%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO111^5 : 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 : n020.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 11:07:39 AM UTC 2026
% Result : Theorem 0.09s 0.27s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 1
% Syntax : Number of formulae : 65 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 579 ( 155 equ; 0 cnn)
% Maximal formula atoms : 12 ( 8 avg)
% Number of connectives : 737 ( 225 ~; 201 |; 0 &; 308 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 227 ( 0 ^; 205 !; 22 ?; 227 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cG,type,
cG: $i > $o ).
thf(tp_cM,type,
cM: $i > $o ).
thf(tp_cN,type,
cN: $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i > $i ).
thf(tp_sK3_SX1,type,
sK3_SX1: $i > $i ).
thf(tp_sK4_SX1,type,
sK4_SX1: $i > $i ).
thf(tp_sK5_SX0,type,
sK5_SX0: $i > $i ).
thf(tp_sK6_SX0,type,
sK6_SX0: $i > $i ).
thf(tp_sK7_SX0,type,
sK7_SX0: $i > $i > $i ).
thf(1,conjecture,
( ( ! [R: $i] : ( cM @ R )
| ? [X: $i] :
~ ( cG @ X )
| ~ ( ! [Y: $i] : ( cM @ Y )
| ? [S: $i] : ( cN @ S ) )
| ~ ( ! [Z: $i] :
~ ( cN @ Z )
| ~ ! [T: $i] : ( cG @ T ) ) )
=> ( ! [R: $i] : ( cM @ R )
| ? [X: $i] :
~ ( cG @ X )
| ~ ! [Y: $i] :
( ( cM @ Y )
| ? [S: $i] : ( cN @ S ) )
| ~ ! [Z: $i] :
( ~ ( cN @ Z )
| ~ ! [T: $i] : ( cG @ T ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM80) ).
thf(2,negated_conjecture,
( ( ( ! [R: $i] : ( cM @ R )
| ? [X: $i] :
~ ( cG @ X )
| ~ ( ! [Y: $i] : ( cM @ Y )
| ? [S: $i] : ( cN @ S ) )
| ~ ( ! [Z: $i] :
~ ( cN @ Z )
| ~ ! [T: $i] : ( cG @ T ) ) )
=> ( ! [R: $i] : ( cM @ R )
| ? [X: $i] :
~ ( cG @ X )
| ~ ! [Y: $i] :
( ( cM @ Y )
| ? [S: $i] : ( cN @ S ) )
| ~ ! [Z: $i] :
( ~ ( cN @ Z )
| ~ ! [T: $i] : ( cG @ T ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [R: $i] : ( cM @ R )
| ? [X: $i] :
~ ( cG @ X )
| ~ ( ! [Y: $i] : ( cM @ Y )
| ? [S: $i] : ( cN @ S ) )
| ~ ( ! [Z: $i] :
~ ( cN @ Z )
| ~ ! [T: $i] : ( cG @ T ) ) )
=> ( ! [R: $i] : ( cM @ R )
| ? [X: $i] :
~ ( cG @ X )
| ~ ! [Y: $i] :
( ( cM @ Y )
| ? [S: $i] : ( cN @ S ) )
| ~ ! [Z: $i] :
( ~ ( cN @ Z )
| ~ ! [T: $i] : ( cG @ T ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [R: $i] : ( cM @ R )
| ? [X: $i] :
~ ( cG @ X )
| ~ ( ! [Y: $i] : ( cM @ Y )
| ? [S: $i] : ( cN @ S ) )
| ~ ( ! [Z: $i] :
~ ( cN @ Z )
| ~ ! [T: $i] : ( cG @ T ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [R: $i] : ( cM @ R )
| ? [X: $i] :
~ ( cG @ X )
| ~ ! [Y: $i] :
( ( cM @ Y )
| ? [S: $i] : ( cN @ S ) )
| ~ ! [Z: $i] :
( ~ ( cN @ Z )
| ~ ! [T: $i] : ( cG @ T ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ( ! [R: $i] : ( cM @ R )
| ? [X: $i] :
~ ( cG @ X )
| ~ ! [Y: $i] :
( ( cM @ Y )
| ? [S: $i] : ( cN @ S ) )
| ~ ! [Z: $i] :
( ~ ( cN @ Z )
| ~ ! [T: $i] : ( cG @ T ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [R: $i] : ( cM @ R )
| ? [X: $i] :
~ ( cG @ X )
| ~ ( ! [Y: $i] : ( cM @ Y )
| ? [S: $i] : ( cN @ S ) )
| ~ ( ! [Z: $i] :
~ ( cN @ Z )
| ~ ! [T: $i] : ( cG @ T ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ( ! [R: $i] : ( cM @ R )
| ? [X: $i] :
~ ( cG @ X )
| ~ ! [Y: $i] :
( ( cM @ Y )
| ? [S: $i] : ( cN @ S ) )
| ~ ! [Z: $i] :
( ~ ( cN @ Z )
| ~ ! [T: $i] : ( cG @ T ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( ! [SX0: $i] : ( cM @ SX0 )
| ~ ! [SX0: $i] :
~ ~ ( cG @ SX0 )
| ~ ! [SX0: $i] :
( ( cM @ SX0 )
| ~ ! [SX1: $i] :
~ ( cN @ SX1 ) )
| ~ ! [SX0: $i] :
( ~ ( cN @ SX0 )
| ~ ! [SX1: $i] : ( cG @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SX0: $i] : ( cM @ SX0 )
| ~ ! [SX0: $i] :
~ ~ ( cG @ SX0 )
| ~ ( ! [SX0: $i] : ( cM @ SX0 )
| ~ ! [SX0: $i] :
~ ( cN @ SX0 ) )
| ~ ( ! [SX0: $i] :
~ ( cN @ SX0 )
| ~ ! [SX0: $i] : ( cG @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: $i] : ( cM @ SX0 )
| ~ ! [SX0: $i] :
~ ~ ( cG @ SX0 )
| ~ ! [SX0: $i] :
( ( cM @ SX0 )
| ~ ! [SX1: $i] :
~ ( cN @ SX1 ) )
| ~ ! [SX0: $i] :
( ~ ( cN @ SX0 )
| ~ ! [SX1: $i] : ( cG @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
( ( ( ! [SX0: $i] : ( cM @ SX0 )
| ~ ! [SX0: $i] :
~ ~ ( cG @ SX0 )
| ~ ( ! [SX0: $i] : ( cM @ SX0 )
| ~ ! [SX0: $i] :
~ ( cN @ SX0 ) ) )
= $true )
| ( ( ~ ( ! [SX0: $i] :
~ ( cN @ SX0 )
| ~ ! [SX0: $i] : ( cG @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [SX0: $i] : ( cM @ SX0 )
| ~ ! [SX0: $i] :
~ ~ ( cG @ SX0 )
| ~ ! [SX0: $i] :
( ( cM @ SX0 )
| ~ ! [SX1: $i] :
~ ( cN @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ! [SX0: $i] :
( ~ ( cN @ SX0 )
| ~ ! [SX1: $i] : ( cG @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(15,plain,
( ( ( ! [SX0: $i] : ( cM @ SX0 )
| ~ ! [SX0: $i] :
~ ~ ( cG @ SX0 ) )
= $true )
| ( ( ~ ( ! [SX0: $i] : ( cM @ SX0 )
| ~ ! [SX0: $i] :
~ ( cN @ SX0 ) ) )
= $true )
| ( ( ~ ( ! [SX0: $i] :
~ ( cN @ SX0 )
| ~ ! [SX0: $i] : ( cG @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(16,plain,
( ( ! [SX0: $i] : ( cM @ SX0 )
| ~ ! [SX0: $i] :
~ ~ ( cG @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
( ( ~ ! [SX0: $i] :
( ( cM @ SX0 )
| ~ ! [SX1: $i] :
~ ( cN @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(18,plain,
( ( ! [SX0: $i] :
( ~ ( cN @ SX0 )
| ~ ! [SX1: $i] : ( cG @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(19,plain,
( ( ( ! [SX0: $i] : ( cM @ SX0 ) )
= $true )
| ( ( ~ ! [SX0: $i] :
~ ~ ( cG @ SX0 ) )
= $true )
| ( ( ~ ( ! [SX0: $i] : ( cM @ SX0 )
| ~ ! [SX0: $i] :
~ ( cN @ SX0 ) ) )
= $true )
| ( ( ~ ( ! [SX0: $i] :
~ ( cN @ SX0 )
| ~ ! [SX0: $i] : ( cG @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(20,plain,
( ( ! [SX0: $i] : ( cM @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(21,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( cG @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(22,plain,
( ( ! [SX0: $i] :
( ( cM @ SX0 )
| ~ ! [SX1: $i] :
~ ( cN @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(23,plain,
! [SV1: $i] :
( ( ~ ( cN @ SV1 )
| ~ ! [SX1: $i] : ( cG @ SX1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(24,plain,
! [SV2: $i] :
( ( ( cM @ SV2 )
= $true )
| ( ( ~ ! [SX0: $i] :
~ ~ ( cG @ SX0 ) )
= $true )
| ( ( ~ ( ! [SX0: $i] : ( cM @ SX0 )
| ~ ! [SX0: $i] :
~ ( cN @ SX0 ) ) )
= $true )
| ( ( ~ ( ! [SX0: $i] :
~ ( cN @ SX0 )
| ~ ! [SX0: $i] : ( cG @ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(25,plain,
( ( cM @ sK1_SX0 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(26,plain,
( ( ! [SX0: $i] :
~ ~ ( cG @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(27,plain,
! [SV3: $i] :
( ( ( cM @ SV3 )
| ~ ! [SX1: $i] :
~ ( cN @ SX1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV1: $i] :
( ( ( ~ ( cN @ SV1 ) )
= $true )
| ( ( ~ ! [SX1: $i] : ( cG @ SX1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV2: $i] :
( ( ( ! [SX0: $i] :
~ ~ ( cG @ SX0 ) )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( ~ ( ! [SX0: $i] : ( cM @ SX0 )
| ~ ! [SX0: $i] :
~ ( cN @ SX0 ) ) )
= $true )
| ( ( ~ ( ! [SX0: $i] :
~ ( cN @ SX0 )
| ~ ! [SX0: $i] : ( cG @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV4: $i] :
( ( ~ ~ ( cG @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV3: $i] :
( ( ( cM @ SV3 )
= $true )
| ( ( ~ ! [SX1: $i] :
~ ( cN @ SX1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV1: $i] :
( ( ( cN @ SV1 )
= $false )
| ( ( ~ ! [SX1: $i] : ( cG @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV2: $i] :
( ( ( ~ ~ ( cG @ ( sK2_SX0 @ SV2 ) ) )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( ~ ( ! [SX0: $i] : ( cM @ SX0 )
| ~ ! [SX0: $i] :
~ ( cN @ SX0 ) ) )
= $true )
| ( ( ~ ( ! [SX0: $i] :
~ ( cN @ SX0 )
| ~ ! [SX0: $i] : ( cG @ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[29]) ).
thf(34,plain,
! [SV4: $i] :
( ( ~ ( cG @ SV4 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV3: $i] :
( ( ( ! [SX1: $i] :
~ ( cN @ SX1 ) )
= $false )
| ( ( cM @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV1: $i] :
( ( ( ! [SX1: $i] : ( cG @ SX1 ) )
= $false )
| ( ( cN @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV2: $i] :
( ( ( ~ ( cG @ ( sK2_SX0 @ SV2 ) ) )
= $true )
| ( ( cM @ SV2 )
= $true )
| ( ( ~ ( ! [SX0: $i] : ( cM @ SX0 )
| ~ ! [SX0: $i] :
~ ( cN @ SX0 ) ) )
= $true )
| ( ( ~ ( ! [SX0: $i] :
~ ( cN @ SX0 )
| ~ ! [SX0: $i] : ( cG @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(38,plain,
! [SV4: $i] :
( ( cG @ SV4 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(39,plain,
! [SV3: $i] :
( ( ( ~ ( cN @ ( sK3_SX1 @ SV3 ) ) )
= $false )
| ( ( cM @ SV3 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(40,plain,
! [SV1: $i] :
( ( ( cG @ ( sK4_SX1 @ SV1 ) )
= $false )
| ( ( cN @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[36]) ).
thf(41,plain,
! [SV2: $i] :
( ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( ~ ( ! [SX0: $i] : ( cM @ SX0 )
| ~ ! [SX0: $i] :
~ ( cN @ SX0 ) ) )
= $true )
| ( ( ~ ( ! [SX0: $i] :
~ ( cN @ SX0 )
| ~ ! [SX0: $i] : ( cG @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV3: $i] :
( ( ( cN @ ( sK3_SX1 @ SV3 ) )
= $true )
| ( ( cM @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(43,plain,
! [SV2: $i] :
( ( ( ! [SX0: $i] : ( cM @ SX0 )
| ~ ! [SX0: $i] :
~ ( cN @ SX0 ) )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( ~ ( ! [SX0: $i] :
~ ( cN @ SX0 )
| ~ ! [SX0: $i] : ( cG @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV2: $i] :
( ( ( ! [SX0: $i] : ( cM @ SX0 ) )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( ~ ( ! [SX0: $i] :
~ ( cN @ SX0 )
| ~ ! [SX0: $i] : ( cG @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(45,plain,
! [SV2: $i] :
( ( ( ~ ! [SX0: $i] :
~ ( cN @ SX0 ) )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( ~ ( ! [SX0: $i] :
~ ( cN @ SX0 )
| ~ ! [SX0: $i] : ( cG @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(46,plain,
! [SV2: $i] :
( ( ( cM @ ( sK5_SX0 @ SV2 ) )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( ~ ( ! [SX0: $i] :
~ ( cN @ SX0 )
| ~ ! [SX0: $i] : ( cG @ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(47,plain,
! [SV2: $i] :
( ( ( ! [SX0: $i] :
~ ( cN @ SX0 ) )
= $true )
| ( ( cM @ SV2 )
= $true )
| ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( ~ ( ! [SX0: $i] :
~ ( cN @ SX0 )
| ~ ! [SX0: $i] : ( cG @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(48,plain,
! [SV2: $i] :
( ( ( ! [SX0: $i] :
~ ( cN @ SX0 )
| ~ ! [SX0: $i] : ( cG @ SX0 ) )
= $false )
| ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( cM @ ( sK5_SX0 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(49,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( cN @ SV5 ) )
= $true )
| ( ( cM @ SV2 )
= $true )
| ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( ~ ( ! [SX0: $i] :
~ ( cN @ SX0 )
| ~ ! [SX0: $i] : ( cG @ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(50,plain,
! [SV2: $i] :
( ( ( ! [SX0: $i] :
~ ( cN @ SX0 ) )
= $false )
| ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( cM @ ( sK5_SX0 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(51,plain,
! [SV2: $i] :
( ( ( ~ ! [SX0: $i] : ( cG @ SX0 ) )
= $false )
| ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( cM @ ( sK5_SX0 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(52,plain,
! [SV2: $i,SV5: $i] :
( ( ( cN @ SV5 )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( ~ ( ! [SX0: $i] :
~ ( cN @ SX0 )
| ~ ! [SX0: $i] : ( cG @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV2: $i] :
( ( ( ~ ( cN @ ( sK6_SX0 @ SV2 ) ) )
= $false )
| ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( cM @ ( sK5_SX0 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[50]) ).
thf(54,plain,
! [SV2: $i] :
( ( ( ! [SX0: $i] : ( cG @ SX0 ) )
= $true )
| ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( cM @ ( sK5_SX0 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(55,plain,
! [SV5: $i,SV2: $i] :
( ( ( ! [SX0: $i] :
~ ( cN @ SX0 )
| ~ ! [SX0: $i] : ( cG @ SX0 ) )
= $false )
| ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( cN @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(56,plain,
! [SV2: $i] :
( ( ( cN @ ( sK6_SX0 @ SV2 ) )
= $true )
| ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( cM @ ( sK5_SX0 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(57,plain,
! [SV2: $i,SV6: $i] :
( ( ( cG @ SV6 )
= $true )
| ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( cM @ ( sK5_SX0 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(58,plain,
! [SV5: $i,SV2: $i] :
( ( ( ! [SX0: $i] :
~ ( cN @ SX0 ) )
= $false )
| ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( cN @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(59,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ! [SX0: $i] : ( cG @ SX0 ) )
= $false )
| ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( cN @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(60,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( cN @ ( sK7_SX0 @ SV5 @ SV2 ) ) )
= $false )
| ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( cN @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[58]) ).
thf(61,plain,
! [SV5: $i,SV2: $i] :
( ( ( ! [SX0: $i] : ( cG @ SX0 ) )
= $true )
| ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( cN @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(62,plain,
! [SV2: $i,SV5: $i] :
( ( ( cN @ ( sK7_SX0 @ SV5 @ SV2 ) )
= $true )
| ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( cN @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(63,plain,
! [SV5: $i,SV2: $i,SV7: $i] :
( ( ( cG @ SV7 )
= $true )
| ( ( cG @ ( sK2_SX0 @ SV2 ) )
= $false )
| ( ( cM @ SV2 )
= $true )
| ( ( cN @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(64,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,63,62,57,56,42,40,38]) ).
thf(65,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO111^5 : 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
% 0.09/0.21 % Computer : n020.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Oct 6 17:33:21 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.27
% 0.09/0.27 No.of.Axioms: 0
% 0.09/0.27
% 0.09/0.27 Length.of.Defs: 0
% 0.09/0.27
% 0.09/0.27 Contains.Choice.Funs: false
% 0.09/0.27 .
% 0.09/0.27
% 0.09/0.27 ********************************
% 0.09/0.27 * All subproblems solved! *
% 0.09/0.27 ********************************
% 0.09/0.27 % 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:64,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.27
% 0.09/0.27 %**** Beginning of derivation protocol ****
% 0.09/0.27 % SZS output start CNFRefutation
% See solution above
% 0.09/0.28
% 0.09/0.28 %**** End of derivation protocol ****
% 0.09/0.28 %**** no. of clauses in derivation: 65 ****
% 0.09/0.28 %**** clause counter: 64 ****
% 0.09/0.28
% 0.09/0.28 % 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:64,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------