%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : LCL947_10 : 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 : n008.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 01:24:32 PM UTC 2026
% Result : Theorem 0.18s 0.56s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 110 ( 44 ~; 45 |; 4 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-5 aty)
% Number of variables : 51 ( 0 sgn 51 !; 0 ?; 37 :)
% 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,
qmltpeq: ( $i * ( $i * '$ki_world' ) ) > $o ).
tff(decl_27,type,
subset: ( $i * ( $i * '$ki_world' ) ) > $o ).
tff(decl_28,type,
union: ( $i * $i ) > $i ).
tff(decl_29,type,
'$ki_exists_in_world_$i': ( $i * '$ki_world' ) > $o ).
tff(decl_48,type,
esk15_5: ( '$ki_world' * ( $i * ( '$ki_world' * ( $i * '$ki_world' ) ) ) ) > '$ki_world' ).
tff(decl_49,type,
esk16_0: '$ki_world' ).
tff(decl_50,type,
esk17_0: $i ).
tff(decl_51,type,
esk18_0: '$ki_world' ).
tff(verify,conjecture,
! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ! [X12] :
( '$ki_exists_in_world_$i'(X1,X12)
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X1,X5)
=> qmltpeq(X5,union(X12,X12),X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
tff(subset_union,axiom,
! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ! [X12] :
( '$ki_exists_in_world_$i'(X1,X12)
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X1,X5)
=> ! [X13] :
( '$ki_exists_in_world_$i'(X5,X13)
=> ! [X7: '$ki_world'] :
( '$ki_accessible'(X5,X7)
=> ( ! [X8: '$ki_world'] :
( '$ki_accessible'(X7,X8)
=> subset(X8,X12,X13) )
=> ! [X8: '$ki_world'] :
( '$ki_accessible'(X7,X8)
=> qmltpeq(X8,union(X12,X13),X13) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_union) ).
tff(mrel_reflexive,axiom,
! [X1: '$ki_world'] : '$ki_accessible'(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
tff(reflexivity_of_subset,axiom,
! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ! [X12] :
( '$ki_exists_in_world_$i'(X1,X12)
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X1,X5)
=> subset(X5,X12,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
tff(c_0_4,negated_conjecture,
~ ! [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
=> ! [X12] :
( '$ki_exists_in_world_$i'(X1,X12)
=> ! [X5: '$ki_world'] :
( '$ki_accessible'(X1,X5)
=> qmltpeq(X5,union(X12,X12),X12) ) ) ),
inference(assume_negation,[status(cth)],[verify]) ).
tff(c_0_5,plain,
! [X100: '$ki_world',X101,X102: '$ki_world',X103,X104: '$ki_world',X106: '$ki_world'] :
( ( ~ '$ki_accessible'('$ki_local_world',X100)
| ~ '$ki_exists_in_world_$i'(X100,X101)
| ~ '$ki_accessible'(X100,X102)
| ~ '$ki_exists_in_world_$i'(X102,X103)
| ~ '$ki_accessible'(X102,X104)
| qmltpeq(X106,union(X101,X103),X103)
| ~ '$ki_accessible'(X104,X106)
| ~ subset(esk15_5(X100,X101,X102,X103,X104),X101,X103) )
& ( ~ '$ki_accessible'('$ki_local_world',X100)
| ~ '$ki_exists_in_world_$i'(X100,X101)
| ~ '$ki_accessible'(X100,X102)
| ~ '$ki_exists_in_world_$i'(X102,X103)
| ~ '$ki_accessible'(X102,X104)
| qmltpeq(X106,union(X101,X103),X103)
| ~ '$ki_accessible'(X104,X106)
| '$ki_accessible'(X104,esk15_5(X100,X101,X102,X103,X104)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subset_union])])])])])]) ).
tff(c_0_6,negated_conjecture,
( ~ qmltpeq(esk18_0,union(esk17_0,esk17_0),esk17_0)
& '$ki_accessible'(esk16_0,esk18_0)
& '$ki_exists_in_world_$i'(esk16_0,esk17_0)
& '$ki_accessible'('$ki_local_world',esk16_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
tcf(c_0_7,plain,
! [X1: '$ki_world',X6,X5: '$ki_world',X4,X3: '$ki_world',X2: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X2)
| ~ '$ki_exists_in_world_$i'(X2,X4)
| ~ '$ki_accessible'(X2,X3)
| ~ '$ki_exists_in_world_$i'(X3,X6)
| ~ '$ki_accessible'(X3,X1)
| ~ '$ki_accessible'(X1,X5)
| qmltpeq(X5,union(X4,X6),X6)
| '$ki_accessible'(X1,esk15_5(X2,X4,X3,X6,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
tcf(c_0_8,negated_conjecture,
'$ki_exists_in_world_$i'(esk16_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
tff(c_0_9,plain,
! [X16: '$ki_world'] : '$ki_accessible'(X16,X16),
inference(variable_rename,[status(thm)],[mrel_reflexive]) ).
tff(c_0_10,plain,
! [X125: '$ki_world',X126,X127: '$ki_world'] :
( subset(X127,X126,X126)
| ~ '$ki_accessible'(X125,X127)
| ~ '$ki_exists_in_world_$i'(X125,X126)
| ~ '$ki_accessible'('$ki_local_world',X125) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[reflexivity_of_subset])])])]) ).
tcf(c_0_11,negated_conjecture,
! [X4,X3: '$ki_world',X2: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'(X2,X1)
| ~ '$ki_accessible'(X3,esk16_0)
| ~ '$ki_accessible'(esk16_0,X2)
| ~ '$ki_accessible'('$ki_local_world',X3)
| ~ '$ki_exists_in_world_$i'(X3,X4)
| '$ki_accessible'(X2,esk15_5(X3,X4,esk16_0,esk17_0,X2))
| qmltpeq(X1,union(X4,esk17_0),esk17_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
tcf(c_0_12,negated_conjecture,
'$ki_accessible'('$ki_local_world',esk16_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
tcf(c_0_13,plain,
! [X1: '$ki_world'] : '$ki_accessible'(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_14,plain,
! [X1: '$ki_world',X4,X2: '$ki_world'] :
( ~ '$ki_accessible'(X1,X2)
| ~ '$ki_exists_in_world_$i'(X1,X4)
| ~ '$ki_accessible'('$ki_local_world',X1)
| subset(X2,X4,X4) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_15,negated_conjecture,
! [X2: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'(X2,X1)
| ~ '$ki_accessible'(esk16_0,X2)
| '$ki_accessible'(X2,esk15_5(esk16_0,esk17_0,esk16_0,esk17_0,X2))
| qmltpeq(X1,union(esk17_0,esk17_0),esk17_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_8]),c_0_12]),c_0_13])]) ).
tcf(c_0_16,negated_conjecture,
'$ki_accessible'(esk16_0,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
tcf(c_0_17,negated_conjecture,
~ qmltpeq(esk18_0,union(esk17_0,esk17_0),esk17_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
tcf(c_0_18,negated_conjecture,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'(esk16_0,X1)
| subset(X1,esk17_0,esk17_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_8]),c_0_12])]) ).
tcf(c_0_19,negated_conjecture,
'$ki_accessible'(esk16_0,esk15_5(esk16_0,esk17_0,esk16_0,esk17_0,esk16_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_13])]),c_0_17]) ).
tcf(c_0_20,plain,
! [X3: '$ki_world',X6,X5: '$ki_world',X4,X2: '$ki_world',X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ '$ki_exists_in_world_$i'(X1,X4)
| ~ '$ki_accessible'(X1,X2)
| ~ '$ki_exists_in_world_$i'(X2,X6)
| ~ '$ki_accessible'(X2,X3)
| ~ '$ki_accessible'(X3,X5)
| ~ subset(esk15_5(X1,X4,X2,X6,X3),X4,X6)
| qmltpeq(X5,union(X4,X6),X6) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
tcf(c_0_21,negated_conjecture,
subset(esk15_5(esk16_0,esk17_0,esk16_0,esk17_0,esk16_0),esk17_0,esk17_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
tcf(c_0_22,negated_conjecture,
! [X1: '$ki_world'] :
( ~ '$ki_accessible'(esk16_0,X1)
| qmltpeq(X1,union(esk17_0,esk17_0),esk17_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_8]),c_0_12]),c_0_13])]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_16]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL947_10 : 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 : n008.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
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 01:14:41 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.18/0.56 % Version: 3.5.1
% 0.18/0.56 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.18/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.18/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.56 % Starting new_bool_1 with 300s (1) cores
% 0.18/0.56 % Starting sh5l with 300s (1) cores
% 0.18/0.56 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 4029045 completed with status 0
% 0.18/0.56 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.18/0.56 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.18/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.18/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.56 % No SInE strategy applied
% 0.18/0.56 % Search class: FGUNS-FSLS33-SFFFFFNN
% 0.18/0.56 % partial match(1): FGUNF-FSLS33-SFFFFFNN
% 0.18/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.18/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.18/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 226s (1) cores
% 0.18/0.56 % Starting new_bool_3 with 226s (1) cores
% 0.18/0.56 % Starting new_bool_1 with 226s (1) cores
% 0.18/0.56 % new_bool_1 with pid 4029053 completed with status 0
% 0.18/0.56 % Result found by new_bool_1
% 0.18/0.56 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.18/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.18/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.56 % No SInE strategy applied
% 0.18/0.56 % Search class: FGUNS-FSLS33-SFFFFFNN
% 0.18/0.56 % partial match(1): FGUNF-FSLS33-SFFFFFNN
% 0.18/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.18/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.18/0.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 226s (1) cores
% 0.18/0.56 % Starting new_bool_3 with 226s (1) cores
% 0.18/0.56 % Starting new_bool_1 with 226s (1) cores
% 0.18/0.56 % Preprocessing time : 0.002 s
% 0.18/0.56 % Presaturation interreduction done
% 0.18/0.56
% 0.18/0.56 % Proof found!
% 0.18/0.56 % SZS status Theorem
% 0.18/0.56 % SZS output start CNFRefutation
% See solution above
% 0.18/0.56 % Parsed axioms : 28
% 0.18/0.56 % Removed by relevancy pruning/SinE : 0
% 0.18/0.56 % Initial clauses : 100
% 0.18/0.56 % Removed in clause preprocessing : 8
% 0.18/0.56 % Initial clauses in saturation : 92
% 0.18/0.56 % Processed clauses : 738
% 0.18/0.56 % ...of these trivial : 0
% 0.18/0.56 % ...subsumed : 80
% 0.18/0.56 % ...remaining for further processing : 658
% 0.18/0.56 % Other redundant clauses eliminated : 0
% 0.18/0.56 % Clauses deleted for lack of memory : 0
% 0.18/0.56 % Backward-subsumed : 0
% 0.18/0.56 % Backward-rewritten : 0
% 0.18/0.56 % Generated clauses : 7177
% 0.18/0.56 % ...of the previous two non-redundant : 7132
% 0.18/0.56 % ...aggressively subsumed : 0
% 0.18/0.56 % Contextual simplify-reflections : 0
% 0.18/0.56 % Paramodulations : 7177
% 0.18/0.56 % Factorizations : 0
% 0.18/0.56 % NegExts : 0
% 0.18/0.56 % Equation resolutions : 0
% 0.18/0.56 % Disequality decompositions : 0
% 0.18/0.56 % Total rewrite steps : 2637
% 0.18/0.56 % ...of those cached : 2623
% 0.18/0.56 % Propositional unsat checks : 0
% 0.18/0.56 % Propositional check models : 0
% 0.18/0.56 % Propositional check unsatisfiable : 0
% 0.18/0.56 % Propositional clauses : 0
% 0.18/0.56 % Propositional clauses after purity: 0
% 0.18/0.56 % Propositional unsat core size : 0
% 0.18/0.56 % Propositional preprocessing time : 0.000
% 0.18/0.56 % Propositional encoding time : 0.000
% 0.18/0.56 % Propositional solver time : 0.000
% 0.18/0.56 % Success case prop preproc time : 0.000
% 0.18/0.56 % Success case prop encoding time : 0.000
% 0.18/0.56 % Success case prop solver time : 0.000
% 0.18/0.56 % Current number of processed clauses : 566
% 0.18/0.56 % Positive orientable unit clauses : 88
% 0.18/0.56 % Positive unorientable unit clauses: 0
% 0.18/0.56 % Negative unit clauses : 1
% 0.18/0.56 % Non-unit-clauses : 477
% 0.18/0.56 % Current number of unprocessed clauses: 6546
% 0.18/0.56 % ...number of literals in the above : 22083
% 0.18/0.56 % Current number of archived formulas : 0
% 0.18/0.56 % Current number of archived clauses : 92
% 0.18/0.56 % Clause-clause subsumption calls (NU) : 30540
% 0.18/0.56 % Rec. Clause-clause subsumption calls : 17823
% 0.18/0.56 % Non-unit clause-clause subsumptions : 80
% 0.18/0.56 % Unit Clause-clause subsumption calls : 1157
% 0.18/0.56 % Rewrite failures with RHS unbound : 0
% 0.18/0.56 % BW rewrite match attempts : 27
% 0.18/0.56 % BW rewrite match successes : 0
% 0.18/0.56 % Condensation attempts : 0
% 0.18/0.56 % Condensation successes : 0
% 0.18/0.56 % Termbank termtop insertions : 210232
% 0.18/0.56 % Search garbage collected termcells : 3290
% 0.18/0.56
% 0.18/0.56 % -------------------------------------------------
% 0.18/0.56 % User time : 0.091 s
% 0.18/0.56 % System time : 0.007 s
% 0.18/0.56 % Total time : 0.098 s
% 0.18/0.56 % Maximum resident set size: 4204 pages
% 0.18/0.56
% 0.18/0.56 % -------------------------------------------------
% 0.18/0.56 % User time : 0.475 s
% 0.18/0.56 % System time : 0.044 s
% 0.18/0.56 % Total time : 0.519 s
% 0.18/0.56 % Maximum resident set size: 4864 pages
% 0.18/0.56 % E exiting
%------------------------------------------------------------------------------