%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : PLA053_5 : 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 01:58:58 PM UTC 2026
% Result : Theorem 0.07s 0.34s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 100 ( 38 ~; 34 |; 14 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 49 !; 4 ?; 29 :)
% 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,
h: ( $i * '$ki_world' ) > $o ).
tff(decl_26,type,
bomb: ( $i * '$ki_world' ) > $o ).
tff(decl_27,type,
defused: ( $i * '$ki_world' ) > $o ).
tff(decl_28,type,
'$ki_exists_in_world_$i': ( $i * '$ki_world' ) > $o ).
tff(decl_29,type,
esk1_0: '$ki_world' ).
tff(decl_30,type,
esk2_0: $i ).
tff(decl_31,type,
esk3_2: ( $i * '$ki_world' ) > $i ).
tff(decl_32,type,
esk4_0: $i ).
tff(verify,conjecture,
! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X1,X3)
=> ? [X7] :
( ( ( h(X1,X7)
& bomb(X1,X3) )
=> defused(X1,X3) )
& '$ki_exists_in_world_$i'(X1,X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(ax2,axiom,
? [X5] :
( ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X1,X3)
=> ( ( h(X1,X5)
& bomb(X1,X3) )
=> ! [X6: '$ki_world'] :
( '$ki_accessible'(X1,X6)
=> bomb(X6,X3) ) ) ) )
& '$ki_exists_in_world_$i'('$ki_local_world',X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
tff('$ki_exists_in_world_$i_const',axiom,
! [X1: '$ki_world',X3] : '$ki_exists_in_world_$i'(X1,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
tff(mrel_universal,axiom,
! [X1: '$ki_world',X2: '$ki_world'] : '$ki_accessible'(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).
tff(ax3,axiom,
! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X1,X3)
=> ? [X7] :
( ! [X6: '$ki_world'] :
( '$ki_accessible'(X1,X6)
=> ( ( h(X6,X7)
& bomb(X6,X3) )
=> defused(X6,X3) ) )
& '$ki_exists_in_world_$i'(X1,X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
tff(c_0_5,negated_conjecture,
~ ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ! [X3] :
( '$ki_exists_in_world_$i'(X1,X3)
=> ? [X7] :
( ( ( h(X1,X7)
& bomb(X1,X3) )
=> defused(X1,X3) )
& '$ki_exists_in_world_$i'(X1,X7) ) ) ),
inference(assume_negation,[status(cth)],[verify]) ).
tff(c_0_6,plain,
! [X16: '$ki_world',X17,X18: '$ki_world'] :
( ( bomb(X18,X17)
| ~ '$ki_accessible'(X16,X18)
| ~ h(X16,esk4_0)
| ~ bomb(X16,X17)
| ~ '$ki_exists_in_world_$i'(X16,X17)
| ~ '$ki_accessible'('$ki_local_world',X16) )
& '$ki_exists_in_world_$i'('$ki_local_world',esk4_0) ),
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_7,plain,
! [X21: '$ki_world',X22] : '$ki_exists_in_world_$i'(X21,X22),
inference(variable_rename,[status(thm)],['$ki_exists_in_world_$i_const']) ).
tff(c_0_8,plain,
! [X25: '$ki_world',X26: '$ki_world'] : '$ki_accessible'(X25,X26),
inference(variable_rename,[status(thm)],[mrel_universal]) ).
tff(c_0_9,negated_conjecture,
! [X10] :
( ( ~ '$ki_exists_in_world_$i'(esk1_0,X10)
| ~ defused(esk1_0,esk2_0) )
& ( ~ '$ki_exists_in_world_$i'(esk1_0,X10)
| h(esk1_0,X10) )
& ( ~ '$ki_exists_in_world_$i'(esk1_0,X10)
| bomb(esk1_0,esk2_0) )
& '$ki_exists_in_world_$i'(esk1_0,esk2_0)
& '$ki_accessible'('$ki_local_world',esk1_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_5])])])])])]) ).
tff(c_0_10,plain,
! [X11: '$ki_world',X12,X14: '$ki_world'] :
( ( ~ '$ki_accessible'('$ki_local_world',X11)
| ~ '$ki_exists_in_world_$i'(X11,X12)
| defused(X14,X12)
| ~ h(X14,esk3_2(X11,X12))
| ~ bomb(X14,X12)
| ~ '$ki_accessible'(X11,X14) )
& ( ~ '$ki_accessible'('$ki_local_world',X11)
| ~ '$ki_exists_in_world_$i'(X11,X12)
| '$ki_exists_in_world_$i'(X11,esk3_2(X11,X12)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])])])]) ).
tcf(c_0_11,plain,
! [X1: '$ki_world',X3,X2: '$ki_world'] :
( ~ '$ki_accessible'(X1,X2)
| ~ h(X1,esk4_0)
| ~ bomb(X1,X3)
| ~ '$ki_exists_in_world_$i'(X1,X3)
| ~ '$ki_accessible'('$ki_local_world',X1)
| bomb(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
tcf(c_0_12,plain,
! [X1: '$ki_world',X3] : '$ki_exists_in_world_$i'(X1,X3),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
tcf(c_0_13,plain,
! [X1: '$ki_world',X2: '$ki_world'] : '$ki_accessible'(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_14,negated_conjecture,
! [X3] :
( ~ '$ki_exists_in_world_$i'(esk1_0,X3)
| h(esk1_0,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_15,plain,
! [X3,X2: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_exists_in_world_$i'(X1,X3)
| ~ h(X2,esk3_2(X1,X3))
| ~ bomb(X2,X3)
| ~ '$ki_accessible'(X1,X2)
| defused(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_16,plain,
! [X1: '$ki_world',X3,X2: '$ki_world'] :
( ~ h(X2,esk4_0)
| ~ bomb(X2,X3)
| bomb(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_13])]) ).
tcf(c_0_17,negated_conjecture,
! [X3] : h(esk1_0,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_12])]) ).
tcf(c_0_18,negated_conjecture,
! [X3] :
( ~ '$ki_exists_in_world_$i'(esk1_0,X3)
| bomb(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_19,negated_conjecture,
! [X3] :
( ~ '$ki_exists_in_world_$i'(esk1_0,X3)
| ~ defused(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_20,plain,
! [X1: '$ki_world',X2: '$ki_world',X3] :
( ~ h(X1,esk3_2(X2,X3))
| ~ bomb(X1,X3)
| defused(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_12]),c_0_13]),c_0_13])]) ).
tcf(c_0_21,negated_conjecture,
! [X1: '$ki_world',X3] :
( ~ bomb(esk1_0,X3)
| bomb(X1,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
tcf(c_0_22,negated_conjecture,
bomb(esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_12])]) ).
tcf(c_0_23,negated_conjecture,
~ defused(esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_12])]) ).
tcf(c_0_24,negated_conjecture,
! [X3] :
( ~ bomb(esk1_0,X3)
| defused(esk1_0,X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
tcf(c_0_25,negated_conjecture,
! [X1: '$ki_world'] : bomb(X1,esk2_0),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : PLA053_5 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Mon Sep 21 03:38:21 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 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
% 0.07/0.34 % Version: 3.5.1
% 0.07/0.34 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.07/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.07/0.34 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.34 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.34 % Starting sh5l with 300s (1) cores
% 0.07/0.34 % new_bool_3 with pid 1479841 completed with status 0
% 0.07/0.34 % Result found by new_bool_3
% 0.07/0.34 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.07/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.07/0.34 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.34 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.34 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.34 % Search class: FHHNS-FFSS21-SFFFFFNN
% 0.07/0.34 % partial match(1): FHHNS-FFSF21-SFFFFFNN
% 0.07/0.34 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.34 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.34 % SubtermCWHack with pid 1479846 completed with status 0
% 0.07/0.34 % Result found by SubtermCWHack
% 0.07/0.34 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.07/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.07/0.34 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.34 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.34 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.34 % Search class: FHHNS-FFSS21-SFFFFFNN
% 0.07/0.34 % partial match(1): FHHNS-FFSF21-SFFFFFNN
% 0.07/0.34 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.34 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.34 % Preprocessing time : 0.001 s
% 0.07/0.34
% 0.07/0.34 % Proof found!
% 0.07/0.34 % SZS status Theorem
% 0.07/0.34 % SZS output start CNFRefutation
% See solution above
% 0.07/0.34 % Parsed axioms : 14
% 0.07/0.34 % Removed by relevancy pruning/SinE : 7
% 0.07/0.34 % Initial clauses : 14
% 0.07/0.34 % Removed in clause preprocessing : 0
% 0.07/0.34 % Initial clauses in saturation : 14
% 0.07/0.34 % Processed clauses : 18
% 0.07/0.34 % ...of these trivial : 3
% 0.07/0.34 % ...subsumed : 0
% 0.07/0.34 % ...remaining for further processing : 15
% 0.07/0.34 % Other redundant clauses eliminated : 0
% 0.07/0.34 % Clauses deleted for lack of memory : 0
% 0.07/0.34 % Backward-subsumed : 0
% 0.07/0.34 % Backward-rewritten : 4
% 0.07/0.34 % Generated clauses : 7
% 0.07/0.34 % ...of the previous two non-redundant : 4
% 0.07/0.34 % ...aggressively subsumed : 0
% 0.07/0.34 % Contextual simplify-reflections : 0
% 0.07/0.34 % Paramodulations : 7
% 0.07/0.34 % Factorizations : 0
% 0.07/0.34 % NegExts : 0
% 0.07/0.34 % Equation resolutions : 0
% 0.07/0.34 % Disequality decompositions : 0
% 0.07/0.34 % Total rewrite steps : 23
% 0.07/0.34 % ...of those cached : 10
% 0.07/0.34 % Propositional unsat checks : 0
% 0.07/0.34 % Propositional check models : 0
% 0.07/0.34 % Propositional check unsatisfiable : 0
% 0.07/0.34 % Propositional clauses : 0
% 0.07/0.34 % Propositional clauses after purity: 0
% 0.07/0.34 % Propositional unsat core size : 0
% 0.07/0.34 % Propositional preprocessing time : 0.000
% 0.07/0.34 % Propositional encoding time : 0.000
% 0.07/0.34 % Propositional solver time : 0.000
% 0.07/0.34 % Success case prop preproc time : 0.000
% 0.07/0.34 % Success case prop encoding time : 0.000
% 0.07/0.34 % Success case prop solver time : 0.000
% 0.07/0.34 % Current number of processed clauses : 11
% 0.07/0.34 % Positive orientable unit clauses : 6
% 0.07/0.34 % Positive unorientable unit clauses: 0
% 0.07/0.34 % Negative unit clauses : 1
% 0.07/0.34 % Non-unit-clauses : 4
% 0.07/0.34 % Current number of unprocessed clauses: 0
% 0.07/0.34 % ...number of literals in the above : 0
% 0.07/0.34 % Current number of archived formulas : 0
% 0.07/0.34 % Current number of archived clauses : 4
% 0.07/0.34 % Clause-clause subsumption calls (NU) : 1
% 0.07/0.34 % Rec. Clause-clause subsumption calls : 0
% 0.07/0.34 % Non-unit clause-clause subsumptions : 0
% 0.07/0.34 % Unit Clause-clause subsumption calls : 0
% 0.07/0.34 % Rewrite failures with RHS unbound : 0
% 0.07/0.34 % BW rewrite match attempts : 4
% 0.07/0.34 % BW rewrite match successes : 4
% 0.07/0.34 % Condensation attempts : 0
% 0.07/0.34 % Condensation successes : 0
% 0.07/0.34 % Termbank termtop insertions : 1065
% 0.07/0.34 % Search garbage collected termcells : 253
% 0.07/0.34
% 0.07/0.34 % -------------------------------------------------
% 0.07/0.34 % User time : 0.003 s
% 0.07/0.34 % System time : 0.001 s
% 0.07/0.34 % Total time : 0.004 s
% 0.07/0.34 % Maximum resident set size: 3640 pages
% 0.07/0.34
% 0.07/0.34 % -------------------------------------------------
% 0.07/0.34 % User time : 0.004 s
% 0.07/0.34 % System time : 0.003 s
% 0.07/0.34 % Total time : 0.007 s
% 0.07/0.34 % Maximum resident set size: 4608 pages
% 0.07/0.34 % E exiting
%------------------------------------------------------------------------------