TSTP Solution File: NUM636^1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM636^1 : 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 : n021.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 11:53:28 EDT 2022
% Result : Theorem 0.41s 0.57s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 111 ( 40 unt; 8 typ; 0 def)
% Number of atoms : 561 ( 226 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 809 ( 132 ~; 126 |; 2 &; 537 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 66 ( 66 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 210 ( 30 ^ 180 !; 0 ?; 210 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_nat,type,
nat: $tType ).
thf(tp_set,type,
set: $tType ).
thf(tp_esti,type,
esti: nat > set > $o ).
thf(tp_n_1,type,
n_1: nat ).
thf(tp_sK1_Xx,type,
sK1_Xx: set > nat ).
thf(tp_setof,type,
setof: ( nat > $o ) > set ).
thf(tp_suc,type,
suc: nat > nat ).
thf(tp_x,type,
x: nat ).
thf(1,axiom,
! [Xx: nat,Xy: nat] :
( ( Xx != Xy )
=> ( ( suc @ Xx )
!= ( suc @ Xy ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz1) ).
thf(2,axiom,
! [Xx: nat] :
( ( suc @ Xx )
!= n_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
thf(3,axiom,
! [Xp: nat > $o,Xs: nat] :
( ( Xp @ Xs )
=> ( esti @ Xs @ ( setof @ Xp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',estii) ).
thf(4,axiom,
! [Xs: set] :
( ( esti @ n_1 @ Xs )
=> ( ! [Xx: nat] :
( ( esti @ Xx @ Xs )
=> ( esti @ ( suc @ Xx ) @ Xs ) )
=> ! [Xx: nat] : ( esti @ Xx @ Xs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
thf(5,axiom,
! [Xp: nat > $o,Xs: nat] :
( ( esti @ Xs @ ( setof @ Xp ) )
=> ( Xp @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',estie) ).
thf(6,conjecture,
( suc @ x )
!= x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz2) ).
thf(7,negated_conjecture,
( ( ( ( suc @ x )
!= x ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ( ( suc @ x )
!= x ) )
= $false ),
inference(unfold_def,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( Xx != Xy )
=> ( ( suc @ Xx )
!= ( suc @ Xy ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [Xx: nat] :
( ( suc @ Xx )
!= n_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [Xp: nat > $o,Xs: nat] :
( ( Xp @ Xs )
=> ( esti @ Xs @ ( setof @ Xp ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [Xs: set] :
( ( esti @ n_1 @ Xs )
=> ( ! [Xx: nat] :
( ( esti @ Xx @ Xs )
=> ( esti @ ( suc @ Xx ) @ Xs ) )
=> ! [Xx: nat] : ( esti @ Xx @ Xs ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ! [Xp: nat > $o,Xs: nat] :
( ( esti @ Xs @ ( setof @ Xp ) )
=> ( Xp @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ~ ( ( ( suc @ x )
!= x ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(15,plain,
( ( ( suc @ x )
= x )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(16,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( Xx = Xy )
| ( ( suc @ Xx )
!= ( suc @ Xy ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(17,plain,
( ( ! [Xx: nat] :
( ( suc @ Xx )
!= n_1 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(18,plain,
( ( ! [Xp: nat > $o,Xs: nat] :
( ~ ( Xp @ Xs )
| ( esti @ Xs @ ( setof @ Xp ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(19,plain,
( ( ! [Xs: set] :
( ~ ( esti @ n_1 @ Xs )
| ( ( esti @ ( sK1_Xx @ Xs ) @ Xs )
& ~ ( esti @ ( suc @ ( sK1_Xx @ Xs ) ) @ Xs ) )
| ! [Xx: nat] : ( esti @ Xx @ Xs ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(20,plain,
( ( ! [Xp: nat > $o,Xs: nat] :
( ~ ( esti @ Xs @ ( setof @ Xp ) )
| ( Xp @ Xs ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(21,plain,
( ( ! [Xp: nat > $o,Xs: nat] :
( ~ ( esti @ Xs @ ( setof @ Xp ) )
| ( Xp @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(22,plain,
( ( ! [Xs: set] :
( ~ ( esti @ n_1 @ Xs )
| ( ( esti @ ( sK1_Xx @ Xs ) @ Xs )
& ~ ( esti @ ( suc @ ( sK1_Xx @ Xs ) ) @ Xs ) )
| ! [Xx: nat] : ( esti @ Xx @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(23,plain,
( ( ! [Xp: nat > $o,Xs: nat] :
( ~ ( Xp @ Xs )
| ( esti @ Xs @ ( setof @ Xp ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(24,plain,
( ( ! [Xx: nat] :
( ( suc @ Xx )
!= n_1 ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(25,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( Xx = Xy )
| ( ( suc @ Xx )
!= ( suc @ Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(26,plain,
( ( ( suc @ x )
= x )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(27,plain,
( ( ! [SX0: set] :
( ~ ( esti @ n_1 @ SX0 )
| ~ ( ~ ( esti @ ( sK1_Xx @ SX0 ) @ SX0 )
| ~ ~ ( esti @ ( suc @ ( sK1_Xx @ SX0 ) ) @ SX0 ) )
| ! [SX1: nat] : ( esti @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(28,plain,
! [SV1: nat > $o] :
( ( ! [SY10: nat] :
( ~ ( esti @ SY10 @ ( setof @ SV1 ) )
| ( SV1 @ SY10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(29,plain,
! [SV2: nat > $o] :
( ( ! [SY11: nat] :
( ~ ( SV2 @ SY11 )
| ( esti @ SY11 @ ( setof @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(30,plain,
! [SV3: nat] :
( ( ( ( suc @ SV3 )
!= n_1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(31,plain,
! [SV4: nat] :
( ( ! [SY12: nat] :
( ( SV4 = SY12 )
| ( ( suc @ SV4 )
!= ( suc @ SY12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(32,plain,
! [SV5: set] :
( ( ~ ( esti @ n_1 @ SV5 )
| ~ ( ~ ( esti @ ( sK1_Xx @ SV5 ) @ SV5 )
| ~ ~ ( esti @ ( suc @ ( sK1_Xx @ SV5 ) ) @ SV5 ) )
| ! [SY13: nat] : ( esti @ SY13 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV1: nat > $o,SV6: nat] :
( ( ~ ( esti @ SV6 @ ( setof @ SV1 ) )
| ( SV1 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(34,plain,
! [SV7: nat,SV2: nat > $o] :
( ( ~ ( SV2 @ SV7 )
| ( esti @ SV7 @ ( setof @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(35,plain,
! [SV3: nat] :
( ( ( suc @ SV3 )
= n_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(36,plain,
! [SV8: nat,SV4: nat] :
( ( ( SV4 = SV8 )
| ( ( suc @ SV4 )
!= ( suc @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(37,plain,
! [SV5: set] :
( ( ( ~ ( esti @ n_1 @ SV5 ) )
= $true )
| ( ( ~ ( ~ ( esti @ ( sK1_Xx @ SV5 ) @ SV5 )
| ~ ~ ( esti @ ( suc @ ( sK1_Xx @ SV5 ) ) @ SV5 ) )
| ! [SY13: nat] : ( esti @ SY13 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV1: nat > $o,SV6: nat] :
( ( ( ~ ( esti @ SV6 @ ( setof @ SV1 ) ) )
= $true )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV7: nat,SV2: nat > $o] :
( ( ( ~ ( SV2 @ SV7 ) )
= $true )
| ( ( esti @ SV7 @ ( setof @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(40,plain,
! [SV8: nat,SV4: nat] :
( ( ( SV4 = SV8 )
= $true )
| ( ( ( ( suc @ SV4 )
!= ( suc @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV5: set] :
( ( ( esti @ n_1 @ SV5 )
= $false )
| ( ( ~ ( ~ ( esti @ ( sK1_Xx @ SV5 ) @ SV5 )
| ~ ~ ( esti @ ( suc @ ( sK1_Xx @ SV5 ) ) @ SV5 ) )
| ! [SY13: nat] : ( esti @ SY13 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV1: nat > $o,SV6: nat] :
( ( ( esti @ SV6 @ ( setof @ SV1 ) )
= $false )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV7: nat,SV2: nat > $o] :
( ( ( SV2 @ SV7 )
= $false )
| ( ( esti @ SV7 @ ( setof @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV8: nat,SV4: nat] :
( ( ( ( suc @ SV4 )
= ( suc @ SV8 ) )
= $false )
| ( ( SV4 = SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV5: set] :
( ( ( ~ ( ~ ( esti @ ( sK1_Xx @ SV5 ) @ SV5 )
| ~ ~ ( esti @ ( suc @ ( sK1_Xx @ SV5 ) ) @ SV5 ) ) )
= $true )
| ( ( ! [SY13: nat] : ( esti @ SY13 @ SV5 ) )
= $true )
| ( ( esti @ n_1 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV5: set] :
( ( ( ~ ( esti @ ( sK1_Xx @ SV5 ) @ SV5 )
| ~ ~ ( esti @ ( suc @ ( sK1_Xx @ SV5 ) ) @ SV5 ) )
= $false )
| ( ( ! [SY13: nat] : ( esti @ SY13 @ SV5 ) )
= $true )
| ( ( esti @ n_1 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(47,plain,
! [SV5: set] :
( ( ( ~ ( esti @ ( sK1_Xx @ SV5 ) @ SV5 ) )
= $false )
| ( ( ! [SY13: nat] : ( esti @ SY13 @ SV5 ) )
= $true )
| ( ( esti @ n_1 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(48,plain,
! [SV5: set] :
( ( ( ~ ~ ( esti @ ( suc @ ( sK1_Xx @ SV5 ) ) @ SV5 ) )
= $false )
| ( ( ! [SY13: nat] : ( esti @ SY13 @ SV5 ) )
= $true )
| ( ( esti @ n_1 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(49,plain,
! [SV5: set] :
( ( ( esti @ ( sK1_Xx @ SV5 ) @ SV5 )
= $true )
| ( ( ! [SY13: nat] : ( esti @ SY13 @ SV5 ) )
= $true )
| ( ( esti @ n_1 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(50,plain,
! [SV5: set] :
( ( ( ~ ( esti @ ( suc @ ( sK1_Xx @ SV5 ) ) @ SV5 ) )
= $true )
| ( ( ! [SY13: nat] : ( esti @ SY13 @ SV5 ) )
= $true )
| ( ( esti @ n_1 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(51,plain,
! [SV5: set,SV9: nat] :
( ( ( esti @ SV9 @ SV5 )
= $true )
| ( ( esti @ ( sK1_Xx @ SV5 ) @ SV5 )
= $true )
| ( ( esti @ n_1 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV5: set] :
( ( ( esti @ ( suc @ ( sK1_Xx @ SV5 ) ) @ SV5 )
= $false )
| ( ( ! [SY13: nat] : ( esti @ SY13 @ SV5 ) )
= $true )
| ( ( esti @ n_1 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(53,plain,
! [SV5: set,SV10: nat] :
( ( ( esti @ SV10 @ SV5 )
= $true )
| ( ( esti @ ( suc @ ( sK1_Xx @ SV5 ) ) @ SV5 )
= $false )
| ( ( esti @ n_1 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(55,plain,
! [SV6: nat] :
( ( ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] : $false ) )
= $false )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[42:[bind(SV1,$thf( ^ [SV19: nat] : $false ))]]) ).
thf(56,plain,
! [SV18: nat > $o,SV6: nat] :
( ( ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] :
~ ( SV18 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV18 @ SV6 ) )
= $true ) ),
inference(prim_subst,[status(thm)],[42:[bind(SV1,$thf( ^ [SV17: nat] : ~ ( SV18 @ SV17 ) ))]]) ).
thf(57,plain,
! [SV6: nat] :
( ( ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] : ( SX0 = n_1 ) ) )
= $false )
| ( ( SV6 = n_1 )
= $true ) ),
inference(prim_subst,[status(thm)],[42:[bind(SV1,$thf( ^ [SV21: nat] : ( SV21 = n_1 ) ))]]) ).
thf(58,plain,
! [SV6: nat] :
( ( ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] : ( SX0 = x ) ) )
= $false )
| ( ( SV6 = x )
= $true ) ),
inference(prim_subst,[status(thm)],[42:[bind(SV1,$thf( ^ [SV22: nat] : ( SV22 = x ) ))]]) ).
thf(59,plain,
! [SV7: nat] :
( ( $true = $false )
| ( ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] : $true ) )
= $true ) ),
inference(prim_subst,[status(thm)],[43:[bind(SV2,$thf( ^ [SV14: nat] : $true ))]]) ).
thf(61,plain,
! [SV7: nat,SV12: nat > $o] :
( ( ( ~ ( SV12 @ SV7 ) )
= $false )
| ( ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] :
~ ( SV12 @ SX0 ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[43:[bind(SV2,$thf( ^ [SV11: nat] : ~ ( SV12 @ SV11 ) ))]]) ).
thf(62,plain,
! [SV7: nat] :
( ( ( SV7 = n_1 )
= $false )
| ( ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] : ( SX0 = n_1 ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[43:[bind(SV2,$thf( ^ [SV15: nat] : ( SV15 = n_1 ) ))]]) ).
thf(63,plain,
! [SV7: nat] :
( ( ( SV7 = x )
= $false )
| ( ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] : ( SX0 = x ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[43:[bind(SV2,$thf( ^ [SV16: nat] : ( SV16 = x ) ))]]) ).
thf(64,plain,
! [SV1: nat > $o,SV6: nat] :
( ( ( SV1 @ SV6 )
= $true )
| ( ( ( SV1 @ SV6 )
= ( ~ ( esti @ SV6 @ ( setof @ SV1 ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[42]) ).
thf(65,plain,
! [SV7: nat,SV2: nat > $o] :
( ( ( SV2 @ SV7 )
= $false )
| ( ( ( SV2 @ SV7 )
= ( ~ ( esti @ SV7 @ ( setof @ SV2 ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[43]) ).
thf(66,plain,
! [SV6: nat,SV1: nat > $o] :
( ( ( ~ ( ( SV1 @ SV6 )
| ~ ( esti @ SV6 @ ( setof @ SV1 ) ) )
| ~ ( ~ ( SV1 @ SV6 )
| ~ ~ ( esti @ SV6 @ ( setof @ SV1 ) ) ) )
= $false )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[64]) ).
thf(67,plain,
! [SV6: nat,SV1: nat > $o] :
( ( ( ( SV1 @ SV6 )
= ( ~ ( esti @ SV6 @ ( setof @ SV1 ) ) ) )
= $false )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[64]) ).
thf(68,plain,
! [SV7: nat,SV2: nat > $o] :
( ( ( ~ ( ( SV2 @ SV7 )
| ~ ( esti @ SV7 @ ( setof @ SV2 ) ) )
| ~ ( ~ ( SV2 @ SV7 )
| ~ ~ ( esti @ SV7 @ ( setof @ SV2 ) ) ) )
= $false )
| ( ( SV2 @ SV7 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[65]) ).
thf(69,plain,
! [SV7: nat,SV2: nat > $o] :
( ( ( ( SV2 @ SV7 )
= ( ~ ( esti @ SV7 @ ( setof @ SV2 ) ) ) )
= $false )
| ( ( SV2 @ SV7 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[65]) ).
thf(70,plain,
! [SV6: nat,SV1: nat > $o] :
( ( ( ~ ( ( SV1 @ SV6 )
| ~ ( esti @ SV6 @ ( setof @ SV1 ) ) ) )
= $false )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(73,plain,
! [SV7: nat,SV2: nat > $o] :
( ( ( ~ ( ~ ( SV2 @ SV7 )
| ~ ~ ( esti @ SV7 @ ( setof @ SV2 ) ) ) )
= $false )
| ( ( SV2 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(74,plain,
! [SV6: nat,SV1: nat > $o] :
( ( ( ( SV1 @ SV6 )
| ~ ( esti @ SV6 @ ( setof @ SV1 ) ) )
= $true )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(77,plain,
! [SV7: nat,SV2: nat > $o] :
( ( ( ~ ( SV2 @ SV7 )
| ~ ~ ( esti @ SV7 @ ( setof @ SV2 ) ) )
= $true )
| ( ( SV2 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(78,plain,
! [SV6: nat,SV1: nat > $o] :
( ( ( SV1 @ SV6 )
= $true )
| ( ( ~ ( esti @ SV6 @ ( setof @ SV1 ) ) )
= $true )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(81,plain,
! [SV7: nat,SV2: nat > $o] :
( ( ( ~ ( SV2 @ SV7 ) )
= $true )
| ( ( ~ ~ ( esti @ SV7 @ ( setof @ SV2 ) ) )
= $true )
| ( ( SV2 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(82,plain,
! [SV1: nat > $o,SV6: nat] :
( ( ( esti @ SV6 @ ( setof @ SV1 ) )
= $false )
| ( ( SV1 @ SV6 )
= $true )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(85,plain,
! [SV7: nat,SV2: nat > $o] :
( ( ( SV2 @ SV7 )
= $false )
| ( ( ~ ~ ( esti @ SV7 @ ( setof @ SV2 ) ) )
= $true )
| ( ( SV2 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(87,plain,
! [SV2: nat > $o,SV7: nat] :
( ( ( ~ ( esti @ SV7 @ ( setof @ SV2 ) ) )
= $false )
| ( ( SV2 @ SV7 )
= $false )
| ( ( SV2 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(89,plain,
! [SV2: nat > $o,SV7: nat] :
( ( ( esti @ SV7 @ ( setof @ SV2 ) )
= $true )
| ( ( SV2 @ SV7 )
= $false )
| ( ( SV2 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(91,plain,
! [SV29: nat > set,SV6: nat,SV28: nat > nat] :
( ( ( ~ ( esti @ ( SV28 @ SV6 ) @ ( SV29 @ SV6 ) ) )
= $true )
| ( ( esti @ ( SV28 @ SV6 ) @ ( SV29 @ SV6 ) )
= $false )
| ( ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] :
~ ( esti @ ( SV28 @ SX0 ) @ ( SV29 @ SX0 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[67:[bind(SV1,$thf( ^ [SX0: nat] : ~ ( esti @ ( SV28 @ SX0 ) @ ( SV29 @ SX0 ) ) ))]]) ).
thf(92,plain,
! [SV6: nat,SV25: nat > $o] :
( ( ( ~ ( SV25 @ SV6 ) )
= $true )
| ( ( ~ ( SV25 @ SV6 ) )
= $true )
| ( ( ~ ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] :
~ ( SV25 @ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[67:[bind(SV1,$thf( ^ [SX0: nat] : ~ ( SV25 @ SX0 ) ))]]) ).
thf(94,plain,
! [SV36: nat > set,SV7: nat,SV35: nat > nat] :
( ( ( ~ ( esti @ ( SV35 @ SV7 ) @ ( SV36 @ SV7 ) ) )
= $false )
| ( ( esti @ ( SV35 @ SV7 ) @ ( SV36 @ SV7 ) )
= $true )
| ( ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] :
~ ( esti @ ( SV35 @ SX0 ) @ ( SV36 @ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[69:[bind(SV2,$thf( ^ [SX0: nat] : ~ ( esti @ ( SV35 @ SX0 ) @ ( SV36 @ SX0 ) ) ))]]) ).
thf(97,plain,
! [SV7: nat,SV32: nat > $o] :
( ( ( ~ ( SV32 @ SV7 ) )
= $false )
| ( ( ~ ( SV32 @ SV7 ) )
= $false )
| ( ( ~ ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] :
~ ( SV32 @ SX0 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[69:[bind(SV2,$thf( ^ [SX0: nat] : ~ ( SV32 @ SX0 ) ))]]) ).
thf(100,plain,
! [SV6: nat,SV25: nat > $o] :
( ( ( SV25 @ SV6 )
= $false )
| ( ( ~ ( SV25 @ SV6 ) )
= $true )
| ( ( ~ ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] :
~ ( SV25 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(101,plain,
! [SV29: nat > set,SV6: nat,SV28: nat > nat] :
( ( ( esti @ ( SV28 @ SV6 ) @ ( SV29 @ SV6 ) )
= $false )
| ( ( esti @ ( SV28 @ SV6 ) @ ( SV29 @ SV6 ) )
= $false )
| ( ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] :
~ ( esti @ ( SV28 @ SX0 ) @ ( SV29 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(103,plain,
! [SV7: nat,SV32: nat > $o] :
( ( ( SV32 @ SV7 )
= $true )
| ( ( ~ ( SV32 @ SV7 ) )
= $false )
| ( ( ~ ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] :
~ ( SV32 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(106,plain,
! [SV36: nat > set,SV7: nat,SV35: nat > nat] :
( ( ( esti @ ( SV35 @ SV7 ) @ ( SV36 @ SV7 ) )
= $true )
| ( ( esti @ ( SV35 @ SV7 ) @ ( SV36 @ SV7 ) )
= $true )
| ( ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] :
~ ( esti @ ( SV35 @ SX0 ) @ ( SV36 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(108,plain,
! [SV6: nat,SV25: nat > $o] :
( ( ( SV25 @ SV6 )
= $false )
| ( ( SV25 @ SV6 )
= $false )
| ( ( ~ ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] :
~ ( SV25 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(109,plain,
! [SV7: nat,SV32: nat > $o] :
( ( ( SV32 @ SV7 )
= $true )
| ( ( SV32 @ SV7 )
= $true )
| ( ( ~ ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] :
~ ( SV32 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(112,plain,
! [SV25: nat > $o,SV6: nat] :
( ( ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] :
~ ( SV25 @ SX0 ) ) )
= $false )
| ( ( SV25 @ SV6 )
= $false )
| ( ( SV25 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(113,plain,
! [SV32: nat > $o,SV7: nat] :
( ( ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] :
~ ( SV32 @ SX0 ) ) )
= $true )
| ( ( SV32 @ SV7 )
= $true )
| ( ( SV32 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(115,plain,
! [SV6: nat,SV18: nat > $o] :
( ( ( SV18 @ SV6 )
= $false )
| ( ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] :
~ ( SV18 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(116,plain,
! [SV7: nat,SV12: nat > $o] :
( ( ( SV12 @ SV7 )
= $true )
| ( ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] :
~ ( SV12 @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(117,plain,
( ( esti @ n_1
@ ( setof
@ ^ [SX0: nat] : ( SX0 = n_1 ) ) )
= $true ),
inference(extuni,[status(esa)],[62:[bind(SV7,$thf( n_1 ))]]) ).
thf(118,plain,
( ( esti @ x
@ ( setof
@ ^ [SX0: nat] : ( SX0 = x ) ) )
= $true ),
inference(extuni,[status(esa)],[63:[bind(SV7,$thf( x ))]]) ).
thf(119,plain,
! [SV1: nat > $o,SV6: nat] :
( ( ( esti @ SV6 @ ( setof @ SV1 ) )
= $false )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(sim,[status(thm)],[82]) ).
thf(120,plain,
! [SV25: nat > $o,SV6: nat] :
( ( ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] :
~ ( SV25 @ SX0 ) ) )
= $false )
| ( ( SV25 @ SV6 )
= $false ) ),
inference(sim,[status(thm)],[112]) ).
thf(121,plain,
! [SV29: nat > set,SV6: nat,SV28: nat > nat] :
( ( ( esti @ ( SV28 @ SV6 ) @ ( SV29 @ SV6 ) )
= $false )
| ( ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] :
~ ( esti @ ( SV28 @ SX0 ) @ ( SV29 @ SX0 ) ) ) )
= $false ) ),
inference(sim,[status(thm)],[101]) ).
thf(122,plain,
! [SV2: nat > $o,SV7: nat] :
( ( ( esti @ SV7 @ ( setof @ SV2 ) )
= $true )
| ( ( SV2 @ SV7 )
= $false ) ),
inference(sim,[status(thm)],[89]) ).
thf(123,plain,
! [SV32: nat > $o,SV7: nat] :
( ( ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] :
~ ( SV32 @ SX0 ) ) )
= $true )
| ( ( SV32 @ SV7 )
= $true ) ),
inference(sim,[status(thm)],[113]) ).
thf(124,plain,
! [SV36: nat > set,SV7: nat,SV35: nat > nat] :
( ( ( esti @ ( SV35 @ SV7 ) @ ( SV36 @ SV7 ) )
= $true )
| ( ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] :
~ ( esti @ ( SV35 @ SX0 ) @ ( SV36 @ SX0 ) ) ) )
= $true ) ),
inference(sim,[status(thm)],[106]) ).
thf(125,plain,
! [SV6: nat] :
( ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] : $false ) )
= $false ),
inference(sim,[status(thm)],[55]) ).
thf(126,plain,
! [SV7: nat] :
( ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] : $true ) )
= $true ),
inference(sim,[status(thm)],[59]) ).
thf(127,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[26,126,125,124,123,122,121,120,119,118,117,116,115,58,57,53,51,44,43,42,35]) ).
thf(128,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM636^1 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n021.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 : Thu Jul 7 03:16:04 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 5
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.34 (rf:0,axioms:5,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:7,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.41/0.57
% 0.41/0.57 ********************************
% 0.41/0.57 * All subproblems solved! *
% 0.41/0.57 ********************************
% 0.41/0.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:127,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.41/0.58
% 0.41/0.58 %**** Beginning of derivation protocol ****
% 0.41/0.58 % SZS output start CNFRefutation
% See solution above
% 0.41/0.58
% 0.41/0.58 %**** End of derivation protocol ****
% 0.41/0.58 %**** no. of clauses in derivation: 103 ****
% 0.41/0.58 %**** clause counter: 127 ****
% 0.41/0.58
% 0.41/0.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:127,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------