%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV256^5 : 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 : n019.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 10:49:49 AM UTC 2026
% Result : Theorem 92.08s 15.66s
% Output : CNFRefutation 92.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 1
% Syntax : Number of formulae : 28 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 155 ( 39 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 228 ( 84 ~; 34 |; 8 &; 91 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 23 ^; 27 !; 6 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_cOPEN,type,
cOPEN: ( a > $o ) > $o ).
thf(tp_sK10_SY65,type,
sK10_SY65: a > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: ( ( a > $o ) > $o ) > a > $o ).
thf(tp_sK2_E,type,
sK2_E: ( ( a > $o ) > a > $o ) > a ).
thf(tp_sK3_E,type,
sK3_E: ( ( a > $o ) > a > ( a > $o ) > $o ) > a > $o ).
thf(tp_sK4_SV50,type,
sK4_SV50: ( ( a > $o ) > a > ( a > $o ) > $o ) > a > $o ).
thf(tp_sK5_SX0,type,
sK5_SX0: ( ( a > $o ) > a > a ) > a > $o ).
thf(tp_sK6_SX0,type,
sK6_SX0: ( ( a > $o ) > a > ( a > $o ) > $o ) > a > $o ).
thf(tp_sK7_SX0,type,
sK7_SX0: ( ( a > $o ) > a > a ) > a > $o ).
thf(tp_sK8_SX0,type,
sK8_SX0: ( ( a > $o ) > a > $o ) > a > $o ).
thf(tp_sK9_E,type,
sK9_E: a ).
thf(1,conjecture,
( ! [K: ( a > $o ) > $o] :
( ! [Xx: a > $o] :
( ( K @ Xx )
=> ( cOPEN @ Xx ) )
=> ( cOPEN
@ ^ [Xx: a] :
? [S: a > $o] :
( ( K @ S )
& ( S @ Xx ) ) ) )
=> ( cOPEN
@ ^ [Xx: a] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM625A_pme) ).
thf(2,negated_conjecture,
( ( ! [K: ( a > $o ) > $o] :
( ! [Xx: a > $o] :
( ( K @ Xx )
=> ( cOPEN @ Xx ) )
=> ( cOPEN
@ ^ [Xx: a] :
? [S: a > $o] :
( ( K @ S )
& ( S @ Xx ) ) ) )
=> ( cOPEN
@ ^ [Xx: a] : $false ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [K: ( a > $o ) > $o] :
( ! [Xx: a > $o] :
( ( K @ Xx )
=> ( cOPEN @ Xx ) )
=> ( cOPEN
@ ^ [Xx: a] :
? [S: a > $o] :
( ( K @ S )
& ( S @ Xx ) ) ) )
=> ( cOPEN
@ ^ [Xx: a] : $false ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [K: ( a > $o ) > $o] :
( ! [Xx: a > $o] :
( ( K @ Xx )
=> ( cOPEN @ Xx ) )
=> ( cOPEN
@ ^ [Xx: a] :
? [S: a > $o] :
( ( K @ S )
& ( S @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( cOPEN
@ ^ [Xx: a] : $false )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ( cOPEN
@ ^ [Xx: a] : $false ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [K: ( a > $o ) > $o] :
( ( ( K @ ( sK1_Xx @ K ) )
& ~ ( cOPEN @ ( sK1_Xx @ K ) ) )
| ( cOPEN
@ ^ [Xx: a] :
? [S: a > $o] :
( ( K @ S )
& ( S @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(8,plain,
( ( ! [K: ( a > $o ) > $o] :
( ( ( K @ ( sK1_Xx @ K ) )
& ~ ( cOPEN @ ( sK1_Xx @ K ) ) )
| ( cOPEN
@ ^ [Xx: a] :
? [S: a > $o] :
( ( K @ S )
& ( S @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(9,plain,
( ( ~ ( cOPEN
@ ^ [Xx: a] : $false ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( ! [SX0: ( a > $o ) > $o] :
( ~ ( ~ ( SX0 @ ( sK1_Xx @ SX0 ) )
| ~ ~ ( cOPEN @ ( sK1_Xx @ SX0 ) ) )
| ( cOPEN
@ ^ [SX1: a] :
~ ! [SX2: a > $o] :
~ ~ ( ~ ( SX0 @ SX2 )
| ~ ( SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(11,plain,
( ( cOPEN
@ ^ [Xx: a] : $false )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: ( a > $o ) > $o] :
( ( ~ ( ~ ( SV1 @ ( sK1_Xx @ SV1 ) )
| ~ ~ ( cOPEN @ ( sK1_Xx @ SV1 ) ) )
| ( cOPEN
@ ^ [SY5: a] :
~ ! [SY6: a > $o] :
~ ~ ( ~ ( SV1 @ SY6 )
| ~ ( SY6 @ SY5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
! [SV1: ( a > $o ) > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK1_Xx @ SV1 ) )
| ~ ~ ( cOPEN @ ( sK1_Xx @ SV1 ) ) ) )
= $true )
| ( ( cOPEN
@ ^ [SY5: a] :
~ ! [SY6: a > $o] :
~ ~ ( ~ ( SV1 @ SY6 )
| ~ ( SY6 @ SY5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(14,plain,
! [SV1: ( a > $o ) > $o] :
( ( ( ~ ( SV1 @ ( sK1_Xx @ SV1 ) )
| ~ ~ ( cOPEN @ ( sK1_Xx @ SV1 ) ) )
= $false )
| ( ( cOPEN
@ ^ [SY5: a] :
~ ! [SY6: a > $o] :
~ ~ ( ~ ( SV1 @ SY6 )
| ~ ( SY6 @ SY5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(15,plain,
! [SV1: ( a > $o ) > $o] :
( ( ( ~ ( SV1 @ ( sK1_Xx @ SV1 ) ) )
= $false )
| ( ( cOPEN
@ ^ [SY5: a] :
~ ! [SY6: a > $o] :
~ ~ ( ~ ( SV1 @ SY6 )
| ~ ( SY6 @ SY5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
! [SV1: ( a > $o ) > $o] :
( ( ( SV1 @ ( sK1_Xx @ SV1 ) )
= $true )
| ( ( cOPEN
@ ^ [SY5: a] :
~ ! [SY6: a > $o] :
~ ~ ( ~ ( SV1 @ SY6 )
| ~ ( SY6 @ SY5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(21,plain,
( ( $false = $true )
| ( ( cOPEN
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ $false
| ~ ( SX1 @ SX0 ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[17:[bind(SV1,$thf( ^ [SV4: a > $o] : $false ))]]) ).
thf(189,plain,
( ( cOPEN
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ $false
| ~ ( SX1 @ SX0 ) ) )
= $true ),
inference(sim,[status(thm)],[21]) ).
thf(190,plain,
( ( ( cOPEN
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ $false
| ~ ( SX1 @ SX0 ) ) )
= ( cOPEN
@ ^ [Xx: a] : $false ) )
= $false ),
inference(res,[status(thm)],[189,11]) ).
thf(191,plain,
( ( ( ~ ! [SY65: a > $o] :
~ ~ ( ~ $false
| ~ ( SY65 @ sK9_E ) ) )
= $true )
| ( $false = $true ) ),
inference(extuni,[status(esa)],[190]) ).
thf(194,plain,
( ( ( ! [SY65: a > $o] :
~ ~ ( ~ $false
| ~ ( SY65 @ sK9_E ) ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(196,plain,
( ( ( ~ ~ ( ~ $false
| ~ ( sK10_SY65 @ sK9_E ) ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_forall_neg,[status(esa)],[194]) ).
thf(198,plain,
( ( ( ~ ( ~ $false
| ~ ( sK10_SY65 @ sK9_E ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(200,plain,
( ( ( ~ $false
| ~ ( sK10_SY65 @ sK9_E ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(202,plain,
( ( ( ~ $false ) = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(205,plain,
( ( $false = $true )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(208,plain,
$false = $true,
inference(sim,[status(thm)],[205]) ).
thf(209,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV256^5 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.20 % Computer : n019.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Oct 6 15:43:46 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 92.08/15.66
% 92.08/15.66 No.of.Axioms: 0
% 92.08/15.66
% 92.08/15.66 Length.of.Defs: 0
% 92.08/15.66
% 92.08/15.66 Contains.Choice.Funs: false
% 92.08/15.66 .............eprover: CPU time limit exceeded, terminating
% 92.08/15.66
% 92.08/15.66
% 92.08/15.66 ********************************
% 92.08/15.66 * All subproblems solved! *
% 92.08/15.66 ********************************
% 92.08/15.66 % SZS status Theorem for /export/starexec/sandbox2/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:208,loop_count:2,foatp_calls:2,translation:fof_full)
% 92.08/15.66
% 92.08/15.66 %**** Beginning of derivation protocol ****
% 92.08/15.66 % SZS output start CNFRefutation
% See solution above
% 92.08/15.66
% 92.08/15.66 %**** End of derivation protocol ****
% 92.08/15.66 %**** no. of clauses in derivation: 28 ****
% 92.08/15.66 %**** clause counter: 208 ****
% 92.08/15.66
% 92.08/15.66 % SZS status Theorem for /export/starexec/sandbox2/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:208,loop_count:2,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------