%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP004^5 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 : Wed Sep 30 08:05:08 AM UTC 2026
% Result : Theorem 11.88s 2.17s
% Output : CNFRefutation 11.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 4 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 258 ( 15 ~; 11 |; 1 &; 224 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 9 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 0 ^; 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
del: $tType ).
thf(decl_23,type,
bool: del ).
thf(decl_25,type,
arr: del > del > del ).
thf(decl_26,type,
mem: $i > del > $o ).
thf(decl_27,type,
ap: $i > $i > $i ).
thf(decl_29,type,
p: $i > $o ).
thf(decl_409,type,
c_2Epred__set_2ECHOICE: del > $i ).
thf(decl_412,type,
c_2Epred__set_2EDELETE: del > $i ).
thf(decl_435,type,
c_2Epred__set_2EREST: del > $i ).
thf(decl_438,type,
c_2Epred__set_2ESUBSET: del > $i ).
thf(decl_466,type,
esk1_0: del ).
thf(decl_467,type,
esk2_0: $i ).
thf(conj_thm_2Epred__set_2EREST__SUBSET,conjecture,
! [X13: del,X197: $i] :
( ( mem @ X197 @ ( arr @ X13 @ bool ) )
=> ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ X13 ) @ ( ap @ ( c_2Epred__set_2EREST @ X13 ) @ X197 ) ) @ X197 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UatzLAcyvt/E---3.1_555335.p',conj_thm_2Epred__set_2EREST__SUBSET) ).
thf(ax_thm_2Epred__set_2EREST__DEF,axiom,
! [X13: del,X197: $i] :
( ( mem @ X197 @ ( arr @ X13 @ bool ) )
=> ( ( ap @ ( c_2Epred__set_2EREST @ X13 ) @ X197 )
= ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ X13 ) @ X197 ) @ ( ap @ ( c_2Epred__set_2ECHOICE @ X13 ) @ X197 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UatzLAcyvt/E---3.1_555335.p',ax_thm_2Epred__set_2EREST__DEF) ).
thf(conj_thm_2Epred__set_2EDELETE__SUBSET,axiom,
! [X13: del,X21: $i] :
( ( mem @ X21 @ X13 )
=> ! [X177: $i] :
( ( mem @ X177 @ ( arr @ X13 @ bool ) )
=> ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ X13 ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ X13 ) @ X177 ) @ X21 ) ) @ X177 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UatzLAcyvt/E---3.1_555335.p',conj_thm_2Epred__set_2EDELETE__SUBSET) ).
thf(ap_tp,axiom,
! [X3: del,X4: del,X5: $i] :
( ( mem @ X5 @ ( arr @ X3 @ X4 ) )
=> ! [X6: $i] :
( ( mem @ X6 @ X3 )
=> ( mem @ ( ap @ X5 @ X6 ) @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UatzLAcyvt/E---3.1_555335.p',ap_tp) ).
thf(mem_c_2Epred__set_2ECHOICE,axiom,
! [X13: del] : ( mem @ ( c_2Epred__set_2ECHOICE @ X13 ) @ ( arr @ ( arr @ X13 @ bool ) @ X13 ) ),
file('/export/starexec/sandbox2/tmp/tmp.UatzLAcyvt/E---3.1_555335.p',mem_c_2Epred__set_2ECHOICE) ).
thf(c_0_5,negated_conjecture,
~ ! [X13: del,X197: $i] :
( ( mem @ X197 @ ( arr @ X13 @ bool ) )
=> ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ X13 ) @ ( ap @ ( c_2Epred__set_2EREST @ X13 ) @ X197 ) ) @ X197 ) ) ),
inference(assume_negation,[status(cth)],[conj_thm_2Epred__set_2EREST__SUBSET]) ).
thf(c_0_6,plain,
! [X3732: del,X3733: $i] :
( ~ ( mem @ X3733 @ ( arr @ X3732 @ bool ) )
| ( ( ap @ ( c_2Epred__set_2EREST @ X3732 ) @ X3733 )
= ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ X3732 ) @ X3733 ) @ ( ap @ ( c_2Epred__set_2ECHOICE @ X3732 ) @ X3733 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax_thm_2Epred__set_2EREST__DEF])])]) ).
thf(c_0_7,negated_conjecture,
( ( mem @ esk2_0 @ ( arr @ esk1_0 @ bool ) )
& ~ ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ esk1_0 ) @ ( ap @ ( c_2Epred__set_2EREST @ esk1_0 ) @ esk2_0 ) ) @ esk2_0 ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
thf(c_0_8,plain,
! [X3848: del,X3849: $i,X3850: $i] :
( ~ ( mem @ X3849 @ X3848 )
| ~ ( mem @ X3850 @ ( arr @ X3848 @ bool ) )
| ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ X3848 ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ X3848 ) @ X3850 ) @ X3849 ) ) @ X3850 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Epred__set_2EDELETE__SUBSET])])])]) ).
thf(c_0_9,plain,
! [X2: $i,X3: del] :
( ( ( ap @ ( c_2Epred__set_2EREST @ X3 ) @ X2 )
= ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ X3 ) @ X2 ) @ ( ap @ ( c_2Epred__set_2ECHOICE @ X3 ) @ X2 ) ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ bool ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
mem @ esk2_0 @ ( arr @ esk1_0 @ bool ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X3689: del,X3690: del,X3691: $i,X3692: $i] :
( ~ ( mem @ X3691 @ ( arr @ X3689 @ X3690 ) )
| ~ ( mem @ X3692 @ X3689 )
| ( mem @ ( ap @ X3691 @ X3692 ) @ X3690 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ap_tp])])])]) ).
thf(c_0_12,plain,
! [X3811: del] : ( mem @ ( c_2Epred__set_2ECHOICE @ X3811 ) @ ( arr @ ( arr @ X3811 @ bool ) @ X3811 ) ),
inference(variable_rename,[status(thm)],[mem_c_2Epred__set_2ECHOICE]) ).
thf(c_0_13,plain,
! [X2: $i,X5: $i,X3: del] :
( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ X3 ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ X3 ) @ X5 ) @ X2 ) ) @ X5 ) )
| ~ ( mem @ X2 @ X3 )
| ~ ( mem @ X5 @ ( arr @ X3 @ bool ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_14,negated_conjecture,
( ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ esk1_0 ) @ esk2_0 ) @ ( ap @ ( c_2Epred__set_2ECHOICE @ esk1_0 ) @ esk2_0 ) )
= ( ap @ ( c_2Epred__set_2EREST @ esk1_0 ) @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_15,negated_conjecture,
~ ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ esk1_0 ) @ ( ap @ ( c_2Epred__set_2EREST @ esk1_0 ) @ esk2_0 ) ) @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_16,plain,
! [X2: $i,X5: $i,X4: del,X3: del] :
( ( mem @ ( ap @ X2 @ X5 ) @ X4 )
| ~ ( mem @ X2 @ ( arr @ X3 @ X4 ) )
| ~ ( mem @ X5 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_17,plain,
! [X3: del] : ( mem @ ( c_2Epred__set_2ECHOICE @ X3 ) @ ( arr @ ( arr @ X3 @ bool ) @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_18,negated_conjecture,
~ ( mem @ ( ap @ ( c_2Epred__set_2ECHOICE @ esk1_0 ) @ esk2_0 ) @ esk1_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_10])]),c_0_15]) ).
thf(c_0_19,plain,
! [X2: $i,X3: del] :
( ( mem @ ( ap @ ( c_2Epred__set_2ECHOICE @ X3 ) @ X2 ) @ X3 )
| ~ ( mem @ X2 @ ( arr @ X3 @ bool ) ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP004^5 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 19:20:33 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.27/0.33 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.UatzLAcyvt/E---3.1_555335.p
% 11.88/2.17 % Version: 3.5.1-ho
% 11.88/2.17 % Preprocessing class: HMLMSMSLSSLNSFA.
% 11.88/2.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.88/2.17 % Starting new_bool_1 with 1500s (5) cores
% 11.88/2.17 % Starting post_as_ho6 with 300s (1) cores
% 11.88/2.17 % Starting post_as_ho8 with 300s (1) cores
% 11.88/2.17 % Starting pre_casc_4 with 300s (1) cores
% 11.88/2.17 % new_bool_1 with pid 555348 completed with status 0
% 11.88/2.17 % Result found by new_bool_1
% 11.88/2.17 % Preprocessing class: HMLMSMSLSSLNSFA.
% 11.88/2.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.88/2.17 % Starting new_bool_1 with 1500s (5) cores
% 11.88/2.17 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 11.88/2.17 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 11.88/2.17 % Search class: HGHSM-SMLM32-DSFFFFNN
% 11.88/2.17 % partial match(1): HGHSM-SMLM32-DSFFFFBN
% 11.88/2.17 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 11.88/2.17 % Starting SubtermCWHack with 151s (1) cores
% 11.88/2.17 % Starting post_as_ho7 with 901s (1) cores
% 11.88/2.17 % Starting post_as_ho8 with 151s (1) cores
% 11.88/2.17 % Starting full_lambda_3 with 151s (1) cores
% 11.88/2.17 % Starting post_as_ho6 with 146s (1) cores
% 11.88/2.17 % post_as_ho8 with pid 555357 completed with status 0
% 11.88/2.17 % Result found by post_as_ho8
% 11.88/2.17 % Preprocessing class: HMLMSMSLSSLNSFA.
% 11.88/2.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.88/2.17 % Starting new_bool_1 with 1500s (5) cores
% 11.88/2.17 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 11.88/2.17 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 11.88/2.17 % Search class: HGHSM-SMLM32-DSFFFFNN
% 11.88/2.17 % partial match(1): HGHSM-SMLM32-DSFFFFBN
% 11.88/2.17 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 11.88/2.17 % Starting SubtermCWHack with 151s (1) cores
% 11.88/2.17 % Starting post_as_ho7 with 901s (1) cores
% 11.88/2.17 % Starting post_as_ho8 with 151s (1) cores
% 11.88/2.17 % Preprocessing time : 0.023 s
% 11.88/2.17 % Presaturation interreduction done
% 11.88/2.17
% 11.88/2.17 % Proof found!
% 11.88/2.17 % SZS status Theorem
% 11.88/2.17 % SZS output start CNFRefutation
% See solution above
% 11.88/2.17 % Parsed axioms : 2697
% 11.88/2.17 % Removed by relevancy pruning/SinE : 2141
% 11.88/2.17 % Initial clauses : 2089
% 11.88/2.17 % Removed in clause preprocessing : 950
% 11.88/2.17 % Initial clauses in saturation : 1139
% 11.88/2.17 % Processed clauses : 2776
% 11.88/2.17 % ...of these trivial : 44
% 11.88/2.17 % ...subsumed : 404
% 11.88/2.17 % ...remaining for further processing : 2328
% 11.88/2.17 % Other redundant clauses eliminated : 353
% 11.88/2.17 % Clauses deleted for lack of memory : 0
% 11.88/2.17 % Backward-subsumed : 2
% 11.88/2.17 % Backward-rewritten : 8
% 11.88/2.17 % Generated clauses : 50776
% 11.88/2.17 % ...of the previous two non-redundant : 49699
% 11.88/2.17 % ...aggressively subsumed : 0
% 11.88/2.17 % Contextual simplify-reflections : 6
% 11.88/2.17 % Paramodulations : 50083
% 11.88/2.17 % Factorizations : 6
% 11.88/2.17 % NegExts : 13
% 11.88/2.17 % Equation resolutions : 367
% 11.88/2.17 % Disequality decompositions : 0
% 11.88/2.17 % Total rewrite steps : 2240
% 11.88/2.17 % ...of those cached : 2059
% 11.88/2.17 % Propositional unsat checks : 0
% 11.88/2.17 % Propositional check models : 0
% 11.88/2.17 % Propositional check unsatisfiable : 0
% 11.88/2.17 % Propositional clauses : 0
% 11.88/2.17 % Propositional clauses after purity: 0
% 11.88/2.17 % Propositional unsat core size : 0
% 11.88/2.17 % Propositional preprocessing time : 0.000
% 11.88/2.17 % Propositional encoding time : 0.000
% 11.88/2.17 % Propositional solver time : 0.000
% 11.88/2.17 % Success case prop preproc time : 0.000
% 11.88/2.17 % Success case prop encoding time : 0.000
% 11.88/2.17 % Success case prop solver time : 0.000
% 11.88/2.17 % Current number of processed clauses : 1322
% 11.88/2.17 % Positive orientable unit clauses : 251
% 11.88/2.17 % Positive unorientable unit clauses: 13
% 11.88/2.17 % Negative unit clauses : 52
% 11.88/2.17 % Non-unit-clauses : 1006
% 11.88/2.17 % Current number of unprocessed clauses: 48814
% 11.88/2.17 % ...number of literals in the above : 287561
% 11.88/2.17 % Current number of archived formulas : 0
% 11.88/2.17 % Current number of archived clauses : 939
% 11.88/2.17 % Clause-clause subsumption calls (NU) : 296965
% 11.88/2.17 % Rec. Clause-clause subsumption calls : 52573
% 11.88/2.17 % Non-unit clause-clause subsumptions : 297
% 11.88/2.17 % Unit Clause-clause subsumption calls : 2378
% 11.88/2.17 % Rewrite failures with RHS unbound : 0
% 11.88/2.17 % BW rewrite match attempts : 7029
% 11.88/2.17 % BW rewrite match successes : 103
% 11.88/2.17 % Condensation attempts : 2776
% 11.88/2.17 % Condensation successes : 21
% 11.88/2.17 % Termbank termtop insertions : 2113615
% 11.88/2.17 % Search garbage collected termcells : 68645
% 11.88/2.17
% 11.88/2.17 % -------------------------------------------------
% 11.88/2.17 % User time : 1.657 s
% 11.88/2.17 % System time : 0.055 s
% 11.88/2.17 % Total time : 1.712 s
% 11.88/2.17 % Maximum resident set size: 15208 pages
% 11.88/2.17
% 11.88/2.17 % -------------------------------------------------
% 11.88/2.17 % User time : 7.831 s
% 11.88/2.17 % System time : 0.271 s
% 11.88/2.17 % Total time : 8.102 s
% 11.88/2.17 % Maximum resident set size: 10752 pages
% 11.88/2.17 % E exiting
%------------------------------------------------------------------------------