%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : PUZ113^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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 : n005.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 10:36:57 AM UTC 2026
% Result : Theorem 0.09s 0.22s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 2
% Syntax : Number of formulae : 50 ( 27 unt; 0 typ; 1 def)
% Number of atoms : 225 ( 85 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 944 ( 146 ~; 98 |; 24 &; 647 @)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 115 ( 2 ^; 113 !; 0 ?; 115 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c1,type,
c1: $i ).
thf(tp_cCKB6_BLACK,type,
cCKB6_BLACK: $i > $i > $o ).
thf(tp_s,type,
s: $i > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY24,type,
sK2_SY24: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i > $i > $o ).
thf(tp_sK4_SY37,type,
sK4_SY37: ( $i > $i > $o ) > $i ).
thf(tp_sK5_SY41,type,
sK5_SY41: ( $i > $i > $o ) > $i ).
thf(cCKB6_BLACK,definition,
( cCKB6_BLACK
= ( ^ [Xu: $i,Xv: $i] :
! [Xw: $i > $i > $o] :
( ( ( Xw @ c1 @ c1 )
& ! [Xj: $i,Xk: $i] :
( ( Xw @ Xj @ Xk )
=> ( ( Xw @ ( s @ ( s @ Xj ) ) @ Xk )
& ( Xw @ ( s @ Xj ) @ ( s @ Xk ) ) ) ) )
=> ( Xw @ Xu @ Xv ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCKB6_BLACK_def) ).
thf(1,conjecture,
! [Xj: $i,Xk: $i] :
( ( cCKB6_BLACK @ Xj @ Xk )
=> ( cCKB6_BLACK @ ( s @ ( s @ Xj ) ) @ ( s @ ( s @ Xk ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCKB6_L11000) ).
thf(2,negated_conjecture,
( ( ! [Xj: $i,Xk: $i] :
( ( cCKB6_BLACK @ Xj @ Xk )
=> ( cCKB6_BLACK @ ( s @ ( s @ Xj ) ) @ ( s @ ( s @ Xk ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i,SY1: $i] :
( ! [SY6: $i > $i > $o] :
( ( ( SY6 @ c1 @ c1 )
& ! [Xj: $i,Xk: $i] :
( ( SY6 @ Xj @ Xk )
=> ( ( SY6 @ ( s @ ( s @ Xj ) ) @ Xk )
& ( SY6 @ ( s @ Xj ) @ ( s @ Xk ) ) ) ) )
=> ( SY6 @ SY0 @ SY1 ) )
=> ! [SY13: $i > $i > $o] :
( ( ( SY13 @ c1 @ c1 )
& ! [Xj: $i,Xk: $i] :
( ( SY13 @ Xj @ Xk )
=> ( ( SY13 @ ( s @ ( s @ Xj ) ) @ Xk )
& ( SY13 @ ( s @ Xj ) @ ( s @ Xk ) ) ) ) )
=> ( SY13 @ ( s @ ( s @ SY0 ) ) @ ( s @ ( s @ SY1 ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,cCKB6_BLACK]) ).
thf(4,plain,
( ( ! [SY24: $i] :
( ! [SY25: $i > $i > $o] :
( ( ( SY25 @ c1 @ c1 )
& ! [Xj: $i,Xk: $i] :
( ( SY25 @ Xj @ Xk )
=> ( ( SY25 @ ( s @ ( s @ Xj ) ) @ Xk )
& ( SY25 @ ( s @ Xj ) @ ( s @ Xk ) ) ) ) )
=> ( SY25 @ sK1_SY0 @ SY24 ) )
=> ! [SY28: $i > $i > $o] :
( ( ( SY28 @ c1 @ c1 )
& ! [Xj: $i,Xk: $i] :
( ( SY28 @ Xj @ Xk )
=> ( ( SY28 @ ( s @ ( s @ Xj ) ) @ Xk )
& ( SY28 @ ( s @ Xj ) @ ( s @ Xk ) ) ) ) )
=> ( SY28 @ ( s @ ( s @ sK1_SY0 ) ) @ ( s @ ( s @ SY24 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY31: $i > $i > $o] :
( ( ( SY31 @ c1 @ c1 )
& ! [Xj: $i,Xk: $i] :
( ( SY31 @ Xj @ Xk )
=> ( ( SY31 @ ( s @ ( s @ Xj ) ) @ Xk )
& ( SY31 @ ( s @ Xj ) @ ( s @ Xk ) ) ) ) )
=> ( SY31 @ sK1_SY0 @ sK2_SY24 ) )
=> ! [SY34: $i > $i > $o] :
( ( ( SY34 @ c1 @ c1 )
& ! [Xj: $i,Xk: $i] :
( ( SY34 @ Xj @ Xk )
=> ( ( SY34 @ ( s @ ( s @ Xj ) ) @ Xk )
& ( SY34 @ ( s @ Xj ) @ ( s @ Xk ) ) ) ) )
=> ( SY34 @ ( s @ ( s @ sK1_SY0 ) ) @ ( s @ ( s @ sK2_SY24 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY31: $i > $i > $o] :
( ( ( SY31 @ c1 @ c1 )
& ! [Xj: $i,Xk: $i] :
( ( SY31 @ Xj @ Xk )
=> ( ( SY31 @ ( s @ ( s @ Xj ) ) @ Xk )
& ( SY31 @ ( s @ Xj ) @ ( s @ Xk ) ) ) ) )
=> ( SY31 @ sK1_SY0 @ sK2_SY24 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY34: $i > $i > $o] :
( ( ( SY34 @ c1 @ c1 )
& ! [Xj: $i,Xk: $i] :
( ( SY34 @ Xj @ Xk )
=> ( ( SY34 @ ( s @ ( s @ Xj ) ) @ Xk )
& ( SY34 @ ( s @ Xj ) @ ( s @ Xk ) ) ) ) )
=> ( SY34 @ ( s @ ( s @ sK1_SY0 ) ) @ ( s @ ( s @ sK2_SY24 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ! [SY34: $i > $i > $o] :
( ( ( SY34 @ c1 @ c1 )
& ! [Xj: $i,Xk: $i] :
( ( SY34 @ Xj @ Xk )
=> ( ( SY34 @ ( s @ ( s @ Xj ) ) @ Xk )
& ( SY34 @ ( s @ Xj ) @ ( s @ Xk ) ) ) ) )
=> ( SY34 @ ( s @ ( s @ sK1_SY0 ) ) @ ( s @ ( s @ sK2_SY24 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [SY31: $i > $i > $o] :
( ( ( SY31 @ c1 @ c1 )
& ! [Xj: $i,Xk: $i] :
( ( SY31 @ Xj @ Xk )
=> ( ( SY31 @ ( s @ ( s @ Xj ) ) @ Xk )
& ( SY31 @ ( s @ Xj ) @ ( s @ Xk ) ) ) ) )
=> ( SY31 @ sK1_SY0 @ sK2_SY24 ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( ~ ! [SY34: $i > $i > $o] :
( ( ( SY34 @ c1 @ c1 )
& ! [Xj: $i,Xk: $i] :
( ( SY34 @ Xj @ Xk )
=> ( ( SY34 @ ( s @ ( s @ Xj ) ) @ Xk )
& ( SY34 @ ( s @ Xj ) @ ( s @ Xk ) ) ) ) )
=> ( SY34 @ ( s @ ( s @ sK1_SY0 ) ) @ ( s @ ( s @ sK2_SY24 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(11,plain,
( ( ! [SX0: $i > $i > $o] :
( ~ ~ ( ~ ( SX0 @ c1 @ c1 )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( SX0 @ SX1 @ SX2 )
| ~ ( ~ ( SX0 @ ( s @ ( s @ SX1 ) ) @ SX2 )
| ~ ( SX0 @ ( s @ SX1 ) @ ( s @ SX2 ) ) ) ) )
| ( SX0 @ sK1_SY0 @ sK2_SY24 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,cCKB6_BLACK]) ).
thf(12,plain,
( ( ~ ! [SX0: $i > $i > $o] :
( ~ ~ ( ~ ( SX0 @ c1 @ c1 )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( SX0 @ SX1 @ SX2 )
| ~ ( ~ ( SX0 @ ( s @ ( s @ SX1 ) ) @ SX2 )
| ~ ( SX0 @ ( s @ SX1 ) @ ( s @ SX2 ) ) ) ) )
| ( SX0 @ ( s @ ( s @ sK1_SY0 ) ) @ ( s @ ( s @ sK2_SY24 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,cCKB6_BLACK]) ).
thf(13,plain,
! [SV1: $i > $i > $o] :
( ( ~ ~ ( ~ ( SV1 @ c1 @ c1 )
| ~ ! [SY37: $i,SY38: $i] :
( ~ ( SV1 @ SY37 @ SY38 )
| ~ ( ~ ( SV1 @ ( s @ ( s @ SY37 ) ) @ SY38 )
| ~ ( SV1 @ ( s @ SY37 ) @ ( s @ SY38 ) ) ) ) )
| ( SV1 @ sK1_SY0 @ sK2_SY24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [SX0: $i > $i > $o] :
( ~ ~ ( ~ ( SX0 @ c1 @ c1 )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( SX0 @ SX1 @ SX2 )
| ~ ( ~ ( SX0 @ ( s @ ( s @ SX1 ) ) @ SX2 )
| ~ ( SX0 @ ( s @ SX1 ) @ ( s @ SX2 ) ) ) ) )
| ( SX0 @ ( s @ ( s @ sK1_SY0 ) ) @ ( s @ ( s @ sK2_SY24 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV1 @ c1 @ c1 )
| ~ ! [SY37: $i,SY38: $i] :
( ~ ( SV1 @ SY37 @ SY38 )
| ~ ( ~ ( SV1 @ ( s @ ( s @ SY37 ) ) @ SY38 )
| ~ ( SV1 @ ( s @ SY37 ) @ ( s @ SY38 ) ) ) ) ) )
= $true )
| ( ( SV1 @ sK1_SY0 @ sK2_SY24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ~ ( ~ ( sK3_SX0 @ c1 @ c1 )
| ~ ! [SY39: $i,SY40: $i] :
( ~ ( sK3_SX0 @ SY39 @ SY40 )
| ~ ( ~ ( sK3_SX0 @ ( s @ ( s @ SY39 ) ) @ SY40 )
| ~ ( sK3_SX0 @ ( s @ SY39 ) @ ( s @ SY40 ) ) ) ) )
| ( sK3_SX0 @ ( s @ ( s @ sK1_SY0 ) ) @ ( s @ ( s @ sK2_SY24 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(17,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( ~ ( SV1 @ c1 @ c1 )
| ~ ! [SY37: $i,SY38: $i] :
( ~ ( SV1 @ SY37 @ SY38 )
| ~ ( ~ ( SV1 @ ( s @ ( s @ SY37 ) ) @ SY38 )
| ~ ( SV1 @ ( s @ SY37 ) @ ( s @ SY38 ) ) ) ) ) )
= $false )
| ( ( SV1 @ sK1_SY0 @ sK2_SY24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ~ ( ~ ( sK3_SX0 @ c1 @ c1 )
| ~ ! [SY39: $i,SY40: $i] :
( ~ ( sK3_SX0 @ SY39 @ SY40 )
| ~ ( ~ ( sK3_SX0 @ ( s @ ( s @ SY39 ) ) @ SY40 )
| ~ ( sK3_SX0 @ ( s @ SY39 ) @ ( s @ SY40 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( sK3_SX0 @ ( s @ ( s @ sK1_SY0 ) ) @ ( s @ ( s @ sK2_SY24 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ c1 @ c1 )
| ~ ! [SY37: $i,SY38: $i] :
( ~ ( SV1 @ SY37 @ SY38 )
| ~ ( ~ ( SV1 @ ( s @ ( s @ SY37 ) ) @ SY38 )
| ~ ( SV1 @ ( s @ SY37 ) @ ( s @ SY38 ) ) ) ) )
= $true )
| ( ( SV1 @ sK1_SY0 @ sK2_SY24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ( ~ ( sK3_SX0 @ c1 @ c1 )
| ~ ! [SY39: $i,SY40: $i] :
( ~ ( sK3_SX0 @ SY39 @ SY40 )
| ~ ( ~ ( sK3_SX0 @ ( s @ ( s @ SY39 ) ) @ SY40 )
| ~ ( sK3_SX0 @ ( s @ SY39 ) @ ( s @ SY40 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ c1 @ c1 ) )
= $true )
| ( ( ~ ! [SY37: $i,SY38: $i] :
( ~ ( SV1 @ SY37 @ SY38 )
| ~ ( ~ ( SV1 @ ( s @ ( s @ SY37 ) ) @ SY38 )
| ~ ( SV1 @ ( s @ SY37 ) @ ( s @ SY38 ) ) ) ) )
= $true )
| ( ( SV1 @ sK1_SY0 @ sK2_SY24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(23,plain,
( ( ~ ( sK3_SX0 @ c1 @ c1 )
| ~ ! [SY39: $i,SY40: $i] :
( ~ ( sK3_SX0 @ SY39 @ SY40 )
| ~ ( ~ ( sK3_SX0 @ ( s @ ( s @ SY39 ) ) @ SY40 )
| ~ ( sK3_SX0 @ ( s @ SY39 ) @ ( s @ SY40 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(24,plain,
! [SV1: $i > $i > $o] :
( ( ( SV1 @ c1 @ c1 )
= $false )
| ( ( ~ ! [SY37: $i,SY38: $i] :
( ~ ( SV1 @ SY37 @ SY38 )
| ~ ( ~ ( SV1 @ ( s @ ( s @ SY37 ) ) @ SY38 )
| ~ ( SV1 @ ( s @ SY37 ) @ ( s @ SY38 ) ) ) ) )
= $true )
| ( ( SV1 @ sK1_SY0 @ sK2_SY24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(25,plain,
( ( ~ ( sK3_SX0 @ c1 @ c1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(26,plain,
( ( ~ ! [SY39: $i,SY40: $i] :
( ~ ( sK3_SX0 @ SY39 @ SY40 )
| ~ ( ~ ( sK3_SX0 @ ( s @ ( s @ SY39 ) ) @ SY40 )
| ~ ( sK3_SX0 @ ( s @ SY39 ) @ ( s @ SY40 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(27,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY37: $i,SY38: $i] :
( ~ ( SV1 @ SY37 @ SY38 )
| ~ ( ~ ( SV1 @ ( s @ ( s @ SY37 ) ) @ SY38 )
| ~ ( SV1 @ ( s @ SY37 ) @ ( s @ SY38 ) ) ) ) )
= $false )
| ( ( SV1 @ c1 @ c1 )
= $false )
| ( ( SV1 @ sK1_SY0 @ sK2_SY24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(28,plain,
( ( sK3_SX0 @ c1 @ c1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(29,plain,
( ( ! [SY39: $i,SY40: $i] :
( ~ ( sK3_SX0 @ SY39 @ SY40 )
| ~ ( ~ ( sK3_SX0 @ ( s @ ( s @ SY39 ) ) @ SY40 )
| ~ ( sK3_SX0 @ ( s @ SY39 ) @ ( s @ SY40 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(30,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY41: $i] :
( ~ ( SV1 @ ( sK4_SY37 @ SV1 ) @ SY41 )
| ~ ( ~ ( SV1 @ ( s @ ( s @ ( sK4_SY37 @ SV1 ) ) ) @ SY41 )
| ~ ( SV1 @ ( s @ ( sK4_SY37 @ SV1 ) ) @ ( s @ SY41 ) ) ) ) )
= $false )
| ( ( SV1 @ c1 @ c1 )
= $false )
| ( ( SV1 @ sK1_SY0 @ sK2_SY24 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(31,plain,
! [SV2: $i] :
( ( ! [SY42: $i] :
( ~ ( sK3_SX0 @ SV2 @ SY42 )
| ~ ( ~ ( sK3_SX0 @ ( s @ ( s @ SV2 ) ) @ SY42 )
| ~ ( sK3_SX0 @ ( s @ SV2 ) @ ( s @ SY42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( sK4_SY37 @ SV1 ) @ ( sK5_SY41 @ SV1 ) )
| ~ ( ~ ( SV1 @ ( s @ ( s @ ( sK4_SY37 @ SV1 ) ) ) @ ( sK5_SY41 @ SV1 ) )
| ~ ( SV1 @ ( s @ ( sK4_SY37 @ SV1 ) ) @ ( s @ ( sK5_SY41 @ SV1 ) ) ) ) )
= $false )
| ( ( SV1 @ c1 @ c1 )
= $false )
| ( ( SV1 @ sK1_SY0 @ sK2_SY24 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(33,plain,
! [SV3: $i,SV2: $i] :
( ( ~ ( sK3_SX0 @ SV2 @ SV3 )
| ~ ( ~ ( sK3_SX0 @ ( s @ ( s @ SV2 ) ) @ SV3 )
| ~ ( sK3_SX0 @ ( s @ SV2 ) @ ( s @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( sK4_SY37 @ SV1 ) @ ( sK5_SY41 @ SV1 ) ) )
= $false )
| ( ( SV1 @ c1 @ c1 )
= $false )
| ( ( SV1 @ sK1_SY0 @ sK2_SY24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(35,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( ~ ( SV1 @ ( s @ ( s @ ( sK4_SY37 @ SV1 ) ) ) @ ( sK5_SY41 @ SV1 ) )
| ~ ( SV1 @ ( s @ ( sK4_SY37 @ SV1 ) ) @ ( s @ ( sK5_SY41 @ SV1 ) ) ) ) )
= $false )
| ( ( SV1 @ c1 @ c1 )
= $false )
| ( ( SV1 @ sK1_SY0 @ sK2_SY24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(36,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ( sK3_SX0 @ SV2 @ SV3 ) )
= $true )
| ( ( ~ ( ~ ( sK3_SX0 @ ( s @ ( s @ SV2 ) ) @ SV3 )
| ~ ( sK3_SX0 @ ( s @ SV2 ) @ ( s @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK4_SY37 @ SV1 ) @ ( sK5_SY41 @ SV1 ) )
= $true )
| ( ( SV1 @ c1 @ c1 )
= $false )
| ( ( SV1 @ sK1_SY0 @ sK2_SY24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(38,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( s @ ( s @ ( sK4_SY37 @ SV1 ) ) ) @ ( sK5_SY41 @ SV1 ) )
| ~ ( SV1 @ ( s @ ( sK4_SY37 @ SV1 ) ) @ ( s @ ( sK5_SY41 @ SV1 ) ) ) )
= $true )
| ( ( SV1 @ c1 @ c1 )
= $false )
| ( ( SV1 @ sK1_SY0 @ sK2_SY24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(39,plain,
! [SV3: $i,SV2: $i] :
( ( ( sK3_SX0 @ SV2 @ SV3 )
= $false )
| ( ( ~ ( ~ ( sK3_SX0 @ ( s @ ( s @ SV2 ) ) @ SV3 )
| ~ ( sK3_SX0 @ ( s @ SV2 ) @ ( s @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( s @ ( s @ ( sK4_SY37 @ SV1 ) ) ) @ ( sK5_SY41 @ SV1 ) ) )
= $true )
| ( ( ~ ( SV1 @ ( s @ ( sK4_SY37 @ SV1 ) ) @ ( s @ ( sK5_SY41 @ SV1 ) ) ) )
= $true )
| ( ( SV1 @ c1 @ c1 )
= $false )
| ( ( SV1 @ sK1_SY0 @ sK2_SY24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ( sK3_SX0 @ ( s @ ( s @ SV2 ) ) @ SV3 )
| ~ ( sK3_SX0 @ ( s @ SV2 ) @ ( s @ SV3 ) ) )
= $false )
| ( ( sK3_SX0 @ SV2 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV1: $i > $i > $o] :
( ( ( SV1 @ ( s @ ( s @ ( sK4_SY37 @ SV1 ) ) ) @ ( sK5_SY41 @ SV1 ) )
= $false )
| ( ( ~ ( SV1 @ ( s @ ( sK4_SY37 @ SV1 ) ) @ ( s @ ( sK5_SY41 @ SV1 ) ) ) )
= $true )
| ( ( SV1 @ c1 @ c1 )
= $false )
| ( ( SV1 @ sK1_SY0 @ sK2_SY24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ( sK3_SX0 @ ( s @ ( s @ SV2 ) ) @ SV3 ) )
= $false )
| ( ( sK3_SX0 @ SV2 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(44,plain,
! [SV3: $i,SV2: $i] :
( ( ( ~ ( sK3_SX0 @ ( s @ SV2 ) @ ( s @ SV3 ) ) )
= $false )
| ( ( sK3_SX0 @ SV2 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV1: $i > $i > $o] :
( ( ( SV1 @ ( s @ ( sK4_SY37 @ SV1 ) ) @ ( s @ ( sK5_SY41 @ SV1 ) ) )
= $false )
| ( ( SV1 @ ( s @ ( s @ ( sK4_SY37 @ SV1 ) ) ) @ ( sK5_SY41 @ SV1 ) )
= $false )
| ( ( SV1 @ c1 @ c1 )
= $false )
| ( ( SV1 @ sK1_SY0 @ sK2_SY24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(46,plain,
! [SV3: $i,SV2: $i] :
( ( ( sK3_SX0 @ ( s @ ( s @ SV2 ) ) @ SV3 )
= $true )
| ( ( sK3_SX0 @ SV2 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(47,plain,
! [SV3: $i,SV2: $i] :
( ( ( sK3_SX0 @ ( s @ SV2 ) @ ( s @ SV3 ) )
= $true )
| ( ( sK3_SX0 @ SV2 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(48,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,47,46,45,37,28]) ).
thf(49,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ113^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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
% 0.09/0.18 % Computer : n005.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 13:59:59 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.22
% 0.09/0.22 No.of.Axioms: 0
% 0.09/0.22
% 0.09/0.22 Length.of.Defs: 277
% 0.09/0.22
% 0.09/0.22 Contains.Choice.Funs: false
% 0.09/0.22 .
% 0.09/0.22
% 0.09/0.22 ********************************
% 0.09/0.22 * All subproblems solved! *
% 0.09/0.22 ********************************
% 0.09/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,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:48,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.22
% 0.09/0.22 %**** Beginning of derivation protocol ****
% 0.09/0.22 % SZS output start CNFRefutation
% See solution above
% 0.09/0.22
% 0.09/0.22 %**** End of derivation protocol ****
% 0.09/0.22 %**** no. of clauses in derivation: 49 ****
% 0.09/0.22 %**** clause counter: 48 ****
% 0.09/0.22
% 0.09/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,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:48,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------