%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NLP266_4 : 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 : n012.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 01:36:01 PM UTC 2026
% Result : Theorem 0.07s 0.35s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 302 ( 0 equ)
% Maximal formula atoms : 57 ( 5 avg)
% Number of connectives : 446 ( 196 ~; 194 |; 34 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 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 : 9 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 169 ( 0 sgn 158 !; 11 ?; 54 :)
% 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,
u: $i ).
tff(decl_26,type,
one: $i ).
tff(decl_27,type,
number: ( $i * ( $i * '$ki_world' ) ) > $o ).
tff(decl_28,type,
string: ( $i * '$ki_world' ) > $o ).
tff(decl_29,type,
in: ( $i * ( $i * ( $i * '$ki_world' ) ) ) > $o ).
tff(decl_30,type,
do: ( $i * ( $i * ( $i * '$ki_world' ) ) ) > $o ).
tff(decl_31,type,
entry_box: ( $i * '$ki_world' ) > $o ).
tff(decl_32,type,
userid: ( $i * ( $i * '$ki_world' ) ) > $o ).
tff(decl_33,type,
'$ki_exists_in_world_$i': ( $i * '$ki_world' ) > $o ).
tff(decl_35,type,
esk2_1: '$ki_world' > $i ).
tff(decl_36,type,
esk3_0: $i ).
tff(decl_37,type,
esk4_4: ( $i * ( $i * ( $i * '$ki_world' ) ) ) > $i ).
tff(decl_38,type,
esk5_0: '$ki_world' ).
tff(decl_39,type,
esk6_4: ( $i * ( $i * ( $i * $i ) ) ) > '$ki_world' ).
tff(decl_40,type,
esk7_4: ( $i * ( $i * ( $i * $i ) ) ) > '$ki_world' ).
tff(decl_41,type,
esk8_4: ( $i * ( $i * ( $i * $i ) ) ) > $i ).
tff(verify,conjecture,
! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ? [X5] :
( ? [X7] :
( ? [X9] :
( ? [X8] :
( ! [X6: '$ki_world'] :
( '$ki_accessible'(X1,X6)
=> ! [X10] :
( '$ki_exists_in_world_$i'(X6,X10)
=> ( do(X6,X8,X9,X10)
=> in(X6,X5,X7,X10) ) ) )
& ! [X6: '$ki_world'] :
( '$ki_accessible'(X1,X6)
=> ( number(X6,X7,one)
& entry_box(X6,X7)
& userid(X6,u,X5) ) )
& '$ki_exists_in_world_$i'(X1,X8) )
& '$ki_exists_in_world_$i'(X1,X9) )
& '$ki_exists_in_world_$i'(X1,X7) )
& '$ki_exists_in_world_$i'(X1,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(ax3,axiom,
! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ! [X8] :
( '$ki_exists_in_world_$i'(X1,X8)
=> ! [X5] :
( '$ki_exists_in_world_$i'(X1,X5)
=> ! [X7] :
( '$ki_exists_in_world_$i'(X1,X7)
=> ( ( entry_box(X1,X7)
& string(X1,X5) )
=> ? [X9] :
( ! [X6: '$ki_world'] :
( '$ki_accessible'(X1,X6)
=> ! [X10] :
( '$ki_exists_in_world_$i'(X6,X10)
=> ( do(X6,X8,X9,X10)
=> in(X6,X5,X7,X10) ) ) )
& '$ki_exists_in_world_$i'(X1,X9) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
tff('$ki_exists_in_world_$i_const',axiom,
! [X1: '$ki_world',X4] : '$ki_exists_in_world_$i'(X1,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
tff(ax1,axiom,
! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ? [X5] :
( ! [X6: '$ki_world'] :
( '$ki_accessible'(X1,X6)
=> ( string(X6,X5)
& userid(X6,u,X5) ) )
& '$ki_exists_in_world_$i'(X1,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
tff(ax2,axiom,
? [X7] :
( ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ( number(X1,X7,one)
& entry_box(X1,X7) ) )
& '$ki_exists_in_world_$i'('$ki_local_world',X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
tff(mrel_transitive,axiom,
! [X1: '$ki_world',X2: '$ki_world',X3: '$ki_world'] :
( ( '$ki_accessible'(X2,X3)
& '$ki_accessible'(X1,X2) )
=> '$ki_accessible'(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_transitive) ).
tff(mrel_reflexive,axiom,
! [X1: '$ki_world'] : '$ki_accessible'(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
tff(c_0_7,negated_conjecture,
~ ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ? [X5] :
( ? [X7] :
( ? [X9] :
( ? [X8] :
( ! [X6: '$ki_world'] :
( '$ki_accessible'(X1,X6)
=> ! [X10] :
( '$ki_exists_in_world_$i'(X6,X10)
=> ( do(X6,X8,X9,X10)
=> in(X6,X5,X7,X10) ) ) )
& ! [X6: '$ki_world'] :
( '$ki_accessible'(X1,X6)
=> ( number(X6,X7,one)
& entry_box(X6,X7)
& userid(X6,u,X5) ) )
& '$ki_exists_in_world_$i'(X1,X8) )
& '$ki_exists_in_world_$i'(X1,X9) )
& '$ki_exists_in_world_$i'(X1,X7) )
& '$ki_exists_in_world_$i'(X1,X5) ) ),
inference(assume_negation,[status(cth)],[verify]) ).
tff(c_0_8,plain,
! [X24: '$ki_world',X25,X26,X27,X29: '$ki_world',X30] :
( ( ~ '$ki_accessible'('$ki_local_world',X24)
| ~ '$ki_exists_in_world_$i'(X24,X25)
| ~ '$ki_exists_in_world_$i'(X24,X26)
| ~ '$ki_exists_in_world_$i'(X24,X27)
| ~ entry_box(X24,X27)
| ~ string(X24,X26)
| in(X29,X26,X27,X30)
| ~ do(X29,X25,esk4_4(X24,X25,X26,X27),X30)
| ~ '$ki_exists_in_world_$i'(X29,X30)
| ~ '$ki_accessible'(X24,X29) )
& ( ~ '$ki_accessible'('$ki_local_world',X24)
| ~ '$ki_exists_in_world_$i'(X24,X25)
| ~ '$ki_exists_in_world_$i'(X24,X26)
| ~ '$ki_exists_in_world_$i'(X24,X27)
| ~ entry_box(X24,X27)
| ~ string(X24,X26)
| '$ki_exists_in_world_$i'(X24,esk4_4(X24,X25,X26,X27)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])])])]) ).
tff(c_0_9,plain,
! [X15: '$ki_world',X16] : '$ki_exists_in_world_$i'(X15,X16),
inference(variable_rename,[status(thm)],['$ki_exists_in_world_$i_const']) ).
tff(c_0_10,negated_conjecture,
! [X32,X33,X34,X35] :
( ( ~ '$ki_exists_in_world_$i'(esk5_0,X32)
| ~ '$ki_exists_in_world_$i'(esk5_0,X33)
| ~ '$ki_exists_in_world_$i'(esk5_0,X34)
| ~ '$ki_exists_in_world_$i'(esk5_0,X35)
| ~ number(esk6_4(X32,X33,X34,X35),X33,one)
| ~ entry_box(esk6_4(X32,X33,X34,X35),X33)
| ~ userid(esk6_4(X32,X33,X34,X35),u,X32)
| ~ in(esk7_4(X32,X33,X34,X35),X32,X33,esk8_4(X32,X33,X34,X35)) )
& ( ~ '$ki_exists_in_world_$i'(esk5_0,X32)
| ~ '$ki_exists_in_world_$i'(esk5_0,X33)
| ~ '$ki_exists_in_world_$i'(esk5_0,X34)
| ~ '$ki_exists_in_world_$i'(esk5_0,X35)
| ~ number(esk6_4(X32,X33,X34,X35),X33,one)
| ~ entry_box(esk6_4(X32,X33,X34,X35),X33)
| ~ userid(esk6_4(X32,X33,X34,X35),u,X32)
| do(esk7_4(X32,X33,X34,X35),X35,X34,esk8_4(X32,X33,X34,X35)) )
& ( ~ '$ki_exists_in_world_$i'(esk5_0,X32)
| ~ '$ki_exists_in_world_$i'(esk5_0,X33)
| ~ '$ki_exists_in_world_$i'(esk5_0,X34)
| ~ '$ki_exists_in_world_$i'(esk5_0,X35)
| ~ number(esk6_4(X32,X33,X34,X35),X33,one)
| ~ entry_box(esk6_4(X32,X33,X34,X35),X33)
| ~ userid(esk6_4(X32,X33,X34,X35),u,X32)
| '$ki_exists_in_world_$i'(esk7_4(X32,X33,X34,X35),esk8_4(X32,X33,X34,X35)) )
& ( ~ '$ki_exists_in_world_$i'(esk5_0,X32)
| ~ '$ki_exists_in_world_$i'(esk5_0,X33)
| ~ '$ki_exists_in_world_$i'(esk5_0,X34)
| ~ '$ki_exists_in_world_$i'(esk5_0,X35)
| ~ number(esk6_4(X32,X33,X34,X35),X33,one)
| ~ entry_box(esk6_4(X32,X33,X34,X35),X33)
| ~ userid(esk6_4(X32,X33,X34,X35),u,X32)
| '$ki_accessible'(esk5_0,esk7_4(X32,X33,X34,X35)) )
& ( ~ '$ki_exists_in_world_$i'(esk5_0,X32)
| ~ '$ki_exists_in_world_$i'(esk5_0,X33)
| ~ '$ki_exists_in_world_$i'(esk5_0,X34)
| ~ '$ki_exists_in_world_$i'(esk5_0,X35)
| '$ki_accessible'(esk5_0,esk6_4(X32,X33,X34,X35))
| ~ in(esk7_4(X32,X33,X34,X35),X32,X33,esk8_4(X32,X33,X34,X35)) )
& ( ~ '$ki_exists_in_world_$i'(esk5_0,X32)
| ~ '$ki_exists_in_world_$i'(esk5_0,X33)
| ~ '$ki_exists_in_world_$i'(esk5_0,X34)
| ~ '$ki_exists_in_world_$i'(esk5_0,X35)
| '$ki_accessible'(esk5_0,esk6_4(X32,X33,X34,X35))
| do(esk7_4(X32,X33,X34,X35),X35,X34,esk8_4(X32,X33,X34,X35)) )
& ( ~ '$ki_exists_in_world_$i'(esk5_0,X32)
| ~ '$ki_exists_in_world_$i'(esk5_0,X33)
| ~ '$ki_exists_in_world_$i'(esk5_0,X34)
| ~ '$ki_exists_in_world_$i'(esk5_0,X35)
| '$ki_accessible'(esk5_0,esk6_4(X32,X33,X34,X35))
| '$ki_exists_in_world_$i'(esk7_4(X32,X33,X34,X35),esk8_4(X32,X33,X34,X35)) )
& ( ~ '$ki_exists_in_world_$i'(esk5_0,X32)
| ~ '$ki_exists_in_world_$i'(esk5_0,X33)
| ~ '$ki_exists_in_world_$i'(esk5_0,X34)
| ~ '$ki_exists_in_world_$i'(esk5_0,X35)
| '$ki_accessible'(esk5_0,esk6_4(X32,X33,X34,X35))
| '$ki_accessible'(esk5_0,esk7_4(X32,X33,X34,X35)) )
& '$ki_accessible'('$ki_local_world',esk5_0) ),
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_7])])])])])]) ).
tcf(c_0_11,plain,
! [X2: '$ki_world',X8,X7,X5,X4,X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_exists_in_world_$i'(X1,X5)
| ~ '$ki_exists_in_world_$i'(X1,X7)
| ~ '$ki_exists_in_world_$i'(X1,X8)
| ~ entry_box(X1,X8)
| ~ string(X1,X7)
| ~ do(X2,X5,esk4_4(X1,X5,X7,X8),X4)
| ~ '$ki_exists_in_world_$i'(X2,X4)
| ~ '$ki_accessible'(X1,X2)
| in(X2,X7,X8,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_12,plain,
! [X1: '$ki_world',X4] : '$ki_exists_in_world_$i'(X1,X4),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_13,negated_conjecture,
! [X8,X7,X5,X4] :
( ~ '$ki_exists_in_world_$i'(esk5_0,X4)
| ~ '$ki_exists_in_world_$i'(esk5_0,X5)
| ~ '$ki_exists_in_world_$i'(esk5_0,X7)
| ~ '$ki_exists_in_world_$i'(esk5_0,X8)
| ~ number(esk6_4(X4,X5,X7,X8),X5,one)
| ~ entry_box(esk6_4(X4,X5,X7,X8),X5)
| ~ userid(esk6_4(X4,X5,X7,X8),u,X4)
| do(esk7_4(X4,X5,X7,X8),X8,X7,esk8_4(X4,X5,X7,X8)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_14,negated_conjecture,
! [X8,X7,X5,X4] :
( ~ '$ki_exists_in_world_$i'(esk5_0,X4)
| ~ '$ki_exists_in_world_$i'(esk5_0,X5)
| ~ '$ki_exists_in_world_$i'(esk5_0,X7)
| ~ '$ki_exists_in_world_$i'(esk5_0,X8)
| ~ number(esk6_4(X4,X5,X7,X8),X5,one)
| ~ entry_box(esk6_4(X4,X5,X7,X8),X5)
| ~ userid(esk6_4(X4,X5,X7,X8),u,X4)
| ~ in(esk7_4(X4,X5,X7,X8),X4,X5,esk8_4(X4,X5,X7,X8)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_15,plain,
! [X2: '$ki_world',X1: '$ki_world',X5,X8,X7,X4] :
( ~ do(X2,X5,esk4_4(X1,X5,X7,X8),X4)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,X2)
| ~ entry_box(X1,X8)
| ~ string(X1,X7)
| in(X2,X7,X8,X4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_12]),c_0_12]),c_0_12])]) ).
tcf(c_0_16,negated_conjecture,
! [X5,X8,X7,X4] :
( ~ userid(esk6_4(X4,X5,X7,X8),u,X4)
| ~ number(esk6_4(X4,X5,X7,X8),X5,one)
| ~ entry_box(esk6_4(X4,X5,X7,X8),X5)
| do(esk7_4(X4,X5,X7,X8),X8,X7,esk8_4(X4,X5,X7,X8)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_12]),c_0_12]),c_0_12]),c_0_12])]) ).
tcf(c_0_17,negated_conjecture,
! [X8,X7,X5,X4] :
( ~ '$ki_exists_in_world_$i'(esk5_0,X4)
| ~ '$ki_exists_in_world_$i'(esk5_0,X5)
| ~ '$ki_exists_in_world_$i'(esk5_0,X7)
| ~ '$ki_exists_in_world_$i'(esk5_0,X8)
| ~ number(esk6_4(X4,X5,X7,X8),X5,one)
| ~ entry_box(esk6_4(X4,X5,X7,X8),X5)
| ~ userid(esk6_4(X4,X5,X7,X8),u,X4)
| '$ki_accessible'(esk5_0,esk7_4(X4,X5,X7,X8)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tff(c_0_18,plain,
! [X19: '$ki_world',X21: '$ki_world'] :
( ( ~ '$ki_accessible'('$ki_local_world',X19)
| ~ '$ki_accessible'(X19,X21)
| string(X21,esk2_1(X19)) )
& ( ~ '$ki_accessible'('$ki_local_world',X19)
| ~ '$ki_accessible'(X19,X21)
| userid(X21,u,esk2_1(X19)) )
& ( ~ '$ki_accessible'('$ki_local_world',X19)
| '$ki_exists_in_world_$i'(X19,esk2_1(X19)) ) ),
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)],[ax1])])])])])]) ).
tcf(c_0_19,negated_conjecture,
! [X8,X7,X5,X4] :
( ~ '$ki_exists_in_world_$i'(esk5_0,X4)
| ~ '$ki_exists_in_world_$i'(esk5_0,X5)
| ~ '$ki_exists_in_world_$i'(esk5_0,X7)
| ~ '$ki_exists_in_world_$i'(esk5_0,X8)
| '$ki_accessible'(esk5_0,esk6_4(X4,X5,X7,X8))
| do(esk7_4(X4,X5,X7,X8),X8,X7,esk8_4(X4,X5,X7,X8)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_20,negated_conjecture,
! [X4,X5,X7,X8] :
( ~ in(esk7_4(X4,X5,X7,X8),X4,X5,esk8_4(X4,X5,X7,X8))
| ~ userid(esk6_4(X4,X5,X7,X8),u,X4)
| ~ number(esk6_4(X4,X5,X7,X8),X5,one)
| ~ entry_box(esk6_4(X4,X5,X7,X8),X5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_12]),c_0_12]),c_0_12]),c_0_12])]) ).
tcf(c_0_21,negated_conjecture,
! [X5,X9,X8,X7,X4,X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,esk7_4(X4,X5,esk4_4(X1,X7,X8,X9),X7))
| ~ number(esk6_4(X4,X5,esk4_4(X1,X7,X8,X9),X7),X5,one)
| ~ string(X1,X8)
| ~ entry_box(X1,X9)
| ~ entry_box(esk6_4(X4,X5,esk4_4(X1,X7,X8,X9),X7),X5)
| ~ userid(esk6_4(X4,X5,esk4_4(X1,X7,X8,X9),X7),u,X4)
| in(esk7_4(X4,X5,esk4_4(X1,X7,X8,X9),X7),X8,X9,esk8_4(X4,X5,esk4_4(X1,X7,X8,X9),X7)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
tcf(c_0_22,negated_conjecture,
! [X5,X8,X7,X4] :
( ~ userid(esk6_4(X4,X5,X7,X8),u,X4)
| ~ number(esk6_4(X4,X5,X7,X8),X5,one)
| ~ entry_box(esk6_4(X4,X5,X7,X8),X5)
| '$ki_accessible'(esk5_0,esk7_4(X4,X5,X7,X8)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_12]),c_0_12]),c_0_12]),c_0_12])]) ).
tcf(c_0_23,plain,
! [X1: '$ki_world',X2: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X2)
| ~ '$ki_accessible'(X2,X1)
| userid(X1,u,esk2_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
tff(c_0_24,plain,
! [X23: '$ki_world'] :
( ( ~ '$ki_accessible'('$ki_local_world',X23)
| number(X23,esk3_0,one) )
& ( ~ '$ki_accessible'('$ki_local_world',X23)
| entry_box(X23,esk3_0) )
& '$ki_exists_in_world_$i'('$ki_local_world',esk3_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax2])])])])])]) ).
tff(c_0_25,plain,
! [X12: '$ki_world',X13: '$ki_world',X14: '$ki_world'] :
( '$ki_accessible'(X12,X14)
| ~ '$ki_accessible'(X13,X14)
| ~ '$ki_accessible'(X12,X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mrel_transitive])])]) ).
tcf(c_0_26,negated_conjecture,
! [X8,X7,X5,X4] :
( ~ '$ki_exists_in_world_$i'(esk5_0,X4)
| ~ '$ki_exists_in_world_$i'(esk5_0,X5)
| ~ '$ki_exists_in_world_$i'(esk5_0,X7)
| ~ '$ki_exists_in_world_$i'(esk5_0,X8)
| ~ in(esk7_4(X4,X5,X7,X8),X4,X5,esk8_4(X4,X5,X7,X8))
| '$ki_accessible'(esk5_0,esk6_4(X4,X5,X7,X8)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_27,negated_conjecture,
! [X4,X5,X7,X8] :
( do(esk7_4(X4,X5,X7,X8),X8,X7,esk8_4(X4,X5,X7,X8))
| '$ki_accessible'(esk5_0,esk6_4(X4,X5,X7,X8)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_12]),c_0_12]),c_0_12]),c_0_12])]) ).
tcf(c_0_28,negated_conjecture,
! [X4,X7,X5,X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,esk7_4(X4,X5,esk4_4(X1,X7,X4,X5),X7))
| ~ number(esk6_4(X4,X5,esk4_4(X1,X7,X4,X5),X7),X5,one)
| ~ string(X1,X4)
| ~ entry_box(X1,X5)
| ~ entry_box(esk6_4(X4,X5,esk4_4(X1,X7,X4,X5),X7),X5)
| ~ userid(esk6_4(X4,X5,esk4_4(X1,X7,X4,X5),X7),u,X4) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
tcf(c_0_29,negated_conjecture,
! [X4,X7,X5,X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,esk6_4(esk2_1(X1),X4,X5,X7))
| ~ number(esk6_4(esk2_1(X1),X4,X5,X7),X4,one)
| ~ entry_box(esk6_4(esk2_1(X1),X4,X5,X7),X4)
| '$ki_accessible'(esk5_0,esk7_4(esk2_1(X1),X4,X5,X7)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
tcf(c_0_30,plain,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| number(X1,esk3_0,one) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
tcf(c_0_31,plain,
! [X1: '$ki_world',X2: '$ki_world',X3: '$ki_world'] :
( ~ '$ki_accessible'(X2,X3)
| ~ '$ki_accessible'(X1,X2)
| '$ki_accessible'(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
tcf(c_0_32,negated_conjecture,
! [X4,X5,X7,X8] :
( ~ in(esk7_4(X4,X5,X7,X8),X4,X5,esk8_4(X4,X5,X7,X8))
| '$ki_accessible'(esk5_0,esk6_4(X4,X5,X7,X8)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_12]),c_0_12]),c_0_12]),c_0_12])]) ).
tcf(c_0_33,negated_conjecture,
! [X5,X9,X8,X7,X4,X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,esk7_4(X4,X5,esk4_4(X1,X7,X8,X9),X7))
| ~ string(X1,X8)
| ~ entry_box(X1,X9)
| '$ki_accessible'(esk5_0,esk6_4(X4,X5,esk4_4(X1,X7,X8,X9),X7))
| in(esk7_4(X4,X5,esk4_4(X1,X7,X8,X9),X7),X8,X9,esk8_4(X4,X5,esk4_4(X1,X7,X8,X9),X7)) ),
inference(spm,[status(thm)],[c_0_15,c_0_27]) ).
tcf(c_0_34,negated_conjecture,
! [X8,X7,X5,X4] :
( ~ '$ki_exists_in_world_$i'(esk5_0,X4)
| ~ '$ki_exists_in_world_$i'(esk5_0,X5)
| ~ '$ki_exists_in_world_$i'(esk5_0,X7)
| ~ '$ki_exists_in_world_$i'(esk5_0,X8)
| '$ki_accessible'(esk5_0,esk6_4(X4,X5,X7,X8))
| '$ki_accessible'(esk5_0,esk7_4(X4,X5,X7,X8)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_35,negated_conjecture,
! [X5,X4,X2: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'('$ki_local_world',X2)
| ~ '$ki_accessible'(X1,esk6_4(esk2_1(X1),X4,esk4_4(X2,X5,esk2_1(X1),X4),X5))
| ~ '$ki_accessible'(X2,esk7_4(esk2_1(X1),X4,esk4_4(X2,X5,esk2_1(X1),X4),X5))
| ~ number(esk6_4(esk2_1(X1),X4,esk4_4(X2,X5,esk2_1(X1),X4),X5),X4,one)
| ~ string(X2,esk2_1(X1))
| ~ entry_box(X2,X4)
| ~ entry_box(esk6_4(esk2_1(X1),X4,esk4_4(X2,X5,esk2_1(X1),X4),X5),X4) ),
inference(spm,[status(thm)],[c_0_28,c_0_23]) ).
tcf(c_0_36,plain,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| entry_box(X1,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
tcf(c_0_37,negated_conjecture,
! [X5,X4,X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,esk6_4(esk2_1(X1),esk3_0,X4,X5))
| ~ entry_box(esk6_4(esk2_1(X1),esk3_0,X4,X5),esk3_0)
| '$ki_accessible'(esk5_0,esk7_4(esk2_1(X1),esk3_0,X4,X5)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
tcf(c_0_38,negated_conjecture,
! [X4,X7,X5,X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,esk7_4(X4,X5,esk4_4(X1,X7,X4,X5),X7))
| ~ string(X1,X4)
| ~ entry_box(X1,X5)
| '$ki_accessible'(esk5_0,esk6_4(X4,X5,esk4_4(X1,X7,X4,X5),X7)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
tcf(c_0_39,negated_conjecture,
! [X4,X5,X7,X8] :
( '$ki_accessible'(esk5_0,esk7_4(X4,X5,X7,X8))
| '$ki_accessible'(esk5_0,esk6_4(X4,X5,X7,X8)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_12]),c_0_12]),c_0_12]),c_0_12])]) ).
tcf(c_0_40,negated_conjecture,
'$ki_accessible'('$ki_local_world',esk5_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_41,negated_conjecture,
! [X4,X2: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'('$ki_local_world',X2)
| ~ '$ki_accessible'(X1,esk6_4(esk2_1(X1),esk3_0,esk4_4(X2,X4,esk2_1(X1),esk3_0),X4))
| ~ '$ki_accessible'(X2,esk7_4(esk2_1(X1),esk3_0,esk4_4(X2,X4,esk2_1(X1),esk3_0),X4))
| ~ string(X2,esk2_1(X1))
| ~ entry_box(esk6_4(esk2_1(X1),esk3_0,esk4_4(X2,X4,esk2_1(X1),esk3_0),X4),esk3_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_30]),c_0_31]),c_0_36]) ).
tcf(c_0_42,negated_conjecture,
! [X5,X4,X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X1,esk6_4(esk2_1(X1),esk3_0,X4,X5))
| '$ki_accessible'(esk5_0,esk7_4(esk2_1(X1),esk3_0,X4,X5)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_36]),c_0_31]) ).
tcf(c_0_43,negated_conjecture,
! [X7,X5,X4] :
( ~ string(esk5_0,X4)
| ~ entry_box(esk5_0,X5)
| '$ki_accessible'(esk5_0,esk6_4(X4,X5,esk4_4(esk5_0,X7,X4,X5),X7)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
tcf(c_0_44,negated_conjecture,
! [X1: '$ki_world',X4,X2: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X2)
| ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_accessible'(X2,esk6_4(esk2_1(X2),esk3_0,esk4_4(X1,X4,esk2_1(X2),esk3_0),X4))
| ~ '$ki_accessible'(X1,esk7_4(esk2_1(X2),esk3_0,esk4_4(X1,X4,esk2_1(X2),esk3_0),X4))
| ~ string(X1,esk2_1(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_36]),c_0_31]) ).
tcf(c_0_45,negated_conjecture,
! [X4] :
( ~ string(esk5_0,esk2_1(esk5_0))
| ~ entry_box(esk5_0,esk3_0)
| '$ki_accessible'(esk5_0,esk7_4(esk2_1(esk5_0),esk3_0,esk4_4(esk5_0,X4,esk2_1(esk5_0),esk3_0),X4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_40])]) ).
tff(c_0_46,plain,
! [X11: '$ki_world'] : '$ki_accessible'(X11,X11),
inference(variable_rename,[status(thm)],[mrel_reflexive]) ).
tcf(c_0_47,negated_conjecture,
( ~ string(esk5_0,esk2_1(esk5_0))
| ~ entry_box(esk5_0,esk3_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_40])]),c_0_43]) ).
tcf(c_0_48,plain,
! [X1: '$ki_world',X2: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X2)
| ~ '$ki_accessible'(X2,X1)
| string(X1,esk2_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
tcf(c_0_49,plain,
! [X1: '$ki_world'] : '$ki_accessible'(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
tcf(c_0_50,negated_conjecture,
~ entry_box(esk5_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_40]),c_0_49])]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_36]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NLP266_4 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Mon Sep 21 01:56:52 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 0.07/0.35 % Version: 3.5.1
% 0.07/0.35 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.07/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.35 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.07/0.35 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.35 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.35 % Starting sh5l with 300s (1) cores
% 0.07/0.35 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1347267 completed with status 0
% 0.07/0.35 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.07/0.35 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.07/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.35 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.07/0.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.35 % No SInE strategy applied
% 0.07/0.35 % Search class: FGHNF-FFMF33-SFFFFFNN
% 0.07/0.35 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.35 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.35 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.07/0.35 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.07/0.35 % Starting new_bool_3 with 136s (1) cores
% 0.07/0.35 % Starting new_bool_1 with 136s (1) cores
% 0.07/0.35 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 1347274 completed with status 0
% 0.07/0.35 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.07/0.35 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.07/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.35 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.07/0.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.35 % No SInE strategy applied
% 0.07/0.35 % Search class: FGHNF-FFMF33-SFFFFFNN
% 0.07/0.35 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.35 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.35 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.07/0.35 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.07/0.35 % Preprocessing time : 0.001 s
% 0.07/0.35 % Presaturation interreduction done
% 0.07/0.35
% 0.07/0.35 % Proof found!
% 0.07/0.35 % SZS status Theorem
% 0.07/0.35 % SZS output start CNFRefutation
% See solution above
% 0.07/0.35 % Parsed axioms : 20
% 0.07/0.35 % Removed by relevancy pruning/SinE : 0
% 0.07/0.35 % Initial clauses : 33
% 0.07/0.35 % Removed in clause preprocessing : 19
% 0.07/0.35 % Initial clauses in saturation : 14
% 0.07/0.35 % Processed clauses : 57
% 0.07/0.35 % ...of these trivial : 0
% 0.07/0.35 % ...subsumed : 5
% 0.07/0.35 % ...remaining for further processing : 52
% 0.07/0.35 % Other redundant clauses eliminated : 0
% 0.07/0.35 % Clauses deleted for lack of memory : 0
% 0.07/0.35 % Backward-subsumed : 7
% 0.07/0.35 % Backward-rewritten : 0
% 0.07/0.35 % Generated clauses : 41
% 0.07/0.35 % ...of the previous two non-redundant : 39
% 0.07/0.35 % ...aggressively subsumed : 0
% 0.07/0.35 % Contextual simplify-reflections : 8
% 0.07/0.35 % Paramodulations : 41
% 0.07/0.35 % Factorizations : 0
% 0.07/0.35 % NegExts : 0
% 0.07/0.35 % Equation resolutions : 0
% 0.07/0.35 % Disequality decompositions : 0
% 0.07/0.35 % Total rewrite steps : 8
% 0.07/0.35 % ...of those cached : 6
% 0.07/0.35 % Propositional unsat checks : 0
% 0.07/0.35 % Propositional check models : 0
% 0.07/0.35 % Propositional check unsatisfiable : 0
% 0.07/0.35 % Propositional clauses : 0
% 0.07/0.35 % Propositional clauses after purity: 0
% 0.07/0.35 % Propositional unsat core size : 0
% 0.07/0.35 % Propositional preprocessing time : 0.000
% 0.07/0.35 % Propositional encoding time : 0.000
% 0.07/0.35 % Propositional solver time : 0.000
% 0.07/0.35 % Success case prop preproc time : 0.000
% 0.07/0.35 % Success case prop encoding time : 0.000
% 0.07/0.35 % Success case prop solver time : 0.000
% 0.07/0.35 % Current number of processed clauses : 31
% 0.07/0.35 % Positive orientable unit clauses : 2
% 0.07/0.35 % Positive unorientable unit clauses: 0
% 0.07/0.35 % Negative unit clauses : 1
% 0.07/0.35 % Non-unit-clauses : 28
% 0.07/0.35 % Current number of unprocessed clauses: 10
% 0.07/0.35 % ...number of literals in the above : 55
% 0.07/0.35 % Current number of archived formulas : 0
% 0.07/0.35 % Current number of archived clauses : 22
% 0.07/0.35 % Clause-clause subsumption calls (NU) : 643
% 0.07/0.35 % Rec. Clause-clause subsumption calls : 166
% 0.07/0.35 % Non-unit clause-clause subsumptions : 19
% 0.07/0.35 % Unit Clause-clause subsumption calls : 13
% 0.07/0.35 % Rewrite failures with RHS unbound : 0
% 0.07/0.35 % BW rewrite match attempts : 2
% 0.07/0.35 % BW rewrite match successes : 0
% 0.07/0.35 % Condensation attempts : 0
% 0.07/0.35 % Condensation successes : 0
% 0.07/0.35 % Termbank termtop insertions : 4092
% 0.07/0.35 % Search garbage collected termcells : 513
% 0.07/0.35
% 0.07/0.35 % -------------------------------------------------
% 0.07/0.35 % User time : 0.006 s
% 0.07/0.35 % System time : 0.002 s
% 0.07/0.35 % Total time : 0.008 s
% 0.07/0.35 % Maximum resident set size: 3648 pages
% 0.07/0.35
% 0.07/0.35 % -------------------------------------------------
% 0.07/0.35 % User time : 0.024 s
% 0.07/0.35 % System time : 0.008 s
% 0.07/0.35 % Total time : 0.032 s
% 0.07/0.35 % Maximum resident set size: 4864 pages
% 0.07/0.35 % E exiting
%------------------------------------------------------------------------------