%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO382^5 : 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 11:08:10 AM UTC 2026
% Result : Theorem 0.09s 0.20s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 1
% Syntax : Number of formulae : 67 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 587 ( 167 equ; 0 cnn)
% Maximal formula atoms : 12 ( 8 avg)
% Number of connectives : 812 ( 168 ~; 142 |; 18 &; 458 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 148 ( 0 ^; 123 !; 25 ?; 148 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cP,type,
cP: $i > $i > $o ).
thf(tp_cQ,type,
cQ: $i > $i > $o ).
thf(tp_cS,type,
cS: $i > $o ).
thf(tp_sK1_Xu,type,
sK1_Xu: $i ).
thf(tp_sK2_Xx,type,
sK2_Xx: $i > $i ).
thf(tp_sK3_Xx,type,
sK3_Xx: $i ).
thf(tp_sK4_Xx,type,
sK4_Xx: $i ).
thf(tp_sK5_SY15,type,
sK5_SY15: $i ).
thf(tp_sK6_Xv,type,
sK6_Xv: $i ).
thf(tp_sK7_Xy,type,
sK7_Xy: $i > $i ).
thf(1,conjecture,
( ( ( ? [Xv: $i] :
! [Xx: $i] : ( cP @ Xx @ Xv )
& ! [Xx: $i] :
( ( cS @ Xx )
=> ? [Xy: $i] : ( cQ @ Xy @ Xx ) )
& ! [Xx: $i,Xy: $i] :
( ( cP @ Xx @ Xy )
=> ~ ( cQ @ Xx @ Xy ) ) )
=> ? [Xu: $i] :
~ ( cS @ Xu ) )
=> ( ( ? [Xv: $i] :
! [Xx: $i] : ( cP @ Xx @ Xv )
& ! [Xx: $i] :
( ( cS @ Xx )
=> ? [Xy: $i] : ( cQ @ Xy @ Xx ) )
& ! [Xx: $i,Xy: $i] :
( ( cP @ Xx @ Xy )
=> ~ ( cQ @ Xx @ Xy ) ) )
=> ? [Xu: $i] :
~ ( cS @ Xu ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM407) ).
thf(2,negated_conjecture,
( ( ( ( ? [Xv: $i] :
! [Xx: $i] : ( cP @ Xx @ Xv )
& ! [Xx: $i] :
( ( cS @ Xx )
=> ? [Xy: $i] : ( cQ @ Xy @ Xx ) )
& ! [Xx: $i,Xy: $i] :
( ( cP @ Xx @ Xy )
=> ~ ( cQ @ Xx @ Xy ) ) )
=> ? [Xu: $i] :
~ ( cS @ Xu ) )
=> ( ( ? [Xv: $i] :
! [Xx: $i] : ( cP @ Xx @ Xv )
& ! [Xx: $i] :
( ( cS @ Xx )
=> ? [Xy: $i] : ( cQ @ Xy @ Xx ) )
& ! [Xx: $i,Xy: $i] :
( ( cP @ Xx @ Xy )
=> ~ ( cQ @ Xx @ Xy ) ) )
=> ? [Xu: $i] :
~ ( cS @ Xu ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ( ? [Xv: $i] :
! [Xx: $i] : ( cP @ Xx @ Xv )
& ! [Xx: $i] :
( ( cS @ Xx )
=> ? [Xy: $i] : ( cQ @ Xy @ Xx ) )
& ! [Xx: $i,Xy: $i] :
( ( cP @ Xx @ Xy )
=> ~ ( cQ @ Xx @ Xy ) ) )
=> ? [Xu: $i] :
~ ( cS @ Xu ) )
=> ( ( ? [Xv: $i] :
! [Xx: $i] : ( cP @ Xx @ Xv )
& ! [Xx: $i] :
( ( cS @ Xx )
=> ? [Xy: $i] : ( cQ @ Xy @ Xx ) )
& ! [Xx: $i,Xy: $i] :
( ( cP @ Xx @ Xy )
=> ~ ( cQ @ Xx @ Xy ) ) )
=> ? [Xu: $i] :
~ ( cS @ Xu ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ( ? [Xv: $i] :
! [Xx: $i] : ( cP @ Xx @ Xv )
& ! [Xx: $i] :
( ( cS @ Xx )
=> ? [Xy: $i] : ( cQ @ Xy @ Xx ) )
& ! [Xx: $i,Xy: $i] :
( ( cP @ Xx @ Xy )
=> ~ ( cQ @ Xx @ Xy ) ) )
=> ? [Xu: $i] :
~ ( cS @ Xu ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ? [Xv: $i] :
! [Xx: $i] : ( cP @ Xx @ Xv ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: $i] :
( ( cS @ Xx )
=> ? [Xy: $i] : ( cQ @ Xy @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( cP @ Xx @ Xy )
=> ~ ( cQ @ Xx @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ? [Xu: $i] :
~ ( cS @ Xu ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ~ ? [Xu: $i] :
~ ( cS @ Xu ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [Xu: $i] : ( cS @ Xu ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(11,plain,
( ( ( ( cP @ sK4_Xx @ sK5_SY15 )
& ( cQ @ sK4_Xx @ sK5_SY15 ) )
| ( ( cS @ sK3_Xx )
& ! [SY14: $i] :
~ ( cQ @ SY14 @ sK3_Xx ) )
| ! [Xv: $i] :
~ ( cP @ ( sK2_Xx @ Xv ) @ Xv )
| ~ ( cS @ sK1_Xu ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(12,plain,
( ( ! [SY16: $i] : ( cP @ SY16 @ sK6_Xv ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(13,plain,
( ( ! [Xx: $i] :
( ~ ( cS @ Xx )
| ( cQ @ ( sK7_Xy @ Xx ) @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(14,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( cP @ Xx @ Xy )
| ~ ( cQ @ Xx @ Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(15,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( cP @ Xx @ Xy )
| ~ ( cQ @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [Xx: $i] :
( ~ ( cS @ Xx )
| ( cQ @ ( sK7_Xy @ Xx ) @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(17,plain,
( ( ! [SY16: $i] : ( cP @ SY16 @ sK6_Xv ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(18,plain,
( ( ( ( cP @ sK4_Xx @ sK5_SY15 )
& ( cQ @ sK4_Xx @ sK5_SY15 ) )
| ( ( cS @ sK3_Xx )
& ! [SY14: $i] :
~ ( cQ @ SY14 @ sK3_Xx ) )
| ! [Xv: $i] :
~ ( cP @ ( sK2_Xx @ Xv ) @ Xv )
| ~ ( cS @ sK1_Xu ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(19,plain,
( ( ! [Xu: $i] : ( cS @ Xu ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(20,plain,
( ( ~ ( ~ ( cP @ sK4_Xx @ sK5_SY15 )
| ~ ( cQ @ sK4_Xx @ sK5_SY15 ) )
| ~ ( ~ ( cS @ sK3_Xx )
| ~ ! [SX0: $i] :
~ ( cQ @ SX0 @ sK3_Xx ) )
| ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 )
| ~ ( cS @ sK1_Xu ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(21,plain,
! [SV1: $i] :
( ( ! [SY17: $i] :
( ~ ( cP @ SV1 @ SY17 )
| ~ ( cQ @ SV1 @ SY17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(22,plain,
! [SV2: $i] :
( ( ~ ( cS @ SV2 )
| ( cQ @ ( sK7_Xy @ SV2 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(23,plain,
! [SV3: $i] :
( ( cP @ SV3 @ sK6_Xv )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(24,plain,
! [SV4: $i] :
( ( cS @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(25,plain,
( ( ( ~ ( ~ ( cP @ sK4_Xx @ sK5_SY15 )
| ~ ( cQ @ sK4_Xx @ sK5_SY15 ) )
| ~ ( ~ ( cS @ sK3_Xx )
| ~ ! [SX0: $i] :
~ ( cQ @ SX0 @ sK3_Xx ) )
| ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(26,plain,
! [SV5: $i,SV1: $i] :
( ( ~ ( cP @ SV1 @ SV5 )
| ~ ( cQ @ SV1 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV2: $i] :
( ( ( ~ ( cS @ SV2 ) )
= $true )
| ( ( cQ @ ( sK7_Xy @ SV2 ) @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(28,plain,
( ( ( ~ ( ~ ( cP @ sK4_Xx @ sK5_SY15 )
| ~ ( cQ @ sK4_Xx @ sK5_SY15 ) ) )
= $true )
| ( ( ~ ( ~ ( cS @ sK3_Xx )
| ~ ! [SX0: $i] :
~ ( cQ @ SX0 @ sK3_Xx ) )
| ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV5: $i,SV1: $i] :
( ( ( ~ ( cP @ SV1 @ SV5 ) )
= $true )
| ( ( ~ ( cQ @ SV1 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV2: $i] :
( ( ( cS @ SV2 )
= $false )
| ( ( cQ @ ( sK7_Xy @ SV2 ) @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
( ( ( ~ ( cP @ sK4_Xx @ sK5_SY15 )
| ~ ( cQ @ sK4_Xx @ sK5_SY15 ) )
= $false )
| ( ( ~ ( ~ ( cS @ sK3_Xx )
| ~ ! [SX0: $i] :
~ ( cQ @ SX0 @ sK3_Xx ) )
| ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV5: $i,SV1: $i] :
( ( ( cP @ SV1 @ SV5 )
= $false )
| ( ( ~ ( cQ @ SV1 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(33,plain,
( ( ( ~ ( cP @ sK4_Xx @ sK5_SY15 ) )
= $false )
| ( ( ~ ( ~ ( cS @ sK3_Xx )
| ~ ! [SX0: $i] :
~ ( cQ @ SX0 @ sK3_Xx ) )
| ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(34,plain,
( ( ( ~ ( cQ @ sK4_Xx @ sK5_SY15 ) )
= $false )
| ( ( ~ ( ~ ( cS @ sK3_Xx )
| ~ ! [SX0: $i] :
~ ( cQ @ SX0 @ sK3_Xx ) )
| ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(35,plain,
! [SV5: $i,SV1: $i] :
( ( ( cQ @ SV1 @ SV5 )
= $false )
| ( ( cP @ SV1 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(36,plain,
( ( ( cP @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( ~ ( cS @ sK3_Xx )
| ~ ! [SX0: $i] :
~ ( cQ @ SX0 @ sK3_Xx ) )
| ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(37,plain,
( ( ( cQ @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( ~ ( cS @ sK3_Xx )
| ~ ! [SX0: $i] :
~ ( cQ @ SX0 @ sK3_Xx ) )
| ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(38,plain,
( ( ( ~ ( ~ ( cS @ sK3_Xx )
| ~ ! [SX0: $i] :
~ ( cQ @ SX0 @ sK3_Xx ) ) )
= $true )
| ( ( ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( cP @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(39,plain,
( ( ( ~ ( ~ ( cS @ sK3_Xx )
| ~ ! [SX0: $i] :
~ ( cQ @ SX0 @ sK3_Xx ) ) )
= $true )
| ( ( ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( cQ @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(40,plain,
( ( ( ~ ( cS @ sK3_Xx )
| ~ ! [SX0: $i] :
~ ( cQ @ SX0 @ sK3_Xx ) )
= $false )
| ( ( ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( cP @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(41,plain,
( ( ( ~ ( cS @ sK3_Xx )
| ~ ! [SX0: $i] :
~ ( cQ @ SX0 @ sK3_Xx ) )
= $false )
| ( ( ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( cQ @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
( ( ( ~ ( cS @ sK3_Xx ) )
= $false )
| ( ( ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( cP @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(43,plain,
( ( ( ~ ! [SX0: $i] :
~ ( cQ @ SX0 @ sK3_Xx ) )
= $false )
| ( ( ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( cP @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(44,plain,
( ( ( ~ ( cS @ sK3_Xx ) )
= $false )
| ( ( ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( cQ @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(45,plain,
( ( ( ~ ! [SX0: $i] :
~ ( cQ @ SX0 @ sK3_Xx ) )
= $false )
| ( ( ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( cQ @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(46,plain,
( ( ( cS @ sK3_Xx )
= $true )
| ( ( ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( cP @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(47,plain,
( ( ( ! [SX0: $i] :
~ ( cQ @ SX0 @ sK3_Xx ) )
= $true )
| ( ( ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( cP @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(48,plain,
( ( ( cS @ sK3_Xx )
= $true )
| ( ( ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( cQ @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(49,plain,
( ( ( ! [SX0: $i] :
~ ( cQ @ SX0 @ sK3_Xx ) )
= $true )
| ( ( ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( cQ @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(50,plain,
! [SV6: $i] :
( ( ( ~ ( cP @ ( sK2_Xx @ SV6 ) @ SV6 ) )
= $true )
| ( ( cS @ sK3_Xx )
= $true )
| ( ( cP @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV7: $i] :
( ( ( ~ ( cQ @ SV7 @ sK3_Xx ) )
= $true )
| ( ( ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( cP @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV8: $i] :
( ( ( ~ ( cP @ ( sK2_Xx @ SV8 ) @ SV8 ) )
= $true )
| ( ( cS @ sK3_Xx )
= $true )
| ( ( cQ @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV9: $i] :
( ( ( ~ ( cQ @ SV9 @ sK3_Xx ) )
= $true )
| ( ( ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( cQ @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV6: $i] :
( ( ( cP @ ( sK2_Xx @ SV6 ) @ SV6 )
= $false )
| ( ( cS @ sK3_Xx )
= $true )
| ( ( cP @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV7: $i] :
( ( ( cQ @ SV7 @ sK3_Xx )
= $false )
| ( ( ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( cP @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV8: $i] :
( ( ( cP @ ( sK2_Xx @ SV8 ) @ SV8 )
= $false )
| ( ( cS @ sK3_Xx )
= $true )
| ( ( cQ @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV9: $i] :
( ( ( cQ @ SV9 @ sK3_Xx )
= $false )
| ( ( ! [SX0: $i] :
~ ( cP @ ( sK2_Xx @ SX0 ) @ SX0 ) )
= $true )
| ( ( cQ @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV6: $i] :
( ( ( cS @ sK1_Xu )
= $false )
| ( ( cP @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( cS @ sK3_Xx )
= $true )
| ( ( cP @ ( sK2_Xx @ SV6 ) @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(59,plain,
! [SV7: $i,SV10: $i] :
( ( ( ~ ( cP @ ( sK2_Xx @ SV10 ) @ SV10 ) )
= $true )
| ( ( cQ @ SV7 @ sK3_Xx )
= $false )
| ( ( cP @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(60,plain,
! [SV8: $i] :
( ( ( cS @ sK1_Xu )
= $false )
| ( ( cQ @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( cS @ sK3_Xx )
= $true )
| ( ( cP @ ( sK2_Xx @ SV8 ) @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV9: $i,SV11: $i] :
( ( ( ~ ( cP @ ( sK2_Xx @ SV11 ) @ SV11 ) )
= $true )
| ( ( cQ @ SV9 @ sK3_Xx )
= $false )
| ( ( cQ @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV7: $i,SV10: $i] :
( ( ( cP @ ( sK2_Xx @ SV10 ) @ SV10 )
= $false )
| ( ( cQ @ SV7 @ sK3_Xx )
= $false )
| ( ( cP @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(63,plain,
! [SV9: $i,SV11: $i] :
( ( ( cP @ ( sK2_Xx @ SV11 ) @ SV11 )
= $false )
| ( ( cQ @ SV9 @ sK3_Xx )
= $false )
| ( ( cQ @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( ~ ( cS @ sK1_Xu ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV10: $i,SV7: $i] :
( ( ( cS @ sK1_Xu )
= $false )
| ( ( cP @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( cQ @ SV7 @ sK3_Xx )
= $false )
| ( ( cP @ ( sK2_Xx @ SV10 ) @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(65,plain,
! [SV11: $i,SV9: $i] :
( ( ( cS @ sK1_Xu )
= $false )
| ( ( cQ @ sK4_Xx @ sK5_SY15 )
= $true )
| ( ( cQ @ SV9 @ sK3_Xx )
= $false )
| ( ( cP @ ( sK2_Xx @ SV11 ) @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(66,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,65,64,60,58,35,30,24]) ).
thf(67,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO382^5 : 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
% 0.09/0.16 % Computer : n006.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Oct 6 17:38:48 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
% 0.09/0.20
% 0.09/0.20 No.of.Axioms: 0
% 0.09/0.20
% 0.09/0.20 Length.of.Defs: 0
% 0.09/0.20
% 0.09/0.20 Contains.Choice.Funs: false
% 0.09/0.20 .
% 0.09/0.20
% 0.09/0.20 ********************************
% 0.09/0.20 * All subproblems solved! *
% 0.09/0.20 ********************************
% 0.09/0.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:66,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.20
% 0.09/0.20 %**** Beginning of derivation protocol ****
% 0.09/0.20 % SZS output start CNFRefutation
% See solution above
% 0.09/0.20
% 0.09/0.20 %**** End of derivation protocol ****
% 0.09/0.20 %**** no. of clauses in derivation: 67 ****
% 0.09/0.20 %**** clause counter: 66 ****
% 0.09/0.20
% 0.09/0.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:66,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------