%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : KRS178+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 : n014.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 0.09s 0.20s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 33 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 180 ( 45 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 361 ( 51 ~; 51 |; 0 &; 253 @)
% ( 3 <=>; 3 =>; 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 : 14 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 98 ( 0 ^; 98 !; 0 ?; 98 :)
% 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_SY10,type,
sK2_SY10: $i > $i > $i ).
thf(tp_sK3_SY14,type,
sK3_SY14: $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] : ( isa @ S1 @ S1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isa_reflexive) ).
thf(15,negated_conjecture,
( ( ! [S1: $i] : ( isa @ S1 @ S1 ) )
= $false ),
inference(negate_conjecture,[status(cth)],[14]) ).
thf(16,plain,
( ( ! [S1: $i] : ( isa @ S1 @ S1 ) )
= $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,
( ( isa @ sK1_S1 @ sK1_S1 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(19,plain,
( ( ~ ( isa @ sK1_S1 @ sK1_S1 ) )
= $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(20,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(21,plain,
( ( ~ ( isa @ sK1_S1 @ sK1_S1 ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(22,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)],[20]) ).
thf(23,plain,
( ( isa @ sK1_S1 @ sK1_S1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(24,plain,
! [SV1: $i] :
( ( ! [SY5: $i] :
~ ( ~ ( ~ ! [SY6: $i,SY7: $i] :
( ~ ( status @ SY6 @ SY7 @ SV1 )
| ( status @ SY6 @ SY7 @ SY5 ) )
| ( isa @ SV1 @ SY5 ) )
| ~ ( ~ ( isa @ SV1 @ SY5 )
| ! [SY8: $i,SY9: $i] :
( ~ ( status @ SY8 @ SY9 @ SV1 )
| ( status @ SY8 @ SY9 @ SY5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(25,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ( ~ ( ~ ! [SY10: $i,SY11: $i] :
( ~ ( status @ SY10 @ SY11 @ SV1 )
| ( status @ SY10 @ SY11 @ SV2 ) )
| ( isa @ SV1 @ SV2 ) )
| ~ ( ~ ( isa @ SV1 @ SV2 )
| ! [SY12: $i,SY13: $i] :
( ~ ( status @ SY12 @ SY13 @ SV1 )
| ( status @ SY12 @ SY13 @ SV2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(26,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ( ~ ! [SY10: $i,SY11: $i] :
( ~ ( status @ SY10 @ SY11 @ SV1 )
| ( status @ SY10 @ SY11 @ SV2 ) )
| ( isa @ SV1 @ SV2 ) )
| ~ ( ~ ( isa @ SV1 @ SV2 )
| ! [SY12: $i,SY13: $i] :
( ~ ( status @ SY12 @ SY13 @ SV1 )
| ( status @ SY12 @ SY13 @ SV2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(27,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ( ~ ! [SY10: $i,SY11: $i] :
( ~ ( status @ SY10 @ SY11 @ SV1 )
| ( status @ SY10 @ SY11 @ SV2 ) )
| ( isa @ SV1 @ SV2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(28,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ( ~ ( isa @ SV1 @ SV2 )
| ! [SY12: $i,SY13: $i] :
( ~ ( status @ SY12 @ SY13 @ SV1 )
| ( status @ SY12 @ SY13 @ SV2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(29,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ! [SY10: $i,SY11: $i] :
( ~ ( status @ SY10 @ SY11 @ SV1 )
| ( status @ SY10 @ SY11 @ SV2 ) )
| ( isa @ SV1 @ SV2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(30,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ( isa @ SV1 @ SV2 )
| ! [SY12: $i,SY13: $i] :
( ~ ( status @ SY12 @ SY13 @ SV1 )
| ( status @ SY12 @ SY13 @ SV2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(31,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ! [SY10: $i,SY11: $i] :
( ~ ( status @ SY10 @ SY11 @ SV1 )
| ( status @ SY10 @ SY11 @ SV2 ) ) )
= $true )
| ( ( isa @ SV1 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ( isa @ SV1 @ SV2 ) )
= $true )
| ( ( ! [SY12: $i,SY13: $i] :
( ~ ( status @ SY12 @ SY13 @ SV1 )
| ( status @ SY12 @ SY13 @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV2: $i,SV1: $i] :
( ( ( ! [SY10: $i,SY11: $i] :
( ~ ( status @ SY10 @ SY11 @ SV1 )
| ( status @ SY10 @ SY11 @ SV2 ) ) )
= $false )
| ( ( isa @ SV1 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV2: $i,SV1: $i] :
( ( ( isa @ SV1 @ SV2 )
= $false )
| ( ( ! [SY12: $i,SY13: $i] :
( ~ ( status @ SY12 @ SY13 @ SV1 )
| ( status @ SY12 @ SY13 @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV1: $i,SV2: $i] :
( ( ( ! [SY14: $i] :
( ~ ( status @ ( sK2_SY10 @ SV2 @ SV1 ) @ SY14 @ SV1 )
| ( status @ ( sK2_SY10 @ SV2 @ SV1 ) @ SY14 @ SV2 ) ) )
= $false )
| ( ( isa @ SV1 @ SV2 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[33]) ).
thf(36,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ! [SY15: $i] :
( ~ ( status @ SV3 @ SY15 @ SV1 )
| ( status @ SV3 @ SY15 @ SV2 ) ) )
= $true )
| ( ( isa @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ( status @ ( sK2_SY10 @ SV2 @ SV1 ) @ ( sK3_SY14 @ SV1 @ SV2 ) @ SV1 )
| ( status @ ( sK2_SY10 @ SV2 @ SV1 ) @ ( sK3_SY14 @ SV1 @ SV2 ) @ SV2 ) )
= $false )
| ( ( isa @ SV1 @ SV2 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(38,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)],[36]) ).
thf(39,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ( status @ ( sK2_SY10 @ SV2 @ SV1 ) @ ( sK3_SY14 @ SV1 @ SV2 ) @ SV1 ) )
= $false )
| ( ( isa @ SV1 @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(40,plain,
! [SV1: $i,SV2: $i] :
( ( ( status @ ( sK2_SY10 @ SV2 @ SV1 ) @ ( sK3_SY14 @ SV1 @ SV2 ) @ SV2 )
= $false )
| ( ( isa @ SV1 @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(41,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)],[38]) ).
thf(42,plain,
! [SV1: $i,SV2: $i] :
( ( ( status @ ( sK2_SY10 @ SV2 @ SV1 ) @ ( sK3_SY14 @ SV1 @ SV2 ) @ SV1 )
= $true )
| ( ( isa @ SV1 @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(43,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)],[41]) ).
thf(44,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,43,42,40]) ).
thf(45,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS178+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 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
% 0.09/0.16 % Computer : n014.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Oct 6 11:41:56 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.20
% 0.09/0.20 No.of.Axioms: 1
% 0.09/0.20
% 0.09/0.20 Length.of.Defs: 0
% 0.09/0.20
% 0.09/0.20 Contains.Choice.Funs: false
% 0.09/0.20 .
% 0.09/0.20
% 0.09/0.20 ********************************
% 0.09/0.20 * All subproblems solved! *
% 0.09/0.20 ********************************
% 0.09/0.20 % SZS status Theorem for /export/starexec/sandbox/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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:44,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.20
% 0.09/0.20 %**** Beginning of derivation protocol ****
% 0.09/0.20 % SZS output start CNFRefutation
% See solution above
% 0.09/0.20
% 0.09/0.20 %**** End of derivation protocol ****
% 0.09/0.20 %**** no. of clauses in derivation: 33 ****
% 0.09/0.20 %**** clause counter: 44 ****
% 0.09/0.20
% 0.09/0.20 % SZS status Theorem for /export/starexec/sandbox/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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:44,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------