%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM637^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:34:43 AM UTC 2026
% Result : Theorem 0.39s 0.30s
% Output : CNFRefutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 96 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 530 ( 203 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 776 ( 127 ~; 120 |; 2 &; 517 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 196 ( 30 ^; 166 !; 0 ?; 196 :)
% 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(2,axiom,
! [Xp: nat > $o,Xs: nat] :
( ( Xp @ Xs )
=> ( esti @ Xs @ ( setof @ Xp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',estii) ).
thf(3,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(4,axiom,
! [Xp: nat > $o,Xs: nat] :
( ( esti @ Xs @ ( setof @ Xp ) )
=> ( Xp @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',estie) ).
thf(5,axiom,
x != n_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).
thf(6,conjecture,
~ ! [Xx_0: nat] :
( x
!= ( suc @ Xx_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz3) ).
thf(7,negated_conjecture,
( ( ~ ! [Xx_0: nat] :
( x
!= ( suc @ Xx_0 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ~ ! [Xx_0: nat] :
( x
!= ( suc @ Xx_0 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [Xp: nat > $o,Xs: nat] :
( ( Xp @ Xs )
=> ( esti @ Xs @ ( setof @ Xp ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,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)],[3]) ).
thf(12,plain,
( ( ! [Xp: nat > $o,Xs: nat] :
( ( esti @ Xs @ ( setof @ Xp ) )
=> ( Xp @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( x != n_1 )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ! [Xx_0: nat] :
( x
!= ( suc @ Xx_0 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(15,plain,
( ( ! [Xx_0: nat] :
( x
!= ( suc @ Xx_0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(17,plain,
( ( ! [Xp: nat > $o,Xs: nat] :
( ~ ( Xp @ Xs )
| ( esti @ Xs @ ( setof @ Xp ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(18,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)],[11]) ).
thf(19,plain,
( ( ! [Xp: nat > $o,Xs: nat] :
( ~ ( esti @ Xs @ ( setof @ Xp ) )
| ( Xp @ Xs ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(20,plain,
( ( x != n_1 )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(21,plain,
( ( x != n_1 )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(22,plain,
( ( ! [Xp: nat > $o,Xs: nat] :
( ~ ( esti @ Xs @ ( setof @ Xp ) )
| ( Xp @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(23,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)],[18]) ).
thf(24,plain,
( ( ! [Xp: nat > $o,Xs: nat] :
( ~ ( Xp @ Xs )
| ( esti @ Xs @ ( setof @ Xp ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(26,plain,
( ( ! [Xx_0: nat] :
( x
!= ( suc @ Xx_0 ) ) )
= $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)],[23]) ).
thf(28,plain,
( ( x = n_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(29,plain,
! [SV1: nat > $o] :
( ( ! [SY9: nat] :
( ~ ( esti @ SY9 @ ( setof @ SV1 ) )
| ( SV1 @ SY9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(30,plain,
! [SV2: nat > $o] :
( ( ! [SY10: nat] :
( ~ ( SV2 @ SY10 )
| ( esti @ SY10 @ ( setof @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(34,plain,
! [SV4: nat] :
( ( x
!= ( suc @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(35,plain,
! [SV5: set] :
( ( ~ ( esti @ n_1 @ SV5 )
| ~ ( ~ ( esti @ ( sK1_Xx @ SV5 ) @ SV5 )
| ~ ~ ( esti @ ( suc @ ( sK1_Xx @ SV5 ) ) @ SV5 ) )
| ! [SY11: nat] : ( esti @ SY11 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(36,plain,
! [SV1: nat > $o,SV6: nat] :
( ( ~ ( esti @ SV6 @ ( setof @ SV1 ) )
| ( SV1 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(37,plain,
! [SV7: nat,SV2: nat > $o] :
( ( ~ ( SV2 @ SV7 )
| ( esti @ SV7 @ ( setof @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(41,plain,
! [SV4: nat] :
( ( x
= ( suc @ SV4 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(42,plain,
! [SV5: set] :
( ( ( ~ ( esti @ n_1 @ SV5 ) )
= $true )
| ( ( ~ ( ~ ( esti @ ( sK1_Xx @ SV5 ) @ SV5 )
| ~ ~ ( esti @ ( suc @ ( sK1_Xx @ SV5 ) ) @ SV5 ) )
| ! [SY11: nat] : ( esti @ SY11 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(43,plain,
! [SV1: nat > $o,SV6: nat] :
( ( ( ~ ( esti @ SV6 @ ( setof @ SV1 ) ) )
= $true )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(44,plain,
! [SV7: nat,SV2: nat > $o] :
( ( ( ~ ( SV2 @ SV7 ) )
= $true )
| ( ( esti @ SV7 @ ( setof @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(48,plain,
! [SV5: set] :
( ( ( esti @ n_1 @ SV5 )
= $false )
| ( ( ~ ( ~ ( esti @ ( sK1_Xx @ SV5 ) @ SV5 )
| ~ ~ ( esti @ ( suc @ ( sK1_Xx @ SV5 ) ) @ SV5 ) )
| ! [SY11: nat] : ( esti @ SY11 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(49,plain,
! [SV1: nat > $o,SV6: nat] :
( ( ( esti @ SV6 @ ( setof @ SV1 ) )
= $false )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(50,plain,
! [SV7: nat,SV2: nat > $o] :
( ( ( SV2 @ SV7 )
= $false )
| ( ( esti @ SV7 @ ( setof @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(51,plain,
! [SV5: set] :
( ( ( ~ ( ~ ( esti @ ( sK1_Xx @ SV5 ) @ SV5 )
| ~ ~ ( esti @ ( suc @ ( sK1_Xx @ SV5 ) ) @ SV5 ) ) )
= $true )
| ( ( ! [SY11: nat] : ( esti @ SY11 @ SV5 ) )
= $true )
| ( ( esti @ n_1 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(52,plain,
! [SV5: set] :
( ( ( ~ ( esti @ ( sK1_Xx @ SV5 ) @ SV5 )
| ~ ~ ( esti @ ( suc @ ( sK1_Xx @ SV5 ) ) @ SV5 ) )
= $false )
| ( ( ! [SY11: nat] : ( esti @ SY11 @ SV5 ) )
= $true )
| ( ( esti @ n_1 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(53,plain,
! [SV5: set] :
( ( ( ~ ( esti @ ( sK1_Xx @ SV5 ) @ SV5 ) )
= $false )
| ( ( ! [SY11: nat] : ( esti @ SY11 @ SV5 ) )
= $true )
| ( ( esti @ n_1 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(54,plain,
! [SV5: set] :
( ( ( ~ ~ ( esti @ ( suc @ ( sK1_Xx @ SV5 ) ) @ SV5 ) )
= $false )
| ( ( ! [SY11: nat] : ( esti @ SY11 @ SV5 ) )
= $true )
| ( ( esti @ n_1 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(55,plain,
! [SV5: set] :
( ( ( esti @ ( sK1_Xx @ SV5 ) @ SV5 )
= $true )
| ( ( ! [SY11: nat] : ( esti @ SY11 @ SV5 ) )
= $true )
| ( ( esti @ n_1 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(56,plain,
! [SV5: set] :
( ( ( ~ ( esti @ ( suc @ ( sK1_Xx @ SV5 ) ) @ SV5 ) )
= $true )
| ( ( ! [SY11: nat] : ( esti @ SY11 @ SV5 ) )
= $true )
| ( ( esti @ n_1 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(57,plain,
! [SV5: set,SV8: nat] :
( ( ( esti @ SV8 @ SV5 )
= $true )
| ( ( esti @ ( sK1_Xx @ SV5 ) @ SV5 )
= $true )
| ( ( esti @ n_1 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(58,plain,
! [SV5: set] :
( ( ( esti @ ( suc @ ( sK1_Xx @ SV5 ) ) @ SV5 )
= $false )
| ( ( ! [SY11: nat] : ( esti @ SY11 @ SV5 ) )
= $true )
| ( ( esti @ n_1 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(59,plain,
! [SV5: set,SV9: nat] :
( ( ( esti @ SV9 @ SV5 )
= $true )
| ( ( esti @ ( suc @ ( sK1_Xx @ SV5 ) ) @ SV5 )
= $false )
| ( ( esti @ n_1 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(64,plain,
! [SV6: nat] :
( ( ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] : $false ) )
= $false )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[49:[bind(SV1,$thf( ^ [SV20: nat] : $false ))]]) ).
thf(65,plain,
! [SV19: nat > $o,SV6: nat] :
( ( ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] :
~ ( SV19 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV19 @ SV6 ) )
= $true ) ),
inference(prim_subst,[status(thm)],[49:[bind(SV1,$thf( ^ [SV18: nat] : ~ ( SV19 @ SV18 ) ))]]) ).
thf(66,plain,
! [SV6: nat] :
( ( ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] : ( SX0 = n_1 ) ) )
= $false )
| ( ( SV6 = n_1 )
= $true ) ),
inference(prim_subst,[status(thm)],[49:[bind(SV1,$thf( ^ [SV16: nat] : ( SV16 = n_1 ) ))]]) ).
thf(67,plain,
! [SV6: nat] :
( ( ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] : ( SX0 = x ) ) )
= $false )
| ( ( SV6 = x )
= $true ) ),
inference(prim_subst,[status(thm)],[49:[bind(SV1,$thf( ^ [SV17: nat] : ( SV17 = x ) ))]]) ).
thf(68,plain,
! [SV7: nat] :
( ( $true = $false )
| ( ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] : $true ) )
= $true ) ),
inference(prim_subst,[status(thm)],[50:[bind(SV2,$thf( ^ [SV15: nat] : $true ))]]) ).
thf(70,plain,
! [SV7: nat,SV13: nat > $o] :
( ( ( ~ ( SV13 @ SV7 ) )
= $false )
| ( ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] :
~ ( SV13 @ SX0 ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[50:[bind(SV2,$thf( ^ [SV12: nat] : ~ ( SV13 @ SV12 ) ))]]) ).
thf(71,plain,
! [SV7: nat] :
( ( ( SV7 = n_1 )
= $false )
| ( ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] : ( SX0 = n_1 ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[50:[bind(SV2,$thf( ^ [SV10: nat] : ( SV10 = n_1 ) ))]]) ).
thf(72,plain,
! [SV7: nat] :
( ( ( SV7 = x )
= $false )
| ( ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] : ( SX0 = x ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[50:[bind(SV2,$thf( ^ [SV11: nat] : ( SV11 = x ) ))]]) ).
thf(74,plain,
! [SV1: nat > $o,SV6: nat] :
( ( ( SV1 @ SV6 )
= $true )
| ( ( ( SV1 @ SV6 )
= ( ~ ( esti @ SV6 @ ( setof @ SV1 ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[49]) ).
thf(75,plain,
! [SV7: nat,SV2: nat > $o] :
( ( ( SV2 @ SV7 )
= $false )
| ( ( ( SV2 @ SV7 )
= ( ~ ( esti @ SV7 @ ( setof @ SV2 ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[50]) ).
thf(78,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)],[74]) ).
thf(79,plain,
! [SV6: nat,SV1: nat > $o] :
( ( ( ( SV1 @ SV6 )
= ( ~ ( esti @ SV6 @ ( setof @ SV1 ) ) ) )
= $false )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[74]) ).
thf(80,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)],[75]) ).
thf(81,plain,
! [SV7: nat,SV2: nat > $o] :
( ( ( ( SV2 @ SV7 )
= ( ~ ( esti @ SV7 @ ( setof @ SV2 ) ) ) )
= $false )
| ( ( SV2 @ SV7 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[75]) ).
thf(84,plain,
! [SV6: nat,SV1: nat > $o] :
( ( ( ~ ( ( SV1 @ SV6 )
| ~ ( esti @ SV6 @ ( setof @ SV1 ) ) ) )
= $false )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(87,plain,
! [SV7: nat,SV2: nat > $o] :
( ( ( ~ ( ~ ( SV2 @ SV7 )
| ~ ~ ( esti @ SV7 @ ( setof @ SV2 ) ) ) )
= $false )
| ( ( SV2 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(90,plain,
! [SV6: nat,SV1: nat > $o] :
( ( ( ( SV1 @ SV6 )
| ~ ( esti @ SV6 @ ( setof @ SV1 ) ) )
= $true )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(93,plain,
! [SV7: nat,SV2: nat > $o] :
( ( ( ~ ( SV2 @ SV7 )
| ~ ~ ( esti @ SV7 @ ( setof @ SV2 ) ) )
= $true )
| ( ( SV2 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(96,plain,
! [SV6: nat,SV1: nat > $o] :
( ( ( SV1 @ SV6 )
= $true )
| ( ( ~ ( esti @ SV6 @ ( setof @ SV1 ) ) )
= $true )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(99,plain,
! [SV7: nat,SV2: nat > $o] :
( ( ( ~ ( SV2 @ SV7 ) )
= $true )
| ( ( ~ ~ ( esti @ SV7 @ ( setof @ SV2 ) ) )
= $true )
| ( ( SV2 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(102,plain,
! [SV1: nat > $o,SV6: nat] :
( ( ( esti @ SV6 @ ( setof @ SV1 ) )
= $false )
| ( ( SV1 @ SV6 )
= $true )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(105,plain,
! [SV7: nat,SV2: nat > $o] :
( ( ( SV2 @ SV7 )
= $false )
| ( ( ~ ~ ( esti @ SV7 @ ( setof @ SV2 ) ) )
= $true )
| ( ( SV2 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(108,plain,
! [SV2: nat > $o,SV7: nat] :
( ( ( ~ ( esti @ SV7 @ ( setof @ SV2 ) ) )
= $false )
| ( ( SV2 @ SV7 )
= $false )
| ( ( SV2 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(111,plain,
! [SV2: nat > $o,SV7: nat] :
( ( ( esti @ SV7 @ ( setof @ SV2 ) )
= $true )
| ( ( SV2 @ SV7 )
= $false )
| ( ( SV2 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(113,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 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[79:[bind(SV1,$thf( ^ [SX0: nat] : ~ ( esti @ ( SV28 @ SX0 ) @ ( SV29 @ SX0 ) ) ))]]) ).
thf(114,plain,
! [SV6: nat,SV25: nat > $o] :
( ( ( ~ ( SV25 @ SV6 ) )
= $true )
| ( ( ~ ( SV25 @ SV6 ) )
= $true )
| ( ( ~ ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] :
~ ( SV25 @ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[79:[bind(SV1,$thf( ^ [SX0: nat] : ~ ( SV25 @ SX0 ) ))]]) ).
thf(116,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 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[81:[bind(SV2,$thf( ^ [SX0: nat] : ~ ( esti @ ( SV35 @ SX0 ) @ ( SV36 @ SX0 ) ) ))]]) ).
thf(119,plain,
! [SV7: nat,SV32: nat > $o] :
( ( ( ~ ( SV32 @ SV7 ) )
= $false )
| ( ( ~ ( SV32 @ SV7 ) )
= $false )
| ( ( ~ ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] :
~ ( SV32 @ SX0 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[81:[bind(SV2,$thf( ^ [SX0: nat] : ~ ( SV32 @ SX0 ) ))]]) ).
thf(121,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)],[114]) ).
thf(122,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)],[113]) ).
thf(124,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)],[119]) ).
thf(127,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)],[116]) ).
thf(129,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)],[121]) ).
thf(130,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)],[124]) ).
thf(133,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)],[129]) ).
thf(134,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)],[130]) ).
thf(137,plain,
! [SV6: nat,SV19: nat > $o] :
( ( ( SV19 @ SV6 )
= $false )
| ( ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] :
~ ( SV19 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(138,plain,
! [SV7: nat,SV13: nat > $o] :
( ( ( SV13 @ SV7 )
= $true )
| ( ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] :
~ ( SV13 @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(140,plain,
( ( esti @ n_1
@ ( setof
@ ^ [SX0: nat] : ( SX0 = n_1 ) ) )
= $true ),
inference(extuni,[status(esa)],[71:[bind(SV7,$thf( n_1 ))]]) ).
thf(141,plain,
( ( esti @ x
@ ( setof
@ ^ [SX0: nat] : ( SX0 = x ) ) )
= $true ),
inference(extuni,[status(esa)],[72:[bind(SV7,$thf( x ))]]) ).
thf(142,plain,
! [SV1: nat > $o,SV6: nat] :
( ( ( esti @ SV6 @ ( setof @ SV1 ) )
= $false )
| ( ( SV1 @ SV6 )
= $true ) ),
inference(sim,[status(thm)],[102]) ).
thf(143,plain,
! [SV25: nat > $o,SV6: nat] :
( ( ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] :
~ ( SV25 @ SX0 ) ) )
= $false )
| ( ( SV25 @ SV6 )
= $false ) ),
inference(sim,[status(thm)],[133]) ).
thf(144,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)],[122]) ).
thf(145,plain,
! [SV2: nat > $o,SV7: nat] :
( ( ( esti @ SV7 @ ( setof @ SV2 ) )
= $true )
| ( ( SV2 @ SV7 )
= $false ) ),
inference(sim,[status(thm)],[111]) ).
thf(146,plain,
! [SV32: nat > $o,SV7: nat] :
( ( ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] :
~ ( SV32 @ SX0 ) ) )
= $true )
| ( ( SV32 @ SV7 )
= $true ) ),
inference(sim,[status(thm)],[134]) ).
thf(147,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)],[127]) ).
thf(148,plain,
! [SV6: nat] :
( ( esti @ SV6
@ ( setof
@ ^ [SX0: nat] : $false ) )
= $false ),
inference(sim,[status(thm)],[64]) ).
thf(149,plain,
! [SV7: nat] :
( ( esti @ SV7
@ ( setof
@ ^ [SX0: nat] : $true ) )
= $true ),
inference(sim,[status(thm)],[68]) ).
thf(150,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,149,148,147,146,145,144,143,142,141,140,138,137,67,66,59,57,50,49,41]) ).
thf(151,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM637^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n017.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 13:26:45 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.39/0.30
% 0.39/0.30 No.of.Axioms: 5
% 0.39/0.30
% 0.39/0.30 Length.of.Defs: 0
% 0.39/0.30
% 0.39/0.30 Contains.Choice.Funs: false
% 0.39/0.30 ..
% 0.39/0.30
% 0.39/0.30 ********************************
% 0.39/0.30 * All subproblems solved! *
% 0.39/0.30 ********************************
% 0.39/0.30 % 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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:150,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.39/0.30
% 0.39/0.30 %**** Beginning of derivation protocol ****
% 0.39/0.30 % SZS output start CNFRefutation
% See solution above
% 0.39/0.30
% 0.39/0.30 %**** End of derivation protocol ****
% 0.39/0.30 %**** no. of clauses in derivation: 96 ****
% 0.39/0.30 %**** clause counter: 150 ****
% 0.39/0.30
% 0.39/0.30 % 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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:150,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------