%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU961^5 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 10:49:18 AM UTC 2026
% Result : Theorem 0.08s 0.13s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 1
% Syntax : Number of formulae : 54 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 243 ( 111 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 631 ( 129 ~; 81 |; 21 &; 368 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 115 ( 115 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 169 ( 61 ^; 108 !; 0 ?; 169 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_Xj,type,
sK1_Xj: $i > $i ).
thf(tp_sK2_SY14,type,
sK2_SY14: $i > $i ).
thf(tp_sK3_SY26,type,
sK3_SY26: ( $i > $i ) > $o ).
thf(tp_sK4_SY16,type,
sK4_SY16: ( ( $i > $i ) > $o ) > $i > $i ).
thf(tp_sK5_Xx,type,
sK5_Xx: ( $i > $i ) > ( $i > $i ) > $i ).
thf(1,conjecture,
( ( ! [Xa: $i,Xb: $i] : ( Xa = Xb )
& ! [Xf: $i > $i,Xg: $i > $i] :
( ! [Xx: $i] :
( ( Xf @ Xx )
= ( Xg @ Xx ) )
=> ( Xf = Xg ) ) )
=> ! [Xj: $i > $i,Xk: $i > $i] :
( ! [Xp: ( $i > $i ) > $o] :
( ( ( Xp @ Xj )
& ! [Xj_0: $i > $i] :
( ( Xp @ Xj_0 )
=> ( Xp
@ ^ [Xx: $i] : ( Xj @ ( Xj_0 @ Xx ) ) ) ) )
=> ( Xp
@ ^ [Xx: $i] : ( Xk @ ( Xj @ Xx ) ) ) )
=> ! [Xp: ( $i > $i ) > $o] :
( ( ( Xp @ Xj )
& ! [Xj_1: $i > $i] :
( ( Xp @ Xj_1 )
=> ( Xp
@ ^ [Xx: $i] : ( Xj @ ( Xj_1 @ Xx ) ) ) ) )
=> ( Xp @ Xk ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM196C_pme) ).
thf(2,negated_conjecture,
( ( ( ! [Xa: $i,Xb: $i] : ( Xa = Xb )
& ! [Xf: $i > $i,Xg: $i > $i] :
( ! [Xx: $i] :
( ( Xf @ Xx )
= ( Xg @ Xx ) )
=> ( Xf = Xg ) ) )
=> ! [Xj: $i > $i,Xk: $i > $i] :
( ! [Xp: ( $i > $i ) > $o] :
( ( ( Xp @ Xj )
& ! [Xj_0: $i > $i] :
( ( Xp @ Xj_0 )
=> ( Xp
@ ^ [Xx: $i] : ( Xj @ ( Xj_0 @ Xx ) ) ) ) )
=> ( Xp
@ ^ [Xx: $i] : ( Xk @ ( Xj @ Xx ) ) ) )
=> ! [Xp: ( $i > $i ) > $o] :
( ( ( Xp @ Xj )
& ! [Xj_1: $i > $i] :
( ( Xp @ Xj_1 )
=> ( Xp
@ ^ [Xx: $i] : ( Xj @ ( Xj_1 @ Xx ) ) ) ) )
=> ( Xp @ Xk ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [Xa: $i,Xb: $i] : ( Xa = Xb )
& ! [Xf: $i > $i,Xg: $i > $i] :
( ! [Xx: $i] :
( ( Xf @ Xx )
= ( Xg @ Xx ) )
=> ( Xf = Xg ) ) )
=> ! [Xj: $i > $i,Xk: $i > $i] :
( ! [Xp: ( $i > $i ) > $o] :
( ( ( Xp @ Xj )
& ! [Xj_0: $i > $i] :
( ( Xp @ Xj_0 )
=> ( Xp
@ ^ [Xx: $i] : ( Xj @ ( Xj_0 @ Xx ) ) ) ) )
=> ( Xp
@ ^ [Xx: $i] : ( Xk @ ( Xj @ Xx ) ) ) )
=> ! [Xp: ( $i > $i ) > $o] :
( ( ( Xp @ Xj )
& ! [Xj_1: $i > $i] :
( ( Xp @ Xj_1 )
=> ( Xp
@ ^ [Xx: $i] : ( Xj @ ( Xj_1 @ Xx ) ) ) ) )
=> ( Xp @ Xk ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xa: $i,Xb: $i] : ( Xa = Xb ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xf: $i > $i,Xg: $i > $i] :
( ! [Xx: $i] :
( ( Xf @ Xx )
= ( Xg @ Xx ) )
=> ( Xf = Xg ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xj: $i > $i,Xk: $i > $i] :
( ! [Xp: ( $i > $i ) > $o] :
( ( ( Xp @ Xj )
& ! [Xj_0: $i > $i] :
( ( Xp @ Xj_0 )
=> ( Xp
@ ^ [Xx: $i] : ( Xj @ ( Xj_0 @ Xx ) ) ) ) )
=> ( Xp
@ ^ [Xx: $i] : ( Xk @ ( Xj @ Xx ) ) ) )
=> ! [Xp: ( $i > $i ) > $o] :
( ( ( Xp @ Xj )
& ! [Xj_1: $i > $i] :
( ( Xp @ Xj_1 )
=> ( Xp
@ ^ [Xx: $i] : ( Xj @ ( Xj_1 @ Xx ) ) ) ) )
=> ( Xp @ Xk ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [Xj: $i > $i,Xk: $i > $i] :
( ! [Xp: ( $i > $i ) > $o] :
( ( ( Xp @ Xj )
& ! [Xj_0: $i > $i] :
( ( Xp @ Xj_0 )
=> ( Xp
@ ^ [Xx: $i] : ( Xj @ ( Xj_0 @ Xx ) ) ) ) )
=> ( Xp
@ ^ [Xx: $i] : ( Xk @ ( Xj @ Xx ) ) ) )
=> ! [Xp: ( $i > $i ) > $o] :
( ( ( Xp @ Xj )
& ! [Xj_1: $i > $i] :
( ( Xp @ Xj_1 )
=> ( Xp
@ ^ [Xx: $i] : ( Xj @ ( Xj_1 @ Xx ) ) ) ) )
=> ( Xp @ Xk ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SY22: ( $i > $i ) > $o] :
( ( ( SY22 @ ( sK4_SY16 @ SY22 ) )
& ~ ( SY22
@ ^ [SY31: $i] : ( sK1_Xj @ ( sK4_SY16 @ SY22 @ SY31 ) ) ) )
| ~ ( SY22 @ sK1_Xj )
| ( SY22
@ ^ [SY25: $i] : ( sK2_SY14 @ ( sK1_Xj @ SY25 ) ) ) )
& ! [SY29: $i > $i] :
( ~ ( sK3_SY26 @ SY29 )
| ( sK3_SY26
@ ^ [SY21: $i] : ( sK1_Xj @ ( SY29 @ SY21 ) ) ) )
& ( sK3_SY26 @ sK1_Xj )
& ~ ( sK3_SY26 @ sK2_SY14 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [Xf: $i > $i,Xg: $i > $i] :
( ( ( Xf @ ( sK5_Xx @ Xg @ Xf ) )
!= ( Xg @ ( sK5_Xx @ Xg @ Xf ) ) )
| ( Xf = Xg ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(10,plain,
( ( ! [Xf: $i > $i,Xg: $i > $i] :
( ( ( Xf @ ( sK5_Xx @ Xg @ Xf ) )
!= ( Xg @ ( sK5_Xx @ Xg @ Xf ) ) )
| ( Xf = Xg ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [Xa: $i,Xb: $i] : ( Xa = Xb ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(12,plain,
( ( ! [SY22: ( $i > $i ) > $o] :
( ( ( SY22 @ ( sK4_SY16 @ SY22 ) )
& ~ ( SY22
@ ^ [SY31: $i] : ( sK1_Xj @ ( sK4_SY16 @ SY22 @ SY31 ) ) ) )
| ~ ( SY22 @ sK1_Xj )
| ( SY22
@ ^ [SY25: $i] : ( sK2_SY14 @ ( sK1_Xj @ SY25 ) ) ) )
& ! [SY29: $i > $i] :
( ~ ( sK3_SY26 @ SY29 )
| ( sK3_SY26
@ ^ [SY21: $i] : ( sK1_Xj @ ( SY29 @ SY21 ) ) ) )
& ( sK3_SY26 @ sK1_Xj )
& ~ ( sK3_SY26 @ sK2_SY14 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ~ ( ~ ! [SX0: ( $i > $i ) > $o] :
( ~ ( ~ ( SX0 @ ( sK4_SY16 @ SX0 ) )
| ~ ~ ( SX0
@ ^ [SX1: $i] : ( sK1_Xj @ ( sK4_SY16 @ SX0 @ SX1 ) ) ) )
| ~ ( SX0 @ sK1_Xj )
| ( SX0
@ ^ [SX1: $i] : ( sK2_SY14 @ ( sK1_Xj @ SX1 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i > $i] :
( ~ ( sK3_SY26 @ SX0 )
| ( sK3_SY26
@ ^ [SX1: $i] : ( sK1_Xj @ ( SX0 @ SX1 ) ) ) )
| ~ ( sK3_SY26 @ sK1_Xj ) )
| ~ ~ ( sK3_SY26 @ sK2_SY14 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(14,plain,
! [SV1: $i > $i] :
( ( ! [SY32: $i > $i] :
( ( ( SV1 @ ( sK5_Xx @ SY32 @ SV1 ) )
!= ( SY32 @ ( sK5_Xx @ SY32 @ SV1 ) ) )
| ( SV1 = SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(15,plain,
! [SV2: $i] :
( ( ! [SY33: $i] : ( SV2 = SY33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(16,plain,
( ( ~ ! [SX0: ( $i > $i ) > $o] :
( ~ ( ~ ( SX0 @ ( sK4_SY16 @ SX0 ) )
| ~ ~ ( SX0
@ ^ [SX1: $i] : ( sK1_Xj @ ( sK4_SY16 @ SX0 @ SX1 ) ) ) )
| ~ ( SX0 @ sK1_Xj )
| ( SX0
@ ^ [SX1: $i] : ( sK2_SY14 @ ( sK1_Xj @ SX1 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i > $i] :
( ~ ( sK3_SY26 @ SX0 )
| ( sK3_SY26
@ ^ [SX1: $i] : ( sK1_Xj @ ( SX0 @ SX1 ) ) ) )
| ~ ( sK3_SY26 @ sK1_Xj ) )
| ~ ~ ( sK3_SY26 @ sK2_SY14 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV3: $i > $i,SV1: $i > $i] :
( ( ( ( SV1 @ ( sK5_Xx @ SV3 @ SV1 ) )
!= ( SV3 @ ( sK5_Xx @ SV3 @ SV1 ) ) )
| ( SV1 = SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV4: $i,SV2: $i] :
( ( SV2 = SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ ! [SX0: ( $i > $i ) > $o] :
( ~ ( ~ ( SX0 @ ( sK4_SY16 @ SX0 ) )
| ~ ~ ( SX0
@ ^ [SX1: $i] : ( sK1_Xj @ ( sK4_SY16 @ SX0 @ SX1 ) ) ) )
| ~ ( SX0 @ sK1_Xj )
| ( SX0
@ ^ [SX1: $i] : ( sK2_SY14 @ ( sK1_Xj @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i > $i] :
( ~ ( sK3_SY26 @ SX0 )
| ( sK3_SY26
@ ^ [SX1: $i] : ( sK1_Xj @ ( SX0 @ SX1 ) ) ) )
| ~ ( sK3_SY26 @ sK1_Xj ) )
| ~ ~ ( sK3_SY26 @ sK2_SY14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(21,plain,
! [SV3: $i > $i,SV1: $i > $i] :
( ( ( ( SV1 @ ( sK5_Xx @ SV3 @ SV1 ) )
!= ( SV3 @ ( sK5_Xx @ SV3 @ SV1 ) ) )
= $true )
| ( ( SV1 = SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(22,plain,
( ( ! [SX0: ( $i > $i ) > $o] :
( ~ ( ~ ( SX0 @ ( sK4_SY16 @ SX0 ) )
| ~ ~ ( SX0
@ ^ [SX1: $i] : ( sK1_Xj @ ( sK4_SY16 @ SX0 @ SX1 ) ) ) )
| ~ ( SX0 @ sK1_Xj )
| ( SX0
@ ^ [SX1: $i] : ( sK2_SY14 @ ( sK1_Xj @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i > $i] :
( ~ ( sK3_SY26 @ SX0 )
| ( sK3_SY26
@ ^ [SX1: $i] : ( sK1_Xj @ ( SX0 @ SX1 ) ) ) )
| ~ ( sK3_SY26 @ sK1_Xj ) )
| ~ ~ ( sK3_SY26 @ sK2_SY14 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV3: $i > $i,SV1: $i > $i] :
( ( ( ( SV1 @ ( sK5_Xx @ SV3 @ SV1 ) )
= ( SV3 @ ( sK5_Xx @ SV3 @ SV1 ) ) )
= $false )
| ( ( SV1 = SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV5: ( $i > $i ) > $o] :
( ( ~ ( ~ ( SV5 @ ( sK4_SY16 @ SV5 ) )
| ~ ~ ( SV5
@ ^ [SY34: $i] : ( sK1_Xj @ ( sK4_SY16 @ SV5 @ SY34 ) ) ) )
| ~ ( SV5 @ sK1_Xj )
| ( SV5
@ ^ [SX1: $i] : ( sK2_SY14 @ ( sK1_Xj @ SX1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( ~ ~ ( ~ ! [SX0: $i > $i] :
( ~ ( sK3_SY26 @ SX0 )
| ( sK3_SY26
@ ^ [SX1: $i] : ( sK1_Xj @ ( SX0 @ SX1 ) ) ) )
| ~ ( sK3_SY26 @ sK1_Xj ) )
| ~ ~ ( sK3_SY26 @ sK2_SY14 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV3: $i > $i,SV1: $i > $i] :
( ( ( ! [SV6: $i] :
( ( SV1 @ SV6 )
= ( SV3 @ SV6 ) ) )
= $true )
| ( ( ( SV1 @ ( sK5_Xx @ SV3 @ SV1 ) )
= ( SV3 @ ( sK5_Xx @ SV3 @ SV1 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV3: $i > $i,SV1: $i > $i] :
( ( ( SV1 = SV3 )
= $true )
| ( ( ( SV1 @ ( sK5_Xx @ SV3 @ SV1 ) )
= ( SV3 @ ( sK5_Xx @ SV3 @ SV1 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV5: ( $i > $i ) > $o] :
( ( ( ~ ( ~ ( SV5 @ ( sK4_SY16 @ SV5 ) )
| ~ ~ ( SV5
@ ^ [SY34: $i] : ( sK1_Xj @ ( sK4_SY16 @ SV5 @ SY34 ) ) ) )
| ~ ( SV5 @ sK1_Xj ) )
= $true )
| ( ( SV5
@ ^ [SX1: $i] : ( sK2_SY14 @ ( sK1_Xj @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(30,plain,
( ( ~ ~ ( ~ ! [SX0: $i > $i] :
( ~ ( sK3_SY26 @ SX0 )
| ( sK3_SY26
@ ^ [SX1: $i] : ( sK1_Xj @ ( SX0 @ SX1 ) ) ) )
| ~ ( sK3_SY26 @ sK1_Xj ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(31,plain,
( ( ~ ~ ( sK3_SY26 @ sK2_SY14 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(32,plain,
! [SV3: $i > $i,SV7: $i,SV1: $i > $i] :
( ( ( ( SV1 @ SV7 )
= ( SV3 @ SV7 ) )
= $true )
| ( ( ( SV1 @ ( sK5_Xx @ SV3 @ SV1 ) )
= ( SV3 @ ( sK5_Xx @ SV3 @ SV1 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV5: ( $i > $i ) > $o] :
( ( ( ~ ( ~ ( SV5 @ ( sK4_SY16 @ SV5 ) )
| ~ ~ ( SV5
@ ^ [SY34: $i] : ( sK1_Xj @ ( sK4_SY16 @ SV5 @ SY34 ) ) ) ) )
= $true )
| ( ( ~ ( SV5 @ sK1_Xj ) )
= $true )
| ( ( SV5
@ ^ [SX1: $i] : ( sK2_SY14 @ ( sK1_Xj @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(34,plain,
( ( ~ ( ~ ! [SX0: $i > $i] :
( ~ ( sK3_SY26 @ SX0 )
| ( sK3_SY26
@ ^ [SX1: $i] : ( sK1_Xj @ ( SX0 @ SX1 ) ) ) )
| ~ ( sK3_SY26 @ sK1_Xj ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(35,plain,
( ( ~ ( sK3_SY26 @ sK2_SY14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(36,plain,
! [SV5: ( $i > $i ) > $o] :
( ( ( ~ ( SV5 @ ( sK4_SY16 @ SV5 ) )
| ~ ~ ( SV5
@ ^ [SY34: $i] : ( sK1_Xj @ ( sK4_SY16 @ SV5 @ SY34 ) ) ) )
= $false )
| ( ( ~ ( SV5 @ sK1_Xj ) )
= $true )
| ( ( SV5
@ ^ [SX1: $i] : ( sK2_SY14 @ ( sK1_Xj @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(37,plain,
( ( ~ ! [SX0: $i > $i] :
( ~ ( sK3_SY26 @ SX0 )
| ( sK3_SY26
@ ^ [SX1: $i] : ( sK1_Xj @ ( SX0 @ SX1 ) ) ) )
| ~ ( sK3_SY26 @ sK1_Xj ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(38,plain,
( ( sK3_SY26 @ sK2_SY14 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV5: ( $i > $i ) > $o] :
( ( ( ~ ( SV5 @ ( sK4_SY16 @ SV5 ) ) )
= $false )
| ( ( ~ ( SV5 @ sK1_Xj ) )
= $true )
| ( ( SV5
@ ^ [SX1: $i] : ( sK2_SY14 @ ( sK1_Xj @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(40,plain,
! [SV5: ( $i > $i ) > $o] :
( ( ( ~ ~ ( SV5
@ ^ [SY34: $i] : ( sK1_Xj @ ( sK4_SY16 @ SV5 @ SY34 ) ) ) )
= $false )
| ( ( ~ ( SV5 @ sK1_Xj ) )
= $true )
| ( ( SV5
@ ^ [SX1: $i] : ( sK2_SY14 @ ( sK1_Xj @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(41,plain,
( ( ~ ! [SX0: $i > $i] :
( ~ ( sK3_SY26 @ SX0 )
| ( sK3_SY26
@ ^ [SX1: $i] : ( sK1_Xj @ ( SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(42,plain,
( ( ~ ( sK3_SY26 @ sK1_Xj ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(43,plain,
! [SV5: ( $i > $i ) > $o] :
( ( ( SV5 @ ( sK4_SY16 @ SV5 ) )
= $true )
| ( ( ~ ( SV5 @ sK1_Xj ) )
= $true )
| ( ( SV5
@ ^ [SX1: $i] : ( sK2_SY14 @ ( sK1_Xj @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(44,plain,
! [SV5: ( $i > $i ) > $o] :
( ( ( ~ ( SV5
@ ^ [SY34: $i] : ( sK1_Xj @ ( sK4_SY16 @ SV5 @ SY34 ) ) ) )
= $true )
| ( ( ~ ( SV5 @ sK1_Xj ) )
= $true )
| ( ( SV5
@ ^ [SX1: $i] : ( sK2_SY14 @ ( sK1_Xj @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(45,plain,
( ( ! [SX0: $i > $i] :
( ~ ( sK3_SY26 @ SX0 )
| ( sK3_SY26
@ ^ [SX1: $i] : ( sK1_Xj @ ( SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(46,plain,
( ( sK3_SY26 @ sK1_Xj )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(47,plain,
! [SV5: ( $i > $i ) > $o] :
( ( ( SV5 @ sK1_Xj )
= $false )
| ( ( SV5 @ ( sK4_SY16 @ SV5 ) )
= $true )
| ( ( SV5
@ ^ [SX1: $i] : ( sK2_SY14 @ ( sK1_Xj @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV5: ( $i > $i ) > $o] :
( ( ( SV5
@ ^ [SY34: $i] : ( sK1_Xj @ ( sK4_SY16 @ SV5 @ SY34 ) ) )
= $false )
| ( ( ~ ( SV5 @ sK1_Xj ) )
= $true )
| ( ( SV5
@ ^ [SX1: $i] : ( sK2_SY14 @ ( sK1_Xj @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV8: $i > $i] :
( ( ~ ( sK3_SY26 @ SV8 )
| ( sK3_SY26
@ ^ [SY36: $i] : ( sK1_Xj @ ( SV8 @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV5: ( $i > $i ) > $o] :
( ( ( SV5 @ sK1_Xj )
= $false )
| ( ( SV5
@ ^ [SY34: $i] : ( sK1_Xj @ ( sK4_SY16 @ SV5 @ SY34 ) ) )
= $false )
| ( ( SV5
@ ^ [SX1: $i] : ( sK2_SY14 @ ( sK1_Xj @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(51,plain,
! [SV8: $i > $i] :
( ( ( ~ ( sK3_SY26 @ SV8 ) )
= $true )
| ( ( sK3_SY26
@ ^ [SY36: $i] : ( sK1_Xj @ ( SV8 @ SY36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV8: $i > $i] :
( ( ( sK3_SY26 @ SV8 )
= $false )
| ( ( sK3_SY26
@ ^ [SY36: $i] : ( sK1_Xj @ ( SV8 @ SY36 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(53,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,52,50,47,46,38,32,28]) ).
thf(54,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU961^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Oct 6 15:38:16 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.13
% 0.08/0.13 No.of.Axioms: 0
% 0.08/0.13
% 0.08/0.13 Length.of.Defs: 0
% 0.08/0.13
% 0.08/0.13 Contains.Choice.Funs: false
% 0.08/0.13 .
% 0.08/0.13
% 0.08/0.13 ********************************
% 0.08/0.13 * All subproblems solved! *
% 0.08/0.13 ********************************
% 0.08/0.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:53,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.13
% 0.08/0.13 %**** Beginning of derivation protocol ****
% 0.08/0.13 % SZS output start CNFRefutation
% See solution above
% 0.08/0.13
% 0.08/0.13 %**** End of derivation protocol ****
% 0.08/0.13 %**** no. of clauses in derivation: 54 ****
% 0.08/0.13 %**** clause counter: 53 ****
% 0.08/0.13
% 0.08/0.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:53,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------