%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO020^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n009.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 11:07:23 AM UTC 2026
% Result : Theorem 0.07s 0.21s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 16 unt; 0 typ; 1 def)
% Number of atoms : 65 ( 14 equ; 0 cnn)
% Maximal formula atoms : 1 ( 4 avg)
% Number of connectives : 80 ( 35 ~; 11 |; 8 &; 21 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 13 ( 2 ^; 11 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_leibeq,type,
leibeq: $o > $o > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $o ).
thf(tp_sK2_SY8,type,
sK2_SY8: $o ).
thf(tp_sK3_SY10,type,
sK3_SY10: $o > $o ).
thf(leibeq,definition,
( leibeq
= ( ^ [X: $o,Y: $o] :
! [P: $o > $o] :
( ( P @ X )
=> ( P @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leibeq) ).
thf(1,conjecture,
! [X: $o,Y: $o] :
( leibeq
@ ( X
& Y )
@ ~ ( ~ X
| ~ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
( ( ! [X: $o,Y: $o] :
( leibeq
@ ( X
& Y )
@ ~ ( ~ X
| ~ Y ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $o,SY1: $o,SY4: $o > $o] :
( ( SY4
@ ( SY0
& SY1 ) )
=> ( SY4
@ ~ ( ~ SY0
| ~ SY1 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,leibeq]) ).
thf(4,plain,
( ( ! [SY8: $o,SY9: $o > $o] :
( ( SY9
@ ( sK1_SY0
& SY8 ) )
=> ( SY9
@ ~ ( ~ sK1_SY0
| ~ SY8 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY10: $o > $o] :
( ( SY10
@ ( sK1_SY0
& sK2_SY8 ) )
=> ( SY10
@ ~ ( ~ sK1_SY0
| ~ sK2_SY8 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ( sK3_SY10
@ ( sK1_SY0
& sK2_SY8 ) )
=> ( sK3_SY10
@ ~ ( ~ sK1_SY0
| ~ sK2_SY8 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( sK3_SY10
@ ( sK1_SY0
& sK2_SY8 ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(8,plain,
( ( sK3_SY10
@ ~ ( ~ sK1_SY0
| ~ sK2_SY8 ) )
= $false ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( sK3_SY10
@ ~ ( ~ sK1_SY0
| ~ sK2_SY8 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( sK3_SY10
@ ( sK1_SY0
& sK2_SY8 ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ( sK3_SY10
@ ~ ( ~ sK1_SY0
| ~ sK2_SY8 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( sK3_SY10
@ ~ ( ~ sK1_SY0
| ~ sK2_SY8 ) )
= $true ),
inference(unfold_def,[status(thm)],[10,leibeq]) ).
thf(13,plain,
( ( sK3_SY10
@ ~ ( ~ sK1_SY0
| ~ sK2_SY8 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[12,13]) ).
thf(15,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO020^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.07/0.17 % Computer : n009.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 17:30:48 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: 151
% 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:1,axioms:1,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:14,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: 15 ****
% 0.07/0.21 %**** clause counter: 14 ****
% 0.07/0.21
% 0.07/0.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:14,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------