%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV405^5 : 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 : n012.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 10:50:03 AM UTC 2026
% Result : Theorem 0.00s 0.13s
% Output : CNFRefutation 0.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 1
% Syntax : Number of formulae : 43 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 195 ( 73 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 225 ( 51 ~; 56 |; 2 &; 112 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 4 ^; 36 !; 4 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cA,type,
cA: $o ).
thf(tp_sK1_V,type,
sK1_V: ( $i > $o ) > $i ).
thf(1,conjecture,
? [U: $i > $o] :
! [V: $i] :
( ( U @ V )
<=> cA ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCOMP1) ).
thf(2,negated_conjecture,
( ( ? [U: $i > $o] :
! [V: $i] :
( ( U @ V )
<=> cA ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [U: $i > $o] :
! [V: $i] :
( ( U @ V )
<=> cA ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ? [U: $i > $o] :
! [V: $i] :
( ( U @ V )
<=> cA ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [U: $i > $o] :
( ( ~ ( U @ ( sK1_V @ U ) )
| ~ cA )
& ( ( U @ ( sK1_V @ U ) )
| cA ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [U: $i > $o] :
( ( ~ ( U @ ( sK1_V @ U ) )
| ~ cA )
& ( ( U @ ( sK1_V @ U ) )
| cA ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SX0: $i > $o] :
~ ( ~ ( ~ ( SX0 @ ( sK1_V @ SX0 ) )
| ~ cA )
| ~ ( ( SX0 @ ( sK1_V @ SX0 ) )
| cA ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
! [SV1: $i > $o] :
( ( ~ ( ~ ( ~ ( SV1 @ ( sK1_V @ SV1 ) )
| ~ cA )
| ~ ( ( SV1 @ ( sK1_V @ SV1 ) )
| cA ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7]) ).
thf(9,plain,
! [SV1: $i > $o] :
( ( ~ ( ~ ( SV1 @ ( sK1_V @ SV1 ) )
| ~ cA )
| ~ ( ( SV1 @ ( sK1_V @ SV1 ) )
| cA ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: $i > $o] :
( ( ~ ( ~ ( SV1 @ ( sK1_V @ SV1 ) )
| ~ cA ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[9]) ).
thf(11,plain,
! [SV1: $i > $o] :
( ( ~ ( ( SV1 @ ( sK1_V @ SV1 ) )
| cA ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i > $o] :
( ( ~ ( SV1 @ ( sK1_V @ SV1 ) )
| ~ cA )
= $true ),
inference(extcnf_not_neg,[status(thm)],[10]) ).
thf(13,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ ( sK1_V @ SV1 ) )
| cA )
= $true ),
inference(extcnf_not_neg,[status(thm)],[11]) ).
thf(14,plain,
! [SV1: $i > $o] :
( ( ( ~ ( SV1 @ ( sK1_V @ SV1 ) ) )
= $true )
| ( ( ~ cA ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ ( sK1_V @ SV1 ) )
= $true )
| ( cA = $true ) ),
inference(extcnf_or_pos,[status(thm)],[13]) ).
thf(16,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ ( sK1_V @ SV1 ) )
= $false )
| ( ( ~ cA ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(17,plain,
! [SV1: $i > $o] :
( ( cA = $false )
| ( ( SV1 @ ( sK1_V @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( $false = $true )
| ( cA = $true ) ),
inference(prim_subst,[status(thm)],[15:[bind(SV1,$thf( ^ [SV4: $i] : $false ))]]) ).
thf(20,plain,
! [SV3: $i > $o] :
( ( ( ~ ( SV3
@ ( sK1_V
@ ^ [SX0: $i] :
~ ( SV3 @ SX0 ) ) ) )
= $true )
| ( cA = $true ) ),
inference(prim_subst,[status(thm)],[15:[bind(SV1,$thf( ^ [SV2: $i] : ~ ( SV3 @ SV2 ) ))]]) ).
thf(21,plain,
( ( cA = $false )
| ( $true = $false ) ),
inference(prim_subst,[status(thm)],[17:[bind(SV1,$thf( ^ [SV5: $i] : $true ))]]) ).
thf(23,plain,
! [SV3: $i > $o] :
( ( cA = $false )
| ( ( ~ ( SV3
@ ( sK1_V
@ ^ [SX0: $i] :
~ ( SV3 @ SX0 ) ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[17:[bind(SV1,$thf( ^ [SV2: $i] : ~ ( SV3 @ SV2 ) ))]]) ).
thf(24,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ ( sK1_V @ SV1 ) )
= $true )
| ( ( ( SV1 @ ( sK1_V @ SV1 ) )
= cA )
= $false ) ),
inference(fac_restr,[status(thm)],[15]) ).
thf(25,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ ( sK1_V @ SV1 ) )
= $false )
| ( ( cA
= ( SV1 @ ( sK1_V @ SV1 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[17]) ).
thf(26,plain,
! [SV1: $i > $o] :
( ( ( ~ ( ( SV1 @ ( sK1_V @ SV1 ) )
| cA )
| ~ ( ~ ( SV1 @ ( sK1_V @ SV1 ) )
| ~ cA ) )
= $false )
| ( ( SV1 @ ( sK1_V @ SV1 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[24]) ).
thf(27,plain,
! [SV1: $i > $o] :
( ( ( ( SV1 @ ( sK1_V @ SV1 ) )
= cA )
= $false )
| ( ( SV1 @ ( sK1_V @ SV1 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[24]) ).
thf(28,plain,
! [SV1: $i > $o] :
( ( ( ~ ( cA
| ( SV1 @ ( sK1_V @ SV1 ) ) )
| ~ ( ~ cA
| ~ ( SV1 @ ( sK1_V @ SV1 ) ) ) )
= $false )
| ( ( SV1 @ ( sK1_V @ SV1 ) )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[25]) ).
thf(30,plain,
! [SV1: $i > $o] :
( ( ( ~ ( ( SV1 @ ( sK1_V @ SV1 ) )
| cA ) )
= $false )
| ( ( SV1 @ ( sK1_V @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(33,plain,
! [SV1: $i > $o] :
( ( ( ~ ( ~ cA
| ~ ( SV1 @ ( sK1_V @ SV1 ) ) ) )
= $false )
| ( ( SV1 @ ( sK1_V @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(34,plain,
! [SV1: $i > $o] :
( ( ( ( SV1 @ ( sK1_V @ SV1 ) )
| cA )
= $true )
| ( ( SV1 @ ( sK1_V @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(37,plain,
! [SV1: $i > $o] :
( ( ( ~ cA
| ~ ( SV1 @ ( sK1_V @ SV1 ) ) )
= $true )
| ( ( SV1 @ ( sK1_V @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(38,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ ( sK1_V @ SV1 ) )
= $true )
| ( cA = $true )
| ( ( SV1 @ ( sK1_V @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV1: $i > $o] :
( ( ( ~ cA ) = $true )
| ( ( ~ ( SV1 @ ( sK1_V @ SV1 ) ) )
= $true )
| ( ( SV1 @ ( sK1_V @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV1: $i > $o] :
( ( cA = $false )
| ( ( ~ ( SV1 @ ( sK1_V @ SV1 ) ) )
= $true )
| ( ( SV1 @ ( sK1_V @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ ( sK1_V @ SV1 ) )
= $false )
| ( cA = $false )
| ( ( SV1 @ ( sK1_V @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(46,plain,
cA = $true,
inference(extuni,[status(esa)],[27:[bind(SV1,$thf( ^ [SX0: $i] : cA ))]]) ).
thf(47,plain,
! [SV3: $i > $o] :
( ( ( SV3
@ ( sK1_V
@ ^ [SX0: $i] :
~ ( SV3 @ SX0 ) ) )
= $false )
| ( cA = $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(48,plain,
! [SV3: $i > $o] :
( ( ( SV3
@ ( sK1_V
@ ^ [SX0: $i] :
~ ( SV3 @ SX0 ) ) )
= $true )
| ( cA = $false ) ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(49,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ ( sK1_V @ SV1 ) )
= $true )
| ( cA = $true ) ),
inference(sim,[status(thm)],[38]) ).
thf(50,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ ( sK1_V @ SV1 ) )
= $false )
| ( cA = $false ) ),
inference(sim,[status(thm)],[45]) ).
thf(51,plain,
cA = $true,
inference(sim,[status(thm)],[19]) ).
thf(52,plain,
cA = $false,
inference(sim,[status(thm)],[21]) ).
thf(53,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[15,52,51,50,49,48,47,46,17]) ).
thf(54,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEV405^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.09 % Computer : n012.cluster.edu
% 0.00/0.09 % Model : x86_64 x86_64
% 0.00/0.09 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.09 % Memory : 8046.5625MB
% 0.00/0.09 % OS : Linux 6.8.0-71-generic
% 0.00/0.09 % CPULimit : 300
% 0.00/0.09 % WCLimit : 300
% 0.00/0.09 % DateTime : Tue Oct 6 15:46:01 UTC 2026
% 0.00/0.09 % CPUTime :
% 0.00/0.09 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.13
% 0.00/0.13 No.of.Axioms: 0
% 0.00/0.13
% 0.00/0.13 Length.of.Defs: 0
% 0.00/0.13
% 0.00/0.13 Contains.Choice.Funs: false
% 0.00/0.13
% 0.00/0.13 ********************************
% 0.00/0.13 * All subproblems solved! *
% 0.00/0.13 ********************************
% 0.00/0.13 % SZS status Theorem for /export/starexec/sandbox2/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:53,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.00/0.13
% 0.00/0.13 %**** Beginning of derivation protocol ****
% 0.00/0.13 % SZS output start CNFRefutation
% See solution above
% 0.00/0.13
% 0.00/0.13 %**** End of derivation protocol ****
% 0.00/0.13 %**** no. of clauses in derivation: 43 ****
% 0.00/0.13 %**** clause counter: 53 ****
% 0.00/0.13
% 0.00/0.13 % SZS status Theorem for /export/starexec/sandbox2/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:53,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------