ Vd198 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(58,plain,
( ( ( vd203 != vd204 )
| ~ ( greater @ vd203 @ vd204 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(59,plain,
( ( ( vd203 != vd204 )
| ~ ( greater @ vd203 @ vd204 ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(60,plain,
( ( ! [Vd198: $i,Vd199: $i] :
( ! [Vd201: $i] :
( Vd198
!= ( vplus @ Vd199 @ Vd201 ) )
| ( less @ Vd199 @ Vd198 ) )
& ! [Vd198: $i,Vd199: $i] :
( ~ ( less @ Vd199 @ Vd198 )
| ( Vd198
= ( vplus @ Vd199 @ ( sK4_Vd201 @ Vd199 @ Vd198 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(61,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ! [Vd196: $i] :
( Vd194
!= ( vplus @ Vd193 @ Vd196 ) )
| ( greater @ Vd194 @ Vd193 ) )
& ! [Vd193: $i,Vd194: $i] :
( ~ ( greater @ Vd194 @ Vd193 )
| ( Vd194
= ( vplus @ Vd193 @ ( sK3_Vd196 @ Vd194 @ Vd193 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(62,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd121
= ( vplus @ Vd120 @ ( sK2_Vd125 @ Vd121 @ Vd120 ) ) )
| ( Vd120 = Vd121 )
| ( Vd120
= ( vplus @ Vd121 @ ( sK1_Vd123 @ Vd121 @ Vd120 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(63,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ! [Vd125: $i] :
( Vd121
!= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(64,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ! [Vd123: $i] :
( Vd120
!= ( vplus @ Vd121 @ Vd123 ) )
| ! [Vd125: $i] :
( Vd121
!= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(65,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ! [Vd123: $i] :
( Vd120
!= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(66,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 = Vd105 )
| ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(67,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(68,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(69,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(70,plain,
( ( ! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(71,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(72,plain,
( ( ! [Vd42: $i,Vd43: $i] :
( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ! [Vd42: $i] :
( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(73,plain,
( ( ! [Vd24: $i] :
( ( Vd24 = v1 )
| ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(74,plain,
( ( ! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(75,plain,
( ( ! [Vd7: $i,Vd8: $i] :
( ( Vd7 = Vd8 )
| ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(76,plain,
( ( ! [Vd3: $i,Vd4: $i] :
( ( ( vsucc @ Vd3 )
!= ( vsucc @ Vd4 ) )
| ( Vd3 = Vd4 ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(77,plain,
( ( ! [Vd1: $i] :
( ( vsucc @ Vd1 )
!= v1 ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(78,plain,
( ( ( greater @ vd203 @ vd204 )
& ( less @ vd203 @ vd204 ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(79,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(80,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( greater @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( SX1
= ( vplus @ SX0 @ ( sK3_Vd196 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(81,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( less @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( SX0
= ( vplus @ SX1 @ ( sK4_Vd201 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(82,plain,
( ( ~ ( ~ ( greater @ vd203 @ vd204 )
| ~ ( less @ vd203 @ vd204 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(83,plain,
( ( ( vd203 != vd204 )
= $true )
| ( ( ~ ( greater @ vd203 @ vd204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(84,plain,
! [SV1: $i] :
( ( ! [SY42: $i] :
( ( SY42
= ( vplus @ SV1 @ ( sK2_Vd125 @ SY42 @ SV1 ) ) )
| ( SV1 = SY42 )
| ( SV1
= ( vplus @ SY42 @ ( sK1_Vd123 @ SY42 @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(85,plain,
! [SV2: $i] :
( ( ! [SY43: $i] :
( ( SV2 != SY43 )
| ! [SY44: $i] :
( SY43
!= ( vplus @ SV2 @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(86,plain,
! [SV3: $i] :
( ( ! [SY45: $i] :
( ! [SY46: $i] :
( SV3
!= ( vplus @ SY45 @ SY46 ) )
| ! [SY47: $i] :
( SY45
!= ( vplus @ SV3 @ SY47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(87,plain,
! [SV4: $i] :
( ( ! [SY48: $i] :
( ( SV4 != SY48 )
| ! [SY49: $i] :
( SV4
!= ( vplus @ SY48 @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(88,plain,
! [SV5: $i] :
( ( ! [SY50: $i] :
( ( SV5 = SY50 )
| ! [SY51: $i] :
( ( vplus @ SY51 @ SV5 )
!= ( vplus @ SY51 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(89,plain,
! [SV6: $i] :
( ( ! [SY52: $i] :
( SY52
!= ( vplus @ SV6 @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(90,plain,
! [SV7: $i] :
( ( ! [SY53: $i] :
( ( vplus @ SY53 @ SV7 )
= ( vplus @ SV7 @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(91,plain,
! [SV8: $i] :
( ( ! [SY54: $i] :
( ( vplus @ ( vsucc @ SV8 ) @ SY54 )
= ( vsucc @ ( vplus @ SV8 @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(92,plain,
! [SV9: $i] :
( ( ( vplus @ v1 @ SV9 )
= ( vsucc @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(93,plain,
! [SV10: $i] :
( ( ! [SY55: $i,SY56: $i] :
( ( vplus @ ( vplus @ SV10 @ SY55 ) @ SY56 )
= ( vplus @ SV10 @ ( vplus @ SY55 @ SY56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(94,plain,
! [SV11: $i] :
( ( ( SV11 = v1 )
| ( SV11
= ( vsucc @ ( vskolem2 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(95,plain,
! [SV12: $i] :
( ( ( vsucc @ SV12 )
!= SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(96,plain,
! [SV13: $i] :
( ( ! [SY57: $i] :
( ( SV13 = SY57 )
| ( ( vsucc @ SV13 )
!= ( vsucc @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(97,plain,
! [SV14: $i] :
( ( ! [SY58: $i] :
( ( ( vsucc @ SV14 )
!= ( vsucc @ SY58 ) )
| ( SV14 = SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(98,plain,
! [SV15: $i] :
( ( ( vsucc @ SV15 )
!= v1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(99,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(100,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( greater @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( SX1
= ( vplus @ SX0 @ ( sK3_Vd196 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(101,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( less @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( SX0
= ( vplus @ SX1 @ ( sK4_Vd201 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(102,plain,
( ( ~ ( greater @ vd203 @ vd204 )
| ~ ( less @ vd203 @ vd204 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(103,plain,
( ( ( vd203 = vd204 )
= $false )
| ( ( ~ ( greater @ vd203 @ vd204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(104,plain,
! [SV1: $i,SV16: $i] :
( ( ( SV16
= ( vplus @ SV1 @ ( sK2_Vd125 @ SV16 @ SV1 ) ) )
| ( SV1 = SV16 )
| ( SV1
= ( vplus @ SV16 @ ( sK1_Vd123 @ SV16 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(105,plain,
! [SV17: $i,SV2: $i] :
( ( ( SV2 != SV17 )
| ! [SY59: $i] :
( SV17
!= ( vplus @ SV2 @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(106,plain,
! [SV18: $i,SV3: $i] :
( ( ! [SY60: $i] :
( SV3
!= ( vplus @ SV18 @ SY60 ) )
| ! [SY61: $i] :
( SV18
!= ( vplus @ SV3 @ SY61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(107,plain,
! [SV19: $i,SV4: $i] :
( ( ( SV4 != SV19 )
| ! [SY62: $i] :
( SV4
!= ( vplus @ SV19 @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(108,plain,
! [SV20: $i,SV5: $i] :
( ( ( SV5 = SV20 )
| ! [SY63: $i] :
( ( vplus @ SY63 @ SV5 )
!= ( vplus @ SY63 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(109,plain,
! [SV6: $i,SV21: $i] :
( ( SV21
!= ( vplus @ SV6 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(110,plain,
! [SV7: $i,SV22: $i] :
( ( ( vplus @ SV22 @ SV7 )
= ( vplus @ SV7 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(111,plain,
! [SV23: $i,SV8: $i] :
( ( ( vplus @ ( vsucc @ SV8 ) @ SV23 )
= ( vsucc @ ( vplus @ SV8 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(112,plain,
! [SV24: $i,SV10: $i] :
( ( ! [SY64: $i] :
( ( vplus @ ( vplus @ SV10 @ SV24 ) @ SY64 )
= ( vplus @ SV10 @ ( vplus @ SV24 @ SY64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(113,plain,
! [SV11: $i] :
( ( ( SV11 = v1 )
= $true )
| ( ( SV11
= ( vsucc @ ( vskolem2 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(114,plain,
! [SV12: $i] :
( ( ( vsucc @ SV12 )
= SV12 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(115,plain,
! [SV25: $i,SV13: $i] :
( ( ( SV13 = SV25 )
| ( ( vsucc @ SV13 )
!= ( vsucc @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(116,plain,
! [SV26: $i,SV14: $i] :
( ( ( ( vsucc @ SV14 )
!= ( vsucc @ SV26 ) )
| ( SV14 = SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(117,plain,
! [SV15: $i] :
( ( ( vsucc @ SV15 )
= v1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(118,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(119,plain,
( ( ~ ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(120,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( greater @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(121,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( SX1
= ( vplus @ SX0 @ ( sK3_Vd196 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(122,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( less @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(123,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( SX0
= ( vplus @ SX1 @ ( sK4_Vd201 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(124,plain,
( ( ~ ( greater @ vd203 @ vd204 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(125,plain,
( ( ~ ( less @ vd203 @ vd204 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(126,plain,
( ( ( greater @ vd203 @ vd204 )
= $false )
| ( ( vd203 = vd204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(127,plain,
! [SV1: $i,SV16: $i] :
( ( ( SV16
= ( vplus @ SV1 @ ( sK2_Vd125 @ SV16 @ SV1 ) ) )
= $true )
| ( ( ( SV1 = SV16 )
| ( SV1
= ( vplus @ SV16 @ ( sK1_Vd123 @ SV16 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(128,plain,
! [SV17: $i,SV2: $i] :
( ( ( SV2 != SV17 )
= $true )
| ( ( ! [SY59: $i] :
( SV17
!= ( vplus @ SV2 @ SY59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(129,plain,
! [SV18: $i,SV3: $i] :
( ( ( ! [SY60: $i] :
( SV3
!= ( vplus @ SV18 @ SY60 ) ) )
= $true )
| ( ( ! [SY61: $i] :
( SV18
!= ( vplus @ SV3 @ SY61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(130,plain,
! [SV19: $i,SV4: $i] :
( ( ( SV4 != SV19 )
= $true )
| ( ( ! [SY62: $i] :
( SV4
!= ( vplus @ SV19 @ SY62 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(131,plain,
! [SV20: $i,SV5: $i] :
( ( ( SV5 = SV20 )
= $true )
| ( ( ! [SY63: $i] :
( ( vplus @ SY63 @ SV5 )
!= ( vplus @ SY63 @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(132,plain,
! [SV6: $i,SV21: $i] :
( ( SV21
= ( vplus @ SV6 @ SV21 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(133,plain,
! [SV27: $i,SV24: $i,SV10: $i] :
( ( ( vplus @ ( vplus @ SV10 @ SV24 ) @ SV27 )
= ( vplus @ SV10 @ ( vplus @ SV24 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(134,plain,
! [SV25: $i,SV13: $i] :
( ( ( SV13 = SV25 )
= $true )
| ( ( ( vsucc @ SV13 )
!= ( vsucc @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(135,plain,
! [SV26: $i,SV14: $i] :
( ( ( ( vsucc @ SV14 )
!= ( vsucc @ SV26 ) )
= $true )
| ( ( SV14 = SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(136,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(137,plain,
( ( ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(138,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( greater @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(139,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( SX1
= ( vplus @ SX0 @ ( sK3_Vd196 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(140,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX0
!= ( vplus @ SX1 @ SX2 ) )
| ( less @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(141,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX1 @ SX0 )
| ( SX0
= ( vplus @ SX1 @ ( sK4_Vd201 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(142,plain,
( ( greater @ vd203 @ vd204 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(143,plain,
( ( less @ vd203 @ vd204 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(144,plain,
! [SV16: $i,SV1: $i] :
( ( ( SV1 = SV16 )
= $true )
| ( ( SV1
= ( vplus @ SV16 @ ( sK1_Vd123 @ SV16 @ SV1 ) ) )
= $true )
| ( ( SV16
= ( vplus @ SV1 @ ( sK2_Vd125 @ SV16 @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(145,plain,
! [SV17: $i,SV2: $i] :
( ( ( SV2 = SV17 )
= $false )
| ( ( ! [SY59: $i] :
( SV17
!= ( vplus @ SV2 @ SY59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(146,plain,
! [SV28: $i,SV18: $i,SV3: $i] :
( ( ( SV3
!= ( vplus @ SV18 @ SV28 ) )
= $true )
| ( ( ! [SY61: $i] :
( SV18
!= ( vplus @ SV3 @ SY61 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(147,plain,
! [SV19: $i,SV4: $i] :
( ( ( SV4 = SV19 )
= $false )
| ( ( ! [SY62: $i] :
( SV4
!= ( vplus @ SV19 @ SY62 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(148,plain,
! [SV20: $i,SV5: $i,SV29: $i] :
( ( ( ( vplus @ SV29 @ SV5 )
!= ( vplus @ SV29 @ SV20 ) )
= $true )
| ( ( SV5 = SV20 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(149,plain,
! [SV25: $i,SV13: $i] :
( ( ( ( vsucc @ SV13 )
= ( vsucc @ SV25 ) )
= $false )
| ( ( SV13 = SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(150,plain,
! [SV26: $i,SV14: $i] :
( ( ( ( vsucc @ SV14 )
= ( vsucc @ SV26 ) )
= $false )
| ( ( SV14 = SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(151,plain,
! [SV30: $i] :
( ( ! [SY65: $i] :
( ( vplus @ SV30 @ ( vsucc @ SY65 ) )
= ( vsucc @ ( vplus @ SV30 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(152,plain,
! [SV31: $i] :
( ( ( vplus @ SV31 @ v1 )
= ( vsucc @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(153,plain,
! [SV32: $i] :
( ( ! [SY66: $i] :
( ! [SY67: $i] :
( SY66
!= ( vplus @ SV32 @ SY67 ) )
| ( greater @ SY66 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(154,plain,
! [SV33: $i] :
( ( ! [SY68: $i] :
( ~ ( greater @ SY68 @ SV33 )
| ( SY68
= ( vplus @ SV33 @ ( sK3_Vd196 @ SY68 @ SV33 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(155,plain,
! [SV34: $i] :
( ( ! [SY69: $i] :
( ! [SY70: $i] :
( SV34
!= ( vplus @ SY69 @ SY70 ) )
| ( less @ SY69 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(156,plain,
! [SV35: $i] :
( ( ! [SY71: $i] :
( ~ ( less @ SY71 @ SV35 )
| ( SV35
= ( vplus @ SY71 @ ( sK4_Vd201 @ SY71 @ SV35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(157,plain,
! [SV36: $i,SV2: $i,SV17: $i] :
( ( ( SV17
!= ( vplus @ SV2 @ SV36 ) )
= $true )
| ( ( SV2 = SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(158,plain,
! [SV28: $i,SV18: $i,SV3: $i] :
( ( ( SV3
= ( vplus @ SV18 @ SV28 ) )
= $false )
| ( ( ! [SY61: $i] :
( SV18
!= ( vplus @ SV3 @ SY61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(159,plain,
! [SV37: $i,SV19: $i,SV4: $i] :
( ( ( SV4
!= ( vplus @ SV19 @ SV37 ) )
= $true )
| ( ( SV4 = SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(160,plain,
! [SV20: $i,SV5: $i,SV29: $i] :
( ( ( ( vplus @ SV29 @ SV5 )
= ( vplus @ SV29 @ SV20 ) )
= $false )
| ( ( SV5 = SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(161,plain,
! [SV38: $i,SV30: $i] :
( ( ( vplus @ SV30 @ ( vsucc @ SV38 ) )
= ( vsucc @ ( vplus @ SV30 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(162,plain,
! [SV32: $i,SV39: $i] :
( ( ! [SY72: $i] :
( SV39
!= ( vplus @ SV32 @ SY72 ) )
| ( greater @ SV39 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(163,plain,
! [SV33: $i,SV40: $i] :
( ( ~ ( greater @ SV40 @ SV33 )
| ( SV40
= ( vplus @ SV33 @ ( sK3_Vd196 @ SV40 @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(164,plain,
! [SV41: $i,SV34: $i] :
( ( ! [SY73: $i] :
( SV34
!= ( vplus @ SV41 @ SY73 ) )
| ( less @ SV41 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(165,plain,
! [SV35: $i,SV42: $i] :
( ( ~ ( less @ SV42 @ SV35 )
| ( SV35
= ( vplus @ SV42 @ ( sK4_Vd201 @ SV42 @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(166,plain,
! [SV36: $i,SV2: $i,SV17: $i] :
( ( ( SV17
= ( vplus @ SV2 @ SV36 ) )
= $false )
| ( ( SV2 = SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(167,plain,
! [SV28: $i,SV43: $i,SV3: $i,SV18: $i] :
( ( ( SV18
!= ( vplus @ SV3 @ SV43 ) )
= $true )
| ( ( SV3
= ( vplus @ SV18 @ SV28 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(168,plain,
! [SV37: $i,SV19: $i,SV4: $i] :
( ( ( SV4
= ( vplus @ SV19 @ SV37 ) )
= $false )
| ( ( SV4 = SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(169,plain,
! [SV32: $i,SV39: $i] :
( ( ( ! [SY72: $i] :
( SV39
!= ( vplus @ SV32 @ SY72 ) ) )
= $true )
| ( ( greater @ SV39 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(170,plain,
! [SV33: $i,SV40: $i] :
( ( ( ~ ( greater @ SV40 @ SV33 ) )
= $true )
| ( ( SV40
= ( vplus @ SV33 @ ( sK3_Vd196 @ SV40 @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(171,plain,
! [SV41: $i,SV34: $i] :
( ( ( ! [SY73: $i] :
( SV34
!= ( vplus @ SV41 @ SY73 ) ) )
= $true )
| ( ( less @ SV41 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(172,plain,
! [SV35: $i,SV42: $i] :
( ( ( ~ ( less @ SV42 @ SV35 ) )
= $true )
| ( ( SV35
= ( vplus @ SV42 @ ( sK4_Vd201 @ SV42 @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(173,plain,
! [SV28: $i,SV43: $i,SV3: $i,SV18: $i] :
( ( ( SV18
= ( vplus @ SV3 @ SV43 ) )
= $false )
| ( ( SV3
= ( vplus @ SV18 @ SV28 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(174,plain,
! [SV44: $i,SV32: $i,SV39: $i] :
( ( ( SV39
!= ( vplus @ SV32 @ SV44 ) )
= $true )
| ( ( greater @ SV39 @ SV32 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(175,plain,
! [SV33: $i,SV40: $i] :
( ( ( greater @ SV40 @ SV33 )
= $false )
| ( ( SV40
= ( vplus @ SV33 @ ( sK3_Vd196 @ SV40 @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(176,plain,
! [SV45: $i,SV41: $i,SV34: $i] :
( ( ( SV34
!= ( vplus @ SV41 @ SV45 ) )
= $true )
| ( ( less @ SV41 @ SV34 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(177,plain,
! [SV35: $i,SV42: $i] :
( ( ( less @ SV42 @ SV35 )
= $false )
| ( ( SV35
= ( vplus @ SV42 @ ( sK4_Vd201 @ SV42 @ SV35 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(178,plain,
! [SV44: $i,SV32: $i,SV39: $i] :
( ( ( SV39
= ( vplus @ SV32 @ SV44 ) )
= $false )
| ( ( greater @ SV39 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(179,plain,
! [SV45: $i,SV41: $i,SV34: $i] :
( ( ( SV34
= ( vplus @ SV41 @ SV45 ) )
= $false )
| ( ( less @ SV41 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(180,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[92,179,178,177,175,173,168,166,161,160,152,150,149,144,143,142,133,132,126,117,114,113,111,110]) ).
thf(181,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[180]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM836+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n017.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 13:36:00 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.54/0.31
% 0.54/0.31 No.of.Axioms: 19
% 0.54/0.31
% 0.54/0.31 Length.of.Defs: 0
% 0.54/0.31
% 0.54/0.31 Contains.Choice.Funs: false
% 0.54/0.31 .....
% 0.54/0.31
% 0.54/0.31 ********************************
% 0.54/0.31 * All subproblems solved! *
% 0.54/0.31 ********************************
% 0.54/0.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:19,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:180,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.54/0.31
% 0.54/0.31 %**** Beginning of derivation protocol ****
% 0.54/0.31 % SZS output start CNFRefutation
% See solution above
% 0.54/0.31
% 0.54/0.31 %**** End of derivation protocol ****
% 0.54/0.31 %**** no. of clauses in derivation: 181 ****
% 0.54/0.31 %**** clause counter: 180 ****
% 0.54/0.31
% 0.54/0.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:19,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:180,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------