TSTP Solution File: NUM638^1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM638^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n017.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 11:53:31 EDT 2022
% Result : Theorem 0.59s 0.78s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 16
% Syntax : Number of formulae : 136 ( 32 unt; 12 typ; 0 def)
% Number of atoms : 970 ( 556 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 561 ( 104 ~; 188 |; 6 &; 245 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 122 ( 54 ^ 68 !; 0 ?; 122 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_nat,type,
nat: $tType ).
thf(tp_n_1,type,
n_1: nat ).
thf(tp_sK1_Xx_0,type,
sK1_Xx_0: nat ).
thf(tp_sK2_SY7,type,
sK2_SY7: nat ).
thf(tp_sK3_REN,type,
sK3_REN: $o ).
thf(tp_sK4_E,type,
sK4_E: nat > nat ).
thf(tp_sK5_E,type,
sK5_E: nat ).
thf(tp_sK6_E,type,
sK6_E: nat ).
thf(tp_sK7_E,type,
sK7_E: nat ).
thf(tp_some,type,
some: ( nat > $o ) > $o ).
thf(tp_suc,type,
suc: nat > nat ).
thf(tp_x,type,
x: nat ).
thf(1,axiom,
! [Xx: nat] :
( ( Xx != n_1 )
=> ( some
@ ^ [Xu: nat] :
( Xx
= ( suc @ Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz3) ).
thf(2,axiom,
! [Xx: nat,Xy: nat] :
( ( ( suc @ Xx )
= ( suc @ Xy ) )
=> ( Xx = Xy ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
thf(3,axiom,
x != n_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).
thf(4,conjecture,
~ ( ! [Xx_0: nat,Xy: nat] :
( ( x
= ( suc @ Xx_0 ) )
=> ( ( x
= ( suc @ Xy ) )
=> ( Xx_0 = Xy ) ) )
=> ~ ( some
@ ^ [Xu: nat] :
( x
= ( suc @ Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz3a) ).
thf(5,negated_conjecture,
( ( ~ ( ! [Xx_0: nat,Xy: nat] :
( ( x
= ( suc @ Xx_0 ) )
=> ( ( x
= ( suc @ Xy ) )
=> ( Xx_0 = Xy ) ) )
=> ~ ( some
@ ^ [Xu: nat] :
( x
= ( suc @ Xu ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( ~ ( ! [Xx_0: nat,Xy: nat] :
( ( x
= ( suc @ Xx_0 ) )
=> ( ( x
= ( suc @ Xy ) )
=> ( Xx_0 = Xy ) ) )
=> ~ ( some
@ ^ [Xu: nat] :
( x
= ( suc @ Xu ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [Xx: nat] :
( ( Xx != n_1 )
=> ( some
@ ^ [Xu: nat] :
( Xx
= ( suc @ Xu ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( ( suc @ Xx )
= ( suc @ Xy ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( ( x != n_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(10,plain,
( ( ! [Xx_0: nat,Xy: nat] :
( ( x
= ( suc @ Xx_0 ) )
=> ( ( x
= ( suc @ Xy ) )
=> ( Xx_0 = Xy ) ) )
=> ~ ( some
@ ^ [Xu: nat] :
( x
= ( suc @ Xu ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(11,plain,
( ( ( sK3_REN
| ~ ( some
@ ^ [Xu: nat] :
( x
= ( suc @ Xu ) ) ) )
& ( sK3_REN
=> ( ( x
= ( suc @ sK1_Xx_0 ) )
& ( x
= ( suc @ sK2_SY7 ) )
& ( sK1_Xx_0 != sK2_SY7 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(12,plain,
( ( ! [Xx: nat] :
( ( Xx = n_1 )
| ( some
@ ^ [Xu: nat] :
( Xx
= ( suc @ Xu ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(13,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( ( suc @ Xx )
!= ( suc @ Xy ) )
| ( Xx = Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(14,plain,
( ( ( x != n_1 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(15,plain,
( ( ( x != n_1 ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( ( suc @ Xx )
!= ( suc @ Xy ) )
| ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(17,plain,
( ( ! [Xx: nat] :
( ( Xx = n_1 )
| ( some
@ ^ [Xu: nat] :
( Xx
= ( suc @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(18,plain,
( ( ( sK3_REN
| ~ ( some
@ ^ [Xu: nat] :
( x
= ( suc @ Xu ) ) ) )
& ( sK3_REN
=> ( ( x
= ( suc @ sK1_Xx_0 ) )
& ( x
= ( suc @ sK2_SY7 ) )
& ( sK1_Xx_0 != sK2_SY7 ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(19,plain,
( ( ~ ( ~ ( sK3_REN
| ~ ( some
@ ^ [SX0: nat] :
( x
= ( suc @ SX0 ) ) ) )
| ~ ( ~ sK3_REN
| ~ ( ( x
!= ( suc @ sK1_Xx_0 ) )
| ~ ~ ( ( x
!= ( suc @ sK2_SY7 ) )
| ~ ( ( sK1_Xx_0 != sK2_SY7 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(20,plain,
( ( x = n_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(21,plain,
! [SV1: nat] :
( ( ! [SY8: nat] :
( ( ( suc @ SV1 )
!= ( suc @ SY8 ) )
| ( SV1 = SY8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(22,plain,
! [SV2: nat] :
( ( ( SV2 = n_1 )
| ( some
@ ^ [SY9: nat] :
( SV2
= ( suc @ SY9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(23,plain,
( ( ~ ( sK3_REN
| ~ ( some
@ ^ [SX0: nat] :
( x
= ( suc @ SX0 ) ) ) )
| ~ ( ~ sK3_REN
| ~ ( ( x
!= ( suc @ sK1_Xx_0 ) )
| ~ ~ ( ( x
!= ( suc @ sK2_SY7 ) )
| ~ ( ( sK1_Xx_0 != sK2_SY7 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV3: nat,SV1: nat] :
( ( ( ( suc @ SV1 )
!= ( suc @ SV3 ) )
| ( SV1 = SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV2: nat] :
( ( ( SV2 = n_1 )
= $true )
| ( ( some
@ ^ [SY9: nat] :
( SV2
= ( suc @ SY9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( ~ ( sK3_REN
| ~ ( some
@ ^ [SX0: nat] :
( x
= ( suc @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(27,plain,
( ( ~ ( ~ sK3_REN
| ~ ( ( x
!= ( suc @ sK1_Xx_0 ) )
| ~ ~ ( ( x
!= ( suc @ sK2_SY7 ) )
| ~ ( ( sK1_Xx_0 != sK2_SY7 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(28,plain,
! [SV3: nat,SV1: nat] :
( ( ( ( ( suc @ SV1 )
!= ( suc @ SV3 ) ) )
= $true )
| ( ( SV1 = SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(29,plain,
( ( sK3_REN
| ~ ( some
@ ^ [SX0: nat] :
( x
= ( suc @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(30,plain,
( ( ~ sK3_REN
| ~ ( ( x
!= ( suc @ sK1_Xx_0 ) )
| ~ ~ ( ( x
!= ( suc @ sK2_SY7 ) )
| ~ ( ( sK1_Xx_0 != sK2_SY7 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(31,plain,
! [SV3: nat,SV1: nat] :
( ( ( ( suc @ SV1 )
= ( suc @ SV3 ) )
= $false )
| ( ( SV1 = SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(32,plain,
( ( sK3_REN = $true )
| ( ( ~ ( some
@ ^ [SX0: nat] :
( x
= ( suc @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(33,plain,
( ( ( ~ sK3_REN )
= $true )
| ( ( ~ ( ( x
!= ( suc @ sK1_Xx_0 ) )
| ~ ~ ( ( x
!= ( suc @ sK2_SY7 ) )
| ~ ( ( sK1_Xx_0 != sK2_SY7 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(34,plain,
( ( ( some
@ ^ [SX0: nat] :
( x
= ( suc @ SX0 ) ) )
= $false )
| ( sK3_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(35,plain,
( ( sK3_REN = $false )
| ( ( ~ ( ( x
!= ( suc @ sK1_Xx_0 ) )
| ~ ~ ( ( x
!= ( suc @ sK2_SY7 ) )
| ~ ( ( sK1_Xx_0 != sK2_SY7 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(36,plain,
( ( ( ( x
!= ( suc @ sK1_Xx_0 ) )
| ~ ~ ( ( x
!= ( suc @ sK2_SY7 ) )
| ~ ( ( sK1_Xx_0 != sK2_SY7 ) ) ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(37,plain,
( ( ( ( x
!= ( suc @ sK1_Xx_0 ) ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(38,plain,
( ( ( ~ ~ ( ( x
!= ( suc @ sK2_SY7 ) )
| ~ ( ( sK1_Xx_0 != sK2_SY7 ) ) ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(39,plain,
( ( ( x
= ( suc @ sK1_Xx_0 ) )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(40,plain,
( ( ( ~ ( ( x
!= ( suc @ sK2_SY7 ) )
| ~ ( ( sK1_Xx_0 != sK2_SY7 ) ) ) )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(41,plain,
( ( ( ( x
!= ( suc @ sK2_SY7 ) )
| ~ ( ( sK1_Xx_0 != sK2_SY7 ) ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(42,plain,
( ( ( ( x
!= ( suc @ sK2_SY7 ) ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(43,plain,
( ( ( ~ ( ( sK1_Xx_0 != sK2_SY7 ) ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(44,plain,
( ( ( x
= ( suc @ sK2_SY7 ) )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(45,plain,
( ( ( ( sK1_Xx_0 != sK2_SY7 ) )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(46,plain,
( ( ( sK1_Xx_0 = sK2_SY7 )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(72,plain,
! [SV4: nat] :
( ( ( SV4 = n_1 )
= $true )
| ( ( some
@ ^ [SX0: nat] :
( SV4
= ( suc @ SX0 ) ) )
= $true ) ),
inference(rename,[status(thm)],[25]) ).
thf(74,plain,
! [SV4: nat] :
( ( ( ( SV4 = n_1 )
= ( x = n_1 ) )
= $false )
| ( ( some
@ ^ [SX0: nat] :
( SV4
= ( suc @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[72,20]) ).
thf(76,plain,
( ( ( some
@ ^ [SX0: nat] :
( n_1
= ( suc @ SX0 ) ) )
= $true )
| ( ( n_1 = x )
= $false ) ),
inference(extuni,[status(esa)],[74:[bind(SV4,$thf( n_1 ))]]) ).
thf(77,plain,
( ( some
@ ^ [SX0: nat] :
( x
= ( suc @ SX0 ) ) )
= $true ),
inference(extuni,[status(esa)],[74:[bind(SV4,$thf( x ))]]) ).
thf(78,plain,
! [SV5: nat,SV6: nat] :
( ( ( ( suc @ SV6 )
= ( suc @ SV5 ) )
= $false )
| ( ( SV6 = SV5 )
= $true ) ),
inference(rename,[status(thm)],[31]) ).
thf(82,plain,
! [SV5: nat,SV6: nat,SV4: nat] :
( ( ( ( ( suc @ SV6 )
= ( suc @ SV5 ) )
= ( SV4 = n_1 ) )
= $false )
| ( ( SV6 = SV5 )
= $true )
| ( ( some
@ ^ [SX0: nat] :
( SV4
= ( suc @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[78,72]) ).
thf(83,plain,
! [SV5: nat,SV6: nat] :
( ( ( ( SV6 = SV5 )
= ( x = n_1 ) )
= $false )
| ( ( ( suc @ SV6 )
= ( suc @ SV5 ) )
= $false ) ),
inference(res,[status(thm)],[78,20]) ).
thf(84,plain,
( ( n_1 = x )
= $false ),
inference(extuni,[status(esa)],[83:[bind(SV6,$thf( n_1 )),bind(SV5,$thf( x ))]]) ).
thf(85,plain,
( ( ( suc @ n_1 )
= ( suc @ x ) )
= $false ),
inference(extuni,[status(esa)],[83:[bind(SV6,$thf( n_1 )),bind(SV5,$thf( x ))]]) ).
thf(86,plain,
( ( x = n_1 )
= $false ),
inference(extuni,[status(esa)],[83:[bind(SV5,$thf( n_1 )),bind(SV6,$thf( x ))]]) ).
thf(87,plain,
( ( ( suc @ x )
= ( suc @ n_1 ) )
= $false ),
inference(extuni,[status(esa)],[83:[bind(SV5,$thf( n_1 )),bind(SV6,$thf( x ))]]) ).
thf(88,plain,
! [SV6: nat,SV5: nat] :
( ( ( some
@ ^ [SX0: nat] :
( ( suc @ SV5 )
= ( suc @ SX0 ) ) )
= $true )
| ( ( SV6 = SV5 )
= $true )
| ( ( ( suc @ SV6 )
= n_1 )
= $false ) ),
inference(extuni,[status(esa)],[82:[bind(SV4,$thf( suc @ SV5 ))]]) ).
thf(89,plain,
! [SV5: nat,SV6: nat] :
( ( ( some
@ ^ [SX0: nat] :
( ( suc @ SV6 )
= ( suc @ SX0 ) ) )
= $true )
| ( ( SV6 = SV5 )
= $true )
| ( ( ( suc @ SV5 )
= n_1 )
= $false ) ),
inference(extuni,[status(esa)],[82:[bind(SV4,$thf( suc @ SV6 ))]]) ).
thf(93,plain,
! [SV4: nat] :
( ( ( ( some
@ ^ [SX0: nat] :
( x
= ( suc @ SX0 ) ) )
= ( some
@ ^ [SX0: nat] :
( SV4
= ( suc @ SX0 ) ) ) )
= $false )
| ( sK3_REN = $true )
| ( ( SV4 = n_1 )
= $true ) ),
inference(res,[status(thm)],[34,72]) ).
thf(98,plain,
( ( ( x = n_1 )
= $true )
| ( sK3_REN = $true ) ),
inference(extuni,[status(esa)],[93:[bind(SV4,$thf( x ))]]) ).
thf(99,plain,
! [SV4: nat] :
( ( ( SV4 = n_1 )
= $true )
| ( sK3_REN = $true )
| ( ( x
= ( suc @ ( sK4_E @ SV4 ) ) )
= $true )
| ( ( SV4
= ( suc @ ( sK4_E @ SV4 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[93]) ).
thf(100,plain,
! [SV4: nat] :
( ( ( SV4 = n_1 )
= $true )
| ( sK3_REN = $true )
| ( ( x
= ( suc @ ( sK4_E @ SV4 ) ) )
= $false )
| ( ( SV4
= ( suc @ ( sK4_E @ SV4 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[93]) ).
thf(102,plain,
! [SV5: nat,SV6: nat] :
( ( ( ( x
= ( suc @ sK1_Xx_0 ) )
= ( ( suc @ SV6 )
= ( suc @ SV5 ) ) )
= $false )
| ( sK3_REN = $false )
| ( ( SV6 = SV5 )
= $true ) ),
inference(res,[status(thm)],[39,78]) ).
thf(107,plain,
( ( ( sK3_REN = sK3_REN )
= $false )
| ( ( x
= ( suc @ sK1_Xx_0 ) )
= $true )
| ( ( some
@ ^ [SX0: nat] :
( x
= ( suc @ SX0 ) ) )
= $false ) ),
inference(res,[status(thm)],[39,34]) ).
thf(109,plain,
( ( ( ( x
= ( suc @ sK1_Xx_0 ) )
= ( x = n_1 ) )
= $false )
| ( sK3_REN = $false ) ),
inference(res,[status(thm)],[39,20]) ).
thf(110,plain,
( ( sK3_REN = $false )
| ( ( x = n_1 )
= $false )
| ( ( ( suc @ sK1_Xx_0 )
= x )
= $false ) ),
inference(extuni,[status(esa)],[109]) ).
thf(111,plain,
( ( sK3_REN = $false )
| ( ( ( suc @ sK1_Xx_0 )
= n_1 )
= $false ) ),
inference(extuni,[status(esa)],[109]) ).
thf(112,plain,
( ( ( some
@ ^ [SX0: nat] :
( x
= ( suc @ SX0 ) ) )
= $false )
| ( ( x
= ( suc @ sK1_Xx_0 ) )
= $true ) ),
inference(extuni,[status(esa)],[107]) ).
thf(113,plain,
! [SV5: nat] :
( ( ( sK1_Xx_0 = SV5 )
= $true )
| ( sK3_REN = $false )
| ( ( x
= ( suc @ SV5 ) )
= $false ) ),
inference(extuni,[status(esa)],[102:[bind(SV6,$thf( sK1_Xx_0 ))]]) ).
thf(114,plain,
! [SV5: nat,SV6: nat] :
( ( ( SV6 = SV5 )
= $true )
| ( sK3_REN = $false )
| ( ( x
= ( suc @ SV5 ) )
= $false )
| ( ( ( suc @ sK1_Xx_0 )
= ( suc @ SV6 ) )
= $false ) ),
inference(extuni,[status(esa)],[102]) ).
thf(115,plain,
! [SV6: nat] :
( ( ( SV6 = sK1_Xx_0 )
= $true )
| ( sK3_REN = $false )
| ( ( x
= ( suc @ SV6 ) )
= $false ) ),
inference(extuni,[status(esa)],[102:[bind(SV5,$thf( sK1_Xx_0 ))]]) ).
thf(116,plain,
! [SV5: nat,SV6: nat] :
( ( ( SV6 = SV5 )
= $true )
| ( sK3_REN = $false )
| ( ( ( suc @ sK1_Xx_0 )
= ( suc @ SV5 ) )
= $false )
| ( ( x
= ( suc @ SV6 ) )
= $false ) ),
inference(extuni,[status(esa)],[102]) ).
thf(118,plain,
! [SV5: nat,SV6: nat] :
( ( ( ( x
= ( suc @ sK2_SY7 ) )
= ( ( suc @ SV6 )
= ( suc @ SV5 ) ) )
= $false )
| ( sK3_REN = $false )
| ( ( SV6 = SV5 )
= $true ) ),
inference(res,[status(thm)],[44,78]) ).
thf(125,plain,
( ( ( sK3_REN = sK3_REN )
= $false )
| ( ( x
= ( suc @ sK2_SY7 ) )
= $true )
| ( ( some
@ ^ [SX0: nat] :
( x
= ( suc @ SX0 ) ) )
= $false ) ),
inference(res,[status(thm)],[44,34]) ).
thf(127,plain,
( ( ( ( x
= ( suc @ sK2_SY7 ) )
= ( x = n_1 ) )
= $false )
| ( sK3_REN = $false ) ),
inference(res,[status(thm)],[44,20]) ).
thf(128,plain,
( ( sK3_REN = $false )
| ( ( x = n_1 )
= $false )
| ( ( ( suc @ sK2_SY7 )
= x )
= $false ) ),
inference(extuni,[status(esa)],[127]) ).
thf(129,plain,
( ( sK3_REN = $false )
| ( ( ( suc @ sK2_SY7 )
= n_1 )
= $false ) ),
inference(extuni,[status(esa)],[127]) ).
thf(130,plain,
( ( ( some
@ ^ [SX0: nat] :
( x
= ( suc @ SX0 ) ) )
= $false )
| ( ( x
= ( suc @ sK2_SY7 ) )
= $true ) ),
inference(extuni,[status(esa)],[125]) ).
thf(131,plain,
! [SV5: nat] :
( ( ( sK2_SY7 = SV5 )
= $true )
| ( sK3_REN = $false )
| ( ( x
= ( suc @ SV5 ) )
= $false ) ),
inference(extuni,[status(esa)],[118:[bind(SV6,$thf( sK2_SY7 ))]]) ).
thf(132,plain,
! [SV5: nat,SV6: nat] :
( ( ( SV6 = SV5 )
= $true )
| ( sK3_REN = $false )
| ( ( x
= ( suc @ SV5 ) )
= $false )
| ( ( ( suc @ sK2_SY7 )
= ( suc @ SV6 ) )
= $false ) ),
inference(extuni,[status(esa)],[118]) ).
thf(133,plain,
! [SV6: nat] :
( ( ( SV6 = sK2_SY7 )
= $true )
| ( sK3_REN = $false )
| ( ( x
= ( suc @ SV6 ) )
= $false ) ),
inference(extuni,[status(esa)],[118:[bind(SV5,$thf( sK2_SY7 ))]]) ).
thf(134,plain,
! [SV5: nat,SV6: nat] :
( ( ( SV6 = SV5 )
= $true )
| ( sK3_REN = $false )
| ( ( ( suc @ sK2_SY7 )
= ( suc @ SV5 ) )
= $false )
| ( ( x
= ( suc @ SV6 ) )
= $false ) ),
inference(extuni,[status(esa)],[118]) ).
thf(136,plain,
! [SV5: nat,SV6: nat] :
( ( ( ( sK1_Xx_0 = sK2_SY7 )
= ( SV6 = SV5 ) )
= $false )
| ( sK3_REN = $false )
| ( ( ( suc @ SV6 )
= ( suc @ SV5 ) )
= $false ) ),
inference(res,[status(thm)],[46,78]) ).
thf(140,plain,
! [SV4: nat] :
( ( ( ( sK1_Xx_0 = sK2_SY7 )
= ( SV4 = n_1 ) )
= $false )
| ( sK3_REN = $false )
| ( ( some
@ ^ [SX0: nat] :
( SV4
= ( suc @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[46,72]) ).
thf(142,plain,
( ( ( ( sK1_Xx_0 = sK2_SY7 )
= ( x
= ( suc @ sK2_SY7 ) ) )
= $false )
| ( sK3_REN = $false )
| ( sK3_REN = $false ) ),
inference(res,[status(thm)],[46,44]) ).
thf(144,plain,
( ( ( ( sK1_Xx_0 = sK2_SY7 )
= ( x
= ( suc @ sK1_Xx_0 ) ) )
= $false )
| ( sK3_REN = $false )
| ( sK3_REN = $false ) ),
inference(res,[status(thm)],[46,39]) ).
thf(148,plain,
( ( sK3_REN = $false )
| ( sK3_REN = $false )
| ( ( sK1_Xx_0
= ( suc @ sK1_Xx_0 ) )
= $false )
| ( ( sK2_SY7 = x )
= $false ) ),
inference(extuni,[status(esa)],[144]) ).
thf(149,plain,
( ( sK3_REN = $false )
| ( sK3_REN = $false )
| ( ( sK2_SY7
= ( suc @ sK1_Xx_0 ) )
= $false )
| ( ( sK1_Xx_0 = x )
= $false ) ),
inference(extuni,[status(esa)],[144]) ).
thf(150,plain,
( ( sK3_REN = $false )
| ( sK3_REN = $false )
| ( ( sK1_Xx_0
= ( suc @ sK2_SY7 ) )
= $false )
| ( ( sK2_SY7 = x )
= $false ) ),
inference(extuni,[status(esa)],[142]) ).
thf(151,plain,
( ( sK3_REN = $false )
| ( sK3_REN = $false )
| ( ( sK2_SY7
= ( suc @ sK2_SY7 ) )
= $false )
| ( ( sK1_Xx_0 = x )
= $false ) ),
inference(extuni,[status(esa)],[142]) ).
thf(152,plain,
( ( ( some
@ ^ [SX0: nat] :
( sK2_SY7
= ( suc @ SX0 ) ) )
= $true )
| ( sK3_REN = $false )
| ( ( sK1_Xx_0 = n_1 )
= $false ) ),
inference(extuni,[status(esa)],[140:[bind(SV4,$thf( sK2_SY7 ))]]) ).
thf(153,plain,
( ( ( some
@ ^ [SX0: nat] :
( sK1_Xx_0
= ( suc @ SX0 ) ) )
= $true )
| ( sK3_REN = $false )
| ( ( sK2_SY7 = n_1 )
= $false ) ),
inference(extuni,[status(esa)],[140:[bind(SV4,$thf( sK1_Xx_0 ))]]) ).
thf(154,plain,
( ( ( sK2_SY7 = sK1_Xx_0 )
= $false )
| ( sK3_REN = $false ) ),
inference(extuni,[status(esa)],[136:[bind(SV5,$thf( sK1_Xx_0 )),bind(SV6,$thf( sK2_SY7 ))]]) ).
thf(155,plain,
( ( ( ( suc @ sK2_SY7 )
= ( suc @ sK1_Xx_0 ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extuni,[status(esa)],[136:[bind(SV5,$thf( sK1_Xx_0 )),bind(SV6,$thf( sK2_SY7 ))]]) ).
thf(156,plain,
( ( ( sK1_Xx_0 = sK2_SY7 )
= $false )
| ( sK3_REN = $false ) ),
inference(extuni,[status(esa)],[136:[bind(SV5,$thf( sK2_SY7 )),bind(SV6,$thf( sK1_Xx_0 ))]]) ).
thf(157,plain,
( ( ( ( suc @ sK1_Xx_0 )
= ( suc @ sK2_SY7 ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extuni,[status(esa)],[136:[bind(SV5,$thf( sK2_SY7 )),bind(SV6,$thf( sK1_Xx_0 ))]]) ).
thf(158,plain,
( ( sK3_REN = $false )
| ( ( sK2_SY7
= ( suc @ sK1_Xx_0 ) )
= $false )
| ( ( sK1_Xx_0 = x )
= $false ) ),
inference(sim,[status(thm)],[149]) ).
thf(159,plain,
( ( sK3_REN = $false )
| ( ( sK1_Xx_0
= ( suc @ sK1_Xx_0 ) )
= $false )
| ( ( sK2_SY7 = x )
= $false ) ),
inference(sim,[status(thm)],[148]) ).
thf(160,plain,
( ( sK3_REN = $false )
| ( ( sK2_SY7
= ( suc @ sK2_SY7 ) )
= $false )
| ( ( sK1_Xx_0 = x )
= $false ) ),
inference(sim,[status(thm)],[151]) ).
thf(161,plain,
( ( sK3_REN = $false )
| ( ( sK1_Xx_0
= ( suc @ sK2_SY7 ) )
= $false )
| ( ( sK2_SY7 = x )
= $false ) ),
inference(sim,[status(thm)],[150]) ).
thf(163,plain,
! [SV5: nat,SV6: nat] :
( ( ( ( n_1 = x )
= ( SV6 = SV5 ) )
= $false )
| ( ( some
@ ^ [SX0: nat] :
( n_1
= ( suc @ SX0 ) ) )
= $true )
| ( ( ( suc @ SV6 )
= ( suc @ SV5 ) )
= $false ) ),
inference(res,[status(thm)],[76,78]) ).
thf(168,plain,
! [SV4: nat] :
( ( ( ( n_1 = x )
= ( SV4 = n_1 ) )
= $false )
| ( ( some
@ ^ [SX0: nat] :
( n_1
= ( suc @ SX0 ) ) )
= $true )
| ( ( some
@ ^ [SX0: nat] :
( SV4
= ( suc @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[76,72]) ).
thf(172,plain,
( ( ( ( n_1 = x )
= ( x
= ( suc @ sK2_SY7 ) ) )
= $false )
| ( ( some
@ ^ [SX0: nat] :
( n_1
= ( suc @ SX0 ) ) )
= $true )
| ( sK3_REN = $false ) ),
inference(res,[status(thm)],[76,44]) ).
thf(174,plain,
( ( ( ( n_1 = x )
= ( x
= ( suc @ sK1_Xx_0 ) ) )
= $false )
| ( ( some
@ ^ [SX0: nat] :
( n_1
= ( suc @ SX0 ) ) )
= $true )
| ( sK3_REN = $false ) ),
inference(res,[status(thm)],[76,39]) ).
thf(176,plain,
( ( ( ( some
@ ^ [SX0: nat] :
( n_1
= ( suc @ SX0 ) ) )
= ( some
@ ^ [SX0: nat] :
( x
= ( suc @ SX0 ) ) ) )
= $false )
| ( ( n_1 = x )
= $false )
| ( sK3_REN = $true ) ),
inference(res,[status(thm)],[76,34]) ).
thf(178,plain,
( ( sK3_REN = $true )
| ( ( n_1 = x )
= $false )
| ( ( n_1
= ( suc @ sK7_E ) )
= $false )
| ( ( ( suc @ sK7_E )
= x )
= $false ) ),
inference(extuni,[status(esa)],[176]) ).
thf(179,plain,
( ( sK3_REN = $true )
| ( ( n_1 = x )
= $false )
| ( ( n_1 = x )
= $false ) ),
inference(extuni,[status(esa)],[176]) ).
thf(180,plain,
( ( sK3_REN = $true )
| ( ( n_1 = x )
= $false )
| ( ( n_1
= ( suc @ sK7_E ) )
= $true )
| ( ( x
= ( suc @ sK7_E ) )
= $true ) ),
inference(extuni,[status(esa)],[176]) ).
thf(181,plain,
( ( sK3_REN = $true )
| ( ( n_1 = x )
= $false )
| ( ( n_1
= ( suc @ sK7_E ) )
= $false )
| ( ( x
= ( suc @ sK7_E ) )
= $false ) ),
inference(extuni,[status(esa)],[176]) ).
thf(182,plain,
( ( sK3_REN = $false )
| ( ( some
@ ^ [SX0: nat] :
( n_1
= ( suc @ SX0 ) ) )
= $true )
| ( ( n_1
= ( suc @ sK1_Xx_0 ) )
= $false ) ),
inference(extuni,[status(esa)],[174]) ).
thf(183,plain,
( ( sK3_REN = $false )
| ( ( some
@ ^ [SX0: nat] :
( n_1
= ( suc @ SX0 ) ) )
= $true )
| ( ( x
= ( suc @ sK1_Xx_0 ) )
= $false )
| ( ( n_1 = x )
= $false ) ),
inference(extuni,[status(esa)],[174]) ).
thf(184,plain,
( ( sK3_REN = $false )
| ( ( some
@ ^ [SX0: nat] :
( n_1
= ( suc @ SX0 ) ) )
= $true )
| ( ( n_1
= ( suc @ sK2_SY7 ) )
= $false ) ),
inference(extuni,[status(esa)],[172]) ).
thf(185,plain,
( ( sK3_REN = $false )
| ( ( some
@ ^ [SX0: nat] :
( n_1
= ( suc @ SX0 ) ) )
= $true )
| ( ( x
= ( suc @ sK2_SY7 ) )
= $false )
| ( ( n_1 = x )
= $false ) ),
inference(extuni,[status(esa)],[172]) ).
thf(186,plain,
( ( ( some
@ ^ [SX0: nat] :
( x
= ( suc @ SX0 ) ) )
= $true )
| ( ( some
@ ^ [SX0: nat] :
( n_1
= ( suc @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[168:[bind(SV4,$thf( x ))]]) ).
thf(187,plain,
( ( ( some
@ ^ [SX0: nat] :
( n_1
= ( suc @ SX0 ) ) )
= $true )
| ( ( some
@ ^ [SX0: nat] :
( n_1
= ( suc @ SX0 ) ) )
= $true )
| ( ( x = n_1 )
= $false ) ),
inference(extuni,[status(esa)],[168:[bind(SV4,$thf( n_1 ))]]) ).
thf(188,plain,
( ( ( x = n_1 )
= $false )
| ( ( some
@ ^ [SX0: nat] :
( n_1
= ( suc @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[163:[bind(SV5,$thf( n_1 )),bind(SV6,$thf( x ))]]) ).
thf(189,plain,
( ( ( ( suc @ x )
= ( suc @ n_1 ) )
= $false )
| ( ( some
@ ^ [SX0: nat] :
( n_1
= ( suc @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[163:[bind(SV5,$thf( n_1 )),bind(SV6,$thf( x ))]]) ).
thf(190,plain,
( ( ( n_1 = x )
= $false )
| ( ( some
@ ^ [SX0: nat] :
( n_1
= ( suc @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[163:[bind(SV5,$thf( x )),bind(SV6,$thf( n_1 ))]]) ).
thf(191,plain,
( ( ( ( suc @ n_1 )
= ( suc @ x ) )
= $false )
| ( ( some
@ ^ [SX0: nat] :
( n_1
= ( suc @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[163:[bind(SV5,$thf( x )),bind(SV6,$thf( n_1 ))]]) ).
thf(192,plain,
( ( sK3_REN = $true )
| ( ( n_1 = x )
= $false ) ),
inference(sim,[status(thm)],[179]) ).
thf(193,plain,
( ( ( some
@ ^ [SX0: nat] :
( n_1
= ( suc @ SX0 ) ) )
= $true )
| ( ( x = n_1 )
= $false ) ),
inference(sim,[status(thm)],[187]) ).
thf(194,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,193,192,191,190,189,188,186,185,184,183,182,181,180,178,161,160,159,158,157,156,155,154,153,152,134,133,132,131,130,129,128,116,115,114,113,112,111,110,100,99,98,89,88,87,86,85,84,78,77,76,72,46,44,39,34]) ).
thf(195,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[194]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM638^1 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 : Thu Jul 7 22:20:00 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 3
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.35 (rf:0,axioms:3,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:5,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.59/0.78
% 0.59/0.78 ********************************
% 0.59/0.78 * All subproblems solved! *
% 0.59/0.78 ********************************
% 0.59/0.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:194,loop_count:10,foatp_calls:3,translation:fof_full)
% 0.59/0.79
% 0.59/0.79 %**** Beginning of derivation protocol ****
% 0.59/0.79 % SZS output start CNFRefutation
% See solution above
% 0.59/0.79
% 0.59/0.79 %**** End of derivation protocol ****
% 0.59/0.79 %**** no. of clauses in derivation: 124 ****
% 0.59/0.79 %**** clause counter: 194 ****
% 0.59/0.79
% 0.59/0.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:194,loop_count:10,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------