%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM705^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 10:35:00 AM UTC 2026
% Result : Theorem 180.50s 30.36s
% Output : CNFRefutation 180.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 5
% Syntax : Number of formulae : 89 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 683 ( 174 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 1168 ( 388 ~; 225 |; 10 &; 487 @)
% ( 0 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 185 ( 29 ^; 156 !; 0 ?; 185 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_nat,type,
nat: $tType ).
thf(tp_lessis,type,
lessis: nat > nat > $o ).
thf(tp_more,type,
more: nat > nat > $o ).
thf(tp_p,type,
p: nat > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: nat ).
thf(tp_sK2_SY15,type,
sK2_SY15: nat ).
thf(tp_sK3_REN,type,
sK3_REN: $o ).
thf(tp_sK4_E,type,
sK4_E: 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_sK8_E,type,
sK8_E: nat ).
thf(tp_sK9_E,type,
sK9_E: nat ).
thf(tp_some,type,
some: ( nat > $o ) > $o ).
thf(1,axiom,
! [Xp: nat > $o] :
( ( some @ Xp )
=> ( some
@ ^ [Xx: nat] :
~ ( ! [Xx_0: nat] :
( ( Xp @ Xx_0 )
=> ( lessis @ Xx @ Xx_0 ) )
=> ~ ( Xp @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz27) ).
thf(2,axiom,
! [Xx: nat,Xy: nat] :
( ( lessis @ Xx @ Xy )
=> ~ ( more @ Xx @ Xy ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10d) ).
thf(4,axiom,
! [Xx: nat,Xy: nat] :
( ( lessis @ Xx @ Xy )
=> ( ~ ( more @ Xy @ Xx )
=> ( Xy = Xx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz14) ).
thf(5,axiom,
some @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s) ).
thf(6,conjecture,
~ ( ! [Xx: nat,Xy: nat] :
( ~ ( ! [Xx_0: nat] :
( ( p @ Xx_0 )
=> ( lessis @ Xx @ Xx_0 ) )
=> ~ ( p @ Xx ) )
=> ( ~ ( ! [Xx_0: nat] :
( ( p @ Xx_0 )
=> ( lessis @ Xy @ Xx_0 ) )
=> ~ ( p @ Xy ) )
=> ( Xx = Xy ) ) )
=> ~ ( some
@ ^ [Xx: nat] :
~ ( ! [Xx_0: nat] :
( ( p @ Xx_0 )
=> ( lessis @ Xx @ Xx_0 ) )
=> ~ ( p @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz27a) ).
thf(7,negated_conjecture,
( ( ~ ( ! [Xx: nat,Xy: nat] :
( ~ ( ! [Xx_0: nat] :
( ( p @ Xx_0 )
=> ( lessis @ Xx @ Xx_0 ) )
=> ~ ( p @ Xx ) )
=> ( ~ ( ! [Xx_0: nat] :
( ( p @ Xx_0 )
=> ( lessis @ Xy @ Xx_0 ) )
=> ~ ( p @ Xy ) )
=> ( Xx = Xy ) ) )
=> ~ ( some
@ ^ [Xx: nat] :
~ ( ! [Xx_0: nat] :
( ( p @ Xx_0 )
=> ( lessis @ Xx @ Xx_0 ) )
=> ~ ( p @ Xx ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ~ ( ! [Xx: nat,Xy: nat] :
( ~ ( ! [Xx_0: nat] :
( ( p @ Xx_0 )
=> ( lessis @ Xx @ Xx_0 ) )
=> ~ ( p @ Xx ) )
=> ( ~ ( ! [Xx_0: nat] :
( ( p @ Xx_0 )
=> ( lessis @ Xy @ Xx_0 ) )
=> ~ ( p @ Xy ) )
=> ( Xx = Xy ) ) )
=> ~ ( some
@ ^ [Xx: nat] :
~ ( ! [Xx_0: nat] :
( ( p @ Xx_0 )
=> ( lessis @ Xx @ Xx_0 ) )
=> ~ ( p @ Xx ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [Xp: nat > $o] :
( ( some @ Xp )
=> ( some
@ ^ [Xx: nat] :
~ ( ! [Xx_0: nat] :
( ( Xp @ Xx_0 )
=> ( lessis @ Xx @ Xx_0 ) )
=> ~ ( Xp @ Xx ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( lessis @ Xx @ Xy )
=> ~ ( more @ Xx @ Xy ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( lessis @ Xx @ Xy )
=> ( ~ ( more @ Xy @ Xx )
=> ( Xy = Xx ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( some @ p )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( ! [Xx_0: nat] :
( ( p @ Xx_0 )
=> ( lessis @ Xx @ Xx_0 ) )
=> ~ ( p @ Xx ) )
=> ( ~ ( ! [Xx_0: nat] :
( ( p @ Xx_0 )
=> ( lessis @ Xy @ Xx_0 ) )
=> ~ ( p @ Xy ) )
=> ( Xx = Xy ) ) )
=> ~ ( some
@ ^ [Xx: nat] :
~ ( ! [Xx_0: nat] :
( ( p @ Xx_0 )
=> ( lessis @ Xx @ Xx_0 ) )
=> ~ ( p @ Xx ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(15,plain,
( ( ( sK3_REN
| ~ ( some
@ ^ [Xx: nat] :
~ ( ! [Xx_0: nat] :
( ( p @ Xx_0 )
=> ( lessis @ Xx @ Xx_0 ) )
=> ~ ( p @ Xx ) ) ) )
& ( sK3_REN
=> ( ! [SY14: nat] :
( ~ ( p @ SY14 )
| ( lessis @ sK1_Xx @ SY14 ) )
& ( p @ sK1_Xx )
& ! [SY17: nat] :
( ~ ( p @ SY17 )
| ( lessis @ sK2_SY15 @ SY17 ) )
& ( p @ sK2_SY15 )
& ( sK1_Xx != sK2_SY15 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(16,plain,
( ( ! [Xp: nat > $o] :
( ~ ( some @ Xp )
| ( some
@ ^ [Xx: nat] :
~ ( ! [Xx_0: nat] :
( ( Xp @ Xx_0 )
=> ( lessis @ Xx @ Xx_0 ) )
=> ~ ( Xp @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(17,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( lessis @ Xx @ Xy )
| ~ ( more @ Xx @ Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(19,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( lessis @ Xx @ Xy )
| ( more @ Xy @ Xx )
| ( Xy = Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(20,plain,
( ( some @ p )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(21,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( lessis @ Xx @ Xy )
| ( more @ Xy @ Xx )
| ( Xy = Xx ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(23,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( lessis @ Xx @ Xy )
| ~ ( more @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(24,plain,
( ( ! [Xp: nat > $o] :
( ~ ( some @ Xp )
| ( some
@ ^ [Xx: nat] :
~ ( ! [Xx_0: nat] :
( ( Xp @ Xx_0 )
=> ( lessis @ Xx @ Xx_0 ) )
=> ~ ( Xp @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(25,plain,
( ( ( sK3_REN
| ~ ( some
@ ^ [Xx: nat] :
~ ( ! [Xx_0: nat] :
( ( p @ Xx_0 )
=> ( lessis @ Xx @ Xx_0 ) )
=> ~ ( p @ Xx ) ) ) )
& ( sK3_REN
=> ( ! [SY14: nat] :
( ~ ( p @ SY14 )
| ( lessis @ sK1_Xx @ SY14 ) )
& ( p @ sK1_Xx )
& ! [SY17: nat] :
( ~ ( p @ SY17 )
| ( lessis @ sK2_SY15 @ SY17 ) )
& ( p @ sK2_SY15 )
& ( sK1_Xx != sK2_SY15 ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(26,plain,
( ( ! [SX0: nat > $o] :
( ~ ( some @ SX0 )
| ( some
@ ^ [SX1: nat] :
~ ( ~ ! [SX2: nat] :
( ~ ( SX0 @ SX2 )
| ( lessis @ SX1 @ SX2 ) )
| ~ ( SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(27,plain,
( ( ~ ( ~ ( sK3_REN
| ~ ( some
@ ^ [SX0: nat] :
~ ( ~ ! [SX1: nat] :
( ~ ( p @ SX1 )
| ( lessis @ SX0 @ SX1 ) )
| ~ ( p @ SX0 ) ) ) )
| ~ ( ~ sK3_REN
| ~ ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK1_Xx @ SX0 ) )
| ~ ( p @ sK1_Xx ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK2_SY15 @ SX0 ) )
| ~ ( p @ sK2_SY15 ) )
| ~ ( ( sK1_Xx != sK2_SY15 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(28,plain,
! [SV1: nat] :
( ( ! [SY18: nat] :
( ~ ( lessis @ SV1 @ SY18 )
| ( more @ SY18 @ SV1 )
| ( SY18 = SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(32,plain,
! [SV3: nat] :
( ( ! [SY19: nat] :
( ~ ( lessis @ SV3 @ SY19 )
| ~ ( more @ SV3 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(33,plain,
! [SV4: nat > $o] :
( ( ~ ( some @ SV4 )
| ( some
@ ^ [SY20: nat] :
~ ( ~ ! [SY21: nat] :
( ~ ( SV4 @ SY21 )
| ( lessis @ SY20 @ SY21 ) )
| ~ ( SV4 @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(34,plain,
( ( ~ ( sK3_REN
| ~ ( some
@ ^ [SX0: nat] :
~ ( ~ ! [SX1: nat] :
( ~ ( p @ SX1 )
| ( lessis @ SX0 @ SX1 ) )
| ~ ( p @ SX0 ) ) ) )
| ~ ( ~ sK3_REN
| ~ ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK1_Xx @ SX0 ) )
| ~ ( p @ sK1_Xx ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK2_SY15 @ SX0 ) )
| ~ ( p @ sK2_SY15 ) )
| ~ ( ( sK1_Xx != sK2_SY15 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(35,plain,
! [SV5: nat,SV1: nat] :
( ( ~ ( lessis @ SV1 @ SV5 )
| ( more @ SV5 @ SV1 )
| ( SV5 = SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(39,plain,
! [SV6: nat,SV3: nat] :
( ( ~ ( lessis @ SV3 @ SV6 )
| ~ ( more @ SV3 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(40,plain,
! [SV4: nat > $o] :
( ( ( ~ ( some @ SV4 ) )
= $true )
| ( ( some
@ ^ [SY20: nat] :
~ ( ~ ! [SY21: nat] :
( ~ ( SV4 @ SY21 )
| ( lessis @ SY20 @ SY21 ) )
| ~ ( SV4 @ SY20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(41,plain,
( ( ~ ( sK3_REN
| ~ ( some
@ ^ [SX0: nat] :
~ ( ~ ! [SX1: nat] :
( ~ ( p @ SX1 )
| ( lessis @ SX0 @ SX1 ) )
| ~ ( p @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(42,plain,
( ( ~ ( ~ sK3_REN
| ~ ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK1_Xx @ SX0 ) )
| ~ ( p @ sK1_Xx ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK2_SY15 @ SX0 ) )
| ~ ( p @ sK2_SY15 ) )
| ~ ( ( sK1_Xx != sK2_SY15 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(43,plain,
! [SV5: nat,SV1: nat] :
( ( ( ~ ( lessis @ SV1 @ SV5 ) )
= $true )
| ( ( ( more @ SV5 @ SV1 )
| ( SV5 = SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(47,plain,
! [SV6: nat,SV3: nat] :
( ( ( ~ ( lessis @ SV3 @ SV6 ) )
= $true )
| ( ( ~ ( more @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(48,plain,
! [SV4: nat > $o] :
( ( ( some @ SV4 )
= $false )
| ( ( some
@ ^ [SY20: nat] :
~ ( ~ ! [SY21: nat] :
( ~ ( SV4 @ SY21 )
| ( lessis @ SY20 @ SY21 ) )
| ~ ( SV4 @ SY20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(49,plain,
( ( sK3_REN
| ~ ( some
@ ^ [SX0: nat] :
~ ( ~ ! [SX1: nat] :
( ~ ( p @ SX1 )
| ( lessis @ SX0 @ SX1 ) )
| ~ ( p @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(50,plain,
( ( ~ sK3_REN
| ~ ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK1_Xx @ SX0 ) )
| ~ ( p @ sK1_Xx ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK2_SY15 @ SX0 ) )
| ~ ( p @ sK2_SY15 ) )
| ~ ( ( sK1_Xx != sK2_SY15 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(51,plain,
! [SV5: nat,SV1: nat] :
( ( ( lessis @ SV1 @ SV5 )
= $false )
| ( ( ( more @ SV5 @ SV1 )
| ( SV5 = SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(52,plain,
! [SV6: nat,SV3: nat] :
( ( ( lessis @ SV3 @ SV6 )
= $false )
| ( ( ~ ( more @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(53,plain,
( ( sK3_REN = $true )
| ( ( ~ ( some
@ ^ [SX0: nat] :
~ ( ~ ! [SX1: nat] :
( ~ ( p @ SX1 )
| ( lessis @ SX0 @ SX1 ) )
| ~ ( p @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(54,plain,
( ( ( ~ sK3_REN ) = $true )
| ( ( ~ ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK1_Xx @ SX0 ) )
| ~ ( p @ sK1_Xx ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK2_SY15 @ SX0 ) )
| ~ ( p @ sK2_SY15 ) )
| ~ ( ( sK1_Xx != sK2_SY15 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV1: nat,SV5: nat] :
( ( ( more @ SV5 @ SV1 )
= $true )
| ( ( SV5 = SV1 )
= $true )
| ( ( lessis @ SV1 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV6: nat,SV3: nat] :
( ( ( more @ SV3 @ SV6 )
= $false )
| ( ( lessis @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(57,plain,
( ( ( some
@ ^ [SX0: nat] :
~ ( ~ ! [SX1: nat] :
( ~ ( p @ SX1 )
| ( lessis @ SX0 @ SX1 ) )
| ~ ( p @ SX0 ) ) )
= $false )
| ( sK3_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(58,plain,
( ( sK3_REN = $false )
| ( ( ~ ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK1_Xx @ SX0 ) )
| ~ ( p @ sK1_Xx ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK2_SY15 @ SX0 ) )
| ~ ( p @ sK2_SY15 ) )
| ~ ( ( sK1_Xx != sK2_SY15 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(59,plain,
( ( ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK1_Xx @ SX0 ) )
| ~ ( p @ sK1_Xx ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK2_SY15 @ SX0 ) )
| ~ ( p @ sK2_SY15 ) )
| ~ ( ( sK1_Xx != sK2_SY15 ) ) ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(60,plain,
( ( ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK1_Xx @ SX0 ) )
| ~ ( p @ sK1_Xx ) ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(61,plain,
( ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK2_SY15 @ SX0 ) )
| ~ ( p @ sK2_SY15 ) )
| ~ ( ( sK1_Xx != sK2_SY15 ) ) ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(62,plain,
( ( ( ~ ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK1_Xx @ SX0 ) )
| ~ ( p @ sK1_Xx ) ) )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(63,plain,
( ( ( ~ ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK2_SY15 @ SX0 ) )
| ~ ( p @ sK2_SY15 ) )
| ~ ( ( sK1_Xx != sK2_SY15 ) ) ) )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(64,plain,
( ( ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK1_Xx @ SX0 ) )
| ~ ( p @ sK1_Xx ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(65,plain,
( ( ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK2_SY15 @ SX0 ) )
| ~ ( p @ sK2_SY15 ) )
| ~ ( ( sK1_Xx != sK2_SY15 ) ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(66,plain,
( ( ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK1_Xx @ SX0 ) ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(67,plain,
( ( ( ~ ( p @ sK1_Xx ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(68,plain,
( ( ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK2_SY15 @ SX0 ) )
| ~ ( p @ sK2_SY15 ) ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(69,plain,
( ( ( ~ ( ( sK1_Xx != sK2_SY15 ) ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(70,plain,
( ( ( ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK1_Xx @ SX0 ) ) )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(71,plain,
( ( ( p @ sK1_Xx )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(72,plain,
( ( ( ~ ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK2_SY15 @ SX0 ) )
| ~ ( p @ sK2_SY15 ) ) )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(73,plain,
( ( ( sK1_Xx != sK2_SY15 )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(74,plain,
! [SV7: nat] :
( ( ( ~ ( p @ SV7 )
| ( lessis @ sK1_Xx @ SV7 ) )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(75,plain,
( ( ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK2_SY15 @ SX0 ) )
| ~ ( p @ sK2_SY15 ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(76,plain,
( ( ( sK1_Xx = sK2_SY15 )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(77,plain,
! [SV7: nat] :
( ( ( ~ ( p @ SV7 ) )
= $true )
| ( ( lessis @ sK1_Xx @ SV7 )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(78,plain,
( ( ( ~ ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK2_SY15 @ SX0 ) ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(79,plain,
( ( ( ~ ( p @ sK2_SY15 ) )
= $false )
| ( sK3_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(80,plain,
! [SV7: nat] :
( ( ( p @ SV7 )
= $false )
| ( ( lessis @ sK1_Xx @ SV7 )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(81,plain,
( ( ( ! [SX0: nat] :
( ~ ( p @ SX0 )
| ( lessis @ sK2_SY15 @ SX0 ) ) )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(82,plain,
( ( ( p @ sK2_SY15 )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(83,plain,
! [SV8: nat] :
( ( ( ~ ( p @ SV8 )
| ( lessis @ sK2_SY15 @ SV8 ) )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(84,plain,
! [SV8: nat] :
( ( ( ~ ( p @ SV8 ) )
= $true )
| ( ( lessis @ sK2_SY15 @ SV8 )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(85,plain,
! [SV8: nat] :
( ( ( p @ SV8 )
= $false )
| ( ( lessis @ sK2_SY15 @ SV8 )
= $true )
| ( sK3_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(90,plain,
! [SV6: nat,SV3: nat] :
( ( ( lessis @ SV3 @ SV6 )
= $false )
| ( ( ( more @ SV3 @ SV6 )
= ( lessis @ SV3 @ SV6 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[56]) ).
thf(94,plain,
! [SV6: nat,SV3: nat] :
( ( ( ~ ( ( more @ SV3 @ SV6 )
| ( lessis @ SV3 @ SV6 ) )
| ~ ( ~ ( more @ SV3 @ SV6 )
| ~ ( lessis @ SV3 @ SV6 ) ) )
= $false )
| ( ( lessis @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[90]) ).
thf(101,plain,
! [SV6: nat,SV3: nat] :
( ( ( ~ ( ~ ( more @ SV3 @ SV6 )
| ~ ( lessis @ SV3 @ SV6 ) ) )
= $false )
| ( ( lessis @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(107,plain,
! [SV6: nat,SV3: nat] :
( ( ( ~ ( more @ SV3 @ SV6 )
| ~ ( lessis @ SV3 @ SV6 ) )
= $true )
| ( ( lessis @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(113,plain,
! [SV6: nat,SV3: nat] :
( ( ( ~ ( more @ SV3 @ SV6 ) )
= $true )
| ( ( ~ ( lessis @ SV3 @ SV6 ) )
= $true )
| ( ( lessis @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(118,plain,
! [SV6: nat,SV3: nat] :
( ( ( more @ SV3 @ SV6 )
= $false )
| ( ( ~ ( lessis @ SV3 @ SV6 ) )
= $true )
| ( ( lessis @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(121,plain,
! [SV6: nat,SV3: nat] :
( ( ( lessis @ SV3 @ SV6 )
= $false )
| ( ( more @ SV3 @ SV6 )
= $false )
| ( ( lessis @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(126,plain,
! [SV6: nat,SV3: nat] :
( ( ( lessis @ SV3 @ SV6 )
= $false )
| ( ( more @ SV3 @ SV6 )
= $false ) ),
inference(sim,[status(thm)],[121]) ).
thf(127,plain,
! [SV10: nat > $o] :
( ( ( some @ SV10 )
= $false )
| ( ( some
@ ^ [SX0: nat] :
~ ( ~ ! [SX1: nat] :
( ~ ( SV10 @ SX1 )
| ( lessis @ SX0 @ SX1 ) )
| ~ ( SV10 @ SX0 ) ) )
= $true ) ),
inference(rename,[status(thm)],[48]) ).
thf(130,plain,
! [SV10: nat > $o] :
( ( ( ( some @ SV10 )
= ( some @ p ) )
= $false )
| ( ( some
@ ^ [SX0: nat] :
~ ( ~ ! [SX1: nat] :
( ~ ( SV10 @ SX1 )
| ( lessis @ SX0 @ SX1 ) )
| ~ ( SV10 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[127,20]) ).
thf(131,plain,
( ( some
@ ^ [SX0: nat] :
~ ( ~ ! [SX1: nat] :
( ~ ( p @ SX1 )
| ( lessis @ SX0 @ SX1 ) )
| ~ ( p @ SX0 ) ) )
= $true ),
inference(extuni,[status(esa)],[130:[bind(SV10,$thf( p ))]]) ).
thf(132,plain,
! [SV10: nat > $o] :
( ( ( ( some
@ ^ [SX0: nat] :
~ ( ~ ! [SX1: nat] :
( ~ ( p @ SX1 )
| ( lessis @ SX0 @ SX1 ) )
| ~ ( p @ SX0 ) ) )
= ( some @ SV10 ) )
= $false )
| ( ( some
@ ^ [SX0: nat] :
~ ( ~ ! [SX1: nat] :
( ~ ( SV10 @ SX1 )
| ( lessis @ SX0 @ SX1 ) )
| ~ ( SV10 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[131,127]) ).
thf(133,plain,
( ( some
@ ^ [SX0: nat] :
~ ( ~ ! [SX1: nat] :
( ~ ~ ( ~ ! [SX2: nat] :
( ~ ( p @ SX2 )
| ( lessis @ SX1 @ SX2 ) )
| ~ ( p @ SX1 ) )
| ( lessis @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX1: nat] :
( ~ ( p @ SX1 )
| ( lessis @ SX0 @ SX1 ) )
| ~ ( p @ SX0 ) ) ) )
= $true ),
inference(extuni,[status(esa)],[132:[bind(SV10,$thf( ^ [SX0: nat] : ~ ( ~ ( ! [SX1: nat] : ( ~ ( p @ SX1 ) | ( lessis @ SX0 @ SX1 ) ) ) | ~ ( p @ SX0 ) ) ))]]) ).
thf(134,plain,
! [SV10: nat > $o] :
( ( ( ( some
@ ^ [SX0: nat] :
~ ( ~ ! [SX1: nat] :
( ~ ~ ( ~ ! [SX2: nat] :
( ~ ( p @ SX2 )
| ( lessis @ SX1 @ SX2 ) )
| ~ ( p @ SX1 ) )
| ( lessis @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX1: nat] :
( ~ ( p @ SX1 )
| ( lessis @ SX0 @ SX1 ) )
| ~ ( p @ SX0 ) ) ) )
= ( some @ SV10 ) )
= $false )
| ( ( some
@ ^ [SX0: nat] :
~ ( ~ ! [SX1: nat] :
( ~ ( SV10 @ SX1 )
| ( lessis @ SX0 @ SX1 ) )
| ~ ( SV10 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[133,127]) ).
thf(135,plain,
( ( some
@ ^ [SX0: nat] :
~ ( ~ ! [SX1: nat] :
( ~ ~ ( ~ ! [SX2: nat] :
( ~ ~ ( ~ ! [SX3: nat] :
( ~ ( p @ SX3 )
| ( lessis @ SX2 @ SX3 ) )
| ~ ( p @ SX2 ) )
| ( lessis @ SX1 @ SX2 ) )
| ~ ~ ( ~ ! [SX2: nat] :
( ~ ( p @ SX2 )
| ( lessis @ SX1 @ SX2 ) )
| ~ ( p @ SX1 ) ) )
| ( lessis @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX1: nat] :
( ~ ~ ( ~ ! [SX2: nat] :
( ~ ( p @ SX2 )
| ( lessis @ SX1 @ SX2 ) )
| ~ ( p @ SX1 ) )
| ( lessis @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX1: nat] :
( ~ ( p @ SX1 )
| ( lessis @ SX0 @ SX1 ) )
| ~ ( p @ SX0 ) ) ) ) )
= $true ),
inference(extuni,[status(esa)],[134:[bind(SV10,$thf( ^ [SX0: nat] : ~ ( ~ ( ! [SX1: nat] : ( ~ ( ~ ( ~ ( ! [SX2: nat] : ( ~ ( p @ SX2 ) | ( lessis @ SX1 @ SX2 ) ) ) | ~ ( p @ SX1 ) ) ) | ( lessis @ SX0 @ SX1 ) ) ) | ~ ( ~ ( ~ ( ! [SX1: nat] : ( ~ ( p @ SX1 ) | ( lessis @ SX0 @ SX1 ) ) ) | ~ ( p @ SX0 ) ) ) ) ))]]) ).
thf(136,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,135,133,131,127,126,85,82,80,76,71,57,56,55]) ).
thf(137,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM705^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n019.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 13:35:31 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 180.50/30.36
% 180.50/30.36 No.of.Axioms: 5
% 180.50/30.36
% 180.50/30.36 Length.of.Defs: 0
% 180.50/30.36
% 180.50/30.36 Contains.Choice.Funs: false
% 180.50/30.36 ..eprover: CPU time limit exceeded, terminating
% 180.50/30.36 .eprover: CPU time limit exceeded, terminating
% 180.50/30.36 .
% 180.50/30.36
% 180.50/30.36 ********************************
% 180.50/30.36 * All subproblems solved! *
% 180.50/30.36 ********************************
% 180.50/30.36 % SZS status Theorem for /export/starexec/sandbox2/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:136,loop_count:5,foatp_calls:3,translation:fof_full)
% 180.50/30.36
% 180.50/30.36 %**** Beginning of derivation protocol ****
% 180.50/30.36 % SZS output start CNFRefutation
% See solution above
% 180.50/30.36
% 180.50/30.36 %**** End of derivation protocol ****
% 180.50/30.36 %**** no. of clauses in derivation: 89 ****
% 180.50/30.36 %**** clause counter: 136 ****
% 180.50/30.36
% 180.50/30.36 % SZS status Theorem for /export/starexec/sandbox2/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:136,loop_count:5,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------