%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL733^5 : 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 10:30:07 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 1
% Syntax : Number of formulae : 40 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 185 ( 55 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 294 ( 74 ~; 47 |; 6 &; 145 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 74 ( 74 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 88 ( 0 ^; 62 !; 26 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_b,type,
b: $tType ).
thf(tp_sK1_Xp,type,
sK1_Xp: ( ( b > $o ) > b ) > b > $o ).
thf(tp_sK2_SY10,type,
sK2_SY10: ( ( b > $o ) > b ) > b ).
thf(tp_sK3_Xf,type,
sK3_Xf: ( b > $o ) > b ).
thf(tp_sK4_Xx,type,
sK4_Xx: b > $o ).
thf(tp_sK5_SY13,type,
sK5_SY13: b ).
thf(tp_sK6_REN,type,
sK6_REN: $o ).
thf(1,conjecture,
( ! [Xr: ( b > $o ) > b > $o] :
( ! [Xx: b > $o] :
? [Xy: b] :
( ? [Xx0: b] : ( Xx @ Xx0 )
=> ( Xx @ Xy ) )
=> ? [Xf: ( b > $o ) > b] :
! [Xx: b > $o] :
( ? [Xx0: b] : ( Xx @ Xx0 )
=> ( Xx @ ( Xf @ Xx ) ) ) )
=> ? [Xj: ( b > $o ) > b] :
! [Xp: b > $o] :
( ? [Xz: b] : ( Xp @ Xz )
=> ( Xp @ ( Xj @ Xp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5310_SUB4) ).
thf(2,negated_conjecture,
( ( ! [Xr: ( b > $o ) > b > $o] :
( ! [Xx: b > $o] :
? [Xy: b] :
( ? [Xx0: b] : ( Xx @ Xx0 )
=> ( Xx @ Xy ) )
=> ? [Xf: ( b > $o ) > b] :
! [Xx: b > $o] :
( ? [Xx0: b] : ( Xx @ Xx0 )
=> ( Xx @ ( Xf @ Xx ) ) ) )
=> ? [Xj: ( b > $o ) > b] :
! [Xp: b > $o] :
( ? [Xz: b] : ( Xp @ Xz )
=> ( Xp @ ( Xj @ Xp ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xr: ( b > $o ) > b > $o] :
( ! [Xx: b > $o] :
? [Xy: b] :
( ? [Xx0: b] : ( Xx @ Xx0 )
=> ( Xx @ Xy ) )
=> ? [Xf: ( b > $o ) > b] :
! [Xx: b > $o] :
( ? [Xx0: b] : ( Xx @ Xx0 )
=> ( Xx @ ( Xf @ Xx ) ) ) )
=> ? [Xj: ( b > $o ) > b] :
! [Xp: b > $o] :
( ? [Xz: b] : ( Xp @ Xz )
=> ( Xp @ ( Xj @ Xp ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xr: ( b > $o ) > b > $o] :
( ! [Xx: b > $o] :
? [Xy: b] :
( ? [Xx0: b] : ( Xx @ Xx0 )
=> ( Xx @ Xy ) )
=> ? [Xf: ( b > $o ) > b] :
! [Xx: b > $o] :
( ? [Xx0: b] : ( Xx @ Xx0 )
=> ( Xx @ ( Xf @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ? [Xj: ( b > $o ) > b] :
! [Xp: b > $o] :
( ? [Xz: b] : ( Xp @ Xz )
=> ( Xp @ ( Xj @ Xp ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ? [Xj: ( b > $o ) > b] :
! [Xp: b > $o] :
( ? [Xz: b] : ( Xp @ Xz )
=> ( Xp @ ( Xj @ Xp ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [Xj: ( b > $o ) > b] :
( ( sK1_Xp @ Xj @ ( sK2_SY10 @ Xj ) )
& ~ ( sK1_Xp @ Xj @ ( Xj @ ( sK1_Xp @ Xj ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ( sK6_REN
| ! [SY11: b > $o] :
( ! [Xx0: b] :
~ ( SY11 @ Xx0 )
| ( SY11 @ ( sK3_Xf @ SY11 ) ) ) )
& ( sK6_REN
=> ( ( sK4_Xx @ sK5_SY13 )
& ! [SY14: b] :
~ ( sK4_Xx @ SY14 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ( sK6_REN
| ! [SY11: b > $o] :
( ! [Xx0: b] :
~ ( SY11 @ Xx0 )
| ( SY11 @ ( sK3_Xf @ SY11 ) ) ) )
& ( sK6_REN
=> ( ( sK4_Xx @ sK5_SY13 )
& ! [SY14: b] :
~ ( sK4_Xx @ SY14 ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [Xj: ( b > $o ) > b] :
( ( sK1_Xp @ Xj @ ( sK2_SY10 @ Xj ) )
& ~ ( sK1_Xp @ Xj @ ( Xj @ ( sK1_Xp @ Xj ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ( ~ ( sK6_REN
| ! [SX0: b > $o] :
( ! [SX1: b] :
~ ( SX0 @ SX1 )
| ( SX0 @ ( sK3_Xf @ SX0 ) ) ) )
| ~ ( ~ sK6_REN
| ~ ( ~ ( sK4_Xx @ sK5_SY13 )
| ~ ! [SX0: b] :
~ ( sK4_Xx @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [SX0: ( b > $o ) > b] :
~ ( ~ ( sK1_Xp @ SX0 @ ( sK2_SY10 @ SX0 ) )
| ~ ~ ( sK1_Xp @ SX0 @ ( SX0 @ ( sK1_Xp @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ( sK6_REN
| ! [SX0: b > $o] :
( ! [SX1: b] :
~ ( SX0 @ SX1 )
| ( SX0 @ ( sK3_Xf @ SX0 ) ) ) )
| ~ ( ~ sK6_REN
| ~ ( ~ ( sK4_Xx @ sK5_SY13 )
| ~ ! [SX0: b] :
~ ( sK4_Xx @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV1: ( b > $o ) > b] :
( ( ~ ( ~ ( sK1_Xp @ SV1 @ ( sK2_SY10 @ SV1 ) )
| ~ ~ ( sK1_Xp @ SV1 @ ( SV1 @ ( sK1_Xp @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( sK6_REN
| ! [SX0: b > $o] :
( ! [SX1: b] :
~ ( SX0 @ SX1 )
| ( SX0 @ ( sK3_Xf @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( ~ sK6_REN
| ~ ( ~ ( sK4_Xx @ sK5_SY13 )
| ~ ! [SX0: b] :
~ ( sK4_Xx @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV1: ( b > $o ) > b] :
( ( ~ ( sK1_Xp @ SV1 @ ( sK2_SY10 @ SV1 ) )
| ~ ~ ( sK1_Xp @ SV1 @ ( SV1 @ ( sK1_Xp @ SV1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( sK6_REN
| ! [SX0: b > $o] :
( ! [SX1: b] :
~ ( SX0 @ SX1 )
| ( SX0 @ ( sK3_Xf @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ sK6_REN
| ~ ( ~ ( sK4_Xx @ sK5_SY13 )
| ~ ! [SX0: b] :
~ ( sK4_Xx @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV1: ( b > $o ) > b] :
( ( ~ ( sK1_Xp @ SV1 @ ( sK2_SY10 @ SV1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV1: ( b > $o ) > b] :
( ( ~ ~ ( sK1_Xp @ SV1 @ ( SV1 @ ( sK1_Xp @ SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(22,plain,
( ( sK6_REN = $true )
| ( ( ! [SX0: b > $o] :
( ! [SX1: b] :
~ ( SX0 @ SX1 )
| ( SX0 @ ( sK3_Xf @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(23,plain,
( ( ( ~ sK6_REN ) = $true )
| ( ( ~ ( ~ ( sK4_Xx @ sK5_SY13 )
| ~ ! [SX0: b] :
~ ( sK4_Xx @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV1: ( b > $o ) > b] :
( ( sK1_Xp @ SV1 @ ( sK2_SY10 @ SV1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
! [SV1: ( b > $o ) > b] :
( ( ~ ( sK1_Xp @ SV1 @ ( SV1 @ ( sK1_Xp @ SV1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV2: b > $o] :
( ( ( ! [SY15: b] :
~ ( SV2 @ SY15 )
| ( SV2 @ ( sK3_Xf @ SV2 ) ) )
= $true )
| ( sK6_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
( ( sK6_REN = $false )
| ( ( ~ ( ~ ( sK4_Xx @ sK5_SY13 )
| ~ ! [SX0: b] :
~ ( sK4_Xx @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV1: ( b > $o ) > b] :
( ( sK1_Xp @ SV1 @ ( SV1 @ ( sK1_Xp @ SV1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV2: b > $o] :
( ( ( ! [SY15: b] :
~ ( SV2 @ SY15 ) )
= $true )
| ( ( SV2 @ ( sK3_Xf @ SV2 ) )
= $true )
| ( sK6_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( ( ~ ( sK4_Xx @ sK5_SY13 )
| ~ ! [SX0: b] :
~ ( sK4_Xx @ SX0 ) )
= $false )
| ( sK6_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV3: b,SV2: b > $o] :
( ( ( ~ ( SV2 @ SV3 ) )
= $true )
| ( ( SV2 @ ( sK3_Xf @ SV2 ) )
= $true )
| ( sK6_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(32,plain,
( ( ( ~ ( sK4_Xx @ sK5_SY13 ) )
= $false )
| ( sK6_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(33,plain,
( ( ( ~ ! [SX0: b] :
~ ( sK4_Xx @ SX0 ) )
= $false )
| ( sK6_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(34,plain,
! [SV3: b,SV2: b > $o] :
( ( ( SV2 @ SV3 )
= $false )
| ( ( SV2 @ ( sK3_Xf @ SV2 ) )
= $true )
| ( sK6_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(35,plain,
( ( ( sK4_Xx @ sK5_SY13 )
= $true )
| ( sK6_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(36,plain,
( ( ( ! [SX0: b] :
~ ( sK4_Xx @ SX0 ) )
= $true )
| ( sK6_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV4: b] :
( ( ( ~ ( sK4_Xx @ SV4 ) )
= $true )
| ( sK6_REN = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(38,plain,
! [SV4: b] :
( ( ( sK4_Xx @ SV4 )
= $false )
| ( sK6_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(39,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,38,35,34,28]) ).
thf(40,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL733^5 : 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
% 0.07/0.19 % Computer : n020.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 12:33:51 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.24
% 0.07/0.24 No.of.Axioms: 0
% 0.07/0.24
% 0.07/0.24 Length.of.Defs: 0
% 0.07/0.24
% 0.07/0.24 Contains.Choice.Funs: false
% 0.07/0.24 .
% 0.07/0.24
% 0.07/0.24 ********************************
% 0.07/0.24 * All subproblems solved! *
% 0.07/0.24 ********************************
% 0.07/0.24 % 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:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:39,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.24
% 0.07/0.24 %**** Beginning of derivation protocol ****
% 0.07/0.24 % SZS output start CNFRefutation
% See solution above
% 0.07/0.24
% 0.07/0.24 %**** End of derivation protocol ****
% 0.07/0.24 %**** no. of clauses in derivation: 40 ****
% 0.07/0.24 %**** clause counter: 39 ****
% 0.07/0.24
% 0.07/0.24 % 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:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:39,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------