%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO039^2 : TPTP v9.3.1. Released v4.1.0.
% 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 : n017.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 11:07:26 AM UTC 2026
% Result : Theorem 0.06s 0.28s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 29 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 231 ( 93 equ; 0 cnn)
% Maximal formula atoms : 3 ( 7 avg)
% Number of connectives : 156 ( 44 ~; 16 |; 0 &; 96 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 1 usr; 2 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_h,type,
h: $o > $i ).
thf(1,conjecture,
( ( h
@ ( ( h @ $false )
= ( h @ ~ $false ) ) )
= ( h @ $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',1) ).
thf(2,negated_conjecture,
( ( ( h
@ ( ( h @ $false )
= ( h @ ~ $false ) ) )
= ( h @ $false ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( h
@ ( ( h @ $false )
= ( h @ ~ $false ) ) )
= ( h @ $false ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ( h
@ ( ( h @ $false )
= ( h @ ~ $false ) ) )
!= ( h @ $false ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ( h
@ ( ( h @ $false )
= ( h @ ~ $false ) ) )
!= ( h @ $false ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(6,plain,
( ( ( h
@ ( ( h @ $false )
= ( h @ ~ $false ) ) )
= ( h @ $false ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5]) ).
thf(7,plain,
( ( ( ( h @ $false )
= ( h @ ~ $false ) )
= $true )
| ( $false = $true ) ),
inference(extuni,[status(esa)],[6]) ).
thf(9,plain,
( ( ( h @ $false )
= ( h @ ~ $false ) )
= $true ),
inference(sim,[status(thm)],[7]) ).
thf(13,plain,
( ( ( ( h @ $false )
= ( h @ ~ $false ) )
= ( ( h
@ ( ( h @ $false )
= ( h @ ~ $false ) ) )
= ( h @ $false ) ) )
= $false ),
inference(res,[status(thm)],[9,6]) ).
thf(15,plain,
( ( ( ~ $false ) = $false )
| ( ( ( h @ $false )
= ( h @ ~ $false ) )
= $false ) ),
inference(extuni,[status(esa)],[13]) ).
thf(16,plain,
( ( ( h @ ~ $false )
= ( h
@ ( ( h @ $false )
= ( h @ ~ $false ) ) ) )
= $false ),
inference(extuni,[status(esa)],[13]) ).
thf(19,plain,
( ( ( ( h @ ~ $false )
= ( h @ $false ) )
= $false )
| ( $false = $true )
| ( ( ( h @ $false )
= ( h @ ~ $false ) )
= $true ) ),
inference(extuni,[status(esa)],[13]) ).
thf(25,plain,
( ( ( ( h @ ~ $false )
= ( h @ $false ) )
= $false )
| ( ( ( h @ $false )
= ( h
@ ( ( h @ $false )
= ( h @ ~ $false ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[13]) ).
thf(32,plain,
( ( $false = $true )
| ( ( ( h @ $false )
= ( h @ ~ $false ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(34,plain,
( ( ( ( h @ ~ $false )
= ( h @ $false ) )
= $false )
| ( ( ( h @ $false )
= ( h @ ~ $false ) )
= $true ) ),
inference(sim,[status(thm)],[19]) ).
thf(35,plain,
( ( ( h @ $false )
= ( h @ ~ $false ) )
= $false ),
inference(sim,[status(thm)],[32]) ).
thf(36,plain,
( ( ( ( h @ ~ $false )
= ( h
@ ( ( h @ $false )
= ( h @ ~ $false ) ) ) )
= ( ( h @ $false )
= ( h @ ~ $false ) ) )
= $false ),
inference(res,[status(thm)],[16,9]) ).
thf(37,plain,
( ( ( ( h @ $false )
= ( h @ ~ $false ) )
= $true )
| ( $false = $true ) ),
inference(extuni,[status(esa)],[36]) ).
thf(39,plain,
( ( ( h
@ ( ( h @ $false )
= ( h @ ~ $false ) ) )
= ( h @ $false ) )
= $false ),
inference(extuni,[status(esa)],[36]) ).
thf(47,plain,
( ( ( ( h @ $false )
= ( h @ ~ $false ) )
= $false )
| ( ( ~ $false ) = $false )
| ( ( ( h @ ~ $false )
= ( h @ $false ) )
= $false ) ),
inference(extuni,[status(esa)],[36]) ).
thf(48,plain,
( ( ( ( h
@ ( ( h @ $false )
= ( h @ ~ $false ) ) )
= ( h @ ~ $false ) )
= $false )
| ( ( ( h @ ~ $false )
= ( h @ $false ) )
= $false ) ),
inference(extuni,[status(esa)],[36]) ).
thf(50,plain,
( ( ( ~ $false ) = $false )
| ( ( ( h @ $false )
= ( h @ ~ $false ) )
= $false ) ),
inference(extuni,[status(esa)],[16]) ).
thf(51,plain,
( ( $false = $true )
| ( ( ( h @ $false )
= ( h @ ~ $false ) )
= $false )
| ( ( ( h @ ~ $false )
= ( h @ $false ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(59,plain,
( ( $false = $true )
| ( ( ( h @ $false )
= ( h @ ~ $false ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(65,plain,
( ( ( ( h @ $false )
= ( h @ ~ $false ) )
= $false )
| ( ( ( h @ ~ $false )
= ( h @ $false ) )
= $false ) ),
inference(sim,[status(thm)],[51]) ).
thf(66,plain,
( ( ( h @ $false )
= ( h @ ~ $false ) )
= $true ),
inference(sim,[status(thm)],[37]) ).
thf(67,plain,
( ( ( h @ $false )
= ( h @ ~ $false ) )
= $false ),
inference(sim,[status(thm)],[59]) ).
thf(68,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[6,67,66,65,48,39,35,34,25,16,9]) ).
thf(69,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO039^2 : TPTP v9.3.1. Released v4.1.0.
% 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
% 0.06/0.19 % Computer : n017.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Oct 6 17:26:30 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.28
% 0.06/0.28 No.of.Axioms: 0
% 0.06/0.28
% 0.06/0.28 Length.of.Defs: 0
% 0.06/0.28
% 0.06/0.28 Contains.Choice.Funs: false
% 0.06/0.28
% 0.06/0.28 ********************************
% 0.06/0.28 * All subproblems solved! *
% 0.06/0.28 ********************************
% 0.06/0.28 % SZS status Theorem for /export/starexec/sandbox/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:68,loop_count:5,foatp_calls:3,translation:fof_experiment)
% 0.06/0.28
% 0.06/0.28 %**** Beginning of derivation protocol ****
% 0.06/0.28 % SZS output start CNFRefutation
% See solution above
% 0.06/0.28
% 0.06/0.28 %**** End of derivation protocol ****
% 0.06/0.28 %**** no. of clauses in derivation: 29 ****
% 0.06/0.28 %**** clause counter: 68 ****
% 0.06/0.28
% 0.06/0.28 % SZS status Theorem for /export/starexec/sandbox/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:68,loop_count:5,foatp_calls:3,translation:fof_experiment)
%------------------------------------------------------------------------------