%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU924^5 : TPTP v9.3.1. Released v4.0.0.
% 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 10:49:14 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 1
% Syntax : Number of formulae : 61 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 410 ( 277 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 344 ( 46 ~; 95 |; 7 &; 177 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 90 ( 90 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 250 ( 154 ^; 96 !; 0 ?; 250 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK10_E,type,
sK10_E: $i > $i ).
thf(tp_sK11_E,type,
sK11_E: $i > $i ).
thf(tp_sK12_E,type,
sK12_E: $i > $i ).
thf(tp_sK13_E,type,
sK13_E: $i > $i ).
thf(tp_sK1_Xz,type,
sK1_Xz: $i ).
thf(tp_sK2_SY7,type,
sK2_SY7: $i > $i ).
thf(tp_sK3_SY17,type,
sK3_SY17: $i ).
thf(tp_sK4_SY19,type,
sK4_SY19: ( ( $i > $i ) > $o ) > $i > $i ).
thf(tp_sK5_SV11,type,
sK5_SV11: $i > $i ).
thf(tp_sK6_SV15,type,
sK6_SV15: $i > $i ).
thf(tp_sK7_SV16,type,
sK7_SV16: $i > $i ).
thf(tp_sK8_E,type,
sK8_E: $i > $i ).
thf(tp_sK9_E,type,
sK9_E: $i > $i ).
thf(1,conjecture,
! [Xz: $i,Xg: $i > $i] :
( ! [Xp: ( $i > $i ) > $o] :
( ( ( Xp
@ ^ [Xx: $i] : Xz )
& ! [Xj: $i > $i] :
( ( Xp @ Xj )
=> ( Xp
@ ^ [Xx: $i] : Xz ) ) )
=> ( Xp @ Xg ) )
=> ! [Xx: $i] :
( ( Xg @ Xx )
= Xz ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM134_pme) ).
thf(2,negated_conjecture,
( ( ! [Xz: $i,Xg: $i > $i] :
( ! [Xp: ( $i > $i ) > $o] :
( ( ( Xp
@ ^ [Xx: $i] : Xz )
& ! [Xj: $i > $i] :
( ( Xp @ Xj )
=> ( Xp
@ ^ [Xx: $i] : Xz ) ) )
=> ( Xp @ Xg ) )
=> ! [Xx: $i] :
( ( Xg @ Xx )
= Xz ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xz: $i,Xg: $i > $i] :
( ! [Xp: ( $i > $i ) > $o] :
( ( ( Xp
@ ^ [Xx: $i] : Xz )
& ! [Xj: $i > $i] :
( ( Xp @ Xj )
=> ( Xp
@ ^ [Xx: $i] : Xz ) ) )
=> ( Xp @ Xg ) )
=> ! [Xx: $i] :
( ( Xg @ Xx )
= Xz ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY7: $i > $i] :
( ! [SY8: ( $i > $i ) > $o] :
( ( ( SY8
@ ^ [SY9: $i] : sK1_Xz )
& ! [SY10: $i > $i] :
( ( SY8 @ SY10 )
=> ( SY8
@ ^ [SY11: $i] : sK1_Xz ) ) )
=> ( SY8 @ SY7 ) )
=> ! [SY12: $i] :
( ( SY7 @ SY12 )
= sK1_Xz ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY13: ( $i > $i ) > $o] :
( ( ( SY13
@ ^ [SY9: $i] : sK1_Xz )
& ! [SY10: $i > $i] :
( ( SY13 @ SY10 )
=> ( SY13
@ ^ [SY11: $i] : sK1_Xz ) ) )
=> ( SY13 @ sK2_SY7 ) )
=> ! [SY17: $i] :
( ( sK2_SY7 @ SY17 )
= sK1_Xz ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY13: ( $i > $i ) > $o] :
( ( ( SY13
@ ^ [SY9: $i] : sK1_Xz )
& ! [SY10: $i > $i] :
( ( SY13 @ SY10 )
=> ( SY13
@ ^ [SY11: $i] : sK1_Xz ) ) )
=> ( SY13 @ sK2_SY7 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY17: $i] :
( ( sK2_SY7 @ SY17 )
= sK1_Xz ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ! [SY17: $i] :
( ( sK2_SY7 @ SY17 )
= sK1_Xz ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [SY13: ( $i > $i ) > $o] :
( ( ( SY13
@ ^ [SY9: $i] : sK1_Xz )
& ! [SY10: $i > $i] :
( ( SY13 @ SY10 )
=> ( SY13
@ ^ [SY11: $i] : sK1_Xz ) ) )
=> ( SY13 @ sK2_SY7 ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( ~ ! [SY17: $i] :
( ( sK2_SY7 @ SY17 )
= sK1_Xz ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(11,plain,
( ( ! [SX0: ( $i > $i ) > $o] :
( ~ ~ ( ~ ( SX0
@ ^ [SX1: $i] : sK1_Xz )
| ~ ! [SX1: $i > $i] :
( ~ ( SX0 @ SX1 )
| ( SX0
@ ^ [SX2: $i] : sK1_Xz ) ) )
| ( SX0 @ sK2_SY7 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [SY17: $i] :
( ( sK2_SY7 @ SY17 )
= sK1_Xz ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(13,plain,
! [SV1: ( $i > $i ) > $o] :
( ( ~ ~ ( ~ ( SV1
@ ^ [SX1: $i] : sK1_Xz )
| ~ ! [SY19: $i > $i] :
( ~ ( SV1 @ SY19 )
| ( SV1
@ ^ [SX2: $i] : sK1_Xz ) ) )
| ( SV1 @ sK2_SY7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ( sK2_SY7 @ sK3_SY17 )
= sK1_Xz )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(15,plain,
! [SV1: ( $i > $i ) > $o] :
( ( ( ~ ~ ( ~ ( SV1
@ ^ [SX1: $i] : sK1_Xz )
| ~ ! [SY19: $i > $i] :
( ~ ( SV1 @ SY19 )
| ( SV1
@ ^ [SX2: $i] : sK1_Xz ) ) ) )
= $true )
| ( ( SV1 @ sK2_SY7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[13]) ).
thf(16,plain,
! [SV1: ( $i > $i ) > $o] :
( ( ( ~ ( ~ ( SV1
@ ^ [SX1: $i] : sK1_Xz )
| ~ ! [SY19: $i > $i] :
( ~ ( SV1 @ SY19 )
| ( SV1
@ ^ [SX2: $i] : sK1_Xz ) ) ) )
= $false )
| ( ( SV1 @ sK2_SY7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(17,plain,
! [SV1: ( $i > $i ) > $o] :
( ( ( ~ ( SV1
@ ^ [SX1: $i] : sK1_Xz )
| ~ ! [SY19: $i > $i] :
( ~ ( SV1 @ SY19 )
| ( SV1
@ ^ [SX2: $i] : sK1_Xz ) ) )
= $true )
| ( ( SV1 @ sK2_SY7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(18,plain,
! [SV1: ( $i > $i ) > $o] :
( ( ( ~ ( SV1
@ ^ [SX1: $i] : sK1_Xz ) )
= $true )
| ( ( ~ ! [SY19: $i > $i] :
( ~ ( SV1 @ SY19 )
| ( SV1
@ ^ [SX2: $i] : sK1_Xz ) ) )
= $true )
| ( ( SV1 @ sK2_SY7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(19,plain,
! [SV1: ( $i > $i ) > $o] :
( ( ( SV1
@ ^ [SX1: $i] : sK1_Xz )
= $false )
| ( ( ~ ! [SY19: $i > $i] :
( ~ ( SV1 @ SY19 )
| ( SV1
@ ^ [SX2: $i] : sK1_Xz ) ) )
= $true )
| ( ( SV1 @ sK2_SY7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(20,plain,
! [SV1: ( $i > $i ) > $o] :
( ( ( ! [SY19: $i > $i] :
( ~ ( SV1 @ SY19 )
| ( SV1
@ ^ [SX2: $i] : sK1_Xz ) ) )
= $false )
| ( ( SV1
@ ^ [SX1: $i] : sK1_Xz )
= $false )
| ( ( SV1 @ sK2_SY7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(21,plain,
! [SV1: ( $i > $i ) > $o] :
( ( ( ~ ( SV1 @ ( sK4_SY19 @ SV1 ) )
| ( SV1
@ ^ [SX2: $i] : sK1_Xz ) )
= $false )
| ( ( SV1
@ ^ [SX1: $i] : sK1_Xz )
= $false )
| ( ( SV1 @ sK2_SY7 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(22,plain,
! [SV1: ( $i > $i ) > $o] :
( ( ( ~ ( SV1 @ ( sK4_SY19 @ SV1 ) ) )
= $false )
| ( ( SV1
@ ^ [SX1: $i] : sK1_Xz )
= $false )
| ( ( SV1 @ sK2_SY7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(23,plain,
! [SV1: ( $i > $i ) > $o] :
( ( ( SV1
@ ^ [SX2: $i] : sK1_Xz )
= $false )
| ( ( SV1
@ ^ [SX1: $i] : sK1_Xz )
= $false )
| ( ( SV1 @ sK2_SY7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(24,plain,
! [SV1: ( $i > $i ) > $o] :
( ( ( SV1 @ ( sK4_SY19 @ SV1 ) )
= $true )
| ( ( SV1
@ ^ [SX1: $i] : sK1_Xz )
= $false )
| ( ( SV1 @ sK2_SY7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(25,plain,
( ( ( ( ^ [SX0: $i] : sK1_Xz )
= ( ^ [SX0: $i] : sK1_Xz ) )
= $false )
| ( ( ( ^ [SX0: $i] : sK1_Xz )
= ( ^ [SX0: $i] : sK1_Xz ) )
= $false )
| ( ( sK2_SY7
= ( ^ [SX0: $i] : sK1_Xz ) )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[23:[bind(SV1,$thf( ^ [SV2: $i > $i] : ( SV2 = ( ^ [SX2: $i] : sK1_Xz ) ) ))]]) ).
thf(26,plain,
( ( sK2_SY7
= ( ^ [SX0: $i] : sK1_Xz ) )
= $true ),
inference(sim,[status(thm)],[25]) ).
thf(27,plain,
( ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) ) )
= ( ^ [SX0: $i] : sK1_Xz ) )
= $true )
| ( ( ( ^ [SX0: $i] : sK1_Xz )
= ( ^ [SX0: $i] : sK1_Xz ) )
= $false )
| ( ( sK2_SY7
= ( ^ [SX0: $i] : sK1_Xz ) )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[24:[bind(SV1,$thf( ^ [SV3: $i > $i] : ( SV3 = ( ^ [SX1: $i] : sK1_Xz ) ) ))]]) ).
thf(28,plain,
( ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) ) )
= ( ^ [SX0: $i] : sK1_Xz ) )
= $true )
| ( ( sK2_SY7
= ( ^ [SX0: $i] : sK1_Xz ) )
= $true ) ),
inference(sim,[status(thm)],[27]) ).
thf(29,plain,
( ( ( sK2_SY7
= ( ^ [SX0: $i] : sK1_Xz ) )
= $true )
| ( ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) ) )
= ( ^ [SX0: $i] : sK1_Xz ) )
= ( sK2_SY7
= ( ^ [SX0: $i] : sK1_Xz ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[28]) ).
thf(30,plain,
! [SV4: $i] :
( ( ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) ) )
= ( ^ [SX0: $i] : sK1_Xz ) )
= ( sK2_SY7
= ( ^ [SX0: $i] : sK1_Xz ) ) )
= $false )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[29]) ).
thf(31,plain,
! [SV5: $i] :
( ( ( sK2_SY7 @ SV5 )
= sK1_Xz )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV6: $i,SV7: $i] :
( ( ( ( sK2_SY7 @ SV6 )
= sK1_Xz )
= $true )
| ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) )
@ SV7 )
= sK1_Xz )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV4: $i] :
( ( ( ~ ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) ) )
= ( ^ [SX0: $i] : sK1_Xz ) )
| ( sK2_SY7
= ( ^ [SX0: $i] : sK1_Xz ) ) )
| ~ ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) ) )
!= ( ^ [SX0: $i] : sK1_Xz ) )
| ( sK2_SY7
!= ( ^ [SX0: $i] : sK1_Xz ) ) ) )
= $false )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[30]) ).
thf(34,plain,
! [SV4: $i] :
( ( ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) ) )
= ( ^ [SX0: $i] : sK1_Xz ) )
= ( sK2_SY7
= ( ^ [SX0: $i] : sK1_Xz ) ) )
= $false )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[30]) ).
thf(35,plain,
! [SV4: $i] :
( ( ( ~ ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) ) )
= ( ^ [SX0: $i] : sK1_Xz ) )
| ( sK2_SY7
= ( ^ [SX0: $i] : sK1_Xz ) ) ) )
= $false )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(36,plain,
! [SV4: $i] :
( ( ( ~ ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) ) )
!= ( ^ [SX0: $i] : sK1_Xz ) )
| ( sK2_SY7
!= ( ^ [SX0: $i] : sK1_Xz ) ) ) )
= $false )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV4: $i] :
( ( ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) ) )
= ( ^ [SX0: $i] : sK1_Xz ) )
| ( sK2_SY7
= ( ^ [SX0: $i] : sK1_Xz ) ) )
= $true )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(38,plain,
! [SV4: $i] :
( ( ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) ) )
!= ( ^ [SX0: $i] : sK1_Xz ) )
| ( sK2_SY7
!= ( ^ [SX0: $i] : sK1_Xz ) ) )
= $true )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(39,plain,
! [SV4: $i] :
( ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) ) )
= ( ^ [SX0: $i] : sK1_Xz ) )
= $true )
| ( ( sK2_SY7
= ( ^ [SX0: $i] : sK1_Xz ) )
= $true )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV4: $i] :
( ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) ) )
!= ( ^ [SX0: $i] : sK1_Xz ) )
= $true )
| ( ( sK2_SY7
!= ( ^ [SX0: $i] : sK1_Xz ) )
= $true )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV4: $i] :
( ( ( ! [SV8: $i] :
( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) )
@ SV8 )
= sK1_Xz ) )
= $true )
| ( ( sK2_SY7
= ( ^ [SX0: $i] : sK1_Xz ) )
= $true )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV4: $i] :
( ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) ) )
= ( ^ [SX0: $i] : sK1_Xz ) )
= $true )
| ( ( sK2_SY7
= ( ^ [SX0: $i] : sK1_Xz ) )
= $true )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV4: $i] :
( ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) ) )
= ( ^ [SX0: $i] : sK1_Xz ) )
= $false )
| ( ( sK2_SY7
!= ( ^ [SX0: $i] : sK1_Xz ) )
= $true )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV4: $i,SV9: $i] :
( ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) )
@ SV9 )
= sK1_Xz )
= $true )
| ( ( sK2_SY7
= ( ^ [SX0: $i] : sK1_Xz ) )
= $true )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV4: $i] :
( ( ( ! [SV10: $i] :
( ( sK2_SY7 @ SV10 )
= sK1_Xz ) )
= $true )
| ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) ) )
= ( ^ [SX0: $i] : sK1_Xz ) )
= $true )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[42]) ).
thf(46,plain,
! [SV4: $i] :
( ( ( sK2_SY7
= ( ^ [SX0: $i] : sK1_Xz ) )
= $true )
| ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) ) )
= ( ^ [SX0: $i] : sK1_Xz ) )
= $true )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV4: $i] :
( ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) ) )
= ( ^ [SX0: $i] : sK1_Xz ) )
= $false )
| ( ( sK2_SY7
!= ( ^ [SX0: $i] : sK1_Xz ) )
= $true )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[43]) ).
thf(49,plain,
! [SV4: $i,SV9: $i] :
( ( ( ! [SV12: $i] :
( ( sK2_SY7 @ SV12 )
= sK1_Xz ) )
= $true )
| ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) )
@ SV9 )
= sK1_Xz )
= $true )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[44]) ).
thf(50,plain,
! [SV4: $i,SV9: $i] :
( ( ( sK2_SY7
= ( ^ [SX0: $i] : sK1_Xz ) )
= $true )
| ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) )
@ SV9 )
= sK1_Xz )
= $true )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[44]) ).
thf(51,plain,
! [SV4: $i,SV13: $i] :
( ( ( ( sK2_SY7 @ SV13 )
= sK1_Xz )
= $true )
| ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) ) )
= ( ^ [SX0: $i] : sK1_Xz ) )
= $true )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(53,plain,
! [SV4: $i] :
( ( ( sK2_SY7
= ( ^ [SX0: $i] : sK1_Xz ) )
= $false )
| ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) ) )
= ( ^ [SX0: $i] : sK1_Xz ) )
= $false )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV4: $i,SV9: $i,SV14: $i] :
( ( ( ( sK2_SY7 @ SV14 )
= sK1_Xz )
= $true )
| ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) )
@ SV9 )
= sK1_Xz )
= $true )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(57,plain,
! [SV4: $i] :
( ( ( sK2_SY7
= ( ^ [SX0: $i] : sK1_Xz ) )
= $false )
| ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) ) )
= ( ^ [SX0: $i] : sK1_Xz ) )
= $false )
| ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[53]) ).
thf(62,plain,
! [SV4: $i,SV9: $i,SV17: $i] :
( ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true )
| ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) )
@ SV9 )
= sK1_Xz )
= $true )
| ( ( ( sK2_SY7 @ SV17 )
= sK1_Xz )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[50]) ).
thf(63,plain,
! [SV4: $i,SV13: $i,SV18: $i] :
( ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true )
| ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) )
@ SV18 )
= sK1_Xz )
= $true )
| ( ( ( sK2_SY7 @ SV13 )
= sK1_Xz )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[51]) ).
thf(64,plain,
! [SV4: $i,SV19: $i,SV20: $i] :
( ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true )
| ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) )
@ SV19 )
= sK1_Xz )
= $true )
| ( ( ( sK2_SY7 @ SV20 )
= sK1_Xz )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[46]) ).
thf(65,plain,
! [SV4: $i] :
( ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true )
| ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) )
@ ( sK10_E @ SV4 ) )
= sK1_Xz )
= $false )
| ( ( ( sK2_SY7 @ ( sK9_E @ SV4 ) )
= sK1_Xz )
= $false ) ),
inference(extuni,[status(esa)],[57]) ).
thf(66,plain,
! [SV4: $i] :
( ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true )
| ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) )
@ ( sK12_E @ SV4 ) )
= sK1_Xz )
= $false )
| ( ( sK1_Xz
= ( sK2_SY7 @ ( sK11_E @ SV4 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[34]) ).
thf(67,plain,
! [SV4: $i] :
( ( ( ( sK2_SY7 @ SV4 )
= sK1_Xz )
= $true )
| ( ( ( sK4_SY19
@ ^ [SX0: $i > $i] :
( SX0
= ( ^ [SX1: $i] : sK1_Xz ) )
@ ( sK13_E @ SV4 ) )
= ( sK2_SY7 @ ( sK13_E @ SV4 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[34]) ).
thf(68,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,67,66,65,64,63,62,54,32,31,28,26,24,23]) ).
thf(69,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU924^5 : TPTP v9.3.1. Released v4.0.0.
% 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 15:33:45 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
% 0.08/0.23
% 0.08/0.23 No.of.Axioms: 0
% 0.08/0.23
% 0.08/0.23 Length.of.Defs: 0
% 0.08/0.23
% 0.08/0.23 Contains.Choice.Funs: false
% 0.08/0.23 .
% 0.08/0.23
% 0.08/0.23 ********************************
% 0.08/0.23 * All subproblems solved! *
% 0.08/0.23 ********************************
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:68,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.08/0.23
% 0.08/0.23 %**** Beginning of derivation protocol ****
% 0.08/0.23 % SZS output start CNFRefutation
% See solution above
% 0.08/0.23
% 0.08/0.23 %**** End of derivation protocol ****
% 0.08/0.23 %**** no. of clauses in derivation: 61 ****
% 0.08/0.23 %**** clause counter: 68 ****
% 0.08/0.23
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:68,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------