%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO105^5 : 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 : n006.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 11:07:38 AM UTC 2026
% Result : Theorem 0.09s 0.21s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 1
% Syntax : Number of formulae : 73 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 432 ( 96 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 886 ( 248 ~; 116 |; 14 &; 471 @)
% ( 3 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 169 ( 0 ^; 141 !; 28 ?; 169 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cP,type,
cP: $i > $i > $i > $o ).
thf(tp_cQ,type,
cQ: $i > $i > $o ).
thf(tp_cR,type,
cR: $i > $o ).
thf(tp_sK1_Xz,type,
sK1_Xz: $i > $i ).
thf(tp_sK2_Xv,type,
sK2_Xv: $i > $i ).
thf(tp_sK3_Xu,type,
sK3_Xu: $i > $i ).
thf(tp_sK4_Xx,type,
sK4_Xx: $i ).
thf(tp_sK5_Xv,type,
sK5_Xv: $i ).
thf(tp_sK6_Xz,type,
sK6_Xz: $i ).
thf(tp_sK7_Xx,type,
sK7_Xx: $i ).
thf(tp_sK8_Xu,type,
sK8_Xu: $i > $i ).
thf(tp_sK9_REN,type,
sK9_REN: $o ).
thf(tp_y,type,
y: $i ).
thf(1,conjecture,
( ~ ( ? [Xx: $i] : ( cQ @ Xx @ y )
=> ~ ! [Xz: $i] :
( ! [Xu: $i] : ( cP @ Xu @ y @ Xz )
=> ~ ? [Xv: $i] : ( cR @ Xv ) ) )
<=> ? [Xx: $i] :
! [Xz: $i] :
? [Xu: $i] :
! [Xv: $i] :
~ ( ( cQ @ Xx @ y )
=> ~ ( ( cP @ Xu @ y @ Xz )
=> ~ ( cR @ Xv ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX2201TEST) ).
thf(2,negated_conjecture,
( ( ~ ( ? [Xx: $i] : ( cQ @ Xx @ y )
=> ~ ! [Xz: $i] :
( ! [Xu: $i] : ( cP @ Xu @ y @ Xz )
=> ~ ? [Xv: $i] : ( cR @ Xv ) ) )
<=> ? [Xx: $i] :
! [Xz: $i] :
? [Xu: $i] :
! [Xv: $i] :
~ ( ( cQ @ Xx @ y )
=> ~ ( ( cP @ Xu @ y @ Xz )
=> ~ ( cR @ Xv ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ~ ( ? [Xx: $i] : ( cQ @ Xx @ y )
=> ~ ! [Xz: $i] :
( ! [Xu: $i] : ( cP @ Xu @ y @ Xz )
=> ~ ? [Xv: $i] : ( cR @ Xv ) ) )
<=> ? [Xx: $i] :
! [Xz: $i] :
? [Xu: $i] :
! [Xv: $i] :
~ ( ( cQ @ Xx @ y )
=> ~ ( ( cP @ Xu @ y @ Xz )
=> ~ ( cR @ Xv ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ( ? [Xx: $i] : ( cQ @ Xx @ y )
=> ~ ! [Xz: $i] :
( ! [Xu: $i] : ( cP @ Xu @ y @ Xz )
=> ~ ? [Xv: $i] : ( cR @ Xv ) ) )
=> ? [Xx: $i] :
! [Xz: $i] :
? [Xu: $i] :
! [Xv: $i] :
~ ( ( cQ @ Xx @ y )
=> ~ ( ( cP @ Xu @ y @ Xz )
=> ~ ( cR @ Xv ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(5,plain,
( ( ? [Xx: $i] :
! [Xz: $i] :
? [Xu: $i] :
! [Xv: $i] :
~ ( ( cQ @ Xx @ y )
=> ~ ( ( cP @ Xu @ y @ Xz )
=> ~ ( cR @ Xv ) ) )
=> ~ ( ? [Xx: $i] : ( cQ @ Xx @ y )
=> ~ ! [Xz: $i] :
( ! [Xu: $i] : ( cP @ Xu @ y @ Xz )
=> ~ ? [Xv: $i] : ( cR @ Xv ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(6,plain,
( ( ~ ( ~ ( ? [Xx: $i] : ( cQ @ Xx @ y )
=> ~ ! [Xz: $i] :
( ! [Xu: $i] : ( cP @ Xu @ y @ Xz )
=> ~ ? [Xv: $i] : ( cR @ Xv ) ) )
=> ? [Xx: $i] :
! [Xz: $i] :
? [Xu: $i] :
! [Xv: $i] :
~ ( ( cQ @ Xx @ y )
=> ~ ( ( cP @ Xu @ y @ Xz )
=> ~ ( cR @ Xv ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ( ? [Xx: $i] :
! [Xz: $i] :
? [Xu: $i] :
! [Xv: $i] :
~ ( ( cQ @ Xx @ y )
=> ~ ( ( cP @ Xu @ y @ Xz )
=> ~ ( cR @ Xv ) ) )
=> ~ ( ? [Xx: $i] : ( cQ @ Xx @ y )
=> ~ ! [Xz: $i] :
( ! [Xu: $i] : ( cP @ Xu @ y @ Xz )
=> ~ ? [Xv: $i] : ( cR @ Xv ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(8,plain,
( ( ( cQ @ sK4_Xx @ y )
& ( ! [Xz: $i] :
~ ( cP @ ( sK3_Xu @ Xz ) @ y @ Xz )
| ! [Xv: $i] :
~ ( cR @ Xv ) )
& ! [Xx: $i] :
( ( ~ ( cQ @ Xx @ y )
| ! [SY8: $i] : ( cP @ SY8 @ y @ ( sK1_Xz @ Xx ) ) )
& ( ~ ( cQ @ Xx @ y )
| ( cR @ ( sK2_Xv @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(9,plain,
( ( ! [SY11: $i] :
( ( cQ @ sK7_Xx @ y )
& ( ~ ( cP @ ( sK8_Xu @ SY11 ) @ y @ SY11 )
| ! [Xv: $i] :
~ ( cR @ Xv ) ) )
& ( ! [Xx: $i] :
~ ( cQ @ Xx @ y )
| sK9_REN )
& ( sK9_REN
=> ( ! [SY10: $i] : ( cP @ SY10 @ y @ sK6_Xz )
& ( cR @ sK5_Xv ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(10,plain,
( ( ( cQ @ sK4_Xx @ y )
& ( ! [Xz: $i] :
~ ( cP @ ( sK3_Xu @ Xz ) @ y @ Xz )
| ! [Xv: $i] :
~ ( cR @ Xv ) )
& ! [Xx: $i] :
( ( ~ ( cQ @ Xx @ y )
| ! [SY8: $i] : ( cP @ SY8 @ y @ ( sK1_Xz @ Xx ) ) )
& ( ~ ( cQ @ Xx @ y )
| ( cR @ ( sK2_Xv @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( ~ ~ ( ~ ( cQ @ sK4_Xx @ y )
| ~ ( ! [SX0: $i] :
~ ( cP @ ( sK3_Xu @ SX0 ) @ y @ SX0 )
| ! [SX0: $i] :
~ ( cR @ SX0 ) ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( cQ @ SX0 @ y )
| ! [SX1: $i] : ( cP @ SX1 @ y @ ( sK1_Xz @ SX0 ) ) )
| ~ ( ~ ( cQ @ SX0 @ y )
| ( cR @ ( sK2_Xv @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
( ( ~ ~ ( ~ ( cQ @ sK4_Xx @ y )
| ~ ( ! [SX0: $i] :
~ ( cP @ ( sK3_Xu @ SX0 ) @ y @ SX0 )
| ! [SX0: $i] :
~ ( cR @ SX0 ) ) )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( cQ @ SX0 @ y )
| ! [SX1: $i] : ( cP @ SX1 @ y @ ( sK1_Xz @ SX0 ) ) )
| ~ ( ~ ( cQ @ SX0 @ y )
| ( cR @ ( sK2_Xv @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(13,plain,
( ( ~ ~ ( ~ ( cQ @ sK4_Xx @ y )
| ~ ( ! [SX0: $i] :
~ ( cP @ ( sK3_Xu @ SX0 ) @ y @ SX0 )
| ! [SX0: $i] :
~ ( cR @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(14,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ ( ~ ( cQ @ SX0 @ y )
| ! [SX1: $i] : ( cP @ SX1 @ y @ ( sK1_Xz @ SX0 ) ) )
| ~ ( ~ ( cQ @ SX0 @ y )
| ( cR @ ( sK2_Xv @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( ~ ( cQ @ sK4_Xx @ y )
| ~ ( ! [SX0: $i] :
~ ( cP @ ( sK3_Xu @ SX0 ) @ y @ SX0 )
| ! [SX0: $i] :
~ ( cR @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( cQ @ SX0 @ y )
| ! [SX1: $i] : ( cP @ SX1 @ y @ ( sK1_Xz @ SX0 ) ) )
| ~ ( ~ ( cQ @ SX0 @ y )
| ( cR @ ( sK2_Xv @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( cQ @ sK4_Xx @ y )
| ~ ( ! [SX0: $i] :
~ ( cP @ ( sK3_Xu @ SX0 ) @ y @ SX0 )
| ! [SX0: $i] :
~ ( cR @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
! [SV1: $i] :
( ( ~ ( ~ ( ~ ( cQ @ SV1 @ y )
| ! [SY14: $i] : ( cP @ SY14 @ y @ ( sK1_Xz @ SV1 ) ) )
| ~ ( ~ ( cQ @ SV1 @ y )
| ( cR @ ( sK2_Xv @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ( cQ @ sK4_Xx @ y ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ( ! [SX0: $i] :
~ ( cP @ ( sK3_Xu @ SX0 ) @ y @ SX0 )
| ! [SX0: $i] :
~ ( cR @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV1: $i] :
( ( ~ ( ~ ( cQ @ SV1 @ y )
| ! [SY14: $i] : ( cP @ SY14 @ y @ ( sK1_Xz @ SV1 ) ) )
| ~ ( ~ ( cQ @ SV1 @ y )
| ( cR @ ( sK2_Xv @ SV1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( cQ @ sK4_Xx @ y )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ! [SX0: $i] :
~ ( cP @ ( sK3_Xu @ SX0 ) @ y @ SX0 )
| ! [SX0: $i] :
~ ( cR @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV1: $i] :
( ( ~ ( ~ ( cQ @ SV1 @ y )
| ! [SY14: $i] : ( cP @ SY14 @ y @ ( sK1_Xz @ SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV1: $i] :
( ( ~ ( ~ ( cQ @ SV1 @ y )
| ( cR @ ( sK2_Xv @ SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( ( ! [SX0: $i] :
~ ( cP @ ( sK3_Xu @ SX0 ) @ y @ SX0 ) )
= $true )
| ( ( ! [SX0: $i] :
~ ( cR @ SX0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV1: $i] :
( ( ~ ( cQ @ SV1 @ y )
| ! [SY14: $i] : ( cP @ SY14 @ y @ ( sK1_Xz @ SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(28,plain,
! [SV1: $i] :
( ( ~ ( cQ @ SV1 @ y )
| ( cR @ ( sK2_Xv @ SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(29,plain,
! [SV2: $i] :
( ( ( ~ ( cP @ ( sK3_Xu @ SV2 ) @ y @ SV2 ) )
= $true )
| ( ( ! [SX0: $i] :
~ ( cR @ SX0 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV1: $i] :
( ( ( ~ ( cQ @ SV1 @ y ) )
= $true )
| ( ( ! [SY14: $i] : ( cP @ SY14 @ y @ ( sK1_Xz @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV1: $i] :
( ( ( ~ ( cQ @ SV1 @ y ) )
= $true )
| ( ( cR @ ( sK2_Xv @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV2: $i] :
( ( ( cP @ ( sK3_Xu @ SV2 ) @ y @ SV2 )
= $false )
| ( ( ! [SX0: $i] :
~ ( cR @ SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV1: $i] :
( ( ( cQ @ SV1 @ y )
= $false )
| ( ( ! [SY14: $i] : ( cP @ SY14 @ y @ ( sK1_Xz @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV1: $i] :
( ( ( cQ @ SV1 @ y )
= $false )
| ( ( cR @ ( sK2_Xv @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV2: $i,SV3: $i] :
( ( ( ~ ( cR @ SV3 ) )
= $true )
| ( ( cP @ ( sK3_Xu @ SV2 ) @ y @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV1: $i,SV4: $i] :
( ( ( cP @ SV4 @ y @ ( sK1_Xz @ SV1 ) )
= $true )
| ( ( cQ @ SV1 @ y )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV2: $i,SV3: $i] :
( ( ( cR @ SV3 )
= $false )
| ( ( cP @ ( sK3_Xu @ SV2 ) @ y @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(38,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[22,37,36,34]) ).
thf(39,plain,
( ( ! [SY11: $i] :
( ( cQ @ sK7_Xx @ y )
& ( ~ ( cP @ ( sK8_Xu @ SY11 ) @ y @ SY11 )
| ! [Xv: $i] :
~ ( cR @ Xv ) ) )
& ( ! [Xx: $i] :
~ ( cQ @ Xx @ y )
| sK9_REN )
& ( sK9_REN
=> ( ! [SY10: $i] : ( cP @ SY10 @ y @ sK6_Xz )
& ( cR @ sK5_Xv ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(40,plain,
( ( ~ ( ~ ! [SX0: $i] :
~ ( ~ ( cQ @ sK7_Xx @ y )
| ~ ( ~ ( cP @ ( sK8_Xu @ SX0 ) @ y @ SX0 )
| ! [SX1: $i] :
~ ( cR @ SX1 ) ) )
| ~ ~ ( ~ ( ! [SX0: $i] :
~ ( cQ @ SX0 @ y )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ! [SX0: $i] : ( cP @ SX0 @ y @ sK6_Xz )
| ~ ( cR @ sK5_Xv ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(41,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ ( cQ @ sK7_Xx @ y )
| ~ ( ~ ( cP @ ( sK8_Xu @ SX0 ) @ y @ SX0 )
| ! [SX1: $i] :
~ ( cR @ SX1 ) ) )
| ~ ~ ( ~ ( ! [SX0: $i] :
~ ( cQ @ SX0 @ y )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ! [SX0: $i] : ( cP @ SX0 @ y @ sK6_Xz )
| ~ ( cR @ sK5_Xv ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(42,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ ( cQ @ sK7_Xx @ y )
| ~ ( ~ ( cP @ ( sK8_Xu @ SX0 ) @ y @ SX0 )
| ! [SX1: $i] :
~ ( cR @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(43,plain,
( ( ~ ~ ( ~ ( ! [SX0: $i] :
~ ( cQ @ SX0 @ y )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ! [SX0: $i] : ( cP @ SX0 @ y @ sK6_Xz )
| ~ ( cR @ sK5_Xv ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(44,plain,
( ( ! [SX0: $i] :
~ ( ~ ( cQ @ sK7_Xx @ y )
| ~ ( ~ ( cP @ ( sK8_Xu @ SX0 ) @ y @ SX0 )
| ! [SX1: $i] :
~ ( cR @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(45,plain,
( ( ~ ( ~ ( ! [SX0: $i] :
~ ( cQ @ SX0 @ y )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ! [SX0: $i] : ( cP @ SX0 @ y @ sK6_Xz )
| ~ ( cR @ sK5_Xv ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(46,plain,
! [SV5: $i] :
( ( ~ ( ~ ( cQ @ sK7_Xx @ y )
| ~ ( ~ ( cP @ ( sK8_Xu @ SV5 ) @ y @ SV5 )
| ! [SX1: $i] :
~ ( cR @ SX1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(47,plain,
( ( ~ ( ! [SX0: $i] :
~ ( cQ @ SX0 @ y )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ! [SX0: $i] : ( cP @ SX0 @ y @ sK6_Xz )
| ~ ( cR @ sK5_Xv ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(48,plain,
! [SV5: $i] :
( ( ~ ( cQ @ sK7_Xx @ y )
| ~ ( ~ ( cP @ ( sK8_Xu @ SV5 ) @ y @ SV5 )
| ! [SX1: $i] :
~ ( cR @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(49,plain,
( ( ~ ( ! [SX0: $i] :
~ ( cQ @ SX0 @ y )
| sK9_REN ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(50,plain,
( ( ~ ( ~ sK9_REN
| ~ ( ~ ! [SX0: $i] : ( cP @ SX0 @ y @ sK6_Xz )
| ~ ( cR @ sK5_Xv ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(51,plain,
( ( ~ ( cQ @ sK7_Xx @ y ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(52,plain,
! [SV5: $i] :
( ( ~ ( ~ ( cP @ ( sK8_Xu @ SV5 ) @ y @ SV5 )
| ! [SX1: $i] :
~ ( cR @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(53,plain,
( ( ! [SX0: $i] :
~ ( cQ @ SX0 @ y )
| sK9_REN )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(54,plain,
( ( ~ sK9_REN
| ~ ( ~ ! [SX0: $i] : ( cP @ SX0 @ y @ sK6_Xz )
| ~ ( cR @ sK5_Xv ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(55,plain,
( ( cQ @ sK7_Xx @ y )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(56,plain,
! [SV5: $i] :
( ( ~ ( cP @ ( sK8_Xu @ SV5 ) @ y @ SV5 )
| ! [SX1: $i] :
~ ( cR @ SX1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(57,plain,
( ( ( ! [SX0: $i] :
~ ( cQ @ SX0 @ y ) )
= $true )
| ( sK9_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(58,plain,
( ( ( ~ sK9_REN ) = $true )
| ( ( ~ ( ~ ! [SX0: $i] : ( cP @ SX0 @ y @ sK6_Xz )
| ~ ( cR @ sK5_Xv ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(59,plain,
! [SV5: $i] :
( ( ( ~ ( cP @ ( sK8_Xu @ SV5 ) @ y @ SV5 ) )
= $true )
| ( ( ! [SX1: $i] :
~ ( cR @ SX1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(60,plain,
! [SV6: $i] :
( ( ( ~ ( cQ @ SV6 @ y ) )
= $true )
| ( sK9_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(61,plain,
( ( sK9_REN = $false )
| ( ( ~ ( ~ ! [SX0: $i] : ( cP @ SX0 @ y @ sK6_Xz )
| ~ ( cR @ sK5_Xv ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(62,plain,
! [SV5: $i] :
( ( ( cP @ ( sK8_Xu @ SV5 ) @ y @ SV5 )
= $false )
| ( ( ! [SX1: $i] :
~ ( cR @ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(63,plain,
! [SV6: $i] :
( ( ( cQ @ SV6 @ y )
= $false )
| ( sK9_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(64,plain,
( ( ( ~ ! [SX0: $i] : ( cP @ SX0 @ y @ sK6_Xz )
| ~ ( cR @ sK5_Xv ) )
= $false )
| ( sK9_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(65,plain,
! [SV5: $i,SV7: $i] :
( ( ( ~ ( cR @ SV7 ) )
= $true )
| ( ( cP @ ( sK8_Xu @ SV5 ) @ y @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(66,plain,
( ( ( ~ ! [SX0: $i] : ( cP @ SX0 @ y @ sK6_Xz ) )
= $false )
| ( sK9_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(67,plain,
( ( ( ~ ( cR @ sK5_Xv ) )
= $false )
| ( sK9_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(68,plain,
! [SV5: $i,SV7: $i] :
( ( ( cR @ SV7 )
= $false )
| ( ( cP @ ( sK8_Xu @ SV5 ) @ y @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(69,plain,
( ( ( ! [SX0: $i] : ( cP @ SX0 @ y @ sK6_Xz ) )
= $true )
| ( sK9_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(70,plain,
( ( ( cR @ sK5_Xv )
= $true )
| ( sK9_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(71,plain,
! [SV8: $i] :
( ( ( cP @ SV8 @ y @ sK6_Xz )
= $true )
| ( sK9_REN = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(72,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[55,71,70,68,63]) ).
thf(73,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[72,38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO105^5 : 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
% 0.09/0.15 % Computer : n006.cluster.edu
% 0.09/0.15 % Model : x86_64 x86_64
% 0.09/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.15 % Memory : 8046.5625MB
% 0.09/0.15 % OS : Linux 6.8.0-71-generic
% 0.09/0.15 % CPULimit : 300
% 0.09/0.15 % WCLimit : 300
% 0.09/0.15 % DateTime : Tue Oct 6 17:32:07 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.21
% 0.09/0.21 No.of.Axioms: 0
% 0.09/0.21
% 0.09/0.21 Length.of.Defs: 0
% 0.09/0.21
% 0.09/0.21 Contains.Choice.Funs: false
% 0.09/0.21 ..
% 0.09/0.21
% 0.09/0.21 ********************************
% 0.09/0.21 * All subproblems solved! *
% 0.09/0.21 ********************************
% 0.09/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,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:72,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.21
% 0.09/0.21 %**** Beginning of derivation protocol ****
% 0.09/0.21 % SZS output start CNFRefutation
% See solution above
% 0.09/0.21
% 0.09/0.21 %**** End of derivation protocol ****
% 0.09/0.21 %**** no. of clauses in derivation: 73 ****
% 0.09/0.21 %**** clause counter: 72 ****
% 0.09/0.21
% 0.09/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,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:72,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------