%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO212^5 : 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 : n008.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 11:07:50 AM UTC 2026
% Result : Theorem 0.09s 0.28s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 43 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 262 ( 73 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 127 ( 45 ~; 42 |; 11 &; 25 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $o ).
thf(tp_b,type,
b: $o ).
thf(tp_sK1_Xp,type,
sK1_Xp: $o > $o ).
thf(1,conjecture,
! [Xp: $o > $o] :
( ( ( Xp @ a )
& ( Xp @ b ) )
=> ( Xp
@ ( a
& b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEMB2) ).
thf(2,negated_conjecture,
( ( ! [Xp: $o > $o] :
( ( ( Xp @ a )
& ( Xp @ b ) )
=> ( Xp
@ ( a
& b ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xp: $o > $o] :
( ( ( Xp @ a )
& ( Xp @ b ) )
=> ( Xp
@ ( a
& b ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ( ( sK1_Xp @ a )
& ( sK1_Xp @ b ) )
=> ( sK1_Xp
@ ( a
& b ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( sK1_Xp @ a )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( sK1_Xp @ b )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( sK1_Xp
@ ( a
& b ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ( sK1_Xp
@ ( a
& b ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( sK1_Xp @ b )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( sK1_Xp @ a )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(11,plain,
( ( ~ ( sK1_Xp
@ ( a
& b ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ~ ( sK1_Xp
@ ~ ( ~ a
| ~ b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(13,plain,
( ( sK1_Xp
@ ~ ( ~ a
| ~ b ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(14,plain,
( ( ( sK1_Xp
@ ~ ( ~ a
| ~ b ) )
= ( sK1_Xp @ a ) )
= $false ),
inference(res,[status(thm)],[13,10]) ).
thf(15,plain,
( ( ( sK1_Xp
@ ~ ( ~ a
| ~ b ) )
= ( sK1_Xp @ b ) )
= $false ),
inference(res,[status(thm)],[13,9]) ).
thf(16,plain,
( ( ( ~ ( ~ a
| ~ b ) )
= $true )
| ( b = $true ) ),
inference(extuni,[status(esa)],[15]) ).
thf(17,plain,
( ( ( ~ ( ~ a
| ~ b ) )
= $false )
| ( b = $false ) ),
inference(extuni,[status(esa)],[15]) ).
thf(18,plain,
( ( ( ~ ( ~ a
| ~ b ) )
= $true )
| ( a = $true ) ),
inference(extuni,[status(esa)],[14]) ).
thf(19,plain,
( ( ( ~ ( ~ a
| ~ b ) )
= $false )
| ( a = $false ) ),
inference(extuni,[status(esa)],[14]) ).
thf(20,plain,
( ( ( ~ a
| ~ b )
= $true )
| ( b = $false ) ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ( ~ a
| ~ b )
= $false )
| ( b = $true ) ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(22,plain,
( ( ( ~ a
| ~ b )
= $true )
| ( a = $false ) ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ( ~ a
| ~ b )
= $false )
| ( a = $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(24,plain,
( ( ( ~ a ) = $true )
| ( ( ~ b ) = $true )
| ( b = $false ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(25,plain,
( ( ( ~ a ) = $false )
| ( b = $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( ( ~ b ) = $false )
| ( b = $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(27,plain,
( ( ( ~ a ) = $true )
| ( ( ~ b ) = $true )
| ( a = $false ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(28,plain,
( ( ( ~ a ) = $false )
| ( a = $true ) ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(29,plain,
( ( ( ~ b ) = $false )
| ( a = $true ) ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(30,plain,
( ( a = $false )
| ( ( ~ b ) = $true )
| ( b = $false ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(31,plain,
( ( a = $true )
| ( b = $true ) ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(32,plain,
( ( b = $true )
| ( b = $true ) ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(33,plain,
( ( a = $false )
| ( ( ~ b ) = $true )
| ( a = $false ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(34,plain,
( ( a = $true )
| ( a = $true ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(35,plain,
( ( b = $true )
| ( a = $true ) ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(36,plain,
( ( b = $false )
| ( a = $false )
| ( b = $false ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(37,plain,
( ( b = $false )
| ( a = $false )
| ( a = $false ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(38,plain,
( ( b = $false )
| ( a = $false ) ),
inference(sim,[status(thm)],[36]) ).
thf(39,plain,
b = $true,
inference(sim,[status(thm)],[32]) ).
thf(40,plain,
( ( b = $false )
| ( a = $false ) ),
inference(sim,[status(thm)],[37]) ).
thf(41,plain,
a = $true,
inference(sim,[status(thm)],[34]) ).
thf(43,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[9,41,40,39,38,35,31,13,10]) ).
thf(44,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO212^5 : 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
% 0.09/0.21 % Computer : n008.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Oct 6 17:34:09 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.28
% 0.09/0.28 No.of.Axioms: 0
% 0.09/0.28
% 0.09/0.28 Length.of.Defs: 0
% 0.09/0.28
% 0.09/0.28 Contains.Choice.Funs: false
% 0.09/0.28
% 0.09/0.28 ********************************
% 0.09/0.28 * All subproblems solved! *
% 0.09/0.28 ********************************
% 0.09/0.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:43,loop_count:5,foatp_calls:2,translation:fof_full)
% 0.09/0.28
% 0.09/0.28 %**** Beginning of derivation protocol ****
% 0.09/0.28 % SZS output start CNFRefutation
% See solution above
% 0.09/0.28
% 0.09/0.28 %**** End of derivation protocol ****
% 0.09/0.28 %**** no. of clauses in derivation: 43 ****
% 0.09/0.28 %**** clause counter: 43 ****
% 0.09/0.28
% 0.09/0.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:43,loop_count:5,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------