%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO003^1 : 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 : 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 11:07:21 AM UTC 2026
% Result : Theorem 0.11s 0.20s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 19 unt; 0 typ; 1 def)
% Number of atoms : 54 ( 21 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 72 ( 5 ~; 4 |; 6 &; 44 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 2 ^; 23 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_leibeq,type,
leibeq: $i > $i > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY10,type,
sK2_SY10: $i ).
thf(tp_sK3_SY13,type,
sK3_SY13: $i > $o ).
thf(leibeq,definition,
( leibeq
= ( ^ [X: $i,Y: $i] :
! [P: $i > $o] :
( ( P @ X )
=> ( P @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leibeq) ).
thf(1,conjecture,
! [X: $i,Y: $i,P: $i > $o] :
( ( ( leibeq @ X @ Y )
& ( P @ X ) )
=> ( P @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
( ( ! [X: $i,Y: $i,P: $i > $o] :
( ( ( leibeq @ X @ Y )
& ( P @ X ) )
=> ( P @ Y ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i,SY1: $i,SY2: $i > $o] :
( ( ! [SY5: $i > $o] :
( ( SY5 @ SY0 )
=> ( SY5 @ SY1 ) )
& ( SY2 @ SY0 ) )
=> ( SY2 @ SY1 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,leibeq]) ).
thf(4,plain,
( ( ! [SY10: $i,SY11: $i > $o] :
( ( ! [SY12: $i > $o] :
( ( SY12 @ sK1_SY0 )
=> ( SY12 @ SY10 ) )
& ( SY11 @ sK1_SY0 ) )
=> ( SY11 @ SY10 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY13: $i > $o] :
( ( ! [SY14: $i > $o] :
( ( SY14 @ sK1_SY0 )
=> ( SY14 @ sK2_SY10 ) )
& ( SY13 @ sK1_SY0 ) )
=> ( SY13 @ sK2_SY10 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ( ! [SY14: $i > $o] :
( ( SY14 @ sK1_SY0 )
=> ( SY14 @ sK2_SY10 ) )
& ( sK3_SY13 @ sK1_SY0 ) )
=> ( sK3_SY13 @ sK2_SY10 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ! [SY14: $i > $o] :
( ( SY14 @ sK1_SY0 )
=> ( SY14 @ sK2_SY10 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(8,plain,
( ( sK3_SY13 @ sK1_SY0 )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(9,plain,
( ( sK3_SY13 @ sK2_SY10 )
= $false ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(10,plain,
( ( ~ ( sK3_SY13 @ sK2_SY10 ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( sK3_SY13 @ sK1_SY0 )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ! [SY14: $i > $o] :
( ( SY14 @ sK1_SY0 )
=> ( SY14 @ sK2_SY10 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(13,plain,
( ( ~ ( sK3_SY13 @ sK2_SY10 ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(14,plain,
( ( ! [SX0: $i > $o] :
( ~ ( SX0 @ sK1_SY0 )
| ( SX0 @ sK2_SY10 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,leibeq]) ).
thf(15,plain,
( ( sK3_SY13 @ sK2_SY10 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(16,plain,
! [SV1: $i > $o] :
( ( ~ ( SV1 @ sK1_SY0 )
| ( SV1 @ sK2_SY10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(17,plain,
! [SV1: $i > $o] :
( ( ( ~ ( SV1 @ sK1_SY0 ) )
= $true )
| ( ( SV1 @ sK2_SY10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(18,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ sK1_SY0 )
= $false )
| ( ( SV1 @ sK2_SY10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(19,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[11,18,15]) ).
thf(20,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO003^1 : 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
% 0.11/0.17 % Computer : n008.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Oct 6 17:31:24 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.20
% 0.11/0.20 No.of.Axioms: 0
% 0.11/0.20
% 0.11/0.20 Length.of.Defs: 151
% 0.11/0.20
% 0.11/0.20 Contains.Choice.Funs: false
% 0.11/0.20
% 0.11/0.20 ********************************
% 0.11/0.20 * All subproblems solved! *
% 0.11/0.20 ********************************
% 0.11/0.20 % 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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:19,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.20
% 0.11/0.20 %**** Beginning of derivation protocol ****
% 0.11/0.20 % SZS output start CNFRefutation
% See solution above
% 0.11/0.20
% 0.11/0.20 %**** End of derivation protocol ****
% 0.11/0.20 %**** no. of clauses in derivation: 20 ****
% 0.11/0.20 %**** clause counter: 19 ****
% 0.11/0.20
% 0.11/0.20 % 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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:19,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------