%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : KRS255+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 10:26:43 AM UTC 2026
% Result : Theorem 0.66s 0.38s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 98 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 624 ( 163 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 1392 ( 390 ~; 182 |; 3 &; 802 @)
% ( 9 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 21 con; 0-3 aty)
% Number of variables : 324 ( 0 ^; 312 !; 12 ?; 324 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cax,type,
cax: $i ).
thf(tp_csa,type,
csa: $i ).
thf(tp_eqv,type,
eqv: $i ).
thf(tp_esa,type,
esa: $i ).
thf(tp_eth,type,
eth: $i ).
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_noc,type,
noc: $i ).
thf(tp_not,type,
not: $i > $i ).
thf(tp_nota,type,
nota: $i > $i > $o ).
thf(tp_sK1_SY28,type,
sK1_SY28: $i > $i > $i ).
thf(tp_sK2_SY26,type,
sK2_SY26: $i > $i > $i ).
thf(tp_sK3_SY20,type,
sK3_SY20: $i > $i > $i ).
thf(tp_sK4_SY35,type,
sK4_SY35: $i > $i > $i ).
thf(tp_sK5_SY33,type,
sK5_SY33: $i > $i > $i > $i ).
thf(tp_sap,type,
sap: $i ).
thf(tp_sat,type,
sat: $i ).
thf(tp_sca,type,
sca: $i ).
thf(tp_status,type,
status: $i > $i > $i > $o ).
thf(tp_tac,type,
tac: $i ).
thf(tp_tau,type,
tau: $i ).
thf(tp_tca,type,
tca: $i ).
thf(tp_thm,type,
thm: $i ).
thf(tp_unp,type,
unp: $i ).
thf(tp_uns,type,
uns: $i ).
thf(tp_wca,type,
wca: $i ).
thf(tp_wec,type,
wec: $i ).
thf(tp_wtc,type,
wtc: $i ).
thf(tp_wth,type,
wth: $i ).
thf(tp_xora,type,
xora: $i > $i > $o ).
thf(13,axiom,
! [S1: $i,S2: $i] :
( ? [Ax: $i,C: $i] :
( ( status @ Ax @ C @ S1 )
& ( status @ Ax @ C @ S2 ) )
<=> ( mighta @ S1 @ S2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mighta) ).
thf(28,axiom,
! [Ax: $i,C: $i] :
( ! [I1: $i] :
( ( model @ I1 @ Ax )
=> ( model @ I1 @ C ) )
<=> ( status @ Ax @ C @ thm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(31,axiom,
! [Ax: $i,C: $i] :
( ( ? [I1: $i] : ( model @ I1 @ Ax )
=> ? [I2: $i] : ( model @ I2 @ C ) )
<=> ( status @ Ax @ C @ sap ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sap) ).
thf(33,conjecture,
mighta @ sap @ thm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mighta_sap_thm) ).
thf(34,negated_conjecture,
( ( mighta @ sap @ thm )
= $false ),
inference(negate_conjecture,[status(cth)],[33]) ).
thf(35,plain,
( ( mighta @ sap @ thm )
= $false ),
inference(unfold_def,[status(thm)],[34]) ).
thf(36,plain,
( ( ! [S1: $i,S2: $i] :
( ? [Ax: $i,C: $i] :
( ( status @ Ax @ C @ S1 )
& ( status @ Ax @ C @ S2 ) )
<=> ( mighta @ S1 @ S2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(37,plain,
( ( ! [Ax: $i,C: $i] :
( ! [I1: $i] :
( ( model @ I1 @ Ax )
=> ( model @ I1 @ C ) )
<=> ( status @ Ax @ C @ thm ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(38,plain,
( ( ! [Ax: $i,C: $i] :
( ( ? [I1: $i] : ( model @ I1 @ Ax )
=> ? [I2: $i] : ( model @ I2 @ C ) )
<=> ( status @ Ax @ C @ sap ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(39,plain,
( ( ~ ( mighta @ sap @ thm ) )
= $true ),
inference(polarity_switch,[status(thm)],[35]) ).
thf(40,plain,
( ( ! [Ax: $i,C: $i] :
( ( ? [I1: $i] : ( model @ I1 @ Ax )
=> ? [I2: $i] : ( model @ I2 @ C ) )
<=> ( status @ Ax @ C @ sap ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(41,plain,
( ( ! [Ax: $i,C: $i] :
( ! [I1: $i] :
( ( model @ I1 @ Ax )
=> ( model @ I1 @ C ) )
<=> ( status @ Ax @ C @ thm ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(42,plain,
( ( ! [S1: $i,S2: $i] :
( ? [Ax: $i,C: $i] :
( ( status @ Ax @ C @ S1 )
& ( status @ Ax @ C @ S2 ) )
<=> ( mighta @ S1 @ S2 ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(43,plain,
( ( ~ ( mighta @ sap @ thm ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(44,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ~ ! [SX2: $i] :
~ ~ ! [SX3: $i] :
~ ~ ( ~ ( status @ SX2 @ SX3 @ SX0 )
| ~ ( status @ SX2 @ SX3 @ SX1 ) )
| ( mighta @ SX0 @ SX1 ) )
| ~ ( ~ ( mighta @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ! [SX3: $i] :
~ ~ ( ~ ( status @ SX2 @ SX3 @ SX0 )
| ~ ( status @ SX2 @ SX3 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(45,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ! [SX2: $i] :
( ~ ( model @ SX2 @ SX0 )
| ( model @ SX2 @ SX1 ) )
| ( status @ SX0 @ SX1 @ thm ) )
| ~ ( ~ ( status @ SX0 @ SX1 @ thm )
| ! [SX2: $i] :
( ~ ( model @ SX2 @ SX0 )
| ( model @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(46,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ~ ~ ! [SX2: $i] :
~ ( model @ SX2 @ SX0 )
| ~ ! [SX2: $i] :
~ ( model @ SX2 @ SX1 ) )
| ( status @ SX0 @ SX1 @ sap ) )
| ~ ( ~ ( status @ SX0 @ SX1 @ sap )
| ~ ~ ! [SX2: $i] :
~ ( model @ SX2 @ SX0 )
| ~ ! [SX2: $i] :
~ ( model @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(47,plain,
( ( mighta @ sap @ thm )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV1: $i] :
( ( ! [SY11: $i] :
~ ( ~ ( ~ ~ ! [SY12: $i] :
~ ~ ! [SY13: $i] :
~ ~ ( ~ ( status @ SY12 @ SY13 @ SV1 )
| ~ ( status @ SY12 @ SY13 @ SY11 ) )
| ( mighta @ SV1 @ SY11 ) )
| ~ ( ~ ( mighta @ SV1 @ SY11 )
| ~ ! [SY14: $i] :
~ ~ ! [SY15: $i] :
~ ~ ( ~ ( status @ SY14 @ SY15 @ SV1 )
| ~ ( status @ SY14 @ SY15 @ SY11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV2: $i] :
( ( ! [SY16: $i] :
~ ( ~ ( ~ ! [SY17: $i] :
( ~ ( model @ SY17 @ SV2 )
| ( model @ SY17 @ SY16 ) )
| ( status @ SV2 @ SY16 @ thm ) )
| ~ ( ~ ( status @ SV2 @ SY16 @ thm )
| ! [SY18: $i] :
( ~ ( model @ SY18 @ SV2 )
| ( model @ SY18 @ SY16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV3: $i] :
( ( ! [SY19: $i] :
~ ( ~ ( ~ ( ~ ~ ! [SY20: $i] :
~ ( model @ SY20 @ SV3 )
| ~ ! [SX2: $i] :
~ ( model @ SX2 @ SY19 ) )
| ( status @ SV3 @ SY19 @ sap ) )
| ~ ( ~ ( status @ SV3 @ SY19 @ sap )
| ~ ~ ! [SY22: $i] :
~ ( model @ SY22 @ SV3 )
| ~ ! [SX2: $i] :
~ ( model @ SX2 @ SY19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( ~ ( ~ ~ ! [SY24: $i] :
~ ~ ! [SY25: $i] :
~ ~ ( ~ ( status @ SY24 @ SY25 @ SV1 )
| ~ ( status @ SY24 @ SY25 @ SV4 ) )
| ( mighta @ SV1 @ SV4 ) )
| ~ ( ~ ( mighta @ SV1 @ SV4 )
| ~ ! [SY26: $i] :
~ ~ ! [SY27: $i] :
~ ~ ( ~ ( status @ SY26 @ SY27 @ SV1 )
| ~ ( status @ SY26 @ SY27 @ SV4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(52,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ! [SY28: $i] :
( ~ ( model @ SY28 @ SV2 )
| ( model @ SY28 @ SV5 ) )
| ( status @ SV2 @ SV5 @ thm ) )
| ~ ( ~ ( status @ SV2 @ SV5 @ thm )
| ! [SY29: $i] :
( ~ ( model @ SY29 @ SV2 )
| ( model @ SY29 @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( ~ ~ ! [SY20: $i] :
~ ( model @ SY20 @ SV3 )
| ~ ! [SY31: $i] :
~ ( model @ SY31 @ SV6 ) )
| ( status @ SV3 @ SV6 @ sap ) )
| ~ ( ~ ( status @ SV3 @ SV6 @ sap )
| ~ ~ ! [SY22: $i] :
~ ( model @ SY22 @ SV3 )
| ~ ! [SY33: $i] :
~ ( model @ SY33 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(54,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( ~ ~ ! [SY24: $i] :
~ ~ ! [SY25: $i] :
~ ~ ( ~ ( status @ SY24 @ SY25 @ SV1 )
| ~ ( status @ SY24 @ SY25 @ SV4 ) )
| ( mighta @ SV1 @ SV4 ) )
| ~ ( ~ ( mighta @ SV1 @ SV4 )
| ~ ! [SY26: $i] :
~ ~ ! [SY27: $i] :
~ ~ ( ~ ( status @ SY26 @ SY27 @ SV1 )
| ~ ( status @ SY26 @ SY27 @ SV4 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(55,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ! [SY28: $i] :
( ~ ( model @ SY28 @ SV2 )
| ( model @ SY28 @ SV5 ) )
| ( status @ SV2 @ SV5 @ thm ) )
| ~ ( ~ ( status @ SV2 @ SV5 @ thm )
| ! [SY29: $i] :
( ~ ( model @ SY29 @ SV2 )
| ( model @ SY29 @ SV5 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(56,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ~ ! [SY20: $i] :
~ ( model @ SY20 @ SV3 )
| ~ ! [SY31: $i] :
~ ( model @ SY31 @ SV6 ) )
| ( status @ SV3 @ SV6 @ sap ) )
| ~ ( ~ ( status @ SV3 @ SV6 @ sap )
| ~ ~ ! [SY22: $i] :
~ ( model @ SY22 @ SV3 )
| ~ ! [SY33: $i] :
~ ( model @ SY33 @ SV6 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(57,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( ~ ~ ! [SY24: $i] :
~ ~ ! [SY25: $i] :
~ ~ ( ~ ( status @ SY24 @ SY25 @ SV1 )
| ~ ( status @ SY24 @ SY25 @ SV4 ) )
| ( mighta @ SV1 @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(58,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( ~ ( mighta @ SV1 @ SV4 )
| ~ ! [SY26: $i] :
~ ~ ! [SY27: $i] :
~ ~ ( ~ ( status @ SY26 @ SY27 @ SV1 )
| ~ ( status @ SY26 @ SY27 @ SV4 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(59,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ! [SY28: $i] :
( ~ ( model @ SY28 @ SV2 )
| ( model @ SY28 @ SV5 ) )
| ( status @ SV2 @ SV5 @ thm ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(60,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ( status @ SV2 @ SV5 @ thm )
| ! [SY29: $i] :
( ~ ( model @ SY29 @ SV2 )
| ( model @ SY29 @ SV5 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(61,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ~ ! [SY20: $i] :
~ ( model @ SY20 @ SV3 )
| ~ ! [SY31: $i] :
~ ( model @ SY31 @ SV6 ) )
| ( status @ SV3 @ SV6 @ sap ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(62,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( ~ ( status @ SV3 @ SV6 @ sap )
| ~ ~ ! [SY22: $i] :
~ ( model @ SY22 @ SV3 )
| ~ ! [SY33: $i] :
~ ( model @ SY33 @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(63,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ~ ! [SY24: $i] :
~ ~ ! [SY25: $i] :
~ ~ ( ~ ( status @ SY24 @ SY25 @ SV1 )
| ~ ( status @ SY24 @ SY25 @ SV4 ) )
| ( mighta @ SV1 @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(64,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( mighta @ SV1 @ SV4 )
| ~ ! [SY26: $i] :
~ ~ ! [SY27: $i] :
~ ~ ( ~ ( status @ SY26 @ SY27 @ SV1 )
| ~ ( status @ SY26 @ SY27 @ SV4 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(65,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ! [SY28: $i] :
( ~ ( model @ SY28 @ SV2 )
| ( model @ SY28 @ SV5 ) )
| ( status @ SV2 @ SV5 @ thm ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(66,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( status @ SV2 @ SV5 @ thm )
| ! [SY29: $i] :
( ~ ( model @ SY29 @ SV2 )
| ( model @ SY29 @ SV5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(67,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( ~ ~ ! [SY20: $i] :
~ ( model @ SY20 @ SV3 )
| ~ ! [SY31: $i] :
~ ( model @ SY31 @ SV6 ) )
| ( status @ SV3 @ SV6 @ sap ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(68,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( status @ SV3 @ SV6 @ sap )
| ~ ~ ! [SY22: $i] :
~ ( model @ SY22 @ SV3 )
| ~ ! [SY33: $i] :
~ ( model @ SY33 @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(69,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ~ ! [SY24: $i] :
~ ~ ! [SY25: $i] :
~ ~ ( ~ ( status @ SY24 @ SY25 @ SV1 )
| ~ ( status @ SY24 @ SY25 @ SV4 ) ) )
= $true )
| ( ( mighta @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(70,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( mighta @ SV1 @ SV4 ) )
= $true )
| ( ( ~ ! [SY26: $i] :
~ ~ ! [SY27: $i] :
~ ~ ( ~ ( status @ SY26 @ SY27 @ SV1 )
| ~ ( status @ SY26 @ SY27 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(71,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ! [SY28: $i] :
( ~ ( model @ SY28 @ SV2 )
| ( model @ SY28 @ SV5 ) ) )
= $true )
| ( ( status @ SV2 @ SV5 @ thm )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(72,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ( status @ SV2 @ SV5 @ thm ) )
= $true )
| ( ( ! [SY29: $i] :
( ~ ( model @ SY29 @ SV2 )
| ( model @ SY29 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(73,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ! [SY20: $i] :
~ ( model @ SY20 @ SV3 )
| ~ ! [SY31: $i] :
~ ( model @ SY31 @ SV6 ) ) )
= $true )
| ( ( status @ SV3 @ SV6 @ sap )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(74,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( status @ SV3 @ SV6 @ sap ) )
= $true )
| ( ( ~ ~ ! [SY22: $i] :
~ ( model @ SY22 @ SV3 )
| ~ ! [SY33: $i] :
~ ( model @ SY33 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(75,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ! [SY24: $i] :
~ ~ ! [SY25: $i] :
~ ~ ( ~ ( status @ SY24 @ SY25 @ SV1 )
| ~ ( status @ SY24 @ SY25 @ SV4 ) ) )
= $false )
| ( ( mighta @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(76,plain,
! [SV4: $i,SV1: $i] :
( ( ( mighta @ SV1 @ SV4 )
= $false )
| ( ( ~ ! [SY26: $i] :
~ ~ ! [SY27: $i] :
~ ~ ( ~ ( status @ SY26 @ SY27 @ SV1 )
| ~ ( status @ SY26 @ SY27 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(77,plain,
! [SV5: $i,SV2: $i] :
( ( ( ! [SY28: $i] :
( ~ ( model @ SY28 @ SV2 )
| ( model @ SY28 @ SV5 ) ) )
= $false )
| ( ( status @ SV2 @ SV5 @ thm )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(78,plain,
! [SV5: $i,SV2: $i] :
( ( ( status @ SV2 @ SV5 @ thm )
= $false )
| ( ( ! [SY29: $i] :
( ~ ( model @ SY29 @ SV2 )
| ( model @ SY29 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(79,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ~ ! [SY20: $i] :
~ ( model @ SY20 @ SV3 )
| ~ ! [SY31: $i] :
~ ( model @ SY31 @ SV6 ) )
= $false )
| ( ( status @ SV3 @ SV6 @ sap )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(80,plain,
! [SV6: $i,SV3: $i] :
( ( ( status @ SV3 @ SV6 @ sap )
= $false )
| ( ( ~ ~ ! [SY22: $i] :
~ ( model @ SY22 @ SV3 )
| ~ ! [SY33: $i] :
~ ( model @ SY33 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(81,plain,
! [SV4: $i,SV1: $i] :
( ( ( ! [SY24: $i] :
~ ~ ! [SY25: $i] :
~ ~ ( ~ ( status @ SY24 @ SY25 @ SV1 )
| ~ ( status @ SY24 @ SY25 @ SV4 ) ) )
= $true )
| ( ( mighta @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(82,plain,
! [SV4: $i,SV1: $i] :
( ( ( ! [SY26: $i] :
~ ~ ! [SY27: $i] :
~ ~ ( ~ ( status @ SY26 @ SY27 @ SV1 )
| ~ ( status @ SY26 @ SY27 @ SV4 ) ) )
= $false )
| ( ( mighta @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(83,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( model @ ( sK1_SY28 @ SV5 @ SV2 ) @ SV2 )
| ( model @ ( sK1_SY28 @ SV5 @ SV2 ) @ SV5 ) )
= $false )
| ( ( status @ SV2 @ SV5 @ thm )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[77]) ).
thf(84,plain,
! [SV5: $i,SV2: $i,SV7: $i] :
( ( ( ~ ( model @ SV7 @ SV2 )
| ( model @ SV7 @ SV5 ) )
= $true )
| ( ( status @ SV2 @ SV5 @ thm )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(85,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ~ ! [SY20: $i] :
~ ( model @ SY20 @ SV3 ) )
= $false )
| ( ( status @ SV3 @ SV6 @ sap )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(86,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ! [SY31: $i] :
~ ( model @ SY31 @ SV6 ) )
= $false )
| ( ( status @ SV3 @ SV6 @ sap )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(87,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ~ ! [SY22: $i] :
~ ( model @ SY22 @ SV3 ) )
= $true )
| ( ( ~ ! [SY33: $i] :
~ ( model @ SY33 @ SV6 ) )
= $true )
| ( ( status @ SV3 @ SV6 @ sap )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(88,plain,
! [SV4: $i,SV1: $i,SV8: $i] :
( ( ( ~ ~ ! [SY34: $i] :
~ ~ ( ~ ( status @ SV8 @ SY34 @ SV1 )
| ~ ( status @ SV8 @ SY34 @ SV4 ) ) )
= $true )
| ( ( mighta @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(89,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ~ ! [SY35: $i] :
~ ~ ( ~ ( status @ ( sK2_SY26 @ SV4 @ SV1 ) @ SY35 @ SV1 )
| ~ ( status @ ( sK2_SY26 @ SV4 @ SV1 ) @ SY35 @ SV4 ) ) )
= $false )
| ( ( mighta @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[82]) ).
thf(90,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( model @ ( sK1_SY28 @ SV5 @ SV2 ) @ SV2 ) )
= $false )
| ( ( status @ SV2 @ SV5 @ thm )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(91,plain,
! [SV2: $i,SV5: $i] :
( ( ( model @ ( sK1_SY28 @ SV5 @ SV2 ) @ SV5 )
= $false )
| ( ( status @ SV2 @ SV5 @ thm )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(92,plain,
! [SV5: $i,SV2: $i,SV7: $i] :
( ( ( ~ ( model @ SV7 @ SV2 ) )
= $true )
| ( ( model @ SV7 @ SV5 )
= $true )
| ( ( status @ SV2 @ SV5 @ thm )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(93,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ! [SY20: $i] :
~ ( model @ SY20 @ SV3 ) )
= $true )
| ( ( status @ SV3 @ SV6 @ sap )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(94,plain,
! [SV3: $i,SV6: $i] :
( ( ( ! [SY31: $i] :
~ ( model @ SY31 @ SV6 ) )
= $true )
| ( ( status @ SV3 @ SV6 @ sap )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(95,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ! [SY22: $i] :
~ ( model @ SY22 @ SV3 ) )
= $false )
| ( ( ~ ! [SY33: $i] :
~ ( model @ SY33 @ SV6 ) )
= $true )
| ( ( status @ SV3 @ SV6 @ sap )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(96,plain,
! [SV4: $i,SV1: $i,SV8: $i] :
( ( ( ~ ! [SY34: $i] :
~ ~ ( ~ ( status @ SV8 @ SY34 @ SV1 )
| ~ ( status @ SV8 @ SY34 @ SV4 ) ) )
= $false )
| ( ( mighta @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(97,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ! [SY35: $i] :
~ ~ ( ~ ( status @ ( sK2_SY26 @ SV4 @ SV1 ) @ SY35 @ SV1 )
| ~ ( status @ ( sK2_SY26 @ SV4 @ SV1 ) @ SY35 @ SV4 ) ) )
= $true )
| ( ( mighta @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(98,plain,
! [SV2: $i,SV5: $i] :
( ( ( model @ ( sK1_SY28 @ SV5 @ SV2 ) @ SV2 )
= $true )
| ( ( status @ SV2 @ SV5 @ thm )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(99,plain,
! [SV5: $i,SV2: $i,SV7: $i] :
( ( ( model @ SV7 @ SV2 )
= $false )
| ( ( model @ SV7 @ SV5 )
= $true )
| ( ( status @ SV2 @ SV5 @ thm )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(100,plain,
! [SV6: $i,SV3: $i] :
( ( ( ! [SY20: $i] :
~ ( model @ SY20 @ SV3 ) )
= $false )
| ( ( status @ SV3 @ SV6 @ sap )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(101,plain,
! [SV3: $i,SV6: $i,SV9: $i] :
( ( ( ~ ( model @ SV9 @ SV6 ) )
= $true )
| ( ( status @ SV3 @ SV6 @ sap )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(102,plain,
! [SV6: $i,SV3: $i] :
( ( ( ! [SY22: $i] :
~ ( model @ SY22 @ SV3 ) )
= $true )
| ( ( ~ ! [SY33: $i] :
~ ( model @ SY33 @ SV6 ) )
= $true )
| ( ( status @ SV3 @ SV6 @ sap )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(103,plain,
! [SV4: $i,SV1: $i,SV8: $i] :
( ( ( ! [SY34: $i] :
~ ~ ( ~ ( status @ SV8 @ SY34 @ SV1 )
| ~ ( status @ SV8 @ SY34 @ SV4 ) ) )
= $true )
| ( ( mighta @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(104,plain,
! [SV1: $i,SV4: $i] :
( ( ( ! [SY35: $i] :
~ ~ ( ~ ( status @ ( sK2_SY26 @ SV4 @ SV1 ) @ SY35 @ SV1 )
| ~ ( status @ ( sK2_SY26 @ SV4 @ SV1 ) @ SY35 @ SV4 ) ) )
= $false )
| ( ( mighta @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(105,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( model @ ( sK3_SY20 @ SV6 @ SV3 ) @ SV3 ) )
= $false )
| ( ( status @ SV3 @ SV6 @ sap )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[100]) ).
thf(106,plain,
! [SV3: $i,SV6: $i,SV9: $i] :
( ( ( model @ SV9 @ SV6 )
= $false )
| ( ( status @ SV3 @ SV6 @ sap )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(107,plain,
! [SV6: $i,SV3: $i,SV10: $i] :
( ( ( ~ ( model @ SV10 @ SV3 ) )
= $true )
| ( ( ~ ! [SY33: $i] :
~ ( model @ SY33 @ SV6 ) )
= $true )
| ( ( status @ SV3 @ SV6 @ sap )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(108,plain,
! [SV4: $i,SV1: $i,SV11: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( status @ SV8 @ SV11 @ SV1 )
| ~ ( status @ SV8 @ SV11 @ SV4 ) ) )
= $true )
| ( ( mighta @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(109,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( status @ ( sK2_SY26 @ SV4 @ SV1 ) @ ( sK4_SY35 @ SV1 @ SV4 ) @ SV1 )
| ~ ( status @ ( sK2_SY26 @ SV4 @ SV1 ) @ ( sK4_SY35 @ SV1 @ SV4 ) @ SV4 ) ) )
= $false )
| ( ( mighta @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[104]) ).
thf(110,plain,
! [SV3: $i,SV6: $i] :
( ( ( model @ ( sK3_SY20 @ SV6 @ SV3 ) @ SV3 )
= $true )
| ( ( status @ SV3 @ SV6 @ sap )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(111,plain,
! [SV6: $i,SV3: $i,SV10: $i] :
( ( ( model @ SV10 @ SV3 )
= $false )
| ( ( ~ ! [SY33: $i] :
~ ( model @ SY33 @ SV6 ) )
= $true )
| ( ( status @ SV3 @ SV6 @ sap )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(112,plain,
! [SV4: $i,SV1: $i,SV11: $i,SV8: $i] :
( ( ( ~ ( ~ ( status @ SV8 @ SV11 @ SV1 )
| ~ ( status @ SV8 @ SV11 @ SV4 ) ) )
= $false )
| ( ( mighta @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(113,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( ~ ( status @ ( sK2_SY26 @ SV4 @ SV1 ) @ ( sK4_SY35 @ SV1 @ SV4 ) @ SV1 )
| ~ ( status @ ( sK2_SY26 @ SV4 @ SV1 ) @ ( sK4_SY35 @ SV1 @ SV4 ) @ SV4 ) ) )
= $true )
| ( ( mighta @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(114,plain,
! [SV3: $i,SV10: $i,SV6: $i] :
( ( ( ! [SY33: $i] :
~ ( model @ SY33 @ SV6 ) )
= $false )
| ( ( model @ SV10 @ SV3 )
= $false )
| ( ( status @ SV3 @ SV6 @ sap )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(115,plain,
! [SV4: $i,SV1: $i,SV11: $i,SV8: $i] :
( ( ( ~ ( status @ SV8 @ SV11 @ SV1 )
| ~ ( status @ SV8 @ SV11 @ SV4 ) )
= $true )
| ( ( mighta @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(116,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( status @ ( sK2_SY26 @ SV4 @ SV1 ) @ ( sK4_SY35 @ SV1 @ SV4 ) @ SV1 )
| ~ ( status @ ( sK2_SY26 @ SV4 @ SV1 ) @ ( sK4_SY35 @ SV1 @ SV4 ) @ SV4 ) )
= $false )
| ( ( mighta @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(117,plain,
! [SV6: $i,SV10: $i,SV3: $i] :
( ( ( ~ ( model @ ( sK5_SY33 @ SV3 @ SV10 @ SV6 ) @ SV6 ) )
= $false )
| ( ( model @ SV10 @ SV3 )
= $false )
| ( ( status @ SV3 @ SV6 @ sap )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[114]) ).
thf(118,plain,
! [SV4: $i,SV1: $i,SV11: $i,SV8: $i] :
( ( ( ~ ( status @ SV8 @ SV11 @ SV1 ) )
= $true )
| ( ( ~ ( status @ SV8 @ SV11 @ SV4 ) )
= $true )
| ( ( mighta @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(119,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( status @ ( sK2_SY26 @ SV4 @ SV1 ) @ ( sK4_SY35 @ SV1 @ SV4 ) @ SV1 ) )
= $false )
| ( ( mighta @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(120,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( status @ ( sK2_SY26 @ SV4 @ SV1 ) @ ( sK4_SY35 @ SV1 @ SV4 ) @ SV4 ) )
= $false )
| ( ( mighta @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(121,plain,
! [SV6: $i,SV10: $i,SV3: $i] :
( ( ( model @ ( sK5_SY33 @ SV3 @ SV10 @ SV6 ) @ SV6 )
= $true )
| ( ( model @ SV10 @ SV3 )
= $false )
| ( ( status @ SV3 @ SV6 @ sap )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(122,plain,
! [SV4: $i,SV1: $i,SV11: $i,SV8: $i] :
( ( ( status @ SV8 @ SV11 @ SV1 )
= $false )
| ( ( ~ ( status @ SV8 @ SV11 @ SV4 ) )
= $true )
| ( ( mighta @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(123,plain,
! [SV1: $i,SV4: $i] :
( ( ( status @ ( sK2_SY26 @ SV4 @ SV1 ) @ ( sK4_SY35 @ SV1 @ SV4 ) @ SV1 )
= $true )
| ( ( mighta @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(124,plain,
! [SV1: $i,SV4: $i] :
( ( ( status @ ( sK2_SY26 @ SV4 @ SV1 ) @ ( sK4_SY35 @ SV1 @ SV4 ) @ SV4 )
= $true )
| ( ( mighta @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(125,plain,
! [SV1: $i,SV4: $i,SV11: $i,SV8: $i] :
( ( ( status @ SV8 @ SV11 @ SV4 )
= $false )
| ( ( status @ SV8 @ SV11 @ SV1 )
= $false )
| ( ( mighta @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(126,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[47,125,124,123,121,110,106,99,98,91]) ).
thf(127,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS255+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n026.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 11:46:16 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.66/0.38
% 0.66/0.38 No.of.Axioms: 3
% 0.66/0.38
% 0.66/0.38 Length.of.Defs: 0
% 0.66/0.38
% 0.66/0.38 Contains.Choice.Funs: false
% 0.66/0.38 ...
% 0.66/0.38
% 0.66/0.38 ********************************
% 0.66/0.38 * All subproblems solved! *
% 0.66/0.38 ********************************
% 0.66/0.38 % SZS status Theorem for /export/starexec/sandbox2/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:126,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.66/0.38
% 0.66/0.38 %**** Beginning of derivation protocol ****
% 0.66/0.38 % SZS output start CNFRefutation
% See solution above
% 0.66/0.38
% 0.66/0.38 %**** End of derivation protocol ****
% 0.66/0.38 %**** no. of clauses in derivation: 98 ****
% 0.66/0.38 %**** clause counter: 126 ****
% 0.66/0.38
% 0.66/0.38 % SZS status Theorem for /export/starexec/sandbox2/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:126,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------