%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO007^1 : 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 : n001.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 0.07s 0.21s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 32 ( 26 unt; 0 typ; 1 def)
% Number of atoms : 139 ( 37 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 91 ( 24 ~; 19 |; 0 &; 29 @)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 2 ^; 16 !; 0 ?; 18 :)
% 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_SX0,type,
sK3_SX0: $o > $o ).
thf(leibeq,definition,
( leibeq
= ( ^ [U: $o,V: $o] :
! [Q: $o > $o] :
( ( Q @ U )
=> ( Q @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leibeq1) ).
thf(1,conjecture,
! [A: $o,B: $o] :
( ( A
<=> B )
=> ( leibeq @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
( ( ! [A: $o,B: $o] :
( ( A
<=> B )
=> ( leibeq @ A @ B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $o,SY1: $o] :
( ( SY0
<=> SY1 )
=> ! [SY4: $o > $o] :
( ( SY4 @ SY0 )
=> ( SY4 @ SY1 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,leibeq]) ).
thf(4,plain,
( ( ! [SY8: $o] :
( ( sK1_SY0
<=> SY8 )
=> ! [SY9: $o > $o] :
( ( SY9 @ sK1_SY0 )
=> ( SY9 @ SY8 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ( sK1_SY0
<=> sK2_SY8 )
=> ! [SY10: $o > $o] :
( ( SY10 @ sK1_SY0 )
=> ( SY10 @ sK2_SY8 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( sK1_SY0
<=> sK2_SY8 )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY10: $o > $o] :
( ( SY10 @ sK1_SY0 )
=> ( SY10 @ sK2_SY8 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ! [SY10: $o > $o] :
( ( SY10 @ sK1_SY0 )
=> ( SY10 @ sK2_SY8 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( sK1_SY0
<=> sK2_SY8 )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( ~ ! [SY10: $o > $o] :
( ( SY10 @ sK1_SY0 )
=> ( SY10 @ sK2_SY8 ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( ~ ( ~ sK1_SY0
| sK2_SY8 )
| ~ ( ~ sK2_SY8
| sK1_SY0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,leibeq]) ).
thf(12,plain,
( ( ~ ! [SX0: $o > $o] :
( ~ ( SX0 @ sK1_SY0 )
| ( SX0 @ sK2_SY8 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,leibeq]) ).
thf(13,plain,
( ( ~ ( ~ sK1_SY0
| sK2_SY8 )
| ~ ( ~ sK2_SY8
| sK1_SY0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [SX0: $o > $o] :
( ~ ( SX0 @ sK1_SY0 )
| ( SX0 @ sK2_SY8 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( ~ sK1_SY0
| sK2_SY8 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( ~ sK2_SY8
| sK1_SY0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
( ( ~ ( sK3_SX0 @ sK1_SY0 )
| ( sK3_SX0 @ sK2_SY8 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(18,plain,
( ( ~ sK1_SY0
| sK2_SY8 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ sK2_SY8
| sK1_SY0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( sK3_SX0 @ sK1_SY0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( sK3_SX0 @ sK2_SY8 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(22,plain,
( ( ( ~ sK1_SY0 ) = $true )
| ( sK2_SY8 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(23,plain,
( ( ( ~ sK2_SY8 ) = $true )
| ( sK1_SY0 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( sK3_SX0 @ sK1_SY0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( sK1_SY0 = $false )
| ( sK2_SY8 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( sK2_SY8 = $false )
| ( sK1_SY0 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( ( sK3_SX0 @ sK1_SY0 )
= ( sK3_SX0 @ sK2_SY8 ) )
= $false ),
inference(res,[status(thm)],[24,21]) ).
thf(28,plain,
( ( sK1_SY0 = $true )
| ( sK2_SY8 = $true ) ),
inference(extuni,[status(esa)],[27]) ).
thf(29,plain,
( ( sK1_SY0 = $false )
| ( sK2_SY8 = $false ) ),
inference(extuni,[status(esa)],[27]) ).
thf(42,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,29,28,26,25,24]) ).
thf(43,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO007^1 : 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 : n001.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
% 0.07/0.17 % DateTime : Tue Oct 6 17:36:54 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: 152
% 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:42,loop_count:5,foatp_calls:2,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: 31 ****
% 0.07/0.21 %**** clause counter: 42 ****
% 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:42,loop_count:5,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------