%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP115^1 : 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 : n014.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 08:04:24 AM UTC 2026
% Result : Theorem 0.20s 0.36s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 26 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 175 ( 28 ~; 26 |; 16 &; 102 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 13 ( 0 ^; 9 !; 4 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
set_b: $tType ).
thf(decl_sort2,type,
b: $tType ).
thf(decl_sort3,type,
a: $tType ).
thf(decl_26,type,
inf_inf_set_b: set_b > set_b > set_b ).
thf(decl_32,type,
bot_bot_set_b: set_b ).
thf(decl_48,type,
topolo1276428102open_b: set_b > $o ).
thf(decl_50,type,
member_b: b > set_b > $o ).
thf(decl_51,type,
a2: b ).
thf(decl_52,type,
f: a > b ).
thf(decl_53,type,
thesis: $o ).
thf(decl_54,type,
x0: a ).
thf(decl_62,type,
esk8_0: set_b ).
thf(decl_63,type,
esk9_0: set_b ).
thf(conj_1,conjecture,
thesis,
file('/export/starexec/sandbox2/tmp/tmp.fGYkbhzmW0/E---3.1_3131331.p',conj_1) ).
thf(fact_1__092_060open_062f_Ax0_A_092_060noteq_062_AA_A_092_060Longrightarrow_062_A_092_060exists_062U_AV_O_Aopen_AU_A_092_060and_062_Aopen_AV_A_092_060and_062_Af_Ax0_A_092_060in_062_AU_A_092_060and_062_AA_A_092_060in_062_AV_A_092_060and_062_AU_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062,axiom,
( ( ( f @ x0 )
!= a2 )
=> ? [X1: set_b,X2: set_b] :
( ( topolo1276428102open_b @ X1 )
& ( topolo1276428102open_b @ X2 )
& ( member_b @ ( f @ x0 ) @ X1 )
& ( member_b @ a2 @ X2 )
& ( ( inf_inf_set_b @ X1 @ X2 )
= bot_bot_set_b ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fGYkbhzmW0/E---3.1_3131331.p',fact_1__092_060open_062f_Ax0_A_092_060noteq_062_AA_A_092_060Longrightarrow_062_A_092_060exists_062U_AV_O_Aopen_AU_A_092_060and_062_Aopen_AV_A_092_060and_062_Af_Ax0_A_092_060in_062_AU_A_092_060and_062_AA_A_092_060in_062_AV_A_092_060and_062_AU_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062) ).
thf(fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062,axiom,
( a2
!= ( f @ x0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.fGYkbhzmW0/E---3.1_3131331.p',fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062) ).
thf(conj_0,hypothesis,
! [X47: set_b,X588: set_b] :
( ( ( topolo1276428102open_b @ X47 )
& ( topolo1276428102open_b @ X588 )
& ( member_b @ ( f @ x0 ) @ X47 )
& ( member_b @ a2 @ X588 )
& ( ( inf_inf_set_b @ X47 @ X588 )
= bot_bot_set_b ) )
=> thesis ),
file('/export/starexec/sandbox2/tmp/tmp.fGYkbhzmW0/E---3.1_3131331.p',conj_0) ).
thf(c_0_4,negated_conjecture,
~ thesis,
inference(assume_negation,[status(cth)],[conj_1]) ).
thf(c_0_5,negated_conjecture,
~ thesis,
inference(fof_simplification,[status(thm)],[c_0_4]) ).
thf(c_0_6,plain,
( ( ( f @ x0 )
!= a2 )
=> ? [X1: set_b,X2: set_b] :
( ( topolo1276428102open_b @ X1 )
& ( topolo1276428102open_b @ X2 )
& ( member_b @ ( f @ x0 ) @ X1 )
& ( member_b @ a2 @ X2 )
& ( ( inf_inf_set_b @ X1 @ X2 )
= bot_bot_set_b ) ) ),
inference(fof_simplification,[status(thm)],[fact_1__092_060open_062f_Ax0_A_092_060noteq_062_AA_A_092_060Longrightarrow_062_A_092_060exists_062U_AV_O_Aopen_AU_A_092_060and_062_Aopen_AV_A_092_060and_062_Af_Ax0_A_092_060in_062_AU_A_092_060and_062_AA_A_092_060in_062_AV_A_092_060and_062_AU_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062]) ).
thf(c_0_7,plain,
( a2
!= ( f @ x0 ) ),
inference(fof_simplification,[status(thm)],[fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062]) ).
thf(c_0_8,hypothesis,
! [X846: set_b,X847: set_b] :
( ~ ( topolo1276428102open_b @ X846 )
| ~ ( topolo1276428102open_b @ X847 )
| ~ ( member_b @ ( f @ x0 ) @ X846 )
| ~ ( member_b @ a2 @ X847 )
| ( ( inf_inf_set_b @ X846 @ X847 )
!= bot_bot_set_b )
| thesis ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_0])])]) ).
thf(c_0_9,negated_conjecture,
~ thesis,
inference(fof_nnf,[status(thm)],[c_0_5]) ).
thf(c_0_10,plain,
( ( ( topolo1276428102open_b @ esk8_0 )
| ( ( f @ x0 )
= a2 ) )
& ( ( topolo1276428102open_b @ esk9_0 )
| ( ( f @ x0 )
= a2 ) )
& ( ( member_b @ ( f @ x0 ) @ esk8_0 )
| ( ( f @ x0 )
= a2 ) )
& ( ( member_b @ a2 @ esk9_0 )
| ( ( f @ x0 )
= a2 ) )
& ( ( ( inf_inf_set_b @ esk8_0 @ esk9_0 )
= bot_bot_set_b )
| ( ( f @ x0 )
= a2 ) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
thf(c_0_11,plain,
( a2
!= ( f @ x0 ) ),
inference(fof_nnf,[status(thm)],[c_0_7]) ).
thf(c_0_12,hypothesis,
! [X1: set_b,X2: set_b] :
( thesis
| ~ ( topolo1276428102open_b @ X1 )
| ~ ( topolo1276428102open_b @ X2 )
| ~ ( member_b @ ( f @ x0 ) @ X1 )
| ~ ( member_b @ a2 @ X2 )
| ( ( inf_inf_set_b @ X1 @ X2 )
!= bot_bot_set_b ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,negated_conjecture,
~ thesis,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
( ( member_b @ ( f @ x0 ) @ esk8_0 )
| ( ( f @ x0 )
= a2 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,plain,
( a2
!= ( f @ x0 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,plain,
( ( topolo1276428102open_b @ esk8_0 )
| ( ( f @ x0 )
= a2 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_17,hypothesis,
! [X2: set_b,X1: set_b] :
( ( ( inf_inf_set_b @ X1 @ X2 )
!= bot_bot_set_b )
| ~ ( member_b @ ( f @ x0 ) @ X1 )
| ~ ( member_b @ a2 @ X2 )
| ~ ( topolo1276428102open_b @ X2 )
| ~ ( topolo1276428102open_b @ X1 ) ),
inference(sr,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_18,plain,
member_b @ ( f @ x0 ) @ esk8_0,
inference(sr,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_19,plain,
topolo1276428102open_b @ esk8_0,
inference(sr,[status(thm)],[c_0_16,c_0_15]) ).
thf(c_0_20,plain,
( ( member_b @ a2 @ esk9_0 )
| ( ( f @ x0 )
= a2 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_21,plain,
( ( ( inf_inf_set_b @ esk8_0 @ esk9_0 )
= bot_bot_set_b )
| ( ( f @ x0 )
= a2 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_22,plain,
( ( topolo1276428102open_b @ esk9_0 )
| ( ( f @ x0 )
= a2 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_23,hypothesis,
! [X1: set_b] :
( ( ( inf_inf_set_b @ esk8_0 @ X1 )
!= bot_bot_set_b )
| ~ ( member_b @ a2 @ X1 )
| ~ ( topolo1276428102open_b @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
thf(c_0_24,plain,
member_b @ a2 @ esk9_0,
inference(sr,[status(thm)],[c_0_20,c_0_15]) ).
thf(c_0_25,plain,
( ( inf_inf_set_b @ esk8_0 @ esk9_0 )
= bot_bot_set_b ),
inference(sr,[status(thm)],[c_0_21,c_0_15]) ).
thf(c_0_26,plain,
topolo1276428102open_b @ esk9_0,
inference(sr,[status(thm)],[c_0_22,c_0_15]) ).
thf(c_0_27,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP115^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n014.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 19:55:44 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 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.fGYkbhzmW0/E---3.1_3131331.p
% 0.20/0.36 % Version: 3.5.1-ho
% 0.20/0.36 % Preprocessing class: HSLSSMSSSSMNSFA.
% 0.20/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.36 % Starting post_as_ho6 with 1500s (5) cores
% 0.20/0.36 % Starting new_bool_3 with 300s (1) cores
% 0.20/0.36 % Starting sh8 with 300s (1) cores
% 0.20/0.36 % Starting post_as_ho1 with 300s (1) cores
% 0.20/0.36 % post_as_ho6 with pid 3131344 completed with status 0
% 0.20/0.36 % Result found by post_as_ho6
% 0.20/0.36 % Preprocessing class: HSLSSMSSSSMNSFA.
% 0.20/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.36 % Starting post_as_ho6 with 1500s (5) cores
% 0.20/0.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true))
% 0.20/0.36 % SinE strategy is GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true)
% 0.20/0.36 % Search class: HGHSM-FFLM31-MSFFFFNN
% 0.20/0.36 % partial match(1): HGHSM-FSLM31-MSFFFFNN
% 0.20/0.36 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.36 % Starting SubtermCWHack with 136s (1) cores
% 0.20/0.36 % Starting post_as_ho6 with 151s (1) cores
% 0.20/0.36 % Starting sh5l with 136s (1) cores
% 0.20/0.36 % Starting new_bool_1 with 136s (1) cores
% 0.20/0.36 % Starting new_bool_2 with 136s (1) cores
% 0.20/0.36 % post_as_ho6 with pid 3131349 completed with status 0
% 0.20/0.36 % Result found by post_as_ho6
% 0.20/0.36 % Preprocessing class: HSLSSMSSSSMNSFA.
% 0.20/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.36 % Starting post_as_ho6 with 1500s (5) cores
% 0.20/0.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true))
% 0.20/0.36 % SinE strategy is GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true)
% 0.20/0.36 % Search class: HGHSM-FFLM31-MSFFFFNN
% 0.20/0.36 % partial match(1): HGHSM-FSLM31-MSFFFFNN
% 0.20/0.36 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.36 % Starting SubtermCWHack with 136s (1) cores
% 0.20/0.36 % Starting post_as_ho6 with 151s (1) cores
% 0.20/0.36 % Preprocessing time : 0.004 s
% 0.20/0.36 % Presaturation interreduction done
% 0.20/0.36
% 0.20/0.36 % Proof found!
% 0.20/0.36 % SZS status Theorem
% 0.20/0.36 % SZS output start CNFRefutation
% See solution above
% 0.20/0.37 % Parsed axioms : 393
% 0.20/0.37 % Removed by relevancy pruning/SinE : 288
% 0.20/0.37 % Initial clauses : 174
% 0.20/0.37 % Removed in clause preprocessing : 7
% 0.20/0.37 % Initial clauses in saturation : 167
% 0.20/0.37 % Processed clauses : 344
% 0.20/0.37 % ...of these trivial : 15
% 0.20/0.37 % ...subsumed : 84
% 0.20/0.37 % ...remaining for further processing : 245
% 0.20/0.37 % Other redundant clauses eliminated : 31
% 0.20/0.37 % Clauses deleted for lack of memory : 0
% 0.20/0.37 % Backward-subsumed : 0
% 0.20/0.37 % Backward-rewritten : 3
% 0.20/0.37 % Generated clauses : 1136
% 0.20/0.37 % ...of the previous two non-redundant : 870
% 0.20/0.37 % ...aggressively subsumed : 0
% 0.20/0.37 % Contextual simplify-reflections : 4
% 0.20/0.37 % Paramodulations : 1100
% 0.20/0.37 % Factorizations : 4
% 0.20/0.37 % NegExts : 0
% 0.20/0.37 % Equation resolutions : 35
% 0.20/0.37 % Disequality decompositions : 0
% 0.20/0.37 % Total rewrite steps : 592
% 0.20/0.37 % ...of those cached : 409
% 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 : 120
% 0.20/0.37 % Positive orientable unit clauses : 33
% 0.20/0.37 % Positive unorientable unit clauses: 3
% 0.20/0.37 % Negative unit clauses : 6
% 0.20/0.37 % Non-unit-clauses : 78
% 0.20/0.37 % Current number of unprocessed clauses: 787
% 0.20/0.37 % ...number of literals in the above : 1919
% 0.20/0.37 % Current number of archived formulas : 0
% 0.20/0.37 % Current number of archived clauses : 111
% 0.20/0.37 % Clause-clause subsumption calls (NU) : 2210
% 0.20/0.37 % Rec. Clause-clause subsumption calls : 1210
% 0.20/0.37 % Non-unit clause-clause subsumptions : 41
% 0.20/0.37 % Unit Clause-clause subsumption calls : 38
% 0.20/0.37 % Rewrite failures with RHS unbound : 0
% 0.20/0.37 % BW rewrite match attempts : 94
% 0.20/0.37 % BW rewrite match successes : 73
% 0.20/0.37 % Condensation attempts : 344
% 0.20/0.37 % Condensation successes : 5
% 0.20/0.37 % Termbank termtop insertions : 24791
% 0.20/0.37 % Search garbage collected termcells : 4986
% 0.20/0.37
% 0.20/0.37 % -------------------------------------------------
% 0.20/0.37 % User time : 0.042 s
% 0.20/0.37 % System time : 0.009 s
% 0.20/0.37 % Total time : 0.051 s
% 0.20/0.37 % Maximum resident set size: 4912 pages
% 0.20/0.37
% 0.20/0.37 % -------------------------------------------------
% 0.20/0.37 % User time : 0.158 s
% 0.20/0.37 % System time : 0.026 s
% 0.20/0.37 % Total time : 0.184 s
% 0.20/0.37 % Maximum resident set size: 5632 pages
% 0.20/0.37 % E exiting
%------------------------------------------------------------------------------