TSTP Solution File: NUM844+2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM844+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 : n008.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 11:55:59 EDT 2022
% Result : Theorem 0.18s 0.40s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 31
% Syntax : Number of formulae : 126 ( 102 unt; 11 typ; 0 def)
% Number of atoms : 359 ( 224 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 768 ( 42 ~; 26 |; 8 &; 684 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 160 ( 0 ^ 160 !; 0 ?; 160 :)
% 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_v1,type,
v1: $i ).
thf(tp_vd411,type,
vd411: $i ).
thf(tp_vd413,type,
vd413: $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,
! [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(10,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(11,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(12,axiom,
! [Vd400: $i] :
( ( vmul @ v1 @ Vd400 )
= Vd400 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
thf(13,axiom,
( ( vmul @ ( vsucc @ vd411 ) @ v1 )
= ( vsucc @ vd411 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(264, 412, 0)') ).
thf(14,axiom,
( ( vsucc @ vd411 )
= ( vsucc @ ( vmul @ vd411 @ v1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(264, 412, 1)') ).
thf(15,axiom,
( ( vsucc @ ( vmul @ vd411 @ v1 ) )
= ( vplus @ ( vmul @ vd411 @ v1 ) @ v1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(264, 412, 2)') ).
thf(16,axiom,
( ( vmul @ ( vsucc @ vd411 ) @ vd413 )
= ( vplus @ ( vmul @ vd411 @ vd413 ) @ vd413 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(265, 414, 0)') ).
thf(17,axiom,
( ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ vd413 ) )
= ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ vd413 ) @ ( vsucc @ vd411 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(266, 415, 0)') ).
thf(18,axiom,
( ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ vd413 ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vplus @ ( vmul @ vd411 @ vd413 ) @ vd413 ) @ ( vsucc @ vd411 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(266, 415, 1)') ).
thf(19,axiom,
( ( vplus @ ( vplus @ ( vmul @ vd411 @ vd413 ) @ vd413 ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ vd413 @ ( vsucc @ vd411 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(266, 415, 2)') ).
thf(20,conjecture,
( ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ vd413 @ ( vsucc @ vd411 ) ) )
= ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ ( vsucc @ vd411 ) @ vd413 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(266, 415, 3)') ).
thf(21,negated_conjecture,
( ( ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ vd413 @ ( vsucc @ vd411 ) ) )
= ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ ( vsucc @ vd411 ) @ vd413 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[20]) ).
thf(22,plain,
( ( ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ vd413 @ ( vsucc @ vd411 ) ) )
= ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ ( vsucc @ vd411 ) @ vd413 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[21]) ).
thf(23,plain,
( ( ! [Vd7: $i,Vd8: $i] :
( ( Vd7 != Vd8 )
=> ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(24,plain,
( ( ! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(25,plain,
( ( ! [Vd24: $i] :
( ( Vd24 != v1 )
=> ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(26,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(27,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(28,plain,
( ( ! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(29,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(30,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(31,plain,
( ( ! [Vd375: $i,Vd376: $i] :
( ( greater @ Vd375 @ Vd376 )
=> ( geq @ Vd375 @ ( vplus @ Vd376 @ v1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(32,plain,
( ( ! [Vd386: $i,Vd387: $i] :
( ( less @ Vd386 @ ( vplus @ Vd387 @ v1 ) )
=> ( leq @ Vd386 @ Vd387 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(33,plain,
( ( ! [Vd396: $i,Vd397: $i] :
( ( ( vmul @ Vd396 @ ( vsucc @ Vd397 ) )
= ( vplus @ ( vmul @ Vd396 @ Vd397 ) @ Vd396 ) )
& ( ( vmul @ Vd396 @ v1 )
= Vd396 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(34,plain,
( ( ! [Vd400: $i] :
( ( vmul @ v1 @ Vd400 )
= Vd400 ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(35,plain,
( ( ( vmul @ ( vsucc @ vd411 ) @ v1 )
= ( vsucc @ vd411 ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(36,plain,
( ( ( vsucc @ vd411 )
= ( vsucc @ ( vmul @ vd411 @ v1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(37,plain,
( ( ( vsucc @ ( vmul @ vd411 @ v1 ) )
= ( vplus @ ( vmul @ vd411 @ v1 ) @ v1 ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(38,plain,
( ( ( vmul @ ( vsucc @ vd411 ) @ vd413 )
= ( vplus @ ( vmul @ vd411 @ vd413 ) @ vd413 ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(39,plain,
( ( ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ vd413 ) )
= ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ vd413 ) @ ( vsucc @ vd411 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(40,plain,
( ( ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ vd413 ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vplus @ ( vmul @ vd411 @ vd413 ) @ vd413 ) @ ( vsucc @ vd411 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(41,plain,
( ( ( vplus @ ( vplus @ ( vmul @ vd411 @ vd413 ) @ vd413 ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ vd413 @ ( vsucc @ vd411 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(42,plain,
( ( ( ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ vd413 @ ( vsucc @ vd411 ) ) )
!= ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ ( vsucc @ vd411 ) @ vd413 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(43,plain,
( ( ! [Vd7: $i,Vd8: $i] :
( ( Vd7 = Vd8 )
| ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(44,plain,
( ( ! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(45,plain,
( ( ! [Vd24: $i] :
( ( Vd24 = v1 )
| ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(46,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)],[26]) ).
thf(47,plain,
( ( ! [Vd375: $i,Vd376: $i] :
( ~ ( greater @ Vd375 @ Vd376 )
| ( geq @ Vd375 @ ( vplus @ Vd376 @ v1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(48,plain,
( ( ! [Vd386: $i,Vd387: $i] :
( ~ ( less @ Vd386 @ ( vplus @ Vd387 @ v1 ) )
| ( leq @ Vd386 @ Vd387 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(49,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)],[33]) ).
thf(50,plain,
( ( ( vplus @ ( vplus @ ( vmul @ vd411 @ vd413 ) @ vd413 ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ vd413 @ ( vsucc @ vd411 ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(51,plain,
( ( ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ vd413 ) @ ( vsucc @ vd411 ) )
= ( vplus @ ( vplus @ ( vmul @ vd411 @ vd413 ) @ vd413 ) @ ( vsucc @ vd411 ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(52,plain,
( ( ( vmul @ ( vsucc @ vd411 ) @ ( vsucc @ vd413 ) )
= ( vplus @ ( vmul @ ( vsucc @ vd411 ) @ vd413 ) @ ( vsucc @ vd411 ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(53,plain,
( ( ( vmul @ ( vsucc @ vd411 ) @ vd413 )
= ( vplus @ ( vmul @ vd411 @ vd413 ) @ vd413 ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(54,plain,
( ( ( vsucc @ ( vmul @ vd411 @ v1 ) )
= ( vplus @ ( vmul @ vd411 @ v1 ) @ v1 ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(55,plain,
( ( ( vsucc @ vd411 )
= ( vsucc @ ( vmul @ vd411 @ v1 ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(56,plain,
( ( ( vmul @ ( vsucc @ vd411 ) @ v1 )
= ( vsucc @ vd411 ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(57,plain,
( ( ! [Vd400: $i] :
( ( vmul @ v1 @ Vd400 )
= Vd400 ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(58,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)],[49]) ).
thf(59,plain,
( ( ! [Vd386: $i,Vd387: $i] :
( ~ ( less @ Vd386 @ ( vplus @ Vd387 @ v1 ) )
| ( leq @ Vd386 @ Vd387 ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(60,plain,
( ( ! [Vd375: $i,Vd376: $i] :
( ~ ( greater @ Vd375 @ Vd376 )
| ( geq @ Vd375 @ ( vplus @ Vd376 @ v1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(61,plain,
( ( ! [Vd78: $i,Vd79: $i] :
( ( vplus @ Vd79 @ Vd78 )
= ( vplus @ Vd78 @ Vd79 ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(62,plain,
( ( ! [Vd68: $i,Vd69: $i] :
( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
= ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(63,plain,
( ( ! [Vd59: $i] :
( ( vplus @ v1 @ Vd59 )
= ( vsucc @ Vd59 ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(64,plain,
( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
= ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(65,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)],[46]) ).
thf(66,plain,
( ( ! [Vd24: $i] :
( ( Vd24 = v1 )
| ( Vd24
= ( vsucc @ ( vskolem2 @ Vd24 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(67,plain,
( ( ! [Vd16: $i] :
( ( vsucc @ Vd16 )
!= Vd16 ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(68,plain,
( ( ! [Vd7: $i,Vd8: $i] :
( ( Vd7 = Vd8 )
| ( ( vsucc @ Vd7 )
!= ( vsucc @ Vd8 ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(69,plain,
( ( ( ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ vd413 @ ( vsucc @ vd411 ) ) )
!= ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ ( vsucc @ vd411 ) @ vd413 ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(70,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)],[65]) ).
thf(71,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)],[58]) ).
thf(72,plain,
! [SV1: $i] :
( ( ( vmul @ v1 @ SV1 )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(73,plain,
! [SV2: $i] :
( ( ! [SY21: $i] :
( ~ ( less @ SV2 @ ( vplus @ SY21 @ v1 ) )
| ( leq @ SV2 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(74,plain,
! [SV3: $i] :
( ( ! [SY22: $i] :
( ~ ( greater @ SV3 @ SY22 )
| ( geq @ SV3 @ ( vplus @ SY22 @ v1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(75,plain,
! [SV4: $i] :
( ( ! [SY23: $i] :
( ( vplus @ SY23 @ SV4 )
= ( vplus @ SV4 @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(76,plain,
! [SV5: $i] :
( ( ! [SY24: $i] :
( ( vplus @ ( vsucc @ SV5 ) @ SY24 )
= ( vsucc @ ( vplus @ SV5 @ SY24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(77,plain,
! [SV6: $i] :
( ( ( vplus @ v1 @ SV6 )
= ( vsucc @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(78,plain,
! [SV7: $i] :
( ( ! [SY25: $i,SY26: $i] :
( ( vplus @ ( vplus @ SV7 @ SY25 ) @ SY26 )
= ( vplus @ SV7 @ ( vplus @ SY25 @ SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(79,plain,
! [SV8: $i] :
( ( ( SV8 = v1 )
| ( SV8
= ( vsucc @ ( vskolem2 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(80,plain,
! [SV9: $i] :
( ( ( ( vsucc @ SV9 )
!= SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(81,plain,
! [SV10: $i] :
( ( ! [SY27: $i] :
( ( SV10 = SY27 )
| ( ( vsucc @ SV10 )
!= ( vsucc @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(82,plain,
( ( ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ vd413 @ ( vsucc @ vd411 ) ) )
= ( vplus @ ( vmul @ vd411 @ vd413 ) @ ( vplus @ ( vsucc @ vd411 ) @ vd413 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(83,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)],[70]) ).
thf(84,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)],[71]) ).
thf(85,plain,
! [SV11: $i,SV2: $i] :
( ( ~ ( less @ SV2 @ ( vplus @ SV11 @ v1 ) )
| ( leq @ SV2 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(86,plain,
! [SV12: $i,SV3: $i] :
( ( ~ ( greater @ SV3 @ SV12 )
| ( geq @ SV3 @ ( vplus @ SV12 @ v1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(87,plain,
! [SV4: $i,SV13: $i] :
( ( ( vplus @ SV13 @ SV4 )
= ( vplus @ SV4 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(88,plain,
! [SV14: $i,SV5: $i] :
( ( ( vplus @ ( vsucc @ SV5 ) @ SV14 )
= ( vsucc @ ( vplus @ SV5 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(89,plain,
! [SV15: $i,SV7: $i] :
( ( ! [SY28: $i] :
( ( vplus @ ( vplus @ SV7 @ SV15 ) @ SY28 )
= ( vplus @ SV7 @ ( vplus @ SV15 @ SY28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(90,plain,
! [SV8: $i] :
( ( ( SV8 = v1 )
= $true )
| ( ( SV8
= ( vsucc @ ( vskolem2 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(91,plain,
! [SV9: $i] :
( ( ( vsucc @ SV9 )
= SV9 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(92,plain,
! [SV16: $i,SV10: $i] :
( ( ( SV10 = SV16 )
| ( ( vsucc @ SV10 )
!= ( vsucc @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(93,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(94,plain,
( ( ~ ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(95,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( vmul @ SX0 @ ( vsucc @ SX1 ) )
= ( vplus @ ( vmul @ SX0 @ SX1 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(96,plain,
( ( ~ ! [SX0: $i] :
( ( vmul @ SX0 @ v1 )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(97,plain,
! [SV11: $i,SV2: $i] :
( ( ( ~ ( less @ SV2 @ ( vplus @ SV11 @ v1 ) ) )
= $true )
| ( ( leq @ SV2 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(98,plain,
! [SV12: $i,SV3: $i] :
( ( ( ~ ( greater @ SV3 @ SV12 ) )
= $true )
| ( ( geq @ SV3 @ ( vplus @ SV12 @ v1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(99,plain,
! [SV17: $i,SV15: $i,SV7: $i] :
( ( ( vplus @ ( vplus @ SV7 @ SV15 ) @ SV17 )
= ( vplus @ SV7 @ ( vplus @ SV15 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(100,plain,
! [SV16: $i,SV10: $i] :
( ( ( SV10 = SV16 )
= $true )
| ( ( ( ( vsucc @ SV10 )
!= ( vsucc @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(101,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
= ( vsucc @ ( vplus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(102,plain,
( ( ! [SX0: $i] :
( ( vplus @ SX0 @ v1 )
= ( vsucc @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(103,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( vmul @ SX0 @ ( vsucc @ SX1 ) )
= ( vplus @ ( vmul @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(104,plain,
( ( ! [SX0: $i] :
( ( vmul @ SX0 @ v1 )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(105,plain,
! [SV11: $i,SV2: $i] :
( ( ( less @ SV2 @ ( vplus @ SV11 @ v1 ) )
= $false )
| ( ( leq @ SV2 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(106,plain,
! [SV12: $i,SV3: $i] :
( ( ( greater @ SV3 @ SV12 )
= $false )
| ( ( geq @ SV3 @ ( vplus @ SV12 @ v1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(107,plain,
! [SV16: $i,SV10: $i] :
( ( ( ( vsucc @ SV10 )
= ( vsucc @ SV16 ) )
= $false )
| ( ( SV10 = SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(108,plain,
! [SV18: $i] :
( ( ! [SY29: $i] :
( ( vplus @ SV18 @ ( vsucc @ SY29 ) )
= ( vsucc @ ( vplus @ SV18 @ SY29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(109,plain,
! [SV19: $i] :
( ( ( vplus @ SV19 @ v1 )
= ( vsucc @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(110,plain,
! [SV20: $i] :
( ( ! [SY30: $i] :
( ( vmul @ SV20 @ ( vsucc @ SY30 ) )
= ( vplus @ ( vmul @ SV20 @ SY30 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(111,plain,
! [SV21: $i] :
( ( ( vmul @ SV21 @ v1 )
= SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(112,plain,
! [SV22: $i,SV18: $i] :
( ( ( vplus @ SV18 @ ( vsucc @ SV22 ) )
= ( vsucc @ ( vplus @ SV18 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(113,plain,
! [SV23: $i,SV20: $i] :
( ( ( vmul @ SV20 @ ( vsucc @ SV23 ) )
= ( vplus @ ( vmul @ SV20 @ SV23 ) @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(114,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[50,113,112,111,109,107,106,105,99,91,90,88,87,82,77,72,56,55,54,53,52,51]) ).
thf(115,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM844+2 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 5 04:53:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 19
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.35 (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:21,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.18/0.40
% 0.18/0.40 ********************************
% 0.18/0.40 * All subproblems solved! *
% 0.18/0.40 ********************************
% 0.18/0.40 % 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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:114,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.41
% 0.18/0.41 %**** Beginning of derivation protocol ****
% 0.18/0.41 % SZS output start CNFRefutation
% See solution above
% 0.18/0.41
% 0.18/0.41 %**** End of derivation protocol ****
% 0.18/0.41 %**** no. of clauses in derivation: 115 ****
% 0.18/0.41 %**** clause counter: 114 ****
% 0.18/0.41
% 0.18/0.41 % 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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:114,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------