TSTP Solution File: NUM851+2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM851+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 11:56:04 EDT 2022
% Result : Theorem 0.92s 1.10s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 43
% Syntax : Number of formulae : 215 ( 157 unt; 16 typ; 0 def)
% Number of atoms : 728 ( 466 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 1237 ( 134 ~; 103 |; 10 &; 978 @)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 440 ( 0 ^ 426 !; 14 ?; 440 :)
% 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_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_v1,type,
v1: $i ).
thf(tp_vd469,type,
vd469: $i ).
thf(tp_vd470,type,
vd470: $i ).
thf(tp_vd471,type,
vd471: $i ).
thf(tp_vd473,type,
vd473: $i ).
thf(tp_vmul,type,
vmul: $i > $i > $i ).
thf(tp_vplus,type,
vplus: $i > $i > $i ).
thf(tp_vskolem2,type,
vskolem2: $i > $i ).
thf(tp_vsucc,type,
vsucc: $i > $i ).
thf(1,axiom,
! [Vd7: $i,Vd8: $i] :
( ( Vd7 != Vd8 )
=> ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
thf(2,axiom,
! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
thf(3,axiom,
! [Vd24: $i] :
( ( Vd24 != v1 )
=> ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
thf(4,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(5,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(6,axiom,
! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(7,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(8,axiom,
! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(9,axiom,
! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
thf(10,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(11,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(12,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(13,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(14,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(15,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(16,axiom,
! [Vd375: $i,Vd376: $i] :
( ( greater @ Vd375 @ Vd376 )
=> ( geq @ Vd375 @ ( vplus @ Vd376 @ v1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(234, 0), 0)') ).
thf(17,axiom,
! [Vd386: $i,Vd387: $i] :
( ( less @ Vd386 @ ( vplus @ Vd387 @ v1 ) )
=> ( leq @ Vd386 @ Vd387 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(241, 0), 0)') ).
thf(18,axiom,
! [Vd396: $i,Vd397: $i] :
( ( ( vmul @ Vd396 @ ( vsucc @ Vd397 ) )
= ( vplus @ ( vmul @ Vd396 @ Vd397 ) @ Vd396 ) )
& ( ( vmul @ Vd396 @ v1 )
= Vd396 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
thf(19,axiom,
! [Vd400: $i] :
( ( vmul @ v1 @ Vd400 )
= Vd400 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
thf(20,axiom,
! [Vd408: $i,Vd409: $i] :
( ( vmul @ ( vsucc @ Vd408 ) @ Vd409 )
= ( vplus @ ( vmul @ Vd408 @ Vd409 ) @ Vd409 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).
thf(21,axiom,
! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
thf(22,axiom,
! [Vd432: $i,Vd433: $i,Vd434: $i] :
( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
= ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
thf(23,axiom,
! [Vd444: $i,Vd445: $i,Vd446: $i] :
( ( vmul @ ( vmul @ Vd444 @ Vd445 ) @ Vd446 )
= ( vmul @ Vd444 @ ( vmul @ Vd445 @ Vd446 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(290, 0), 0)') ).
thf(24,axiom,
greater @ vd470 @ vd471,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(antec(302), 472, 0)') ).
thf(25,axiom,
( vd470
= ( vplus @ vd471 @ vd473 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq(302)), 474, 0)') ).
thf(26,axiom,
( ( vmul @ vd470 @ vd469 )
= ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct2(conseq(302)), 475, 0)') ).
thf(27,conjecture,
( ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 )
= ( vplus @ ( vmul @ vd471 @ vd469 ) @ ( vmul @ vd473 @ vd469 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct2(conseq(302)), 475, 1)') ).
thf(28,negated_conjecture,
( ( ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 )
= ( vplus @ ( vmul @ vd471 @ vd469 ) @ ( vmul @ vd473 @ vd469 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[27]) ).
thf(29,plain,
( ( ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 )
= ( vplus @ ( vmul @ vd471 @ vd469 ) @ ( vmul @ vd473 @ vd469 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[28]) ).
thf(30,plain,
( ( ! [Vd7: $i,Vd8: $i] :
( ( Vd7 != Vd8 )
=> ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(31,plain,
( ( ! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(32,plain,
( ( ! [Vd24: $i] :
( ( Vd24 != v1 )
=> ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(33,plain,
( ( ! [Vd42: $i,Vd43: $i] :
( ( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
= ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
& ( ( vplus @ Vd42 @ v1 )
= ( vsucc @ Vd42 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(34,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(35,plain,
( ( ! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(36,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(37,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(38,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(39,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 != Vd105 )
=> ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(40,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(41,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ~ ? [Vd123: $i] :
( Vd120
= ( vplus @ Vd121 @ Vd123 ) )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(42,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ~ ? [Vd125: $i] :
( Vd121
= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(43,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)],[14]) ).
thf(44,plain,
( ( ! [Vd193: $i,Vd194: $i] :
( ( greater @ Vd194 @ Vd193 )
<=> ? [Vd196: $i] :
( Vd194
= ( vplus @ Vd193 @ Vd196 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(45,plain,
( ( ! [Vd375: $i,Vd376: $i] :
( ( greater @ Vd375 @ Vd376 )
=> ( geq @ Vd375 @ ( vplus @ Vd376 @ v1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(46,plain,
( ( ! [Vd386: $i,Vd387: $i] :
( ( less @ Vd386 @ ( vplus @ Vd387 @ v1 ) )
=> ( leq @ Vd386 @ Vd387 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(47,plain,
( ( ! [Vd396: $i,Vd397: $i] :
( ( ( vmul @ Vd396 @ ( vsucc @ Vd397 ) )
= ( vplus @ ( vmul @ Vd396 @ Vd397 ) @ Vd396 ) )
& ( ( vmul @ Vd396 @ v1 )
= Vd396 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(48,plain,
( ( ! [Vd400: $i] :
( ( vmul @ v1 @ Vd400 )
= Vd400 ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(49,plain,
( ( ! [Vd408: $i,Vd409: $i] :
( ( vmul @ ( vsucc @ Vd408 ) @ Vd409 )
= ( vplus @ ( vmul @ Vd408 @ Vd409 ) @ Vd409 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(50,plain,
( ( ! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(51,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)],[22]) ).
thf(52,plain,
( ( ! [Vd444: $i,Vd445: $i,Vd446: $i] :
( ( vmul @ ( vmul @ Vd444 @ Vd445 ) @ Vd446 )
= ( vmul @ Vd444 @ ( vmul @ Vd445 @ Vd446 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(53,plain,
( ( greater @ vd470 @ vd471 )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(54,plain,
( ( vd470
= ( vplus @ vd471 @ vd473 ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(55,plain,
( ( ( vmul @ vd470 @ vd469 )
= ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(56,plain,
( ( ( ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 )
!= ( vplus @ ( vmul @ vd471 @ vd469 ) @ ( vmul @ vd473 @ vd469 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[29]) ).
thf(57,plain,
( ( ! [Vd7: $i,Vd8: $i] :
( ( Vd7 = Vd8 )
| ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(58,plain,
( ( ! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(59,plain,
( ( ! [Vd24: $i] :
( ( Vd24 = v1 )
| ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(60,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)],[33]) ).
thf(61,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(62,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 = Vd105 )
| ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(63,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ! [Vd123: $i] :
( Vd120
!= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(64,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ! [Vd123: $i] :
( Vd120
!= ( vplus @ Vd121 @ Vd123 ) )
| ! [Vd125: $i] :
( Vd121
!= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(65,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ! [Vd125: $i] :
( Vd121
!= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(66,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)],[43]) ).
thf(67,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)],[44]) ).
thf(68,plain,
( ( ! [Vd375: $i,Vd376: $i] :
( ~ ( greater @ Vd375 @ Vd376 )
| ( geq @ Vd375 @ ( vplus @ Vd376 @ v1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(69,plain,
( ( ! [Vd386: $i,Vd387: $i] :
( ~ ( less @ Vd386 @ ( vplus @ Vd387 @ v1 ) )
| ( leq @ Vd386 @ Vd387 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(70,plain,
( ( ! [Vd396: $i,Vd397: $i] :
( ( vmul @ Vd396 @ ( vsucc @ Vd397 ) )
= ( vplus @ ( vmul @ Vd396 @ Vd397 ) @ Vd396 ) )
& ! [Vd396: $i] :
( ( vmul @ Vd396 @ v1 )
= Vd396 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(71,plain,
( ( ( vmul @ vd470 @ vd469 )
= ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(72,plain,
( ( vd470
= ( vplus @ vd471 @ vd473 ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(73,plain,
( ( greater @ vd470 @ vd471 )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(74,plain,
( ( ! [Vd444: $i,Vd445: $i,Vd446: $i] :
( ( vmul @ ( vmul @ Vd444 @ Vd445 ) @ Vd446 )
= ( vmul @ Vd444 @ ( vmul @ Vd445 @ Vd446 ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(75,plain,
( ( ! [Vd432: $i,Vd433: $i,Vd434: $i] :
( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
= ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(76,plain,
( ( ! [Vd418: $i,Vd419: $i] :
( ( vmul @ Vd418 @ Vd419 )
= ( vmul @ Vd419 @ Vd418 ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(77,plain,
( ( ! [Vd408: $i,Vd409: $i] :
( ( vmul @ ( vsucc @ Vd408 ) @ Vd409 )
= ( vplus @ ( vmul @ Vd408 @ Vd409 ) @ Vd409 ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(78,plain,
( ( ! [Vd400: $i] :
( ( vmul @ v1 @ Vd400 )
= Vd400 ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(79,plain,
( ( ! [Vd396: $i,Vd397: $i] :
( ( vmul @ Vd396 @ ( vsucc @ Vd397 ) )
= ( vplus @ ( vmul @ Vd396 @ Vd397 ) @ Vd396 ) )
& ! [Vd396: $i] :
( ( vmul @ Vd396 @ v1 )
= Vd396 ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(80,plain,
( ( ! [Vd386: $i,Vd387: $i] :
( ~ ( less @ Vd386 @ ( vplus @ Vd387 @ v1 ) )
| ( leq @ Vd386 @ Vd387 ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(81,plain,
( ( ! [Vd375: $i,Vd376: $i] :
( ~ ( greater @ Vd375 @ Vd376 )
| ( geq @ Vd375 @ ( vplus @ Vd376 @ v1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(82,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)],[67]) ).
thf(83,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)],[66]) ).
thf(84,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ! [Vd125: $i] :
( Vd121
!= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(85,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ! [Vd123: $i] :
( Vd120
!= ( vplus @ Vd121 @ Vd123 ) )
| ! [Vd125: $i] :
( Vd121
!= ( vplus @ Vd120 @ Vd125 ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(86,plain,
( ( ! [Vd120: $i,Vd121: $i] :
( ( Vd120 != Vd121 )
| ! [Vd123: $i] :
( Vd120
!= ( vplus @ Vd121 @ Vd123 ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(87,plain,
( ( ! [Vd104: $i,Vd105: $i] :
( ( Vd104 = Vd105 )
| ! [Vd107: $i] :
( ( vplus @ Vd107 @ Vd104 )
!= ( vplus @ Vd107 @ Vd105 ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(88,plain,
( ( ! [Vd92: $i,Vd93: $i] :
( Vd93
!= ( vplus @ Vd92 @ Vd93 ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(89,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(90,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(91,plain,
( ( ! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(92,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(93,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)],[60]) ).
thf(94,plain,
( ( ! [Vd24: $i] :
( ( Vd24 = v1 )
| ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(95,plain,
( ( ! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(96,plain,
( ( ! [Vd7: $i,Vd8: $i] :
( ( Vd7 = Vd8 )
| ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(97,plain,
( ( ( ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 )
!= ( vplus @ ( vmul @ vd471 @ vd469 ) @ ( vmul @ vd473 @ vd469 ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(98,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)],[93]) ).
thf(99,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( vmul @ SX0 @ ( vsucc @ SX1 ) )
= ( vplus @ ( vmul @ SX0 @ SX1 ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ( vmul @ SX0 @ v1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[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 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(101,plain,
! [SV1: $i] :
( ( ! [SY53: $i,SY54: $i] :
( ( vmul @ ( vmul @ SV1 @ SY53 ) @ SY54 )
= ( vmul @ SV1 @ ( vmul @ SY53 @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(102,plain,
! [SV2: $i] :
( ( ! [SY55: $i,SY56: $i] :
( ( vmul @ SV2 @ ( vplus @ SY55 @ SY56 ) )
= ( vplus @ ( vmul @ SV2 @ SY55 ) @ ( vmul @ SV2 @ SY56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(103,plain,
! [SV3: $i] :
( ( ! [SY57: $i] :
( ( vmul @ SV3 @ SY57 )
= ( vmul @ SY57 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(104,plain,
! [SV4: $i] :
( ( ! [SY58: $i] :
( ( vmul @ ( vsucc @ SV4 ) @ SY58 )
= ( vplus @ ( vmul @ SV4 @ SY58 ) @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(105,plain,
! [SV5: $i] :
( ( ( vmul @ v1 @ SV5 )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(106,plain,
! [SV6: $i] :
( ( ! [SY59: $i] :
( ~ ( less @ SV6 @ ( vplus @ SY59 @ v1 ) )
| ( leq @ SV6 @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(107,plain,
! [SV7: $i] :
( ( ! [SY60: $i] :
( ~ ( greater @ SV7 @ SY60 )
| ( geq @ SV7 @ ( vplus @ SY60 @ v1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(108,plain,
! [SV8: $i] :
( ( ! [SY61: $i] :
( ( SY61
= ( vplus @ SV8 @ ( sK2_Vd125 @ SY61 @ SV8 ) ) )
| ( SV8 = SY61 )
| ( SV8
= ( vplus @ SY61 @ ( sK1_Vd123 @ SY61 @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(109,plain,
! [SV9: $i] :
( ( ! [SY62: $i] :
( ( SV9 != SY62 )
| ! [SY63: $i] :
( SY62
!= ( vplus @ SV9 @ SY63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(110,plain,
! [SV10: $i] :
( ( ! [SY64: $i] :
( ! [SY65: $i] :
( SV10
!= ( vplus @ SY64 @ SY65 ) )
| ! [SY66: $i] :
( SY64
!= ( vplus @ SV10 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(111,plain,
! [SV11: $i] :
( ( ! [SY67: $i] :
( ( SV11 != SY67 )
| ! [SY68: $i] :
( SV11
!= ( vplus @ SY67 @ SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(112,plain,
! [SV12: $i] :
( ( ! [SY69: $i] :
( ( SV12 = SY69 )
| ! [SY70: $i] :
( ( vplus @ SY70 @ SV12 )
!= ( vplus @ SY70 @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(113,plain,
! [SV13: $i] :
( ( ! [SY71: $i] :
( SY71
!= ( vplus @ SV13 @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(114,plain,
! [SV14: $i] :
( ( ! [SY72: $i] :
( ( vplus @ SY72 @ SV14 )
= ( vplus @ SV14 @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(115,plain,
! [SV15: $i] :
( ( ! [SY73: $i] :
( ( vplus @ ( vsucc @ SV15 ) @ SY73 )
= ( vsucc @ ( vplus @ SV15 @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(116,plain,
! [SV16: $i] :
( ( ( vplus @ v1 @ SV16 )
= ( vsucc @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(117,plain,
! [SV17: $i] :
( ( ! [SY74: $i,SY75: $i] :
( ( vplus @ ( vplus @ SV17 @ SY74 ) @ SY75 )
= ( vplus @ SV17 @ ( vplus @ SY74 @ SY75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(118,plain,
! [SV18: $i] :
( ( ( SV18 = v1 )
| ( SV18
= ( vsucc @ ( vskolem2 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(119,plain,
! [SV19: $i] :
( ( ( ( vsucc @ SV19 )
!= SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(120,plain,
! [SV20: $i] :
( ( ! [SY76: $i] :
( ( SV20 = SY76 )
| ( ( vsucc @ SV20 )
!= ( vsucc @ SY76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(121,plain,
( ( ( vmul @ ( vplus @ vd471 @ vd473 ) @ vd469 )
= ( vplus @ ( vmul @ vd471 @ vd469 ) @ ( vmul @ vd473 @ vd469 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(122,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)],[98]) ).
thf(123,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( vmul @ SX0 @ ( vsucc @ SX1 ) )
= ( vplus @ ( vmul @ SX0 @ SX1 ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ( vmul @ SX0 @ v1 )
= SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(124,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)],[100]) ).
thf(125,plain,
! [SV21: $i,SV1: $i] :
( ( ! [SY77: $i] :
( ( vmul @ ( vmul @ SV1 @ SV21 ) @ SY77 )
= ( vmul @ SV1 @ ( vmul @ SV21 @ SY77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(126,plain,
! [SV22: $i,SV2: $i] :
( ( ! [SY78: $i] :
( ( vmul @ SV2 @ ( vplus @ SV22 @ SY78 ) )
= ( vplus @ ( vmul @ SV2 @ SV22 ) @ ( vmul @ SV2 @ SY78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(127,plain,
! [SV23: $i,SV3: $i] :
( ( ( vmul @ SV3 @ SV23 )
= ( vmul @ SV23 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(128,plain,
! [SV24: $i,SV4: $i] :
( ( ( vmul @ ( vsucc @ SV4 ) @ SV24 )
= ( vplus @ ( vmul @ SV4 @ SV24 ) @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(129,plain,
! [SV25: $i,SV6: $i] :
( ( ~ ( less @ SV6 @ ( vplus @ SV25 @ v1 ) )
| ( leq @ SV6 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(130,plain,
! [SV26: $i,SV7: $i] :
( ( ~ ( greater @ SV7 @ SV26 )
| ( geq @ SV7 @ ( vplus @ SV26 @ v1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(131,plain,
! [SV8: $i,SV27: $i] :
( ( ( SV27
= ( vplus @ SV8 @ ( sK2_Vd125 @ SV27 @ SV8 ) ) )
| ( SV8 = SV27 )
| ( SV8
= ( vplus @ SV27 @ ( sK1_Vd123 @ SV27 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(132,plain,
! [SV28: $i,SV9: $i] :
( ( ( SV9 != SV28 )
| ! [SY79: $i] :
( SV28
!= ( vplus @ SV9 @ SY79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(133,plain,
! [SV29: $i,SV10: $i] :
( ( ! [SY80: $i] :
( SV10
!= ( vplus @ SV29 @ SY80 ) )
| ! [SY81: $i] :
( SV29
!= ( vplus @ SV10 @ SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(134,plain,
! [SV30: $i,SV11: $i] :
( ( ( SV11 != SV30 )
| ! [SY82: $i] :
( SV11
!= ( vplus @ SV30 @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(135,plain,
! [SV31: $i,SV12: $i] :
( ( ( SV12 = SV31 )
| ! [SY83: $i] :
( ( vplus @ SY83 @ SV12 )
!= ( vplus @ SY83 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(136,plain,
! [SV13: $i,SV32: $i] :
( ( ( SV32
!= ( vplus @ SV13 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(137,plain,
! [SV14: $i,SV33: $i] :
( ( ( vplus @ SV33 @ SV14 )
= ( vplus @ SV14 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(138,plain,
! [SV34: $i,SV15: $i] :
( ( ( vplus @ ( vsucc @ SV15 ) @ SV34 )
= ( vsucc @ ( vplus @ SV15 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(139,plain,
! [SV35: $i,SV17: $i] :
( ( ! [SY84: $i] :
( ( vplus @ ( vplus @ SV17 @ SV35 ) @ SY84 )
= ( vplus @ SV17 @ ( vplus @ SV35 @ SY84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(140,plain,
! [SV18: $i] :
( ( ( SV18 = v1 )
= $true )
| ( ( SV18
= ( vsucc @ ( vskolem2 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(141,plain,
! [SV19: $i] :
( ( ( vsucc @ SV19 )
= SV19 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(142,plain,
! [SV36: $i,SV20: $i] :
( ( ( SV20 = SV36 )
| ( ( vsucc @ SV20 )
!= ( vsucc @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(143,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(144,plain,
( ( ~ ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(145,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( vmul @ SX0 @ ( vsucc @ SX1 ) )
= ( vplus @ ( vmul @ SX0 @ SX1 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(146,plain,
( ( ~ ! [SX0: $i] :
( ( vmul @ SX0 @ v1 )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(147,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( greater @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(148,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( SX1
= ( vplus @ SX0 @ ( sK3_Vd196 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(149,plain,
! [SV37: $i,SV21: $i,SV1: $i] :
( ( ( vmul @ ( vmul @ SV1 @ SV21 ) @ SV37 )
= ( vmul @ SV1 @ ( vmul @ SV21 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(150,plain,
! [SV38: $i,SV22: $i,SV2: $i] :
( ( ( vmul @ SV2 @ ( vplus @ SV22 @ SV38 ) )
= ( vplus @ ( vmul @ SV2 @ SV22 ) @ ( vmul @ SV2 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(151,plain,
! [SV25: $i,SV6: $i] :
( ( ( ~ ( less @ SV6 @ ( vplus @ SV25 @ v1 ) ) )
= $true )
| ( ( leq @ SV6 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(152,plain,
! [SV26: $i,SV7: $i] :
( ( ( ~ ( greater @ SV7 @ SV26 ) )
= $true )
| ( ( geq @ SV7 @ ( vplus @ SV26 @ v1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(153,plain,
! [SV8: $i,SV27: $i] :
( ( ( SV27
= ( vplus @ SV8 @ ( sK2_Vd125 @ SV27 @ SV8 ) ) )
= $true )
| ( ( ( SV8 = SV27 )
| ( SV8
= ( vplus @ SV27 @ ( sK1_Vd123 @ SV27 @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(154,plain,
! [SV28: $i,SV9: $i] :
( ( ( ( SV9 != SV28 ) )
= $true )
| ( ( ! [SY79: $i] :
( SV28
!= ( vplus @ SV9 @ SY79 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(155,plain,
! [SV29: $i,SV10: $i] :
( ( ( ! [SY80: $i] :
( SV10
!= ( vplus @ SV29 @ SY80 ) ) )
= $true )
| ( ( ! [SY81: $i] :
( SV29
!= ( vplus @ SV10 @ SY81 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(156,plain,
! [SV30: $i,SV11: $i] :
( ( ( ( SV11 != SV30 ) )
= $true )
| ( ( ! [SY82: $i] :
( SV11
!= ( vplus @ SV30 @ SY82 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(157,plain,
! [SV31: $i,SV12: $i] :
( ( ( SV12 = SV31 )
= $true )
| ( ( ! [SY83: $i] :
( ( vplus @ SY83 @ SV12 )
!= ( vplus @ SY83 @ SV31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(158,plain,
! [SV13: $i,SV32: $i] :
( ( SV32
= ( vplus @ SV13 @ SV32 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(159,plain,
! [SV39: $i,SV35: $i,SV17: $i] :
( ( ( vplus @ ( vplus @ SV17 @ SV35 ) @ SV39 )
= ( vplus @ SV17 @ ( vplus @ SV35 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(160,plain,
! [SV36: $i,SV20: $i] :
( ( ( SV20 = SV36 )
= $true )
| ( ( ( ( vsucc @ SV20 )
!= ( vsucc @ SV36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(161,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(162,plain,
( ( ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(163,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( vmul @ SX0 @ ( vsucc @ SX1 ) )
= ( vplus @ ( vmul @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(164,plain,
( ( ! [SX0: $i] :
( ( vmul @ SX0 @ v1 )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(165,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( SX1
!= ( vplus @ SX0 @ SX2 ) )
| ( greater @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(166,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( greater @ SX1 @ SX0 )
| ( SX1
= ( vplus @ SX0 @ ( sK3_Vd196 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(167,plain,
! [SV25: $i,SV6: $i] :
( ( ( less @ SV6 @ ( vplus @ SV25 @ v1 ) )
= $false )
| ( ( leq @ SV6 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(168,plain,
! [SV26: $i,SV7: $i] :
( ( ( greater @ SV7 @ SV26 )
= $false )
| ( ( geq @ SV7 @ ( vplus @ SV26 @ v1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(169,plain,
! [SV27: $i,SV8: $i] :
( ( ( SV8 = SV27 )
= $true )
| ( ( SV8
= ( vplus @ SV27 @ ( sK1_Vd123 @ SV27 @ SV8 ) ) )
= $true )
| ( ( SV27
= ( vplus @ SV8 @ ( sK2_Vd125 @ SV27 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(170,plain,
! [SV28: $i,SV9: $i] :
( ( ( SV9 = SV28 )
= $false )
| ( ( ! [SY79: $i] :
( SV28
!= ( vplus @ SV9 @ SY79 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(171,plain,
! [SV40: $i,SV29: $i,SV10: $i] :
( ( ( ( SV10
!= ( vplus @ SV29 @ SV40 ) ) )
= $true )
| ( ( ! [SY81: $i] :
( SV29
!= ( vplus @ SV10 @ SY81 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(172,plain,
! [SV30: $i,SV11: $i] :
( ( ( SV11 = SV30 )
= $false )
| ( ( ! [SY82: $i] :
( SV11
!= ( vplus @ SV30 @ SY82 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(173,plain,
! [SV31: $i,SV12: $i,SV41: $i] :
( ( ( ( ( vplus @ SV41 @ SV12 )
!= ( vplus @ SV41 @ SV31 ) ) )
= $true )
| ( ( SV12 = SV31 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(174,plain,
! [SV36: $i,SV20: $i] :
( ( ( ( vsucc @ SV20 )
= ( vsucc @ SV36 ) )
= $false )
| ( ( SV20 = SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(175,plain,
! [SV42: $i] :
( ( ! [SY85: $i] :
( ( vplus @ SV42 @ ( vsucc @ SY85 ) )
= ( vsucc @ ( vplus @ SV42 @ SY85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(176,plain,
! [SV43: $i] :
( ( ( vplus @ SV43 @ v1 )
= ( vsucc @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(177,plain,
! [SV44: $i] :
( ( ! [SY86: $i] :
( ( vmul @ SV44 @ ( vsucc @ SY86 ) )
= ( vplus @ ( vmul @ SV44 @ SY86 ) @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(178,plain,
! [SV45: $i] :
( ( ( vmul @ SV45 @ v1 )
= SV45 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(179,plain,
! [SV46: $i] :
( ( ! [SY87: $i] :
( ! [SY88: $i] :
( SY87
!= ( vplus @ SV46 @ SY88 ) )
| ( greater @ SY87 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(180,plain,
! [SV47: $i] :
( ( ! [SY89: $i] :
( ~ ( greater @ SY89 @ SV47 )
| ( SY89
= ( vplus @ SV47 @ ( sK3_Vd196 @ SY89 @ SV47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(181,plain,
! [SV48: $i,SV9: $i,SV28: $i] :
( ( ( ( SV28
!= ( vplus @ SV9 @ SV48 ) ) )
= $true )
| ( ( SV9 = SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(182,plain,
! [SV40: $i,SV29: $i,SV10: $i] :
( ( ( SV10
= ( vplus @ SV29 @ SV40 ) )
= $false )
| ( ( ! [SY81: $i] :
( SV29
!= ( vplus @ SV10 @ SY81 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(183,plain,
! [SV49: $i,SV30: $i,SV11: $i] :
( ( ( ( SV11
!= ( vplus @ SV30 @ SV49 ) ) )
= $true )
| ( ( SV11 = SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(184,plain,
! [SV31: $i,SV12: $i,SV41: $i] :
( ( ( ( vplus @ SV41 @ SV12 )
= ( vplus @ SV41 @ SV31 ) )
= $false )
| ( ( SV12 = SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(185,plain,
! [SV50: $i,SV42: $i] :
( ( ( vplus @ SV42 @ ( vsucc @ SV50 ) )
= ( vsucc @ ( vplus @ SV42 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(186,plain,
! [SV51: $i,SV44: $i] :
( ( ( vmul @ SV44 @ ( vsucc @ SV51 ) )
= ( vplus @ ( vmul @ SV44 @ SV51 ) @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(187,plain,
! [SV46: $i,SV52: $i] :
( ( ! [SY90: $i] :
( SV52
!= ( vplus @ SV46 @ SY90 ) )
| ( greater @ SV52 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(188,plain,
! [SV47: $i,SV53: $i] :
( ( ~ ( greater @ SV53 @ SV47 )
| ( SV53
= ( vplus @ SV47 @ ( sK3_Vd196 @ SV53 @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(189,plain,
! [SV48: $i,SV9: $i,SV28: $i] :
( ( ( SV28
= ( vplus @ SV9 @ SV48 ) )
= $false )
| ( ( SV9 = SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(190,plain,
! [SV40: $i,SV54: $i,SV10: $i,SV29: $i] :
( ( ( ( SV29
!= ( vplus @ SV10 @ SV54 ) ) )
= $true )
| ( ( SV10
= ( vplus @ SV29 @ SV40 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(191,plain,
! [SV49: $i,SV30: $i,SV11: $i] :
( ( ( SV11
= ( vplus @ SV30 @ SV49 ) )
= $false )
| ( ( SV11 = SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(192,plain,
! [SV46: $i,SV52: $i] :
( ( ( ! [SY90: $i] :
( SV52
!= ( vplus @ SV46 @ SY90 ) ) )
= $true )
| ( ( greater @ SV52 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(193,plain,
! [SV47: $i,SV53: $i] :
( ( ( ~ ( greater @ SV53 @ SV47 ) )
= $true )
| ( ( SV53
= ( vplus @ SV47 @ ( sK3_Vd196 @ SV53 @ SV47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(194,plain,
! [SV40: $i,SV54: $i,SV10: $i,SV29: $i] :
( ( ( SV29
= ( vplus @ SV10 @ SV54 ) )
= $false )
| ( ( SV10
= ( vplus @ SV29 @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(195,plain,
! [SV55: $i,SV46: $i,SV52: $i] :
( ( ( ( SV52
!= ( vplus @ SV46 @ SV55 ) ) )
= $true )
| ( ( greater @ SV52 @ SV46 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(196,plain,
! [SV47: $i,SV53: $i] :
( ( ( greater @ SV53 @ SV47 )
= $false )
| ( ( SV53
= ( vplus @ SV47 @ ( sK3_Vd196 @ SV53 @ SV47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(197,plain,
! [SV55: $i,SV46: $i,SV52: $i] :
( ( ( SV52
= ( vplus @ SV46 @ SV55 ) )
= $false )
| ( ( greater @ SV52 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(198,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[71,197,196,194,191,189,186,185,184,178,176,174,169,168,167,159,158,150,149,141,140,138,137,128,127,121,116,105,73,72]) ).
thf(199,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM851+2 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 5 14:10:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 26
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.36 .
% 0.13/0.37 (rf:0,axioms:26,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:28,loop_count:0,foatp_calls:0,translation:fof_full)...........
% 0.92/1.10
% 0.92/1.10 ********************************
% 0.92/1.10 * All subproblems solved! *
% 0.92/1.10 ********************************
% 0.92/1.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:26,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:198,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.92/1.11
% 0.92/1.11 %**** Beginning of derivation protocol ****
% 0.92/1.11 % SZS output start CNFRefutation
% See solution above
% 0.92/1.11
% 0.92/1.11 %**** End of derivation protocol ****
% 0.92/1.11 %**** no. of clauses in derivation: 199 ****
% 0.92/1.11 %**** clause counter: 198 ****
% 0.92/1.11
% 0.92/1.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:26,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:198,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------