%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL944_8 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 : Thu Sep 24 01:17:46 PM UTC 2026
% Result : Theorem 140.47s 36.10s
% Output : CNFRefutation 140.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 51 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 252 ( 0 equ)
% Maximal formula atoms : 40 ( 4 avg)
% Number of connectives : 323 ( 122 ~; 149 |; 17 &)
% ( 0 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 2 con; 0-2 aty)
% Number of variables : 114 ( 0 sgn 114 !; 0 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
'$ki_world': $tType ).
tff(decl_23,type,
'$ki_local_world': '$ki_world' ).
tff(decl_24,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(decl_25,type,
r2: '$ki_world' > $o ).
tff(decl_51,type,
or_2: '$ki_world' > $o ).
tff(decl_57,type,
is_a_theorem: ( $i * '$ki_world' ) > $o ).
tff(decl_60,type,
or: ( $i * $i ) > $i ).
tff(decl_62,type,
implies: ( $i * $i ) > $i ).
tff(decl_63,type,
'$ki_exists_in_world_$i': ( $i * '$ki_world' ) > $o ).
tff(decl_146,type,
esk83_1: '$ki_world' > '$ki_world' ).
tff(decl_147,type,
esk84_1: '$ki_world' > '$ki_world' ).
tff(decl_148,type,
esk85_1: '$ki_world' > $i ).
tff(decl_149,type,
esk86_1: '$ki_world' > '$ki_world' ).
tff(decl_150,type,
esk87_1: '$ki_world' > $i ).
tff(decl_151,type,
esk88_1: '$ki_world' > '$ki_world' ).
tff(decl_218,type,
esk155_1: '$ki_world' > '$ki_world' ).
tff(decl_219,type,
esk156_1: '$ki_world' > '$ki_world' ).
tff(decl_220,type,
esk157_1: '$ki_world' > $i ).
tff(decl_221,type,
esk158_1: '$ki_world' > '$ki_world' ).
tff(decl_222,type,
esk159_1: '$ki_world' > $i ).
tff(decl_223,type,
esk160_1: '$ki_world' > '$ki_world' ).
tff(decl_251,type,
esk188_0: '$ki_world' ).
tff(r2_0,axiom,
( ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ( ! [X3: '$ki_world'] :
( '$ki_accessible'(X1,X3)
=> ! [X12] :
( '$ki_exists_in_world_$i'(X3,X12)
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X3,X5)
=> ! [X13] :
( '$ki_exists_in_world_$i'(X5,X13)
=> ! [X6: '$ki_world'] :
( '$ki_accessible'(X5,X6)
=> is_a_theorem(X6,implies(X13,or(X12,X13))) ) ) ) ) )
=> ! [X3: '$ki_world'] :
( '$ki_accessible'(X1,X3)
=> r2(X3) ) ) )
& ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ( ! [X3: '$ki_world'] :
( '$ki_accessible'(X1,X3)
=> r2(X3) )
=> ! [X3: '$ki_world'] :
( '$ki_accessible'(X1,X3)
=> ! [X12] :
( '$ki_exists_in_world_$i'(X3,X12)
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X3,X5)
=> ! [X13] :
( '$ki_exists_in_world_$i'(X5,X13)
=> ! [X6: '$ki_world'] :
( '$ki_accessible'(X5,X6)
=> is_a_theorem(X6,implies(X13,or(X12,X13))) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2_0) ).
tff(mrel_reflexive,axiom,
! [X1: '$ki_world'] : '$ki_accessible'(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
tff(verify,conjecture,
! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> r2(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(or_2_0,axiom,
( ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ( ! [X3: '$ki_world'] :
( '$ki_accessible'(X1,X3)
=> ! [X2] :
( '$ki_exists_in_world_$i'(X3,X2)
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X3,X5)
=> ! [X4] :
( '$ki_exists_in_world_$i'(X5,X4)
=> ! [X6: '$ki_world'] :
( '$ki_accessible'(X5,X6)
=> is_a_theorem(X6,implies(X4,or(X2,X4))) ) ) ) ) )
=> ! [X3: '$ki_world'] :
( '$ki_accessible'(X1,X3)
=> or_2(X3) ) ) )
& ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ( ! [X3: '$ki_world'] :
( '$ki_accessible'(X1,X3)
=> or_2(X3) )
=> ! [X3: '$ki_world'] :
( '$ki_accessible'(X1,X3)
=> ! [X2] :
( '$ki_exists_in_world_$i'(X3,X2)
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X3,X5)
=> ! [X4] :
( '$ki_exists_in_world_$i'(X5,X4)
=> ! [X6: '$ki_world'] :
( '$ki_accessible'(X5,X6)
=> is_a_theorem(X6,implies(X4,or(X2,X4))) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_2_0) ).
tff(hilbert_or_2,axiom,
! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> or_2(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_2) ).
tff(c_0_5,plain,
! [X447: '$ki_world',X449: '$ki_world',X450,X451: '$ki_world',X452,X453: '$ki_world',X454: '$ki_world',X460: '$ki_world'] :
( ( ~ '$ki_accessible'('$ki_local_world',X454)
| r2(X460)
| ~ '$ki_accessible'(X454,X460)
| ~ is_a_theorem(esk160_1(X454),implies(esk159_1(X454),or(esk157_1(X454),esk159_1(X454)))) )
& ( ~ '$ki_accessible'('$ki_local_world',X454)
| r2(X460)
| ~ '$ki_accessible'(X454,X460)
| '$ki_accessible'(esk158_1(X454),esk160_1(X454)) )
& ( ~ '$ki_accessible'('$ki_local_world',X454)
| r2(X460)
| ~ '$ki_accessible'(X454,X460)
| '$ki_exists_in_world_$i'(esk158_1(X454),esk159_1(X454)) )
& ( ~ '$ki_accessible'('$ki_local_world',X454)
| r2(X460)
| ~ '$ki_accessible'(X454,X460)
| '$ki_accessible'(esk156_1(X454),esk158_1(X454)) )
& ( ~ '$ki_accessible'('$ki_local_world',X454)
| r2(X460)
| ~ '$ki_accessible'(X454,X460)
| '$ki_exists_in_world_$i'(esk156_1(X454),esk157_1(X454)) )
& ( ~ '$ki_accessible'('$ki_local_world',X454)
| r2(X460)
| ~ '$ki_accessible'(X454,X460)
| '$ki_accessible'(X454,esk156_1(X454)) )
& ( ~ '$ki_accessible'('$ki_local_world',X447)
| is_a_theorem(X453,implies(X452,or(X450,X452)))
| ~ '$ki_accessible'(X451,X453)
| ~ '$ki_exists_in_world_$i'(X451,X452)
| ~ '$ki_accessible'(X449,X451)
| ~ '$ki_exists_in_world_$i'(X449,X450)
| ~ '$ki_accessible'(X447,X449)
| ~ r2(esk155_1(X447)) )
& ( ~ '$ki_accessible'('$ki_local_world',X447)
| is_a_theorem(X453,implies(X452,or(X450,X452)))
| ~ '$ki_accessible'(X451,X453)
| ~ '$ki_exists_in_world_$i'(X451,X452)
| ~ '$ki_accessible'(X449,X451)
| ~ '$ki_exists_in_world_$i'(X449,X450)
| ~ '$ki_accessible'(X447,X449)
| '$ki_accessible'(X447,esk155_1(X447)) ) ),
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)],[r2_0])])])])])]) ).
tff(c_0_6,plain,
! [X15: '$ki_world'] : '$ki_accessible'(X15,X15),
inference(variable_rename,[status(thm)],[mrel_reflexive]) ).
tff(c_0_7,negated_conjecture,
~ ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> r2(X1) ),
inference(assume_negation,[status(cth)],[verify]) ).
tff(c_0_8,plain,
! [X279: '$ki_world',X281: '$ki_world',X282,X283: '$ki_world',X284,X285: '$ki_world',X286: '$ki_world',X292: '$ki_world'] :
( ( ~ '$ki_accessible'('$ki_local_world',X286)
| or_2(X292)
| ~ '$ki_accessible'(X286,X292)
| ~ is_a_theorem(esk88_1(X286),implies(esk87_1(X286),or(esk85_1(X286),esk87_1(X286)))) )
& ( ~ '$ki_accessible'('$ki_local_world',X286)
| or_2(X292)
| ~ '$ki_accessible'(X286,X292)
| '$ki_accessible'(esk86_1(X286),esk88_1(X286)) )
& ( ~ '$ki_accessible'('$ki_local_world',X286)
| or_2(X292)
| ~ '$ki_accessible'(X286,X292)
| '$ki_exists_in_world_$i'(esk86_1(X286),esk87_1(X286)) )
& ( ~ '$ki_accessible'('$ki_local_world',X286)
| or_2(X292)
| ~ '$ki_accessible'(X286,X292)
| '$ki_accessible'(esk84_1(X286),esk86_1(X286)) )
& ( ~ '$ki_accessible'('$ki_local_world',X286)
| or_2(X292)
| ~ '$ki_accessible'(X286,X292)
| '$ki_exists_in_world_$i'(esk84_1(X286),esk85_1(X286)) )
& ( ~ '$ki_accessible'('$ki_local_world',X286)
| or_2(X292)
| ~ '$ki_accessible'(X286,X292)
| '$ki_accessible'(X286,esk84_1(X286)) )
& ( ~ '$ki_accessible'('$ki_local_world',X279)
| is_a_theorem(X285,implies(X284,or(X282,X284)))
| ~ '$ki_accessible'(X283,X285)
| ~ '$ki_exists_in_world_$i'(X283,X284)
| ~ '$ki_accessible'(X281,X283)
| ~ '$ki_exists_in_world_$i'(X281,X282)
| ~ '$ki_accessible'(X279,X281)
| ~ or_2(esk83_1(X279)) )
& ( ~ '$ki_accessible'('$ki_local_world',X279)
| is_a_theorem(X285,implies(X284,or(X282,X284)))
| ~ '$ki_accessible'(X283,X285)
| ~ '$ki_exists_in_world_$i'(X283,X284)
| ~ '$ki_accessible'(X281,X283)
| ~ '$ki_exists_in_world_$i'(X281,X282)
| ~ '$ki_accessible'(X279,X281)
| '$ki_accessible'(X279,esk83_1(X279)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_2_0])])])])])]) ).
tcf(c_0_9,plain,
! [X3: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,X3)
| r2(X3)
| '$ki_accessible'(X1,esk156_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
tcf(c_0_10,plain,
! [X1: '$ki_world'] : '$ki_accessible'(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
tff(c_0_11,negated_conjecture,
( ~ r2(esk188_0)
& '$ki_accessible'('$ki_local_world',esk188_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
tcf(c_0_12,plain,
! [X2,X4,X3: '$ki_world',X6: '$ki_world',X5: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X5,X6)
| ~ '$ki_exists_in_world_$i'(X5,X4)
| ~ '$ki_accessible'(X3,X5)
| ~ '$ki_exists_in_world_$i'(X3,X2)
| ~ '$ki_accessible'(X1,X3)
| is_a_theorem(X6,implies(X4,or(X2,X4)))
| '$ki_accessible'(X1,esk83_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_13,plain,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| '$ki_accessible'('$ki_local_world',esk156_1('$ki_local_world'))
| r2(X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
tcf(c_0_14,negated_conjecture,
'$ki_accessible'('$ki_local_world',esk188_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
tcf(c_0_15,negated_conjecture,
~ r2(esk188_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
tcf(c_0_16,plain,
! [X3: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,X3)
| r2(X3)
| '$ki_exists_in_world_$i'(esk156_1(X1),esk157_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
tcf(c_0_17,plain,
! [X1: '$ki_world',X2,X4,X5: '$ki_world',X3: '$ki_world'] :
( ~ '$ki_accessible'(X5,X3)
| ~ '$ki_accessible'(X3,X1)
| ~ '$ki_accessible'('$ki_local_world',X5)
| ~ '$ki_exists_in_world_$i'(X5,X4)
| ~ '$ki_exists_in_world_$i'(X3,X2)
| '$ki_accessible'('$ki_local_world',esk83_1('$ki_local_world'))
| is_a_theorem(X1,implies(X2,or(X4,X2))) ),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
tcf(c_0_18,negated_conjecture,
'$ki_accessible'('$ki_local_world',esk156_1('$ki_local_world')),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
tcf(c_0_19,plain,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| r2(X1)
| '$ki_exists_in_world_$i'(esk156_1('$ki_local_world'),esk157_1('$ki_local_world')) ),
inference(spm,[status(thm)],[c_0_16,c_0_10]) ).
tcf(c_0_20,plain,
! [X3: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,X3)
| r2(X3)
| '$ki_accessible'(esk156_1(X1),esk158_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
tcf(c_0_21,negated_conjecture,
! [X4,X3: '$ki_world',X2,X1: '$ki_world'] :
( ~ '$ki_accessible'(X3,X1)
| ~ '$ki_accessible'(esk156_1('$ki_local_world'),X3)
| ~ '$ki_exists_in_world_$i'(X3,X2)
| ~ '$ki_exists_in_world_$i'(esk156_1('$ki_local_world'),X4)
| '$ki_accessible'('$ki_local_world',esk83_1('$ki_local_world'))
| is_a_theorem(X1,implies(X2,or(X4,X2))) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
tcf(c_0_22,negated_conjecture,
'$ki_exists_in_world_$i'(esk156_1('$ki_local_world'),esk157_1('$ki_local_world')),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_14]),c_0_15]) ).
tcf(c_0_23,plain,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| '$ki_accessible'(esk156_1('$ki_local_world'),esk158_1('$ki_local_world'))
| r2(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_10]) ).
tcf(c_0_24,plain,
! [X3: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,X3)
| r2(X3)
| '$ki_exists_in_world_$i'(esk158_1(X1),esk159_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
tcf(c_0_25,negated_conjecture,
! [X3: '$ki_world',X2,X1: '$ki_world'] :
( ~ '$ki_accessible'(X3,X1)
| ~ '$ki_accessible'(esk156_1('$ki_local_world'),X3)
| ~ '$ki_exists_in_world_$i'(X3,X2)
| '$ki_accessible'('$ki_local_world',esk83_1('$ki_local_world'))
| is_a_theorem(X1,implies(X2,or(esk157_1('$ki_local_world'),X2))) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
tcf(c_0_26,negated_conjecture,
'$ki_accessible'(esk156_1('$ki_local_world'),esk158_1('$ki_local_world')),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_14]),c_0_15]) ).
tcf(c_0_27,plain,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| r2(X1)
| '$ki_exists_in_world_$i'(esk158_1('$ki_local_world'),esk159_1('$ki_local_world')) ),
inference(spm,[status(thm)],[c_0_24,c_0_10]) ).
tcf(c_0_28,plain,
! [X3: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,X3)
| r2(X3)
| '$ki_accessible'(esk158_1(X1),esk160_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
tcf(c_0_29,negated_conjecture,
! [X2,X1: '$ki_world'] :
( ~ '$ki_accessible'(esk158_1('$ki_local_world'),X1)
| ~ '$ki_exists_in_world_$i'(esk158_1('$ki_local_world'),X2)
| '$ki_accessible'('$ki_local_world',esk83_1('$ki_local_world'))
| is_a_theorem(X1,implies(X2,or(esk157_1('$ki_local_world'),X2))) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
tcf(c_0_30,negated_conjecture,
'$ki_exists_in_world_$i'(esk158_1('$ki_local_world'),esk159_1('$ki_local_world')),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_14]),c_0_15]) ).
tcf(c_0_31,plain,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| '$ki_accessible'(esk158_1('$ki_local_world'),esk160_1('$ki_local_world'))
| r2(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_10]) ).
tcf(c_0_32,plain,
! [X3: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,X3)
| ~ is_a_theorem(esk160_1(X1),implies(esk159_1(X1),or(esk157_1(X1),esk159_1(X1))))
| r2(X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
tcf(c_0_33,negated_conjecture,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'(esk158_1('$ki_local_world'),X1)
| '$ki_accessible'('$ki_local_world',esk83_1('$ki_local_world'))
| is_a_theorem(X1,implies(esk159_1('$ki_local_world'),or(esk157_1('$ki_local_world'),esk159_1('$ki_local_world')))) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
tcf(c_0_34,negated_conjecture,
'$ki_accessible'(esk158_1('$ki_local_world'),esk160_1('$ki_local_world')),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_14]),c_0_15]) ).
tcf(c_0_35,plain,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ is_a_theorem(esk160_1('$ki_local_world'),implies(esk159_1('$ki_local_world'),or(esk157_1('$ki_local_world'),esk159_1('$ki_local_world'))))
| r2(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_10]) ).
tcf(c_0_36,negated_conjecture,
( '$ki_accessible'('$ki_local_world',esk83_1('$ki_local_world'))
| is_a_theorem(esk160_1('$ki_local_world'),implies(esk159_1('$ki_local_world'),or(esk157_1('$ki_local_world'),esk159_1('$ki_local_world')))) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
tff(c_0_37,plain,
! [X558: '$ki_world'] :
( or_2(X558)
| ~ '$ki_accessible'('$ki_local_world',X558) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[hilbert_or_2])])]) ).
tcf(c_0_38,negated_conjecture,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| '$ki_accessible'('$ki_local_world',esk83_1('$ki_local_world'))
| r2(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
tcf(c_0_39,plain,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| or_2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
tcf(c_0_40,negated_conjecture,
'$ki_accessible'('$ki_local_world',esk83_1('$ki_local_world')),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_14]),c_0_15]) ).
tcf(c_0_41,plain,
! [X2,X4,X3: '$ki_world',X6: '$ki_world',X5: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X5,X6)
| ~ '$ki_exists_in_world_$i'(X5,X4)
| ~ '$ki_accessible'(X3,X5)
| ~ '$ki_exists_in_world_$i'(X3,X2)
| ~ '$ki_accessible'(X1,X3)
| ~ or_2(esk83_1(X1))
| is_a_theorem(X6,implies(X4,or(X2,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_42,negated_conjecture,
or_2(esk83_1('$ki_local_world')),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
tcf(c_0_43,negated_conjecture,
! [X1: '$ki_world',X2,X4,X5: '$ki_world',X3: '$ki_world'] :
( ~ '$ki_accessible'(X5,X3)
| ~ '$ki_accessible'(X3,X1)
| ~ '$ki_accessible'('$ki_local_world',X5)
| ~ '$ki_exists_in_world_$i'(X5,X4)
| ~ '$ki_exists_in_world_$i'(X3,X2)
| is_a_theorem(X1,implies(X2,or(X4,X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_10])]) ).
tcf(c_0_44,negated_conjecture,
! [X4,X3: '$ki_world',X2,X1: '$ki_world'] :
( ~ '$ki_accessible'(X3,X1)
| ~ '$ki_accessible'(esk156_1('$ki_local_world'),X3)
| ~ '$ki_exists_in_world_$i'(X3,X2)
| ~ '$ki_exists_in_world_$i'(esk156_1('$ki_local_world'),X4)
| is_a_theorem(X1,implies(X2,or(X4,X2))) ),
inference(spm,[status(thm)],[c_0_43,c_0_18]) ).
tcf(c_0_45,negated_conjecture,
! [X3: '$ki_world',X2,X1: '$ki_world'] :
( ~ '$ki_accessible'(X3,X1)
| ~ '$ki_accessible'(esk156_1('$ki_local_world'),X3)
| ~ '$ki_exists_in_world_$i'(X3,X2)
| is_a_theorem(X1,implies(X2,or(esk157_1('$ki_local_world'),X2))) ),
inference(spm,[status(thm)],[c_0_44,c_0_22]) ).
tcf(c_0_46,negated_conjecture,
! [X2,X1: '$ki_world'] :
( ~ '$ki_accessible'(esk158_1('$ki_local_world'),X1)
| ~ '$ki_exists_in_world_$i'(esk158_1('$ki_local_world'),X2)
| is_a_theorem(X1,implies(X2,or(esk157_1('$ki_local_world'),X2))) ),
inference(spm,[status(thm)],[c_0_45,c_0_26]) ).
tcf(c_0_47,negated_conjecture,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'(esk158_1('$ki_local_world'),X1)
| is_a_theorem(X1,implies(esk159_1('$ki_local_world'),or(esk157_1('$ki_local_world'),esk159_1('$ki_local_world')))) ),
inference(spm,[status(thm)],[c_0_46,c_0_30]) ).
tcf(c_0_48,negated_conjecture,
is_a_theorem(esk160_1('$ki_local_world'),implies(esk159_1('$ki_local_world'),or(esk157_1('$ki_local_world'),esk159_1('$ki_local_world')))),
inference(spm,[status(thm)],[c_0_47,c_0_34]) ).
tcf(c_0_49,plain,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| r2(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_48])]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_14]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL944_8 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/15.66 % Computer : n006.cluster.edu
% 0.16/15.66 % Model : x86_64 x86_64
% 0.16/15.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/15.66 % Memory : 8046.5625MB
% 0.16/15.66 % OS : Linux 6.8.0-71-generic
% 0.16/15.66 % CPULimit : 300
% 0.16/15.66 % WCLimit : 300
% 0.16/15.66 % DateTime : Mon Sep 21 01:13:30 UTC 2026
% 0.16/15.66 % CPUTime :
% 0.16/15.66 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/15.70 Running first-order theorem proving
% 0.21/15.71 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 140.47/36.10 % Version: 3.5.1
% 140.47/36.10 % Preprocessing class: FSLSSMSSSSSNFFN.
% 140.47/36.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 140.47/36.10 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 140.47/36.10 % Starting new_bool_3 with 300s (1) cores
% 140.47/36.10 % Starting new_bool_1 with 300s (1) cores
% 140.47/36.10 % Starting sh5l with 300s (1) cores
% 140.47/36.10 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1693444 completed with status 0
% 140.47/36.10 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 140.47/36.10 % Preprocessing class: FSLSSMSSSSSNFFN.
% 140.47/36.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 140.47/36.10 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 140.47/36.10 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 140.47/36.10 % No SInE strategy applied
% 140.47/36.10 % Search class: FGUNS-FSLF31-MFFFFFNN
% 140.47/36.10 % partial match(3): FGHNF-FSLF11-MFFFFFNN
% 140.47/36.10 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 140.47/36.10 % Starting SubtermCWHack with 136s (1) cores
% 140.47/36.10 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 140.47/36.10 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 140.47/36.10 % Starting new_bool_3 with 136s (1) cores
% 140.47/36.10 % Starting new_bool_1 with 136s (1) cores
% 140.47/36.10 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1693452 completed with status 0
% 140.47/36.10 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 140.47/36.10 % Preprocessing class: FSLSSMSSSSSNFFN.
% 140.47/36.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 140.47/36.10 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 140.47/36.10 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 140.47/36.10 % No SInE strategy applied
% 140.47/36.10 % Search class: FGUNS-FSLF31-MFFFFFNN
% 140.47/36.10 % partial match(3): FGHNF-FSLF11-MFFFFFNN
% 140.47/36.10 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 140.47/36.10 % Starting SubtermCWHack with 136s (1) cores
% 140.47/36.10 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 140.47/36.10 % Preprocessing time : 0.005 s
% 140.47/36.10 % Presaturation interreduction done
% 140.47/36.10
% 140.47/36.10 % Proof found!
% 140.47/36.10 % SZS status Theorem
% 140.47/36.10 % SZS output start CNFRefutation
% See solution above
% 140.47/36.10 % Parsed axioms : 110
% 140.47/36.10 % Removed by relevancy pruning/SinE : 0
% 140.47/36.10 % Initial clauses : 333
% 140.47/36.10 % Removed in clause preprocessing : 42
% 140.47/36.10 % Initial clauses in saturation : 291
% 140.47/36.10 % Processed clauses : 21107
% 140.47/36.10 % ...of these trivial : 0
% 140.47/36.10 % ...subsumed : 3085
% 140.47/36.10 % ...remaining for further processing : 18022
% 140.47/36.10 % Other redundant clauses eliminated : 0
% 140.47/36.10 % Clauses deleted for lack of memory : 0
% 140.47/36.10 % Backward-subsumed : 964
% 140.47/36.10 % Backward-rewritten : 23
% 140.47/36.10 % Generated clauses : 528915
% 140.47/36.10 % ...of the previous two non-redundant : 528641
% 140.47/36.10 % ...aggressively subsumed : 0
% 140.47/36.10 % Contextual simplify-reflections : 0
% 140.47/36.10 % Paramodulations : 528915
% 140.47/36.10 % Factorizations : 0
% 140.47/36.10 % NegExts : 0
% 140.47/36.10 % Equation resolutions : 0
% 140.47/36.10 % Disequality decompositions : 0
% 140.47/36.10 % Total rewrite steps : 276
% 140.47/36.10 % ...of those cached : 218
% 140.47/36.10 % Propositional unsat checks : 3
% 140.47/36.10 % Propositional check models : 3
% 140.47/36.10 % Propositional check unsatisfiable : 0
% 140.47/36.10 % Propositional clauses : 0
% 140.47/36.10 % Propositional clauses after purity: 0
% 140.47/36.10 % Propositional unsat core size : 0
% 140.47/36.10 % Propositional preprocessing time : 0.000
% 140.47/36.10 % Propositional encoding time : 0.302
% 140.47/36.10 % Propositional solver time : 0.031
% 140.47/36.10 % Success case prop preproc time : 0.000
% 140.47/36.10 % Success case prop encoding time : 0.000
% 140.47/36.10 % Success case prop solver time : 0.000
% 140.47/36.10 % Current number of processed clauses : 16745
% 140.47/36.10 % Positive orientable unit clauses : 121
% 140.47/36.10 % Positive unorientable unit clauses: 0
% 140.47/36.10 % Negative unit clauses : 1
% 140.47/36.10 % Non-unit-clauses : 16623
% 140.47/36.10 % Current number of unprocessed clauses: 507958
% 140.47/36.10 % ...number of literals in the above : 2574108
% 140.47/36.10 % Current number of archived formulas : 0
% 140.47/36.10 % Current number of archived clauses : 1277
% 140.47/36.10 % Clause-clause subsumption calls (NU) : 128228423
% 140.47/36.10 % Rec. Clause-clause subsumption calls : 19399746
% 140.47/36.10 % Non-unit clause-clause subsumptions : 4049
% 140.47/36.10 % Unit Clause-clause subsumption calls : 370158
% 140.47/36.10 % Rewrite failures with RHS unbound : 0
% 140.47/36.10 % BW rewrite match attempts : 20
% 140.47/36.10 % BW rewrite match successes : 12
% 140.47/36.10 % Condensation attempts : 0
% 140.47/36.10 % Condensation successes : 0
% 140.47/36.10 % Termbank termtop insertions : 11361843
% 140.47/36.10 % Search garbage collected termcells : 8607
% 140.47/36.10
% 140.47/36.10 % -------------------------------------------------
% 140.47/36.10 % User time : 19.279 s
% 140.47/36.10 % System time : 0.331 s
% 140.47/36.10 % Total time : 19.609 s
% 140.47/36.10 % Maximum resident set size: 5092 pages
% 140.47/36.10
% 140.47/36.10 % -------------------------------------------------
% 140.47/36.10 % User time : 97.207 s
% 140.47/36.10 % System time : 2.490 s
% 140.47/36.10 % Total time : 99.697 s
% 140.47/36.10 % Maximum resident set size: 5120 pages
% 140.47/36.10 % E exiting
%------------------------------------------------------------------------------