%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL944^8 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 Sep 30 08:12:52 AM UTC 2026
% Result : Theorem 3.51s 0.85s
% Output : CNFRefutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 60 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 327 ( 10 equ; 0 cnn)
% Maximal formula atoms : 40 ( 5 avg)
% Number of connectives : 1083 ( 133 ~; 154 |; 19 &; 737 @)
% ( 0 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 8 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 26 usr; 3 con; 0-3 aty)
% Number of variables : 144 ( 30 ^; 114 !; 0 ?; 144 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mworld: $tType ).
thf(decl_23,type,
mrel: mworld > mworld > $o ).
thf(decl_24,type,
mactual: mworld ).
thf(decl_25,type,
mlocal: ( mworld > $o ) > $o ).
thf(decl_27,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(decl_29,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(decl_31,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(decl_33,type,
eiw_di: $i > mworld > $o ).
thf(decl_34,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(decl_36,type,
r2: mworld > $o ).
thf(decl_62,type,
or_2: mworld > $o ).
thf(decl_68,type,
is_a_theorem: $i > mworld > $o ).
thf(decl_71,type,
or: $i > $i > $i ).
thf(decl_73,type,
implies: $i > $i > $i ).
thf(decl_156,type,
esk83_1: mworld > mworld ).
thf(decl_157,type,
esk84_1: mworld > mworld ).
thf(decl_158,type,
esk85_1: mworld > $i ).
thf(decl_159,type,
esk86_1: mworld > mworld ).
thf(decl_160,type,
esk87_1: mworld > $i ).
thf(decl_161,type,
esk88_1: mworld > mworld ).
thf(decl_228,type,
esk155_1: mworld > mworld ).
thf(decl_229,type,
esk156_1: mworld > mworld ).
thf(decl_230,type,
esk157_1: mworld > $i ).
thf(decl_231,type,
esk158_1: mworld > mworld ).
thf(decl_232,type,
esk159_1: mworld > $i ).
thf(decl_233,type,
esk160_1: mworld > mworld ).
thf(decl_261,type,
esk188_0: mworld ).
thf(mlocal_def,axiom,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pCwQBaUklG/E---3.1_2360211.p',mlocal_def) ).
thf(mand_def,axiom,
( mand
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
& ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pCwQBaUklG/E---3.1_2360211.p',mand_def) ).
thf(mimplies_def,axiom,
( mimplies
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pCwQBaUklG/E---3.1_2360211.p',mimplies_def) ).
thf(mbox_def,axiom,
( mbox
= ( ^ [X1: mworld > $o,X3: mworld] :
! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( X1 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pCwQBaUklG/E---3.1_2360211.p',mbox_def) ).
thf(mforall_di_def,axiom,
( mforall_di
= ( ^ [X7: $i > mworld > $o,X3: mworld] :
! [X6: $i] :
( ( eiw_di @ X6 @ X3 )
=> ( X7 @ X6 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pCwQBaUklG/E---3.1_2360211.p',mforall_di_def) ).
thf(r2_0,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ r2 )
@ ( mbox
@ ( mforall_di
@ ^ [X32: $i] :
( mbox
@ ( mforall_di
@ ^ [X33: $i] : ( mbox @ ( is_a_theorem @ ( implies @ X33 @ ( or @ X32 @ X33 ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [X32: $i] :
( mbox
@ ( mforall_di
@ ^ [X33: $i] : ( mbox @ ( is_a_theorem @ ( implies @ X33 @ ( or @ X32 @ X33 ) ) ) ) ) ) ) )
@ ( mbox @ r2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pCwQBaUklG/E---3.1_2360211.p',r2_0) ).
thf(principia_r2,conjecture,
mlocal @ ( mbox @ r2 ),
file('/export/starexec/sandbox2/tmp/tmp.pCwQBaUklG/E---3.1_2360211.p',principia_r2) ).
thf(or_2_0,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ or_2 )
@ ( mbox
@ ( mforall_di
@ ^ [X6: $i] :
( mbox
@ ( mforall_di
@ ^ [X9: $i] : ( mbox @ ( is_a_theorem @ ( implies @ X9 @ ( or @ X6 @ X9 ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [X6: $i] :
( mbox
@ ( mforall_di
@ ^ [X9: $i] : ( mbox @ ( is_a_theorem @ ( implies @ X9 @ ( or @ X6 @ X9 ) ) ) ) ) ) ) )
@ ( mbox @ or_2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pCwQBaUklG/E---3.1_2360211.p',or_2_0) ).
thf(mrel_reflexive,axiom,
! [X3: mworld] : ( mrel @ X3 @ X3 ),
file('/export/starexec/sandbox2/tmp/tmp.pCwQBaUklG/E---3.1_2360211.p',mrel_reflexive) ).
thf(hilbert_or_2,axiom,
mlocal @ ( mbox @ or_2 ),
file('/export/starexec/sandbox2/tmp/tmp.pCwQBaUklG/E---3.1_2360211.p',hilbert_or_2) ).
thf(c_0_10,plain,
( mlocal
= ( ^ [Z0: mworld > $o] : ( Z0 @ mactual ) ) ),
inference(fof_simplification,[status(thm)],[mlocal_def]) ).
thf(c_0_11,plain,
( mand
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand_def]) ).
thf(c_0_12,plain,
( mimplies
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies_def]) ).
thf(c_0_13,plain,
( mbox
= ( ^ [Z0: mworld > $o,Z1: mworld] :
! [X5: mworld] :
( ( mrel @ Z1 @ X5 )
=> ( Z0 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_def]) ).
thf(c_0_14,plain,
( mforall_di
= ( ^ [Z0: $i > mworld > $o,Z1: mworld] :
! [X6: $i] :
( ( eiw_di @ X6 @ Z1 )
=> ( Z0 @ X6 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mforall_di_def]) ).
thf(c_0_15,plain,
( ! [X473: mworld] :
( ( mrel @ mactual @ X473 )
=> ( ! [X467: mworld] :
( ( mrel @ X473 @ X467 )
=> ( r2 @ X467 ) )
=> ! [X472: mworld] :
( ( mrel @ X473 @ X472 )
=> ! [X471: $i] :
( ( eiw_di @ X471 @ X472 )
=> ! [X470: mworld] :
( ( mrel @ X472 @ X470 )
=> ! [X469: $i] :
( ( eiw_di @ X469 @ X470 )
=> ! [X468: mworld] :
( ( mrel @ X470 @ X468 )
=> ( is_a_theorem @ ( implies @ X469 @ ( or @ X471 @ X469 ) ) @ X468 ) ) ) ) ) ) ) )
& ! [X480: mworld] :
( ( mrel @ mactual @ X480 )
=> ( ! [X478: mworld] :
( ( mrel @ X480 @ X478 )
=> ! [X477: $i] :
( ( eiw_di @ X477 @ X478 )
=> ! [X476: mworld] :
( ( mrel @ X478 @ X476 )
=> ! [X475: $i] :
( ( eiw_di @ X475 @ X476 )
=> ! [X474: mworld] :
( ( mrel @ X476 @ X474 )
=> ( is_a_theorem @ ( implies @ X475 @ ( or @ X477 @ X475 ) ) @ X474 ) ) ) ) ) )
=> ! [X479: mworld] :
( ( mrel @ X480 @ X479 )
=> ( r2 @ X479 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[r2_0]),c_0_10]),c_0_11]),c_0_12]),c_0_13]),c_0_14]) ).
thf(c_0_16,negated_conjecture,
~ ( mlocal @ ( mbox @ r2 ) ),
inference(assume_negation,[status(cth)],[principia_r2]) ).
thf(c_0_17,plain,
( ! [X305: mworld] :
( ( mrel @ mactual @ X305 )
=> ( ! [X299: mworld] :
( ( mrel @ X305 @ X299 )
=> ( or_2 @ X299 ) )
=> ! [X304: mworld] :
( ( mrel @ X305 @ X304 )
=> ! [X303: $i] :
( ( eiw_di @ X303 @ X304 )
=> ! [X302: mworld] :
( ( mrel @ X304 @ X302 )
=> ! [X301: $i] :
( ( eiw_di @ X301 @ X302 )
=> ! [X300: mworld] :
( ( mrel @ X302 @ X300 )
=> ( is_a_theorem @ ( implies @ X301 @ ( or @ X303 @ X301 ) ) @ X300 ) ) ) ) ) ) ) )
& ! [X312: mworld] :
( ( mrel @ mactual @ X312 )
=> ( ! [X310: mworld] :
( ( mrel @ X312 @ X310 )
=> ! [X309: $i] :
( ( eiw_di @ X309 @ X310 )
=> ! [X308: mworld] :
( ( mrel @ X310 @ X308 )
=> ! [X307: $i] :
( ( eiw_di @ X307 @ X308 )
=> ! [X306: mworld] :
( ( mrel @ X308 @ X306 )
=> ( is_a_theorem @ ( implies @ X307 @ ( or @ X309 @ X307 ) ) @ X306 ) ) ) ) ) )
=> ! [X311: mworld] :
( ( mrel @ X312 @ X311 )
=> ( or_2 @ X311 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[or_2_0]),c_0_10]),c_0_11]),c_0_12]),c_0_13]),c_0_14]) ).
thf(c_0_18,plain,
! [X1020: mworld,X1022: mworld,X1023: $i,X1024: mworld,X1025: $i,X1026: mworld,X1027: mworld,X1033: mworld] :
( ( ( mrel @ X1020 @ ( esk155_1 @ X1020 ) )
| ~ ( mrel @ X1020 @ X1022 )
| ~ ( eiw_di @ X1023 @ X1022 )
| ~ ( mrel @ X1022 @ X1024 )
| ~ ( eiw_di @ X1025 @ X1024 )
| ~ ( mrel @ X1024 @ X1026 )
| ( is_a_theorem @ ( implies @ X1025 @ ( or @ X1023 @ X1025 ) ) @ X1026 )
| ~ ( mrel @ mactual @ X1020 ) )
& ( ~ ( r2 @ ( esk155_1 @ X1020 ) )
| ~ ( mrel @ X1020 @ X1022 )
| ~ ( eiw_di @ X1023 @ X1022 )
| ~ ( mrel @ X1022 @ X1024 )
| ~ ( eiw_di @ X1025 @ X1024 )
| ~ ( mrel @ X1024 @ X1026 )
| ( is_a_theorem @ ( implies @ X1025 @ ( or @ X1023 @ X1025 ) ) @ X1026 )
| ~ ( mrel @ mactual @ X1020 ) )
& ( ( mrel @ X1027 @ ( esk156_1 @ X1027 ) )
| ~ ( mrel @ X1027 @ X1033 )
| ( r2 @ X1033 )
| ~ ( mrel @ mactual @ X1027 ) )
& ( ( eiw_di @ ( esk157_1 @ X1027 ) @ ( esk156_1 @ X1027 ) )
| ~ ( mrel @ X1027 @ X1033 )
| ( r2 @ X1033 )
| ~ ( mrel @ mactual @ X1027 ) )
& ( ( mrel @ ( esk156_1 @ X1027 ) @ ( esk158_1 @ X1027 ) )
| ~ ( mrel @ X1027 @ X1033 )
| ( r2 @ X1033 )
| ~ ( mrel @ mactual @ X1027 ) )
& ( ( eiw_di @ ( esk159_1 @ X1027 ) @ ( esk158_1 @ X1027 ) )
| ~ ( mrel @ X1027 @ X1033 )
| ( r2 @ X1033 )
| ~ ( mrel @ mactual @ X1027 ) )
& ( ( mrel @ ( esk158_1 @ X1027 ) @ ( esk160_1 @ X1027 ) )
| ~ ( mrel @ X1027 @ X1033 )
| ( r2 @ X1033 )
| ~ ( mrel @ mactual @ X1027 ) )
& ( ~ ( is_a_theorem @ ( implies @ ( esk159_1 @ X1027 ) @ ( or @ ( esk157_1 @ X1027 ) @ ( esk159_1 @ X1027 ) ) ) @ ( esk160_1 @ X1027 ) )
| ~ ( mrel @ X1027 @ X1033 )
| ( r2 @ X1033 )
| ~ ( mrel @ mactual @ X1027 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])])]) ).
thf(c_0_19,plain,
! [X588: mworld] : ( mrel @ X588 @ X588 ),
inference(variable_rename,[status(thm)],[mrel_reflexive]) ).
thf(c_0_20,negated_conjecture,
~ ! [X587: mworld] :
( ( mrel @ mactual @ X587 )
=> ( r2 @ X587 ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_16,c_0_10]),c_0_13]) ).
thf(c_0_21,plain,
! [X852: mworld,X854: mworld,X855: $i,X856: mworld,X857: $i,X858: mworld,X859: mworld,X865: mworld] :
( ( ( mrel @ X852 @ ( esk83_1 @ X852 ) )
| ~ ( mrel @ X852 @ X854 )
| ~ ( eiw_di @ X855 @ X854 )
| ~ ( mrel @ X854 @ X856 )
| ~ ( eiw_di @ X857 @ X856 )
| ~ ( mrel @ X856 @ X858 )
| ( is_a_theorem @ ( implies @ X857 @ ( or @ X855 @ X857 ) ) @ X858 )
| ~ ( mrel @ mactual @ X852 ) )
& ( ~ ( or_2 @ ( esk83_1 @ X852 ) )
| ~ ( mrel @ X852 @ X854 )
| ~ ( eiw_di @ X855 @ X854 )
| ~ ( mrel @ X854 @ X856 )
| ~ ( eiw_di @ X857 @ X856 )
| ~ ( mrel @ X856 @ X858 )
| ( is_a_theorem @ ( implies @ X857 @ ( or @ X855 @ X857 ) ) @ X858 )
| ~ ( mrel @ mactual @ X852 ) )
& ( ( mrel @ X859 @ ( esk84_1 @ X859 ) )
| ~ ( mrel @ X859 @ X865 )
| ( or_2 @ X865 )
| ~ ( mrel @ mactual @ X859 ) )
& ( ( eiw_di @ ( esk85_1 @ X859 ) @ ( esk84_1 @ X859 ) )
| ~ ( mrel @ X859 @ X865 )
| ( or_2 @ X865 )
| ~ ( mrel @ mactual @ X859 ) )
& ( ( mrel @ ( esk84_1 @ X859 ) @ ( esk86_1 @ X859 ) )
| ~ ( mrel @ X859 @ X865 )
| ( or_2 @ X865 )
| ~ ( mrel @ mactual @ X859 ) )
& ( ( eiw_di @ ( esk87_1 @ X859 ) @ ( esk86_1 @ X859 ) )
| ~ ( mrel @ X859 @ X865 )
| ( or_2 @ X865 )
| ~ ( mrel @ mactual @ X859 ) )
& ( ( mrel @ ( esk86_1 @ X859 ) @ ( esk88_1 @ X859 ) )
| ~ ( mrel @ X859 @ X865 )
| ( or_2 @ X865 )
| ~ ( mrel @ mactual @ X859 ) )
& ( ~ ( is_a_theorem @ ( implies @ ( esk87_1 @ X859 ) @ ( or @ ( esk85_1 @ X859 ) @ ( esk87_1 @ X859 ) ) ) @ ( esk88_1 @ X859 ) )
| ~ ( mrel @ X859 @ X865 )
| ( or_2 @ X865 )
| ~ ( mrel @ mactual @ X859 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])])]) ).
thf(c_0_22,plain,
! [X5: mworld,X3: mworld] :
( ( mrel @ X3 @ ( esk156_1 @ X3 ) )
| ( r2 @ X5 )
| ~ ( mrel @ X3 @ X5 )
| ~ ( mrel @ mactual @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_23,plain,
! [X3: mworld] : ( mrel @ X3 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_24,negated_conjecture,
( ( mrel @ mactual @ esk188_0 )
& ~ ( r2 @ esk188_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
thf(c_0_25,plain,
! [X5: mworld,X9: $i,X6: $i,X36: mworld,X35: mworld,X3: mworld] :
( ( mrel @ X3 @ ( esk83_1 @ X3 ) )
| ( is_a_theorem @ ( implies @ X9 @ ( or @ X6 @ X9 ) ) @ X36 )
| ~ ( mrel @ X3 @ X5 )
| ~ ( eiw_di @ X6 @ X5 )
| ~ ( mrel @ X5 @ X35 )
| ~ ( eiw_di @ X9 @ X35 )
| ~ ( mrel @ X35 @ X36 )
| ~ ( mrel @ mactual @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_26,plain,
! [X3: mworld] :
( ( mrel @ mactual @ ( esk156_1 @ mactual ) )
| ( r2 @ X3 )
| ~ ( mrel @ mactual @ X3 ) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_27,negated_conjecture,
mrel @ mactual @ esk188_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_28,negated_conjecture,
~ ( r2 @ esk188_0 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_29,plain,
! [X5: mworld,X3: mworld] :
( ( eiw_di @ ( esk157_1 @ X3 ) @ ( esk156_1 @ X3 ) )
| ( r2 @ X5 )
| ~ ( mrel @ X3 @ X5 )
| ~ ( mrel @ mactual @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_30,plain,
! [X3: mworld,X5: mworld,X9: $i,X6: $i,X35: mworld] :
( ( is_a_theorem @ ( implies @ X6 @ ( or @ X9 @ X6 ) ) @ X3 )
| ( mrel @ mactual @ ( esk83_1 @ mactual ) )
| ~ ( mrel @ mactual @ X5 )
| ~ ( eiw_di @ X6 @ X35 )
| ~ ( eiw_di @ X9 @ X5 )
| ~ ( mrel @ X35 @ X3 )
| ~ ( mrel @ X5 @ X35 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
thf(c_0_31,negated_conjecture,
mrel @ mactual @ ( esk156_1 @ mactual ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
thf(c_0_32,plain,
! [X3: mworld] :
( ( eiw_di @ ( esk157_1 @ mactual ) @ ( esk156_1 @ mactual ) )
| ( r2 @ X3 )
| ~ ( mrel @ mactual @ X3 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
thf(c_0_33,plain,
! [X5: mworld,X3: mworld] :
( ( mrel @ ( esk156_1 @ X3 ) @ ( esk158_1 @ X3 ) )
| ( r2 @ X5 )
| ~ ( mrel @ X3 @ X5 )
| ~ ( mrel @ mactual @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_34,negated_conjecture,
! [X9: $i,X6: $i,X5: mworld,X3: mworld] :
( ( is_a_theorem @ ( implies @ X6 @ ( or @ X9 @ X6 ) ) @ X3 )
| ( mrel @ mactual @ ( esk83_1 @ mactual ) )
| ~ ( eiw_di @ X9 @ ( esk156_1 @ mactual ) )
| ~ ( mrel @ ( esk156_1 @ mactual ) @ X5 )
| ~ ( eiw_di @ X6 @ X5 )
| ~ ( mrel @ X5 @ X3 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_35,negated_conjecture,
eiw_di @ ( esk157_1 @ mactual ) @ ( esk156_1 @ mactual ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_27]),c_0_28]) ).
thf(c_0_36,plain,
! [X3: mworld] :
( ( mrel @ ( esk156_1 @ mactual ) @ ( esk158_1 @ mactual ) )
| ( r2 @ X3 )
| ~ ( mrel @ mactual @ X3 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_23]) ).
thf(c_0_37,plain,
! [X5: mworld,X3: mworld] :
( ( eiw_di @ ( esk159_1 @ X3 ) @ ( esk158_1 @ X3 ) )
| ( r2 @ X5 )
| ~ ( mrel @ X3 @ X5 )
| ~ ( mrel @ mactual @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_38,plain,
! [X578: mworld] :
( ( mrel @ mactual @ X578 )
=> ( or_2 @ X578 ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[hilbert_or_2,c_0_10]),c_0_13]) ).
thf(c_0_39,negated_conjecture,
! [X6: $i,X5: mworld,X3: mworld] :
( ( is_a_theorem @ ( implies @ X6 @ ( or @ ( esk157_1 @ mactual ) @ X6 ) ) @ X3 )
| ( mrel @ mactual @ ( esk83_1 @ mactual ) )
| ~ ( mrel @ ( esk156_1 @ mactual ) @ X5 )
| ~ ( eiw_di @ X6 @ X5 )
| ~ ( mrel @ X5 @ X3 ) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_40,negated_conjecture,
mrel @ ( esk156_1 @ mactual ) @ ( esk158_1 @ mactual ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_27]),c_0_28]) ).
thf(c_0_41,plain,
! [X3: mworld] :
( ( eiw_di @ ( esk159_1 @ mactual ) @ ( esk158_1 @ mactual ) )
| ( r2 @ X3 )
| ~ ( mrel @ mactual @ X3 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_23]) ).
thf(c_0_42,plain,
! [X5: mworld,X3: mworld] :
( ( mrel @ ( esk158_1 @ X3 ) @ ( esk160_1 @ X3 ) )
| ( r2 @ X5 )
| ~ ( mrel @ X3 @ X5 )
| ~ ( mrel @ mactual @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_43,plain,
! [X1131: mworld] :
( ~ ( mrel @ mactual @ X1131 )
| ( or_2 @ X1131 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])]) ).
thf(c_0_44,negated_conjecture,
! [X6: $i,X3: mworld] :
( ( is_a_theorem @ ( implies @ X6 @ ( or @ ( esk157_1 @ mactual ) @ X6 ) ) @ X3 )
| ( mrel @ mactual @ ( esk83_1 @ mactual ) )
| ~ ( eiw_di @ X6 @ ( esk158_1 @ mactual ) )
| ~ ( mrel @ ( esk158_1 @ mactual ) @ X3 ) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
thf(c_0_45,negated_conjecture,
eiw_di @ ( esk159_1 @ mactual ) @ ( esk158_1 @ mactual ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_27]),c_0_28]) ).
thf(c_0_46,plain,
! [X3: mworld] :
( ( mrel @ ( esk158_1 @ mactual ) @ ( esk160_1 @ mactual ) )
| ( r2 @ X3 )
| ~ ( mrel @ mactual @ X3 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_23]) ).
thf(c_0_47,plain,
! [X5: mworld,X3: mworld] :
( ( r2 @ X5 )
| ~ ( is_a_theorem @ ( implies @ ( esk159_1 @ X3 ) @ ( or @ ( esk157_1 @ X3 ) @ ( esk159_1 @ X3 ) ) ) @ ( esk160_1 @ X3 ) )
| ~ ( mrel @ X3 @ X5 )
| ~ ( mrel @ mactual @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_48,plain,
! [X5: mworld,X9: $i,X6: $i,X36: mworld,X35: mworld,X3: mworld] :
( ( is_a_theorem @ ( implies @ X9 @ ( or @ X6 @ X9 ) ) @ X36 )
| ~ ( or_2 @ ( esk83_1 @ X3 ) )
| ~ ( mrel @ X3 @ X5 )
| ~ ( eiw_di @ X6 @ X5 )
| ~ ( mrel @ X5 @ X35 )
| ~ ( eiw_di @ X9 @ X35 )
| ~ ( mrel @ X35 @ X36 )
| ~ ( mrel @ mactual @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_49,plain,
! [X3: mworld] :
( ( or_2 @ X3 )
| ~ ( mrel @ mactual @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_50,negated_conjecture,
! [X3: mworld] :
( ( is_a_theorem @ ( implies @ ( esk159_1 @ mactual ) @ ( or @ ( esk157_1 @ mactual ) @ ( esk159_1 @ mactual ) ) ) @ X3 )
| ( mrel @ mactual @ ( esk83_1 @ mactual ) )
| ~ ( mrel @ ( esk158_1 @ mactual ) @ X3 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_51,negated_conjecture,
mrel @ ( esk158_1 @ mactual ) @ ( esk160_1 @ mactual ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_27]),c_0_28]) ).
thf(c_0_52,negated_conjecture,
! [X3: mworld] :
( ~ ( is_a_theorem @ ( implies @ ( esk159_1 @ X3 ) @ ( or @ ( esk157_1 @ X3 ) @ ( esk159_1 @ X3 ) ) ) @ ( esk160_1 @ X3 ) )
| ~ ( mrel @ mactual @ X3 )
| ~ ( mrel @ X3 @ esk188_0 ) ),
inference(spm,[status(thm)],[c_0_28,c_0_47]) ).
thf(c_0_53,plain,
! [X3: mworld,X6: $i,X5: mworld,X35: mworld,X9: $i,X36: mworld] :
( ( is_a_theorem @ ( implies @ X6 @ ( or @ X9 @ X6 ) ) @ X3 )
| ~ ( mrel @ mactual @ ( esk83_1 @ X5 ) )
| ~ ( mrel @ mactual @ X5 )
| ~ ( eiw_di @ X6 @ X35 )
| ~ ( eiw_di @ X9 @ X36 )
| ~ ( mrel @ X35 @ X3 )
| ~ ( mrel @ X36 @ X35 )
| ~ ( mrel @ X5 @ X36 ) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
thf(c_0_54,negated_conjecture,
( ( is_a_theorem @ ( implies @ ( esk159_1 @ mactual ) @ ( or @ ( esk157_1 @ mactual ) @ ( esk159_1 @ mactual ) ) ) @ ( esk160_1 @ mactual ) )
| ( mrel @ mactual @ ( esk83_1 @ mactual ) ) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
thf(c_0_55,negated_conjecture,
! [X3: mworld,X35: mworld,X5: mworld,X36: mworld] :
( ~ ( mrel @ mactual @ ( esk83_1 @ X3 ) )
| ~ ( eiw_di @ ( esk159_1 @ X5 ) @ X35 )
| ~ ( eiw_di @ ( esk157_1 @ X5 ) @ X36 )
| ~ ( mrel @ X35 @ ( esk160_1 @ X5 ) )
| ~ ( mrel @ mactual @ X5 )
| ~ ( mrel @ X5 @ esk188_0 )
| ~ ( mrel @ mactual @ X3 )
| ~ ( mrel @ X36 @ X35 )
| ~ ( mrel @ X3 @ X36 ) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
thf(c_0_56,negated_conjecture,
mrel @ mactual @ ( esk83_1 @ mactual ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_54]),c_0_23]),c_0_27])]) ).
thf(c_0_57,negated_conjecture,
! [X3: mworld,X35: mworld,X5: mworld] :
( ~ ( eiw_di @ ( esk159_1 @ X3 ) @ X5 )
| ~ ( eiw_di @ ( esk157_1 @ X3 ) @ X35 )
| ~ ( mrel @ X5 @ ( esk160_1 @ X3 ) )
| ~ ( mrel @ mactual @ X3 )
| ~ ( mrel @ X3 @ esk188_0 )
| ~ ( mrel @ mactual @ X35 )
| ~ ( mrel @ X35 @ X5 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_23])]) ).
thf(c_0_58,negated_conjecture,
! [X3: mworld] :
( ~ ( eiw_di @ ( esk157_1 @ mactual ) @ X3 )
| ~ ( mrel @ X3 @ ( esk158_1 @ mactual ) )
| ~ ( mrel @ mactual @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_45]),c_0_51]),c_0_23]),c_0_27])]) ).
thf(c_0_59,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_35]),c_0_40]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL944^8 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n003.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 10:52:58 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.23/0.26 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.pCwQBaUklG/E---3.1_2360211.p
% 3.51/0.85 % Version: 3.5.1-ho
% 3.51/0.85 % Preprocessing class: HSLSSMSSMLLNHSN.
% 3.51/0.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.51/0.85 % Starting almost_fo_3 with 1500s (5) cores
% 3.51/0.85 % Starting sh10 with 300s (1) cores
% 3.51/0.85 % Starting new_ho_16 with 300s (1) cores
% 3.51/0.85 % Starting post_as_ho11 with 300s (1) cores
% 3.51/0.85 % new_ho_16 with pid 2360226 completed with status 9
% 3.51/0.85 % almost_fo_3 with pid 2360224 completed with status 0
% 3.51/0.85 % Result found by almost_fo_3
% 3.51/0.85 % Preprocessing class: HSLSSMSSMLLNHSN.
% 3.51/0.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.51/0.85 % Starting almost_fo_3 with 1500s (5) cores
% 3.51/0.85 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.51/0.85 % No SInE strategy applied
% 3.51/0.85 % Search class: HGUNS-FSLF31-MHSSMFNN
% 3.51/0.85 % partial match(2): HGUNM-FSLF32-MHSSMFNN
% 3.51/0.85 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 3.51/0.85 % Starting SubtermCWHack with 151s (1) cores
% 3.51/0.85 % Starting almost_fo_3 with 329s (1) cores
% 3.51/0.85 % Starting ho_unfolding_7 with 329s (1) cores
% 3.51/0.85 % Starting new_bool_3 with 329s (1) cores
% 3.51/0.85 % Starting new_bool_1 with 329s (1) cores
% 3.51/0.85 % almost_fo_3 with pid 2360242 completed with status 0
% 3.51/0.85 % Result found by almost_fo_3
% 3.51/0.85 % Preprocessing class: HSLSSMSSMLLNHSN.
% 3.51/0.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.51/0.85 % Starting almost_fo_3 with 1500s (5) cores
% 3.51/0.85 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.51/0.85 % No SInE strategy applied
% 3.51/0.85 % Search class: HGUNS-FSLF31-MHSSMFNN
% 3.51/0.85 % partial match(2): HGUNM-FSLF32-MHSSMFNN
% 3.51/0.85 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 3.51/0.85 % Starting SubtermCWHack with 151s (1) cores
% 3.51/0.85 % Starting almost_fo_3 with 329s (1) cores
% 3.51/0.85 % Preprocessing time : 0.009 s
% 3.51/0.85 % Presaturation interreduction done
% 3.51/0.85
% 3.51/0.85 % Proof found!
% 3.51/0.85 % SZS status Theorem
% 3.51/0.85 % SZS output start CNFRefutation
% See solution above
% 3.51/0.85 % Parsed axioms : 130
% 3.51/0.85 % Removed by relevancy pruning/SinE : 0
% 3.51/0.85 % Initial clauses : 343
% 3.51/0.85 % Removed in clause preprocessing : 52
% 3.51/0.85 % Initial clauses in saturation : 291
% 3.51/0.85 % Processed clauses : 2596
% 3.51/0.85 % ...of these trivial : 0
% 3.51/0.85 % ...subsumed : 85
% 3.51/0.85 % ...remaining for further processing : 2511
% 3.51/0.85 % Other redundant clauses eliminated : 0
% 3.51/0.85 % Clauses deleted for lack of memory : 0
% 3.51/0.85 % Backward-subsumed : 0
% 3.51/0.85 % Backward-rewritten : 106
% 3.51/0.85 % Generated clauses : 2798
% 3.51/0.85 % ...of the previous two non-redundant : 2797
% 3.51/0.85 % ...aggressively subsumed : 0
% 3.51/0.85 % Contextual simplify-reflections : 0
% 3.51/0.85 % Paramodulations : 2798
% 3.51/0.85 % Factorizations : 0
% 3.51/0.85 % NegExts : 0
% 3.51/0.85 % Equation resolutions : 0
% 3.51/0.85 % Disequality decompositions : 0
% 3.51/0.85 % Total rewrite steps : 138
% 3.51/0.85 % ...of those cached : 121
% 3.51/0.85 % Propositional unsat checks : 0
% 3.51/0.85 % Propositional check models : 0
% 3.51/0.85 % Propositional check unsatisfiable : 0
% 3.51/0.85 % Propositional clauses : 0
% 3.51/0.85 % Propositional clauses after purity: 0
% 3.51/0.85 % Propositional unsat core size : 0
% 3.51/0.85 % Propositional preprocessing time : 0.000
% 3.51/0.85 % Propositional encoding time : 0.000
% 3.51/0.85 % Propositional solver time : 0.000
% 3.51/0.85 % Success case prop preproc time : 0.000
% 3.51/0.85 % Success case prop encoding time : 0.000
% 3.51/0.85 % Success case prop solver time : 0.000
% 3.51/0.85 % Current number of processed clauses : 2115
% 3.51/0.85 % Positive orientable unit clauses : 17
% 3.51/0.85 % Positive unorientable unit clauses: 0
% 3.51/0.85 % Negative unit clauses : 2
% 3.51/0.85 % Non-unit-clauses : 2096
% 3.51/0.85 % Current number of unprocessed clauses: 767
% 3.51/0.85 % ...number of literals in the above : 6221
% 3.51/0.85 % Current number of archived formulas : 0
% 3.51/0.85 % Current number of archived clauses : 396
% 3.51/0.85 % Clause-clause subsumption calls (NU) : 1285401
% 3.51/0.85 % Rec. Clause-clause subsumption calls : 382310
% 3.51/0.85 % Non-unit clause-clause subsumptions : 85
% 3.51/0.85 % Unit Clause-clause subsumption calls : 4267
% 3.51/0.85 % Rewrite failures with RHS unbound : 0
% 3.51/0.85 % BW rewrite match attempts : 16
% 3.51/0.85 % BW rewrite match successes : 14
% 3.51/0.85 % Condensation attempts : 0
% 3.51/0.85 % Condensation successes : 0
% 3.51/0.85 % Termbank termtop insertions : 135878
% 3.51/0.85 % Search garbage collected termcells : 27588
% 3.51/0.85
% 3.51/0.85 % -------------------------------------------------
% 3.51/0.85 % User time : 0.503 s
% 3.51/0.85 % System time : 0.021 s
% 3.51/0.85 % Total time : 0.524 s
% 3.51/0.85 % Maximum resident set size: 7912 pages
% 3.51/0.85
% 3.51/0.85 % -------------------------------------------------
% 3.51/0.85 % User time : 2.351 s
% 3.51/0.85 % System time : 0.158 s
% 3.51/0.85 % Total time : 2.509 s
% 3.51/0.85 % Maximum resident set size: 4864 pages
% 3.51/0.85 % E exiting
%------------------------------------------------------------------------------