%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : KRS179+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 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 : n005.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 10:26:36 AM UTC 2026
% Result : Theorem 0.06s 0.24s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 40 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 213 ( 52 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 411 ( 51 ~; 51 |; 6 &; 291 @)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 107 ( 0 ^; 107 !; 0 ?; 107 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_isa,type,
isa: $i > $i > $o ).
thf(tp_mighta,type,
mighta: $i > $i > $o ).
thf(tp_model,type,
model: $i > $i > $o ).
thf(tp_nevera,type,
nevera: $i > $i > $o ).
thf(tp_not,type,
not: $i > $i ).
thf(tp_nota,type,
nota: $i > $i > $o ).
thf(tp_sK1_S1,type,
sK1_S1: $i ).
thf(tp_sK2_SY7,type,
sK2_SY7: $i ).
thf(tp_sK3_SY9,type,
sK3_SY9: $i ).
thf(tp_sK4_SY15,type,
sK4_SY15: $i > $i > $i ).
thf(tp_sK5_SY19,type,
sK5_SY19: $i > $i > $i ).
thf(tp_status,type,
status: $i > $i > $i > $o ).
thf(tp_xora,type,
xora: $i > $i > $o ).
thf(12,axiom,
! [S1: $i,S2: $i] :
( ! [Ax: $i,C: $i] :
( ( status @ Ax @ C @ S1 )
=> ( status @ Ax @ C @ S2 ) )
<=> ( isa @ S1 @ S2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isa) ).
thf(14,conjecture,
! [S1: $i,S2: $i,S3: $i] :
( ( ( isa @ S1 @ S2 )
& ( isa @ S2 @ S3 ) )
=> ( isa @ S1 @ S3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isa_transitive) ).
thf(15,negated_conjecture,
( ( ! [S1: $i,S2: $i,S3: $i] :
( ( ( isa @ S1 @ S2 )
& ( isa @ S2 @ S3 ) )
=> ( isa @ S1 @ S3 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[14]) ).
thf(16,plain,
( ( ! [S1: $i,S2: $i,S3: $i] :
( ( ( isa @ S1 @ S2 )
& ( isa @ S2 @ S3 ) )
=> ( isa @ S1 @ S3 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [S1: $i,S2: $i] :
( ! [Ax: $i,C: $i] :
( ( status @ Ax @ C @ S1 )
=> ( status @ Ax @ C @ S2 ) )
<=> ( isa @ S1 @ S2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(18,plain,
( ( ! [SY7: $i,SY8: $i] :
( ( ( isa @ sK1_S1 @ SY7 )
& ( isa @ SY7 @ SY8 ) )
=> ( isa @ sK1_S1 @ SY8 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(19,plain,
( ( ! [SY9: $i] :
( ( ( isa @ sK1_S1 @ sK2_SY7 )
& ( isa @ sK2_SY7 @ SY9 ) )
=> ( isa @ sK1_S1 @ SY9 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(20,plain,
( ( ( ( isa @ sK1_S1 @ sK2_SY7 )
& ( isa @ sK2_SY7 @ sK3_SY9 ) )
=> ( isa @ sK1_S1 @ sK3_SY9 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(21,plain,
( ( isa @ sK1_S1 @ sK2_SY7 )
= $true ),
inference(standard_cnf,[status(thm)],[20]) ).
thf(22,plain,
( ( isa @ sK2_SY7 @ sK3_SY9 )
= $true ),
inference(standard_cnf,[status(thm)],[20]) ).
thf(23,plain,
( ( isa @ sK1_S1 @ sK3_SY9 )
= $false ),
inference(standard_cnf,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ( isa @ sK1_S1 @ sK3_SY9 ) )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(25,plain,
( ( ! [S1: $i,S2: $i] :
( ! [Ax: $i,C: $i] :
( ( status @ Ax @ C @ S1 )
=> ( status @ Ax @ C @ S2 ) )
<=> ( isa @ S1 @ S2 ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(26,plain,
( ( isa @ sK2_SY7 @ sK3_SY9 )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(27,plain,
( ( isa @ sK1_S1 @ sK2_SY7 )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(28,plain,
( ( ~ ( isa @ sK1_S1 @ sK3_SY9 ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(29,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( status @ SX2 @ SX3 @ SX0 )
| ( status @ SX2 @ SX3 @ SX1 ) )
| ( isa @ SX0 @ SX1 ) )
| ~ ( ~ ( isa @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] :
( ~ ( status @ SX2 @ SX3 @ SX0 )
| ( status @ SX2 @ SX3 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(30,plain,
( ( isa @ sK1_S1 @ sK3_SY9 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(31,plain,
! [SV1: $i] :
( ( ! [SY10: $i] :
~ ( ~ ( ~ ! [SY11: $i,SY12: $i] :
( ~ ( status @ SY11 @ SY12 @ SV1 )
| ( status @ SY11 @ SY12 @ SY10 ) )
| ( isa @ SV1 @ SY10 ) )
| ~ ( ~ ( isa @ SV1 @ SY10 )
| ! [SY13: $i,SY14: $i] :
( ~ ( status @ SY13 @ SY14 @ SV1 )
| ( status @ SY13 @ SY14 @ SY10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ( ~ ( ~ ! [SY15: $i,SY16: $i] :
( ~ ( status @ SY15 @ SY16 @ SV1 )
| ( status @ SY15 @ SY16 @ SV2 ) )
| ( isa @ SV1 @ SV2 ) )
| ~ ( ~ ( isa @ SV1 @ SV2 )
| ! [SY17: $i,SY18: $i] :
( ~ ( status @ SY17 @ SY18 @ SV1 )
| ( status @ SY17 @ SY18 @ SV2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(33,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ( ~ ! [SY15: $i,SY16: $i] :
( ~ ( status @ SY15 @ SY16 @ SV1 )
| ( status @ SY15 @ SY16 @ SV2 ) )
| ( isa @ SV1 @ SV2 ) )
| ~ ( ~ ( isa @ SV1 @ SV2 )
| ! [SY17: $i,SY18: $i] :
( ~ ( status @ SY17 @ SY18 @ SV1 )
| ( status @ SY17 @ SY18 @ SV2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(34,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ( ~ ! [SY15: $i,SY16: $i] :
( ~ ( status @ SY15 @ SY16 @ SV1 )
| ( status @ SY15 @ SY16 @ SV2 ) )
| ( isa @ SV1 @ SV2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(35,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ( ~ ( isa @ SV1 @ SV2 )
| ! [SY17: $i,SY18: $i] :
( ~ ( status @ SY17 @ SY18 @ SV1 )
| ( status @ SY17 @ SY18 @ SV2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(36,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ! [SY15: $i,SY16: $i] :
( ~ ( status @ SY15 @ SY16 @ SV1 )
| ( status @ SY15 @ SY16 @ SV2 ) )
| ( isa @ SV1 @ SV2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(37,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ( isa @ SV1 @ SV2 )
| ! [SY17: $i,SY18: $i] :
( ~ ( status @ SY17 @ SY18 @ SV1 )
| ( status @ SY17 @ SY18 @ SV2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(38,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ! [SY15: $i,SY16: $i] :
( ~ ( status @ SY15 @ SY16 @ SV1 )
| ( status @ SY15 @ SY16 @ SV2 ) ) )
= $true )
| ( ( isa @ SV1 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ( isa @ SV1 @ SV2 ) )
= $true )
| ( ( ! [SY17: $i,SY18: $i] :
( ~ ( status @ SY17 @ SY18 @ SV1 )
| ( status @ SY17 @ SY18 @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV2: $i,SV1: $i] :
( ( ( ! [SY15: $i,SY16: $i] :
( ~ ( status @ SY15 @ SY16 @ SV1 )
| ( status @ SY15 @ SY16 @ SV2 ) ) )
= $false )
| ( ( isa @ SV1 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV2: $i,SV1: $i] :
( ( ( isa @ SV1 @ SV2 )
= $false )
| ( ( ! [SY17: $i,SY18: $i] :
( ~ ( status @ SY17 @ SY18 @ SV1 )
| ( status @ SY17 @ SY18 @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV1: $i,SV2: $i] :
( ( ( ! [SY19: $i] :
( ~ ( status @ ( sK4_SY15 @ SV2 @ SV1 ) @ SY19 @ SV1 )
| ( status @ ( sK4_SY15 @ SV2 @ SV1 ) @ SY19 @ SV2 ) ) )
= $false )
| ( ( isa @ SV1 @ SV2 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(43,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ! [SY20: $i] :
( ~ ( status @ SV3 @ SY20 @ SV1 )
| ( status @ SV3 @ SY20 @ SV2 ) ) )
= $true )
| ( ( isa @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ( status @ ( sK4_SY15 @ SV2 @ SV1 ) @ ( sK5_SY19 @ SV1 @ SV2 ) @ SV1 )
| ( status @ ( sK4_SY15 @ SV2 @ SV1 ) @ ( sK5_SY19 @ SV1 @ SV2 ) @ SV2 ) )
= $false )
| ( ( isa @ SV1 @ SV2 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[42]) ).
thf(45,plain,
! [SV2: $i,SV1: $i,SV4: $i,SV3: $i] :
( ( ( ~ ( status @ SV3 @ SV4 @ SV1 )
| ( status @ SV3 @ SV4 @ SV2 ) )
= $true )
| ( ( isa @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ( status @ ( sK4_SY15 @ SV2 @ SV1 ) @ ( sK5_SY19 @ SV1 @ SV2 ) @ SV1 ) )
= $false )
| ( ( isa @ SV1 @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(47,plain,
! [SV1: $i,SV2: $i] :
( ( ( status @ ( sK4_SY15 @ SV2 @ SV1 ) @ ( sK5_SY19 @ SV1 @ SV2 ) @ SV2 )
= $false )
| ( ( isa @ SV1 @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(48,plain,
! [SV2: $i,SV1: $i,SV4: $i,SV3: $i] :
( ( ( ~ ( status @ SV3 @ SV4 @ SV1 ) )
= $true )
| ( ( status @ SV3 @ SV4 @ SV2 )
= $true )
| ( ( isa @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV1: $i,SV2: $i] :
( ( ( status @ ( sK4_SY15 @ SV2 @ SV1 ) @ ( sK5_SY19 @ SV1 @ SV2 ) @ SV1 )
= $true )
| ( ( isa @ SV1 @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(50,plain,
! [SV2: $i,SV1: $i,SV4: $i,SV3: $i] :
( ( ( status @ SV3 @ SV4 @ SV1 )
= $false )
| ( ( status @ SV3 @ SV4 @ SV2 )
= $true )
| ( ( isa @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(51,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[26,50,49,47,30,27]) ).
thf(52,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS179+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.19 % Computer : n005.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Oct 6 11:41:59 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.24
% 0.06/0.24 No.of.Axioms: 1
% 0.06/0.24
% 0.06/0.24 Length.of.Defs: 0
% 0.06/0.24
% 0.06/0.24 Contains.Choice.Funs: false
% 0.06/0.24 .
% 0.06/0.24
% 0.06/0.24 ********************************
% 0.06/0.24 * All subproblems solved! *
% 0.06/0.24 ********************************
% 0.06/0.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:51,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.06/0.24
% 0.06/0.24 %**** Beginning of derivation protocol ****
% 0.06/0.24 % SZS output start CNFRefutation
% See solution above
% 0.06/0.24
% 0.06/0.24 %**** End of derivation protocol ****
% 0.06/0.24 %**** no. of clauses in derivation: 40 ****
% 0.06/0.24 %**** clause counter: 51 ****
% 0.06/0.24
% 0.06/0.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:51,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------