%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL962_16 : 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 : n005.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 01:18:10 PM UTC 2026
% Result : Theorem 0.11s 0.43s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 74 ( 34 ~; 26 |; 3 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
'$ki_world': $tType ).
tff(decl_sort2,type,
'$ki_index': $tType ).
tff(decl_23,type,
'$ki_local_world': '$ki_world' ).
tff(decl_24,type,
'$ki_accessible': ( '$ki_world' * ( '$ki_world' * '$ki_index' ) ) > $o ).
tff(decl_25,type,
'#idx(a)': '$ki_index' ).
tff(decl_26,type,
'#idx(b)': '$ki_index' ).
tff(decl_27,type,
p: '$ki_world' > $o ).
tff(decl_28,type,
esk1_0: '$ki_world' ).
tff(decl_29,type,
esk2_1: '$ki_world' > '$ki_world' ).
tff(verify,conjecture,
! [X1: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',X1)
=> ~ p(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff('mrel_transitive_#idx(a)',axiom,
! [X1: '$ki_world',X2: '$ki_world',X3: '$ki_world'] :
( ( '$ki_accessible'('#idx(a)',X2,X3)
& '$ki_accessible'('#idx(a)',X1,X2) )
=> '$ki_accessible'('#idx(a)',X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_transitive_#idx(a)') ).
tff(ab_axiom_2,axiom,
( ~ ! [X1: '$ki_world'] :
( '$ki_accessible'('#idx(b)','$ki_local_world',X1)
=> p(X1) )
=> ! [X1: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',X1)
=> ~ ! [X4: '$ki_world'] :
( '$ki_accessible'('#idx(b)',X1,X4)
=> p(X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_axiom_2) ).
tff('mrel_reflexive_#idx(a)',axiom,
! [X1: '$ki_world'] : '$ki_accessible'('#idx(a)',X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_reflexive_#idx(a)') ).
tff(not_a_axiom_1,axiom,
~ p('$ki_local_world'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_a_axiom_1) ).
tff('mrel_reflexive_#idx(b)',axiom,
! [X1: '$ki_world'] : '$ki_accessible'('#idx(b)',X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_reflexive_#idx(b)') ).
tff(ab_axiom_1,axiom,
! [X1: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',X1)
=> ( p(X1)
=> ! [X4: '$ki_world'] :
( '$ki_accessible'('#idx(b)',X1,X4)
=> p(X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_axiom_1) ).
tff(c_0_7,negated_conjecture,
~ ! [X1: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',X1)
=> ~ p(X1) ),
inference(assume_negation,[status(cth)],[verify]) ).
tff(c_0_8,negated_conjecture,
~ ! [X1: '$ki_world'] :
( '$ki_accessible'('#idx(a)','$ki_local_world',X1)
=> ~ p(X1) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
tff(c_0_9,plain,
! [X12: '$ki_world',X13: '$ki_world',X14: '$ki_world'] :
( '$ki_accessible'('#idx(a)',X12,X14)
| ~ '$ki_accessible'('#idx(a)',X13,X14)
| ~ '$ki_accessible'('#idx(a)',X12,X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['mrel_transitive_#idx(a)'])])]) ).
tff(c_0_10,negated_conjecture,
( p(esk1_0)
& '$ki_accessible'('#idx(a)','$ki_local_world',esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
tff(c_0_11,plain,
! [X8: '$ki_world',X9: '$ki_world'] :
( ( p(X8)
| ~ '$ki_accessible'('#idx(b)','$ki_local_world',X8)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X9)
| ~ p(esk2_1(X9)) )
& ( p(X8)
| ~ '$ki_accessible'('#idx(b)','$ki_local_world',X8)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X9)
| '$ki_accessible'('#idx(b)',X9,esk2_1(X9)) ) ),
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)],[ab_axiom_2])])])])])]) ).
tcf(c_0_12,plain,
! [X1: '$ki_world',X2: '$ki_world',X3: '$ki_world'] :
( ~ '$ki_accessible'('#idx(a)',X2,X3)
| ~ '$ki_accessible'('#idx(a)',X1,X2)
| '$ki_accessible'('#idx(a)',X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_13,negated_conjecture,
'$ki_accessible'('#idx(a)','$ki_local_world',esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tff(c_0_14,plain,
! [X11: '$ki_world'] : '$ki_accessible'('#idx(a)',X11,X11),
inference(variable_rename,[status(thm)],['mrel_reflexive_#idx(a)']) ).
tff(c_0_15,plain,
~ p('$ki_local_world'),
inference(fof_simplification,[status(thm)],[not_a_axiom_1]) ).
tcf(c_0_16,plain,
! [X1: '$ki_world',X2: '$ki_world'] :
( ~ '$ki_accessible'('#idx(b)','$ki_local_world',X2)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X1)
| p(X2)
| '$ki_accessible'('#idx(b)',X1,esk2_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
tcf(c_0_17,negated_conjecture,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'('#idx(a)',X1,'$ki_local_world')
| '$ki_accessible'('#idx(a)',X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
tcf(c_0_18,plain,
! [X1: '$ki_world'] : '$ki_accessible'('#idx(a)',X1,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
tff(c_0_19,plain,
! [X15: '$ki_world'] : '$ki_accessible'('#idx(b)',X15,X15),
inference(variable_rename,[status(thm)],['mrel_reflexive_#idx(b)']) ).
tff(c_0_20,plain,
~ p('$ki_local_world'),
inference(fof_nnf,[status(thm)],[c_0_15]) ).
tff(c_0_21,plain,
! [X6: '$ki_world',X7: '$ki_world'] :
( p(X7)
| ~ '$ki_accessible'('#idx(b)',X6,X7)
| ~ p(X6)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X6) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ab_axiom_1])])])]) ).
tcf(c_0_22,negated_conjecture,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'('#idx(b)','$ki_local_world',X1)
| '$ki_accessible'('#idx(b)',esk1_0,esk2_1(esk1_0))
| p(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
tcf(c_0_23,plain,
! [X1: '$ki_world'] : '$ki_accessible'('#idx(b)',X1,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
tcf(c_0_24,plain,
~ p('$ki_local_world'),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
tcf(c_0_25,plain,
! [X1: '$ki_world',X2: '$ki_world'] :
( ~ '$ki_accessible'('#idx(b)',X1,X2)
| ~ p(X1)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X1)
| p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
tcf(c_0_26,negated_conjecture,
'$ki_accessible'('#idx(b)',esk1_0,esk2_1(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
tcf(c_0_27,negated_conjecture,
p(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_28,plain,
! [X1: '$ki_world',X2: '$ki_world'] :
( ~ '$ki_accessible'('#idx(b)','$ki_local_world',X2)
| ~ '$ki_accessible'('#idx(a)','$ki_local_world',X1)
| ~ p(esk2_1(X1))
| p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
tcf(c_0_29,negated_conjecture,
p(esk2_1(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_13])]) ).
tcf(c_0_30,negated_conjecture,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'('#idx(b)','$ki_local_world',X1)
| p(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_13])]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_30]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL962_16 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 01:14:18 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.43 % Version: 3.5.1
% 0.11/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.43 % Starting sh5l with 300s (1) cores
% 0.11/0.43 % new_bool_3 with pid 2223685 completed with status 0
% 0.11/0.43 % Result found by new_bool_3
% 0.11/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.43 % Search class: FGUNS-FFSF11-SFFFFFNN
% 0.11/0.43 % partial match(1): FGUNF-FFSF11-SFFFFFNN
% 0.11/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.43 % SubtermCWHack with pid 2223691 completed with status 0
% 0.11/0.43 % Result found by SubtermCWHack
% 0.11/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.43 % Search class: FGUNS-FFSF11-SFFFFFNN
% 0.11/0.43 % partial match(1): FGUNF-FFSF11-SFFFFFNN
% 0.11/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.43 % Preprocessing time : 0.001 s
% 0.11/0.43
% 0.11/0.43 % Proof found!
% 0.11/0.43 % SZS status Theorem
% 0.11/0.43 % SZS output start CNFRefutation
% See solution above
% 0.11/0.43 % Parsed axioms : 15
% 0.11/0.43 % Removed by relevancy pruning/SinE : 7
% 0.11/0.43 % Initial clauses : 10
% 0.11/0.43 % Removed in clause preprocessing : 0
% 0.11/0.43 % Initial clauses in saturation : 10
% 0.11/0.43 % Processed clauses : 21
% 0.11/0.43 % ...of these trivial : 0
% 0.11/0.43 % ...subsumed : 2
% 0.11/0.43 % ...remaining for further processing : 19
% 0.11/0.43 % Other redundant clauses eliminated : 0
% 0.11/0.43 % Clauses deleted for lack of memory : 0
% 0.11/0.43 % Backward-subsumed : 2
% 0.11/0.43 % Backward-rewritten : 2
% 0.11/0.43 % Generated clauses : 21
% 0.11/0.43 % ...of the previous two non-redundant : 17
% 0.11/0.43 % ...aggressively subsumed : 0
% 0.11/0.43 % Contextual simplify-reflections : 0
% 0.11/0.43 % Paramodulations : 21
% 0.11/0.43 % Factorizations : 0
% 0.11/0.43 % NegExts : 0
% 0.11/0.43 % Equation resolutions : 0
% 0.11/0.43 % Disequality decompositions : 0
% 0.11/0.43 % Total rewrite steps : 9
% 0.11/0.43 % ...of those cached : 3
% 0.11/0.43 % Propositional unsat checks : 0
% 0.11/0.43 % Propositional check models : 0
% 0.11/0.43 % Propositional check unsatisfiable : 0
% 0.11/0.43 % Propositional clauses : 0
% 0.11/0.43 % Propositional clauses after purity: 0
% 0.11/0.43 % Propositional unsat core size : 0
% 0.11/0.43 % Propositional preprocessing time : 0.000
% 0.11/0.43 % Propositional encoding time : 0.000
% 0.11/0.43 % Propositional solver time : 0.000
% 0.11/0.43 % Success case prop preproc time : 0.000
% 0.11/0.43 % Success case prop encoding time : 0.000
% 0.11/0.43 % Success case prop solver time : 0.000
% 0.11/0.43 % Current number of processed clauses : 15
% 0.11/0.43 % Positive orientable unit clauses : 7
% 0.11/0.43 % Positive unorientable unit clauses: 0
% 0.11/0.43 % Negative unit clauses : 1
% 0.11/0.43 % Non-unit-clauses : 7
% 0.11/0.43 % Current number of unprocessed clauses: 6
% 0.11/0.43 % ...number of literals in the above : 16
% 0.11/0.43 % Current number of archived formulas : 0
% 0.11/0.43 % Current number of archived clauses : 4
% 0.11/0.43 % Clause-clause subsumption calls (NU) : 8
% 0.11/0.43 % Rec. Clause-clause subsumption calls : 7
% 0.11/0.43 % Non-unit clause-clause subsumptions : 3
% 0.11/0.43 % Unit Clause-clause subsumption calls : 0
% 0.11/0.43 % Rewrite failures with RHS unbound : 0
% 0.11/0.43 % BW rewrite match attempts : 4
% 0.11/0.43 % BW rewrite match successes : 2
% 0.11/0.43 % Condensation attempts : 0
% 0.11/0.43 % Condensation successes : 0
% 0.11/0.43 % Termbank termtop insertions : 1159
% 0.11/0.43 % Search garbage collected termcells : 143
% 0.11/0.43
% 0.11/0.43 % -------------------------------------------------
% 0.11/0.43 % User time : 0.007 s
% 0.11/0.43 % System time : 0.000 s
% 0.11/0.43 % Total time : 0.007 s
% 0.11/0.43 % Maximum resident set size: 3636 pages
% 0.11/0.43
% 0.11/0.43 % -------------------------------------------------
% 0.11/0.43 % User time : 0.010 s
% 0.11/0.43 % System time : 0.003 s
% 0.11/0.43 % Total time : 0.013 s
% 0.11/0.43 % Maximum resident set size: 4864 pages
% 0.11/0.43 % E exiting
%------------------------------------------------------------------------------