%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP005^5 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:03:58 AM UTC 2026
% Result : Theorem 1.05s 1.88s
% Output : CNFRefutation 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 14 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 156 ( 6 ~; 2 |; 1 &; 144 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 30 ( 0 ^; 30 !; 0 ?; 30 :)
% 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_200,type,
c_2Epair_2ECURRY: del > del > del > $i ).
thf(decl_208,type,
c_2Epair_2EUNCURRY: del > del > del > $i ).
thf(decl_500,type,
c_2Eset__relation_2Erel__to__reln: del > del > $i ).
thf(decl_501,type,
c_2Eset__relation_2Ereln__to__rel: del > del > $i ).
thf(decl_516,type,
esk1_0: del ).
thf(decl_517,type,
esk2_0: del ).
thf(decl_518,type,
esk3_0: $i ).
thf(conj_thm_2Eset__relation_2Erel__to__reln__inv,conjecture,
! [X13: del,X20: del,X207: $i] :
( ( mem @ X207 @ ( arr @ X13 @ ( arr @ X20 @ bool ) ) )
=> ( ( ap @ ( c_2Eset__relation_2Ereln__to__rel @ X13 @ X20 ) @ ( ap @ ( c_2Eset__relation_2Erel__to__reln @ X13 @ X20 ) @ X207 ) )
= X207 ) ),
file('/export/starexec/sandbox/tmp/tmp.JFXNQ5Krxw/E---3.1_1693503.p',conj_thm_2Eset__relation_2Erel__to__reln__inv) ).
thf(conj_thm_2Eset__relation_2Ereln__to__rel__IS__CURRY,axiom,
! [X13: del,X20: del] :
( ( c_2Eset__relation_2Ereln__to__rel @ X13 @ X20 )
= ( c_2Epair_2ECURRY @ X13 @ X20 @ bool ) ),
file('/export/starexec/sandbox/tmp/tmp.JFXNQ5Krxw/E---3.1_1693503.p',conj_thm_2Eset__relation_2Ereln__to__rel__IS__CURRY) ).
thf(conj_thm_2Eset__relation_2Erel__to__reln__IS__UNCURRY,axiom,
! [X13: del,X20: del] :
( ( c_2Eset__relation_2Erel__to__reln @ X13 @ X20 )
= ( c_2Epair_2EUNCURRY @ X13 @ X20 @ bool ) ),
file('/export/starexec/sandbox/tmp/tmp.JFXNQ5Krxw/E---3.1_1693503.p',conj_thm_2Eset__relation_2Erel__to__reln__IS__UNCURRY) ).
thf(conj_thm_2Epair_2ECURRY__UNCURRY__THM,axiom,
! [X13: del,X20: del,X72: del,X29: $i] :
( ( mem @ X29 @ ( arr @ X13 @ ( arr @ X20 @ X72 ) ) )
=> ( ( ap @ ( c_2Epair_2ECURRY @ X13 @ X20 @ X72 ) @ ( ap @ ( c_2Epair_2EUNCURRY @ X13 @ X20 @ X72 ) @ X29 ) )
= X29 ) ),
file('/export/starexec/sandbox/tmp/tmp.JFXNQ5Krxw/E---3.1_1693503.p',conj_thm_2Epair_2ECURRY__UNCURRY__THM) ).
thf(c_0_4,negated_conjecture,
~ ! [X13: del,X20: del,X207: $i] :
( ( mem @ X207 @ ( arr @ X13 @ ( arr @ X20 @ bool ) ) )
=> ( ( ap @ ( c_2Eset__relation_2Ereln__to__rel @ X13 @ X20 ) @ ( ap @ ( c_2Eset__relation_2Erel__to__reln @ X13 @ X20 ) @ X207 ) )
= X207 ) ),
inference(assume_negation,[status(cth)],[conj_thm_2Eset__relation_2Erel__to__reln__inv]) ).
thf(c_0_5,negated_conjecture,
( ( mem @ esk3_0 @ ( arr @ esk1_0 @ ( arr @ esk2_0 @ bool ) ) )
& ( ( ap @ ( c_2Eset__relation_2Ereln__to__rel @ esk1_0 @ esk2_0 ) @ ( ap @ ( c_2Eset__relation_2Erel__to__reln @ esk1_0 @ esk2_0 ) @ esk3_0 ) )
!= esk3_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
thf(c_0_6,plain,
! [X3389: del,X3390: del] :
( ( c_2Eset__relation_2Ereln__to__rel @ X3389 @ X3390 )
= ( c_2Epair_2ECURRY @ X3389 @ X3390 @ bool ) ),
inference(variable_rename,[status(thm)],[conj_thm_2Eset__relation_2Ereln__to__rel__IS__CURRY]) ).
thf(c_0_7,plain,
! [X3377: del,X3378: del] :
( ( c_2Eset__relation_2Erel__to__reln @ X3377 @ X3378 )
= ( c_2Epair_2EUNCURRY @ X3377 @ X3378 @ bool ) ),
inference(variable_rename,[status(thm)],[conj_thm_2Eset__relation_2Erel__to__reln__IS__UNCURRY]) ).
thf(c_0_8,negated_conjecture,
( ( ap @ ( c_2Eset__relation_2Ereln__to__rel @ esk1_0 @ esk2_0 ) @ ( ap @ ( c_2Eset__relation_2Erel__to__reln @ esk1_0 @ esk2_0 ) @ esk3_0 ) )
!= esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,plain,
! [X3: del,X4: del] :
( ( c_2Eset__relation_2Ereln__to__rel @ X3 @ X4 )
= ( c_2Epair_2ECURRY @ X3 @ X4 @ bool ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
! [X3: del,X4: del] :
( ( c_2Eset__relation_2Erel__to__reln @ X3 @ X4 )
= ( c_2Epair_2EUNCURRY @ X3 @ X4 @ bool ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X4174: del,X4175: del,X4176: del,X4177: $i] :
( ~ ( mem @ X4177 @ ( arr @ X4174 @ ( arr @ X4175 @ X4176 ) ) )
| ( ( ap @ ( c_2Epair_2ECURRY @ X4174 @ X4175 @ X4176 ) @ ( ap @ ( c_2Epair_2EUNCURRY @ X4174 @ X4175 @ X4176 ) @ X4177 ) )
= X4177 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Epair_2ECURRY__UNCURRY__THM])])]) ).
thf(c_0_12,negated_conjecture,
( ( ap @ ( c_2Epair_2ECURRY @ esk1_0 @ esk2_0 @ bool ) @ ( ap @ ( c_2Epair_2EUNCURRY @ esk1_0 @ esk2_0 @ bool ) @ esk3_0 ) )
!= esk3_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
thf(c_0_13,plain,
! [X2: $i,X3: del,X4: del,X13: del] :
( ( ( ap @ ( c_2Epair_2ECURRY @ X3 @ X4 @ X13 ) @ ( ap @ ( c_2Epair_2EUNCURRY @ X3 @ X4 @ X13 ) @ X2 ) )
= X2 )
| ~ ( mem @ X2 @ ( arr @ X3 @ ( arr @ X4 @ X13 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_14,negated_conjecture,
mem @ esk3_0 @ ( arr @ esk1_0 @ ( arr @ esk2_0 @ bool ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP005^5 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.16 % Computer : n001.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Sep 29 19:27:07 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.76/0.87 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.JFXNQ5Krxw/E---3.1_1693503.p
% 1.05/1.88 % Version: 3.5.1-ho
% 1.05/1.88 % Preprocessing class: HMLMSMSLSSLNSFA.
% 1.05/1.88 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.05/1.88 % Starting new_bool_1 with 1500s (5) cores
% 1.05/1.88 % Starting post_as_ho6 with 300s (1) cores
% 1.05/1.88 % Starting post_as_ho8 with 300s (1) cores
% 1.05/1.88 % Starting pre_casc_4 with 300s (1) cores
% 1.05/1.88 % pre_casc_4 with pid 1693519 completed with status 0
% 1.05/1.88 % Result found by pre_casc_4
% 1.05/1.88 % Preprocessing class: HMLMSMSLSSLNSFA.
% 1.05/1.88 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.05/1.88 % Starting new_bool_1 with 1500s (5) cores
% 1.05/1.88 % Starting post_as_ho6 with 300s (1) cores
% 1.05/1.88 % Starting post_as_ho8 with 300s (1) cores
% 1.05/1.88 % Starting pre_casc_4 with 300s (1) cores
% 1.05/1.88 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 1.05/1.88 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 1.05/1.88 % Search class: HGHSM-FMLM32-DSFFFFNN
% 1.05/1.88 % partial match(2): HGHSM-SMLM32-DSFFFFBN
% 1.05/1.88 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.05/1.88 % Starting SubtermCWHack with 28s (1) cores
% 1.05/1.88 % SubtermCWHack with pid 1693520 completed with status 0
% 1.05/1.88 % Result found by SubtermCWHack
% 1.05/1.88 % Preprocessing class: HMLMSMSLSSLNSFA.
% 1.05/1.88 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.05/1.88 % Starting new_bool_1 with 1500s (5) cores
% 1.05/1.88 % Starting post_as_ho6 with 300s (1) cores
% 1.05/1.88 % Starting post_as_ho8 with 300s (1) cores
% 1.05/1.88 % Starting pre_casc_4 with 300s (1) cores
% 1.05/1.88 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 1.05/1.88 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 1.05/1.88 % Search class: HGHSM-FMLM32-DSFFFFNN
% 1.05/1.88 % partial match(2): HGHSM-SMLM32-DSFFFFBN
% 1.05/1.88 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.05/1.88 % Starting SubtermCWHack with 28s (1) cores
% 1.05/1.88 % Preprocessing time : 0.019 s
% 1.05/1.88
% 1.05/1.88 % Proof found!
% 1.05/1.88 % SZS status Theorem
% 1.05/1.88 % SZS output start CNFRefutation
% See solution above
% 1.05/1.88 % Parsed axioms : 3387
% 1.05/1.88 % Removed by relevancy pruning/SinE : 3000
% 1.05/1.88 % Initial clauses : 1770
% 1.05/1.88 % Removed in clause preprocessing : 917
% 1.05/1.88 % Initial clauses in saturation : 853
% 1.05/1.88 % Processed clauses : 2283
% 1.05/1.88 % ...of these trivial : 84
% 1.05/1.88 % ...subsumed : 1152
% 1.05/1.88 % ...remaining for further processing : 1047
% 1.05/1.88 % Other redundant clauses eliminated : 57
% 1.05/1.88 % Clauses deleted for lack of memory : 0
% 1.05/1.88 % Backward-subsumed : 143
% 1.05/1.88 % Backward-rewritten : 16
% 1.05/1.88 % Generated clauses : 40284
% 1.05/1.88 % ...of the previous two non-redundant : 39303
% 1.05/1.88 % ...aggressively subsumed : 0
% 1.05/1.88 % Contextual simplify-reflections : 4
% 1.05/1.88 % Paramodulations : 40220
% 1.05/1.88 % Factorizations : 0
% 1.05/1.88 % NegExts : 0
% 1.05/1.88 % Equation resolutions : 64
% 1.05/1.88 % Disequality decompositions : 0
% 1.05/1.88 % Total rewrite steps : 3123
% 1.05/1.88 % ...of those cached : 2813
% 1.05/1.88 % Propositional unsat checks : 0
% 1.05/1.88 % Propositional check models : 0
% 1.05/1.88 % Propositional check unsatisfiable : 0
% 1.05/1.88 % Propositional clauses : 0
% 1.05/1.88 % Propositional clauses after purity: 0
% 1.05/1.88 % Propositional unsat core size : 0
% 1.05/1.88 % Propositional preprocessing time : 0.000
% 1.05/1.88 % Propositional encoding time : 0.000
% 1.05/1.88 % Propositional solver time : 0.000
% 1.05/1.88 % Success case prop preproc time : 0.000
% 1.05/1.88 % Success case prop encoding time : 0.000
% 1.05/1.88 % Success case prop solver time : 0.000
% 1.05/1.88 % Current number of processed clauses : 868
% 1.05/1.88 % Positive orientable unit clauses : 178
% 1.05/1.88 % Positive unorientable unit clauses: 0
% 1.05/1.88 % Negative unit clauses : 35
% 1.05/1.88 % Non-unit-clauses : 655
% 1.05/1.88 % Current number of unprocessed clauses: 36659
% 1.05/1.88 % ...number of literals in the above : 197621
% 1.05/1.88 % Current number of archived formulas : 0
% 1.05/1.88 % Current number of archived clauses : 159
% 1.05/1.88 % Clause-clause subsumption calls (NU) : 38340
% 1.05/1.88 % Rec. Clause-clause subsumption calls : 16351
% 1.05/1.88 % Non-unit clause-clause subsumptions : 833
% 1.05/1.88 % Unit Clause-clause subsumption calls : 554
% 1.05/1.88 % Rewrite failures with RHS unbound : 0
% 1.05/1.88 % BW rewrite match attempts : 1249
% 1.05/1.88 % BW rewrite match successes : 77
% 1.05/1.88 % Condensation attempts : 0
% 1.05/1.88 % Condensation successes : 0
% 1.05/1.88 % Termbank termtop insertions : 1297691
% 1.05/1.88 % Search garbage collected termcells : 79531
% 1.05/1.88
% 1.05/1.88 % -------------------------------------------------
% 1.05/1.88 % User time : 0.690 s
% 1.05/1.88 % System time : 0.052 s
% 1.05/1.88 % Total time : 0.742 s
% 1.05/1.88 % Maximum resident set size: 16564 pages
% 1.05/1.88
% 1.05/1.88 % -------------------------------------------------
% 1.05/1.88 % User time : 0.899 s
% 1.05/1.88 % System time : 0.070 s
% 1.05/1.88 % Total time : 0.969 s
% 1.05/1.88 % Maximum resident set size: 12288 pages
% 1.05/1.88 % E exiting
%------------------------------------------------------------------------------