%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL579^1 : TPTP v9.3.1. Released v3.6.0.
% 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 : n013.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 10:29:26 AM UTC 2026
% Result : Theorem 0.11s 0.25s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 26 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 30 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 95 ( 18 ~; 8 |; 2 &; 49 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 0 ^; 25 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_SY4,type,
sK2_SY4: $i ).
thf(tp_sK3_SY8,type,
sK3_SY8: $i > $o ).
thf(1,conjecture,
! [X: $i,Y: $i] :
( ! [P: $i > $o] :
( ( P @ X )
=> ( P @ Y ) )
=> ! [P: $i > $o] :
( ( P @ Y )
=> ( P @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a) ).
thf(2,negated_conjecture,
( ( ! [X: $i,Y: $i] :
( ! [P: $i > $o] :
( ( P @ X )
=> ( P @ Y ) )
=> ! [P: $i > $o] :
( ( P @ Y )
=> ( P @ X ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [X: $i,Y: $i] :
( ! [P: $i > $o] :
( ( P @ X )
=> ( P @ Y ) )
=> ! [P: $i > $o] :
( ( P @ Y )
=> ( P @ X ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY4: $i] :
( ! [SY5: $i > $o] :
( ( SY5 @ sK1_X )
=> ( SY5 @ SY4 ) )
=> ! [SY6: $i > $o] :
( ( SY6 @ SY4 )
=> ( SY6 @ sK1_X ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY7: $i > $o] :
( ( SY7 @ sK1_X )
=> ( SY7 @ sK2_SY4 ) )
=> ! [SY8: $i > $o] :
( ( SY8 @ sK2_SY4 )
=> ( SY8 @ sK1_X ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY7: $i > $o] :
( ( SY7 @ sK1_X )
=> ( SY7 @ sK2_SY4 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY8: $i > $o] :
( ( SY8 @ sK2_SY4 )
=> ( SY8 @ sK1_X ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ! [SY8: $i > $o] :
( ( SY8 @ sK2_SY4 )
=> ( SY8 @ sK1_X ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ( sK3_SY8 @ sK2_SY4 )
& ~ ( sK3_SY8 @ sK1_X ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( ! [SY7: $i > $o] :
( ~ ( SY7 @ sK1_X )
| ( SY7 @ sK2_SY4 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(11,plain,
( ( ! [SY7: $i > $o] :
( ~ ( SY7 @ sK1_X )
| ( SY7 @ sK2_SY4 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(12,plain,
( ( ( sK3_SY8 @ sK2_SY4 )
& ~ ( sK3_SY8 @ sK1_X ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ~ ( ~ ( sK3_SY8 @ sK2_SY4 )
| ~ ~ ( sK3_SY8 @ sK1_X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(14,plain,
! [SV1: $i > $o] :
( ( ~ ( SV1 @ sK1_X )
| ( SV1 @ sK2_SY4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(15,plain,
( ( ~ ( sK3_SY8 @ sK2_SY4 )
| ~ ~ ( sK3_SY8 @ sK1_X ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(16,plain,
! [SV1: $i > $o] :
( ( ( ~ ( SV1 @ sK1_X ) )
= $true )
| ( ( SV1 @ sK2_SY4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( sK3_SY8 @ sK2_SY4 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ~ ( sK3_SY8 @ sK1_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(19,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ sK1_X )
= $false )
| ( ( SV1 @ sK2_SY4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( sK3_SY8 @ sK2_SY4 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ( sK3_SY8 @ sK1_X ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(22,plain,
( ( sK3_SY8 @ sK1_X )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(23,plain,
( ( ( sK1_X = sK1_X )
= $false )
| ( ( sK2_SY4 = sK1_X )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[19:[bind(SV1,$thf( ^ [SV2: $i] : ( SV2 = sK1_X ) ))]]) ).
thf(24,plain,
( ( sK2_SY4 = sK1_X )
= $true ),
inference(sim,[status(thm)],[23]) ).
thf(25,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,24,22]) ).
thf(26,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL579^1 : TPTP v9.3.1. Released v3.6.0.
% 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
% 0.11/0.19 % Computer : n013.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Oct 6 12:23:36 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.25
% 0.11/0.25 No.of.Axioms: 0
% 0.11/0.25
% 0.11/0.25 Length.of.Defs: 0
% 0.11/0.25
% 0.11/0.25 Contains.Choice.Funs: false
% 0.11/0.25
% 0.11/0.25 ********************************
% 0.11/0.25 * All subproblems solved! *
% 0.11/0.25 ********************************
% 0.11/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:25,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.11/0.25
% 0.11/0.25 %**** Beginning of derivation protocol ****
% 0.11/0.25 % SZS output start CNFRefutation
% See solution above
% 0.11/0.25
% 0.11/0.25 %**** End of derivation protocol ****
% 0.11/0.25 %**** no. of clauses in derivation: 26 ****
% 0.11/0.25 %**** clause counter: 25 ****
% 0.11/0.25
% 0.11/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:25,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------