%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV233^5 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 10:49:47 AM UTC 2026
% Result : Theorem 0.08s 0.20s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 47 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 229 ( 59 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 242 ( 52 ~; 34 |; 12 &; 117 @)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 0 ^; 48 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cD,type,
cD: $i > $o ).
thf(tp_cE,type,
cE: $i > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: $i > $o ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(1,conjecture,
! [Xx: $i > $o] :
( ! [Xx0: $i] :
( ( Xx @ Xx0 )
=> ( ( cD @ Xx0 )
& ( cE @ Xx0 ) ) )
=> ( ! [Xx0: $i] :
( ( Xx @ Xx0 )
=> ( cD @ Xx0 ) )
& ! [Xx0: $i] :
( ( Xx @ Xx0 )
=> ( cE @ Xx0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM46_pme) ).
thf(2,negated_conjecture,
( ( ! [Xx: $i > $o] :
( ! [Xx0: $i] :
( ( Xx @ Xx0 )
=> ( ( cD @ Xx0 )
& ( cE @ Xx0 ) ) )
=> ( ! [Xx0: $i] :
( ( Xx @ Xx0 )
=> ( cD @ Xx0 ) )
& ! [Xx0: $i] :
( ( Xx @ Xx0 )
=> ( cE @ Xx0 ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i > $o] :
( ! [Xx0: $i] :
( ( Xx @ Xx0 )
=> ( ( cD @ Xx0 )
& ( cE @ Xx0 ) ) )
=> ( ! [Xx0: $i] :
( ( Xx @ Xx0 )
=> ( cD @ Xx0 ) )
& ! [Xx0: $i] :
( ( Xx @ Xx0 )
=> ( cE @ Xx0 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY4: $i] :
( ( sK1_Xx @ SY4 )
=> ( ( cD @ SY4 )
& ( cE @ SY4 ) ) )
=> ( ! [SY5: $i] :
( ( sK1_Xx @ SY5 )
=> ( cD @ SY5 ) )
& ! [SY6: $i] :
( ( sK1_Xx @ SY6 )
=> ( cE @ SY6 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY4: $i] :
( ( sK1_Xx @ SY4 )
=> ( ( cD @ SY4 )
& ( cE @ SY4 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [SY5: $i] :
( ( sK1_Xx @ SY5 )
=> ( cD @ SY5 ) )
& ! [SY6: $i] :
( ( sK1_Xx @ SY6 )
=> ( cE @ SY6 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( ! [SY5: $i] :
( ( sK1_Xx @ SY5 )
=> ( cD @ SY5 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[6]) ).
thf(8,plain,
( ( ! [SY6: $i] :
( ( sK1_Xx @ SY6 )
=> ( cE @ SY6 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[6]) ).
thf(9,plain,
( ( ~ ! [SY5: $i] :
( ( sK1_Xx @ SY5 )
=> ( cD @ SY5 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ! [SY6: $i] :
( ( sK1_Xx @ SY6 )
=> ( cE @ SY6 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(11,plain,
( ( ! [SY4: $i] :
( ( sK1_Xx @ SY4 )
=> ( ( cD @ SY4 )
& ( cE @ SY4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(12,plain,
( ( ~ ! [SY5: $i] :
( ( sK1_Xx @ SY5 )
=> ( cD @ SY5 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK1_Xx @ SX0 )
| ( cD @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [SX0: $i] :
( ~ ( sK1_Xx @ SX0 )
| ~ ( ~ ( cD @ SX0 )
| ~ ( cE @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(15,plain,
( ( ! [SX0: $i] :
( ~ ( sK1_Xx @ SX0 )
| ( cD @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(16,plain,
! [SV1: $i] :
( ( ~ ( sK1_Xx @ SV1 )
| ~ ( ~ ( cD @ SV1 )
| ~ ( cE @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( sK1_Xx @ sK2_SX0 )
| ( cD @ sK2_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(18,plain,
! [SV1: $i] :
( ( ( ~ ( sK1_Xx @ SV1 ) )
= $true )
| ( ( ~ ( ~ ( cD @ SV1 )
| ~ ( cE @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ( sK1_Xx @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( cD @ sK2_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV1: $i] :
( ( ( sK1_Xx @ SV1 )
= $false )
| ( ( ~ ( ~ ( cD @ SV1 )
| ~ ( cE @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( sK1_Xx @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
! [SV1: $i] :
( ( ( ~ ( cD @ SV1 )
| ~ ( cE @ SV1 ) )
= $false )
| ( ( sK1_Xx @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(24,plain,
! [SV1: $i] :
( ( ( ~ ( cD @ SV1 ) )
= $false )
| ( ( sK1_Xx @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(25,plain,
! [SV1: $i] :
( ( ( ~ ( cE @ SV1 ) )
= $false )
| ( ( sK1_Xx @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(26,plain,
! [SV1: $i] :
( ( ( cD @ SV1 )
= $true )
| ( ( sK1_Xx @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(27,plain,
! [SV1: $i] :
( ( ( cE @ SV1 )
= $true )
| ( ( sK1_Xx @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(28,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,27,26,22]) ).
thf(29,plain,
( ( ! [SY4: $i] :
( ( sK1_Xx @ SY4 )
=> ( ( cD @ SY4 )
& ( cE @ SY4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(30,plain,
( ( ~ ! [SY6: $i] :
( ( sK1_Xx @ SY6 )
=> ( cE @ SY6 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(31,plain,
( ( ! [SX0: $i] :
( ~ ( sK1_Xx @ SX0 )
| ~ ( ~ ( cD @ SX0 )
| ~ ( cE @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(32,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK1_Xx @ SX0 )
| ( cE @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(33,plain,
! [SV2: $i] :
( ( ~ ( sK1_Xx @ SV2 )
| ~ ( ~ ( cD @ SV2 )
| ~ ( cE @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(34,plain,
( ( ! [SX0: $i] :
( ~ ( sK1_Xx @ SX0 )
| ( cE @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV2: $i] :
( ( ( ~ ( sK1_Xx @ SV2 ) )
= $true )
| ( ( ~ ( ~ ( cD @ SV2 )
| ~ ( cE @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(36,plain,
( ( ~ ( sK1_Xx @ sK3_SX0 )
| ( cE @ sK3_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[34]) ).
thf(37,plain,
! [SV2: $i] :
( ( ( sK1_Xx @ SV2 )
= $false )
| ( ( ~ ( ~ ( cD @ SV2 )
| ~ ( cE @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(38,plain,
( ( ~ ( sK1_Xx @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(39,plain,
( ( cE @ sK3_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(40,plain,
! [SV2: $i] :
( ( ( ~ ( cD @ SV2 )
| ~ ( cE @ SV2 ) )
= $false )
| ( ( sK1_Xx @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(41,plain,
( ( sK1_Xx @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(42,plain,
! [SV2: $i] :
( ( ( ~ ( cD @ SV2 ) )
= $false )
| ( ( sK1_Xx @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(43,plain,
! [SV2: $i] :
( ( ( ~ ( cE @ SV2 ) )
= $false )
| ( ( sK1_Xx @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(44,plain,
! [SV2: $i] :
( ( ( cD @ SV2 )
= $true )
| ( ( sK1_Xx @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(45,plain,
! [SV2: $i] :
( ( ( cE @ SV2 )
= $true )
| ( ( sK1_Xx @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(46,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[39,45,44,41]) ).
thf(47,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[46,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV233^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n002.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Oct 6 15:47:38 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.20
% 0.08/0.20 No.of.Axioms: 0
% 0.08/0.20
% 0.08/0.20 Length.of.Defs: 0
% 0.08/0.20
% 0.08/0.20 Contains.Choice.Funs: false
% 0.08/0.20
% 0.08/0.20 ********************************
% 0.08/0.20 * All subproblems solved! *
% 0.08/0.20 ********************************
% 0.08/0.20 % SZS status Theorem for /export/starexec/sandbox2/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:46,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.20
% 0.08/0.20 %**** Beginning of derivation protocol ****
% 0.08/0.20 % SZS output start CNFRefutation
% See solution above
% 0.08/0.20
% 0.08/0.20 %**** End of derivation protocol ****
% 0.08/0.20 %**** no. of clauses in derivation: 47 ****
% 0.08/0.20 %**** clause counter: 46 ****
% 0.08/0.20
% 0.08/0.20 % SZS status Theorem for /export/starexec/sandbox2/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:46,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------