%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP199^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:04:39 AM UTC 2026
% Result : Theorem 0.20s 0.37s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 24 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 236 ( 5 ~; 0 |; 0 &; 231 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 52 ( 3 ^; 49 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
variable: $tType ).
thf(decl_sort2,type,
real: $tType ).
thf(decl_sort3,type,
set_variable: $tType ).
thf(decl_sort4,type,
char: $tType ).
thf(decl_25,type,
denota1419872369iation: ( variable > real ) > ( variable > real ) > set_variable > $o ).
thf(decl_34,type,
zero_zero_real: real ).
thf(decl_41,type,
sup_sup_set_variable: set_variable > set_variable > set_variable ).
thf(decl_67,type,
bot_bot_set_variable: set_variable ).
thf(decl_80,type,
insert_variable: variable > set_variable > set_variable ).
thf(decl_90,type,
dVar: char > variable ).
thf(decl_91,type,
rVar: char > variable ).
thf(decl_102,type,
f: real > variable > real ).
thf(decl_104,type,
u: set_variable ).
thf(decl_105,type,
omega: variable > real ).
thf(decl_109,type,
x: char ).
thf(fact_151_insert__is__Un,axiom,
( insert_variable
= ( ^ [X235: variable] : ( sup_sup_set_variable @ ( insert_variable @ X235 @ bot_bot_set_variable ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LCrEfNsin6/E---3.1_2996663.p',fact_151_insert__is__Un) ).
thf(fact_84_sup__commute,axiom,
( sup_sup_set_variable
= ( ^ [X123: set_variable,X124: set_variable] : ( sup_sup_set_variable @ X124 @ X123 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LCrEfNsin6/E---3.1_2996663.p',fact_84_sup__commute) ).
thf(conj_0,conjecture,
denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( sup_sup_set_variable @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) @ u ),
file('/export/starexec/sandbox2/tmp/tmp.LCrEfNsin6/E---3.1_2996663.p',conj_0) ).
thf(fact_2_Un__insert__left,axiom,
! [X3: variable,X4: set_variable,X5: set_variable] :
( ( sup_sup_set_variable @ ( insert_variable @ X3 @ X4 ) @ X5 )
= ( insert_variable @ X3 @ ( sup_sup_set_variable @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LCrEfNsin6/E---3.1_2996663.p',fact_2_Un__insert__left) ).
thf(fact_4_Un__insert__right,axiom,
! [X9: set_variable,X3: variable,X4: set_variable] :
( ( sup_sup_set_variable @ X9 @ ( insert_variable @ X3 @ X4 ) )
= ( insert_variable @ X3 @ ( sup_sup_set_variable @ X9 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LCrEfNsin6/E---3.1_2996663.p',fact_4_Un__insert__right) ).
thf(fact_64_insert__commute,axiom,
! [X82: variable,X83: variable,X9: set_variable] :
( ( insert_variable @ X82 @ ( insert_variable @ X83 @ X9 ) )
= ( insert_variable @ X83 @ ( insert_variable @ X82 @ X9 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LCrEfNsin6/E---3.1_2996663.p',fact_64_insert__commute) ).
thf(fact_9_sup__bot__left,axiom,
! [X16: set_variable] :
( ( sup_sup_set_variable @ bot_bot_set_variable @ X16 )
= X16 ),
file('/export/starexec/sandbox2/tmp/tmp.LCrEfNsin6/E---3.1_2996663.p',fact_9_sup__bot__left) ).
thf(fact_0_uv,axiom,
denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LCrEfNsin6/E---3.1_2996663.p',fact_0_uv) ).
thf(c_0_8,plain,
! [X622: variable] :
( ( insert_variable @ X622 )
= ( sup_sup_set_variable @ ( insert_variable @ X622 @ bot_bot_set_variable ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_151_insert__is__Un])]) ).
thf(c_0_9,plain,
! [X614: set_variable,X615: set_variable] :
( ( sup_sup_set_variable @ X614 @ X615 )
= ( sup_sup_set_variable @ X615 @ X614 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_84_sup__commute])]) ).
thf(c_0_10,plain,
! [X739: variable] :
( ( insert_variable @ X739 )
= ( sup_sup_set_variable @ ( insert_variable @ X739 @ bot_bot_set_variable ) ) ),
inference(variable_rename,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
~ ( denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( sup_sup_set_variable @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) @ u ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_12,plain,
! [X673: set_variable,X674: set_variable] :
( ( sup_sup_set_variable @ X673 @ X674 )
= ( sup_sup_set_variable @ X674 @ X673 ) ),
inference(variable_rename,[status(thm)],[c_0_9]) ).
thf(c_0_13,plain,
! [X3: variable] :
( ( insert_variable @ X3 )
= ( sup_sup_set_variable @ ( insert_variable @ X3 @ bot_bot_set_variable ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
~ ( denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( sup_sup_set_variable @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) @ u ) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
thf(c_0_15,plain,
! [X714: variable,X715: set_variable,X716: set_variable] :
( ( sup_sup_set_variable @ ( insert_variable @ X714 @ X715 ) @ X716 )
= ( insert_variable @ X714 @ ( sup_sup_set_variable @ X715 @ X716 ) ) ),
inference(variable_rename,[status(thm)],[fact_2_Un__insert__left]) ).
thf(c_0_16,plain,
! [X717: set_variable,X718: variable,X719: set_variable] :
( ( sup_sup_set_variable @ X717 @ ( insert_variable @ X718 @ X719 ) )
= ( insert_variable @ X718 @ ( sup_sup_set_variable @ X717 @ X719 ) ) ),
inference(variable_rename,[status(thm)],[fact_4_Un__insert__right]) ).
thf(c_0_17,plain,
! [X5: set_variable,X4: set_variable] :
( ( sup_sup_set_variable @ X4 @ X5 )
= ( sup_sup_set_variable @ X5 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_18,plain,
! [X3: variable,X4: set_variable] :
( ( sup_sup_set_variable @ ( insert_variable @ X3 @ bot_bot_set_variable ) @ X4 )
= ( insert_variable @ X3 @ X4 ) ),
inference(arg_cong,[status(thm)],[c_0_13]) ).
thf(c_0_19,negated_conjecture,
~ ( denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( sup_sup_set_variable @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) @ u ) ),
inference(fof_nnf,[status(thm)],[c_0_14]) ).
thf(c_0_20,plain,
! [X3: variable,X4: set_variable,X5: set_variable] :
( ( sup_sup_set_variable @ ( insert_variable @ X3 @ X4 ) @ X5 )
= ( insert_variable @ X3 @ ( sup_sup_set_variable @ X4 @ X5 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_21,plain,
! [X3: variable,X4: set_variable,X5: set_variable] :
( ( sup_sup_set_variable @ X4 @ ( insert_variable @ X3 @ X5 ) )
= ( insert_variable @ X3 @ ( sup_sup_set_variable @ X4 @ X5 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_22,plain,
! [X722: variable,X723: variable,X724: set_variable] :
( ( insert_variable @ X722 @ ( insert_variable @ X723 @ X724 ) )
= ( insert_variable @ X723 @ ( insert_variable @ X722 @ X724 ) ) ),
inference(variable_rename,[status(thm)],[fact_64_insert__commute]) ).
thf(c_0_23,plain,
! [X647: set_variable] :
( ( sup_sup_set_variable @ bot_bot_set_variable @ X647 )
= X647 ),
inference(variable_rename,[status(thm)],[fact_9_sup__bot__left]) ).
thf(c_0_24,plain,
! [X3: variable,X4: set_variable] :
( ( sup_sup_set_variable @ X4 @ ( insert_variable @ X3 @ bot_bot_set_variable ) )
= ( insert_variable @ X3 @ X4 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_25,negated_conjecture,
~ ( denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( sup_sup_set_variable @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) @ u ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_26,plain,
! [X3: variable,X4: set_variable,X5: set_variable] :
( ( sup_sup_set_variable @ ( insert_variable @ X3 @ X4 ) @ X5 )
= ( sup_sup_set_variable @ X4 @ ( insert_variable @ X3 @ X5 ) ) ),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_27,plain,
! [X3: variable,X35: variable,X4: set_variable] :
( ( insert_variable @ X3 @ ( insert_variable @ X35 @ X4 ) )
= ( insert_variable @ X35 @ ( insert_variable @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_28,plain,
! [X4: set_variable] :
( ( sup_sup_set_variable @ bot_bot_set_variable @ X4 )
= X4 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_29,plain,
denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ),
inference(split_conjunct,[status(thm)],[fact_0_uv]) ).
thf(c_0_30,plain,
! [X3: variable,X35: variable,X4: set_variable] :
( ( sup_sup_set_variable @ X4 @ ( insert_variable @ X3 @ ( insert_variable @ X35 @ bot_bot_set_variable ) ) )
= ( insert_variable @ X3 @ ( insert_variable @ X35 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_21,c_0_24]) ).
thf(c_0_31,negated_conjecture,
~ ( denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ u ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_26]),c_0_27]),c_0_28]) ).
thf(c_0_32,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP199^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n003.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 20:12:44 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.20/0.28 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.LCrEfNsin6/E---3.1_2996663.p
% 0.20/0.37 % Version: 3.5.1-ho
% 0.20/0.37 % Preprocessing class: HSLSSMSMSSMNHSA.
% 0.20/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.37 % Starting ehoh_best2 with 1500s (5) cores
% 0.20/0.37 % Starting additional_ho_6 with 300s (1) cores
% 0.20/0.37 % Starting new_bool_5 with 300s (1) cores
% 0.20/0.37 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.37 % new_bool_5 with pid 2996722 completed with status 0
% 0.20/0.37 % Result found by new_bool_5
% 0.20/0.37 % Preprocessing class: HSLSSMSMSSMNHSA.
% 0.20/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.37 % Starting ehoh_best2 with 1500s (5) cores
% 0.20/0.37 % Starting additional_ho_6 with 300s (1) cores
% 0.20/0.37 % Starting new_bool_5 with 300s (1) cores
% 0.20/0.37 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 0.20/0.37 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.20/0.37 % Search class: HGUSM-FFMF31-MHSFFFBN
% 0.20/0.37 % partial match(3): HGUSM-FSLM31-MHSFFFBN
% 0.20/0.37 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.37 % Starting SubtermCWHack with 28s (1) cores
% 0.20/0.37 % SubtermCWHack with pid 2996726 completed with status 0
% 0.20/0.37 % Result found by SubtermCWHack
% 0.20/0.37 % Preprocessing class: HSLSSMSMSSMNHSA.
% 0.20/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.37 % Starting ehoh_best2 with 1500s (5) cores
% 0.20/0.37 % Starting additional_ho_6 with 300s (1) cores
% 0.20/0.37 % Starting new_bool_5 with 300s (1) cores
% 0.20/0.37 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 0.20/0.37 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.20/0.37 % Search class: HGUSM-FFMF31-MHSFFFBN
% 0.20/0.37 % partial match(3): HGUSM-FSLM31-MHSFFFBN
% 0.20/0.37 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.37 % Starting SubtermCWHack with 28s (1) cores
% 0.20/0.37 % Preprocessing time : 0.003 s
% 0.20/0.37
% 0.20/0.37 % Proof found!
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % SZS output start CNFRefutation
% See solution above
% 0.20/0.37 % Parsed axioms : 462
% 0.20/0.37 % Removed by relevancy pruning/SinE : 404
% 0.20/0.37 % Initial clauses : 99
% 0.20/0.37 % Removed in clause preprocessing : 5
% 0.20/0.37 % Initial clauses in saturation : 94
% 0.20/0.37 % Processed clauses : 858
% 0.20/0.37 % ...of these trivial : 30
% 0.20/0.37 % ...subsumed : 712
% 0.20/0.37 % ...remaining for further processing : 116
% 0.20/0.37 % Other redundant clauses eliminated : 30
% 0.20/0.37 % Clauses deleted for lack of memory : 0
% 0.20/0.37 % Backward-subsumed : 0
% 0.20/0.37 % Backward-rewritten : 10
% 0.20/0.37 % Generated clauses : 1843
% 0.20/0.37 % ...of the previous two non-redundant : 1509
% 0.20/0.37 % ...aggressively subsumed : 0
% 0.20/0.37 % Contextual simplify-reflections : 0
% 0.20/0.37 % Paramodulations : 1811
% 0.20/0.37 % Factorizations : 0
% 0.20/0.37 % NegExts : 0
% 0.20/0.37 % Equation resolutions : 39
% 0.20/0.37 % Disequality decompositions : 0
% 0.20/0.37 % Total rewrite steps : 910
% 0.20/0.37 % ...of those cached : 668
% 0.20/0.37 % Propositional unsat checks : 0
% 0.20/0.37 % Propositional check models : 0
% 0.20/0.37 % Propositional check unsatisfiable : 0
% 0.20/0.37 % Propositional clauses : 0
% 0.20/0.37 % Propositional clauses after purity: 0
% 0.20/0.37 % Propositional unsat core size : 0
% 0.20/0.37 % Propositional preprocessing time : 0.000
% 0.20/0.37 % Propositional encoding time : 0.000
% 0.20/0.37 % Propositional solver time : 0.000
% 0.20/0.37 % Success case prop preproc time : 0.000
% 0.20/0.37 % Success case prop encoding time : 0.000
% 0.20/0.37 % Success case prop solver time : 0.000
% 0.20/0.37 % Current number of processed clauses : 90
% 0.20/0.37 % Positive orientable unit clauses : 19
% 0.20/0.37 % Positive unorientable unit clauses: 7
% 0.20/0.37 % Negative unit clauses : 10
% 0.20/0.37 % Non-unit-clauses : 54
% 0.20/0.37 % Current number of unprocessed clauses: 702
% 0.20/0.37 % ...number of literals in the above : 1346
% 0.20/0.37 % Current number of archived formulas : 0
% 0.20/0.37 % Current number of archived clauses : 11
% 0.20/0.37 % Clause-clause subsumption calls (NU) : 1935
% 0.20/0.37 % Rec. Clause-clause subsumption calls : 1914
% 0.20/0.37 % Non-unit clause-clause subsumptions : 384
% 0.20/0.37 % Unit Clause-clause subsumption calls : 42
% 0.20/0.37 % Rewrite failures with RHS unbound : 0
% 0.20/0.37 % BW rewrite match attempts : 72
% 0.20/0.37 % BW rewrite match successes : 58
% 0.20/0.37 % Condensation attempts : 0
% 0.20/0.37 % Condensation successes : 0
% 0.20/0.37 % Termbank termtop insertions : 21588
% 0.20/0.37 % Search garbage collected termcells : 3612
% 0.20/0.37
% 0.20/0.37 % -------------------------------------------------
% 0.20/0.37 % User time : 0.041 s
% 0.20/0.37 % System time : 0.008 s
% 0.20/0.37 % Total time : 0.049 s
% 0.20/0.37 % Maximum resident set size: 4892 pages
% 0.20/0.37
% 0.20/0.37 % -------------------------------------------------
% 0.20/0.37 % User time : 0.053 s
% 0.20/0.37 % System time : 0.016 s
% 0.20/0.37 % Total time : 0.068 s
% 0.20/0.37 % Maximum resident set size: 5632 pages
% 0.20/0.37 % E exiting
%------------------------------------------------------------------------------