%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO253^5 : 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 : n026.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 11:07:56 AM UTC 2026
% Result : Theorem 0.07s 0.21s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 1
% Syntax : Number of formulae : 46 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 315 ( 84 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 251 ( 130 ~; 91 |; 10 &; 20 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 1 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 0 ^; 6 !; 4 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_p,type,
p: $o ).
thf(1,conjecture,
? [Xf: $o > $o] :
( ( Xf
@ ( p
& ~ p ) )
& ~ ( Xf
@ ( p
| ~ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM124) ).
thf(2,negated_conjecture,
( ( ? [Xf: $o > $o] :
( ( Xf
@ ( p
& ~ p ) )
& ~ ( Xf
@ ( p
| ~ p ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [Xf: $o > $o] :
( ( Xf
@ ( p
& ~ p ) )
& ~ ( Xf
@ ( p
| ~ p ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ? [Xf: $o > $o] :
( ( Xf
@ ( p
& ~ p ) )
& ~ ( Xf
@ ( p
| ~ p ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xf: $o > $o] :
( ~ ( Xf
@ ( p
& ~ p ) )
| ( Xf
@ ( p
| ~ p ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [Xf: $o > $o] :
( ~ ( Xf
@ ( p
& ~ p ) )
| ( Xf
@ ( p
| ~ p ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SX0: $o > $o] :
( ~ ( SX0
@ ~ ( ~ p
| ~ ~ p ) )
| ( SX0
@ ( p
| ~ p ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
! [SV1: $o > $o] :
( ( ~ ( SV1
@ ~ ( ~ p
| ~ ~ p ) )
| ( SV1
@ ( p
| ~ p ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[7]) ).
thf(9,plain,
( ( ~ $true
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ $false
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ~ ( ~ p
| ~ ~ p )
| p
| ~ p )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[7]) ).
thf(12,plain,
( ( ~ ~ ~ ( ~ p
| ~ ~ p )
| ~ ( p
| ~ p ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[7]) ).
thf(13,plain,
! [SV1: $o > $o] :
( ( ( ~ ( SV1
@ ~ ( ~ p
| ~ ~ p ) ) )
= $true )
| ( ( SV1
@ ( p
| ~ p ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8]) ).
thf(14,plain,
( ( ( ~ $true ) = $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[9]) ).
thf(15,plain,
( ( ( ~ $false ) = $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[10]) ).
thf(16,plain,
( ( ( ~ ~ ( ~ p
| ~ ~ p ) )
= $true )
| ( ( p
| ~ p )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[11]) ).
thf(17,plain,
( ( ( ~ ~ ~ ( ~ p
| ~ ~ p ) )
= $true )
| ( ( ~ ( p
| ~ p ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(18,plain,
! [SV1: $o > $o] :
( ( ( SV1
@ ~ ( ~ p
| ~ ~ p ) )
= $false )
| ( ( SV1
@ ( p
| ~ p ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(19,plain,
( ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(20,plain,
( ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(21,plain,
( ( ( ~ ( ~ p
| ~ ~ p ) )
= $false )
| ( ( p
| ~ p )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(22,plain,
( ( ( ~ ~ ( ~ p
| ~ ~ p ) )
= $false )
| ( ( ~ ( p
| ~ p ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(23,plain,
( ( ( ~ p
| ~ ~ p )
= $true )
| ( ( p
| ~ p )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(24,plain,
( ( ( ~ ( ~ p
| ~ ~ p ) )
= $true )
| ( ( ~ ( p
| ~ p ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(25,plain,
( ( ( ~ p ) = $true )
| ( ( ~ ~ p )
= $true )
| ( ( p
| ~ p )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(26,plain,
( ( ( ~ p
| ~ ~ p )
= $false )
| ( ( ~ ( p
| ~ p ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(27,plain,
( ( p = $false )
| ( ( ~ ~ p )
= $true )
| ( ( p
| ~ p )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(28,plain,
( ( ( ~ p ) = $false )
| ( ( ~ ( p
| ~ p ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(29,plain,
( ( ( ~ ~ p )
= $false )
| ( ( ~ ( p
| ~ p ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
( ( ( ~ p ) = $false )
| ( p = $false )
| ( ( p
| ~ p )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
( ( p = $true )
| ( ( ~ ( p
| ~ p ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(32,plain,
( ( ( ~ p ) = $true )
| ( ( ~ ( p
| ~ p ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(33,plain,
( ( p = $true )
| ( p = $false )
| ( ( p
| ~ p )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(34,plain,
( ( ( p
| ~ p )
= $false )
| ( p = $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(35,plain,
( ( p = $false )
| ( ( ~ ( p
| ~ p ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(36,plain,
( ( p = $true )
| ( ( ~ p ) = $true )
| ( p = $false )
| ( p = $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(37,plain,
( ( p = $false )
| ( p = $true ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(38,plain,
( ( ( ~ p ) = $false )
| ( p = $true ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(39,plain,
( ( ( p
| ~ p )
= $false )
| ( p = $false ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(40,plain,
( ( p = $false )
| ( p = $true )
| ( p = $false )
| ( p = $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(41,plain,
( ( p = $true )
| ( p = $true ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(42,plain,
( ( p = $false )
| ( p = $false ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(43,plain,
( ( ( ~ p ) = $false )
| ( p = $false ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(44,plain,
( ( p = $true )
| ( p = $false ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(45,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,44,42,41,40,37,20,19]) ).
thf(46,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO253^5 : 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
% 0.07/0.18 % Computer : n026.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 17:37:06 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.21
% 0.07/0.21 No.of.Axioms: 0
% 0.07/0.21
% 0.07/0.21 Length.of.Defs: 0
% 0.07/0.21
% 0.07/0.21 Contains.Choice.Funs: false
% 0.07/0.21
% 0.07/0.21 ********************************
% 0.07/0.21 * All subproblems solved! *
% 0.07/0.21 ********************************
% 0.07/0.21 % 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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:45,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.21
% 0.07/0.21 %**** Beginning of derivation protocol ****
% 0.07/0.21 % SZS output start CNFRefutation
% See solution above
% 0.07/0.21
% 0.07/0.21 %**** End of derivation protocol ****
% 0.07/0.21 %**** no. of clauses in derivation: 46 ****
% 0.07/0.21 %**** clause counter: 45 ****
% 0.07/0.21
% 0.07/0.21 % 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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:45,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------