%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP177^1 : 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 : n005.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 08:04:36 AM UTC 2026
% Result : Theorem 0.23s 0.34s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 14 ( 0 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 53 ( 6 ~; 2 |; 0 &; 44 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
b: $tType ).
thf(decl_sort2,type,
set_b: $tType ).
thf(decl_sort3,type,
labele1159362096nt_a_b: $tType ).
thf(decl_55,type,
labele1424214014nt_a_b: labele1159362096nt_a_b > set_b ).
thf(decl_166,type,
member_b: b > set_b > $o ).
thf(decl_167,type,
g: labele1159362096nt_a_b ).
thf(decl_170,type,
f: b > b ).
thf(decl_172,type,
x: b ).
thf(conj_0,conjecture,
member_b @ x @ ( labele1424214014nt_a_b @ g ),
file('/export/starexec/sandbox2/tmp/tmp.eQHxyUTN3J/E---3.1_2143109.p',conj_0) ).
thf(fact_0__092_060open_062_092_060And_062xa_O_A_092_060lbrakk_062f_Axa_A_092_060in_062_Avertices_AG_059_Axa_A_092_060notin_062_Avertices_AG_092_060rbrakk_062_A_092_060Longrightarrow_062_AFalse_092_060close_062,axiom,
! [X1: b] :
( ( member_b @ ( f @ X1 ) @ ( labele1424214014nt_a_b @ g ) )
=> ( member_b @ X1 @ ( labele1424214014nt_a_b @ g ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.eQHxyUTN3J/E---3.1_2143109.p',fact_0__092_060open_062_092_060And_062xa_O_A_092_060lbrakk_062f_Axa_A_092_060in_062_Avertices_AG_059_Axa_A_092_060notin_062_Avertices_AG_092_060rbrakk_062_A_092_060Longrightarrow_062_AFalse_092_060close_062) ).
thf(fact_2_fv_I1_J,axiom,
member_b @ ( f @ x ) @ ( labele1424214014nt_a_b @ g ),
file('/export/starexec/sandbox2/tmp/tmp.eQHxyUTN3J/E---3.1_2143109.p',fact_2_fv_I1_J) ).
thf(c_0_3,negated_conjecture,
~ ( member_b @ x @ ( labele1424214014nt_a_b @ g ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_4,negated_conjecture,
~ ( member_b @ x @ ( labele1424214014nt_a_b @ g ) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
thf(c_0_5,plain,
! [X1509: b] :
( ~ ( member_b @ ( f @ X1509 ) @ ( labele1424214014nt_a_b @ g ) )
| ( member_b @ X1509 @ ( labele1424214014nt_a_b @ g ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_0__092_060open_062_092_060And_062xa_O_A_092_060lbrakk_062f_Axa_A_092_060in_062_Avertices_AG_059_Axa_A_092_060notin_062_Avertices_AG_092_060rbrakk_062_A_092_060Longrightarrow_062_AFalse_092_060close_062])])]) ).
thf(c_0_6,negated_conjecture,
~ ( member_b @ x @ ( labele1424214014nt_a_b @ g ) ),
inference(fof_nnf,[status(thm)],[c_0_4]) ).
thf(c_0_7,plain,
! [X1: b] :
( ( member_b @ X1 @ ( labele1424214014nt_a_b @ g ) )
| ~ ( member_b @ ( f @ X1 ) @ ( labele1424214014nt_a_b @ g ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,plain,
member_b @ ( f @ x ) @ ( labele1424214014nt_a_b @ g ),
inference(split_conjunct,[status(thm)],[fact_2_fv_I1_J]) ).
thf(c_0_9,negated_conjecture,
~ ( member_b @ x @ ( labele1424214014nt_a_b @ g ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP177^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n005.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 20:06:30 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.27 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.eQHxyUTN3J/E---3.1_2143109.p
% 0.23/0.34 % Version: 3.5.1-ho
% 0.23/0.34 % partial match(1): HSLMSMSMSSMNSFA
% 0.23/0.34 % Preprocessing class: HSLMSMSMSSMCSFA.
% 0.23/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.34 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.23/0.34 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.23/0.34 % Starting full_lambda_6 with 300s (1) cores
% 0.23/0.34 % Starting ehoh_best_sine with 300s (1) cores
% 0.23/0.34 % full_lambda_6 with pid 2143125 completed with status 0
% 0.23/0.34 % Result found by full_lambda_6
% 0.23/0.34 % partial match(1): HSLMSMSMSSMNSFA
% 0.23/0.34 % Preprocessing class: HSLMSMSMSSMCSFA.
% 0.23/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.34 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.23/0.34 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.23/0.34 % Starting full_lambda_6 with 300s (1) cores
% 0.23/0.34 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountTerms,hypos,4,,4,20000,1.0,true))
% 0.23/0.34 % SinE strategy is GSinE(CountTerms,hypos,4,,4,20000,1.0,true)
% 0.23/0.34 % Search class: HGHSM-FSLM31-DSFFFFBN
% 0.23/0.34 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.34 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.34 % SubtermCWHack with pid 2143127 completed with status 0
% 0.23/0.34 % Result found by SubtermCWHack
% 0.23/0.34 % partial match(1): HSLMSMSMSSMNSFA
% 0.23/0.34 % Preprocessing class: HSLMSMSMSSMCSFA.
% 0.23/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.34 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.23/0.34 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.23/0.34 % Starting full_lambda_6 with 300s (1) cores
% 0.23/0.34 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountTerms,hypos,4,,4,20000,1.0,true))
% 0.23/0.34 % SinE strategy is GSinE(CountTerms,hypos,4,,4,20000,1.0,true)
% 0.23/0.34 % Search class: HGHSM-FSLM31-DSFFFFBN
% 0.23/0.34 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.34 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.34 % Preprocessing time : 0.005 s
% 0.23/0.34
% 0.23/0.34 % Proof found!
% 0.23/0.34 % SZS status Theorem
% 0.23/0.34 % SZS output start CNFRefutation
% See solution above
% 0.23/0.34 % Parsed axioms : 563
% 0.23/0.34 % Removed by relevancy pruning/SinE : 349
% 0.23/0.34 % Initial clauses : 332
% 0.23/0.34 % Removed in clause preprocessing : 15
% 0.23/0.34 % Initial clauses in saturation : 317
% 0.23/0.34 % Processed clauses : 170
% 0.23/0.34 % ...of these trivial : 6
% 0.23/0.34 % ...subsumed : 33
% 0.23/0.34 % ...remaining for further processing : 131
% 0.23/0.34 % Other redundant clauses eliminated : 32
% 0.23/0.34 % Clauses deleted for lack of memory : 0
% 0.23/0.34 % Backward-subsumed : 1
% 0.23/0.34 % Backward-rewritten : 7
% 0.23/0.34 % Generated clauses : 171
% 0.23/0.34 % ...of the previous two non-redundant : 85
% 0.23/0.34 % ...aggressively subsumed : 0
% 0.23/0.34 % Contextual simplify-reflections : 0
% 0.23/0.34 % Paramodulations : 134
% 0.23/0.34 % Factorizations : 0
% 0.23/0.34 % NegExts : 0
% 0.23/0.34 % Equation resolutions : 37
% 0.23/0.34 % Disequality decompositions : 0
% 0.23/0.34 % Total rewrite steps : 78
% 0.23/0.34 % ...of those cached : 35
% 0.23/0.34 % Propositional unsat checks : 0
% 0.23/0.34 % Propositional check models : 0
% 0.23/0.34 % Propositional check unsatisfiable : 0
% 0.23/0.34 % Propositional clauses : 0
% 0.23/0.34 % Propositional clauses after purity: 0
% 0.23/0.34 % Propositional unsat core size : 0
% 0.23/0.34 % Propositional preprocessing time : 0.000
% 0.23/0.34 % Propositional encoding time : 0.000
% 0.23/0.34 % Propositional solver time : 0.000
% 0.23/0.34 % Success case prop preproc time : 0.000
% 0.23/0.34 % Success case prop encoding time : 0.000
% 0.23/0.34 % Success case prop solver time : 0.000
% 0.23/0.34 % Current number of processed clauses : 107
% 0.23/0.34 % Positive orientable unit clauses : 55
% 0.23/0.34 % Positive unorientable unit clauses: 0
% 0.23/0.34 % Negative unit clauses : 5
% 0.23/0.34 % Non-unit-clauses : 47
% 0.23/0.34 % Current number of unprocessed clauses: 229
% 0.23/0.34 % ...number of literals in the above : 607
% 0.23/0.34 % Current number of archived formulas : 0
% 0.23/0.34 % Current number of archived clauses : 8
% 0.23/0.34 % Clause-clause subsumption calls (NU) : 300
% 0.23/0.34 % Rec. Clause-clause subsumption calls : 296
% 0.23/0.34 % Non-unit clause-clause subsumptions : 16
% 0.23/0.34 % Unit Clause-clause subsumption calls : 251
% 0.23/0.34 % Rewrite failures with RHS unbound : 0
% 0.23/0.34 % BW rewrite match attempts : 17
% 0.23/0.34 % BW rewrite match successes : 7
% 0.23/0.34 % Condensation attempts : 0
% 0.23/0.34 % Condensation successes : 0
% 0.23/0.34 % Termbank termtop insertions : 30638
% 0.23/0.34 % Search garbage collected termcells : 9161
% 0.23/0.34
% 0.23/0.34 % -------------------------------------------------
% 0.23/0.34 % User time : 0.022 s
% 0.23/0.34 % System time : 0.009 s
% 0.23/0.34 % Total time : 0.032 s
% 0.23/0.34 % Maximum resident set size: 6104 pages
% 0.23/0.34
% 0.23/0.34 % -------------------------------------------------
% 0.23/0.34 % User time : 0.044 s
% 0.23/0.34 % System time : 0.015 s
% 0.23/0.34 % Total time : 0.059 s
% 0.23/0.34 % Maximum resident set size: 6144 pages
% 0.23/0.34 % E exiting
%------------------------------------------------------------------------------