%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP075^1 : 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 : n004.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 08:04:17 AM UTC 2026
% Result : Theorem 0.20s 0.32s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 3 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 175 ( 28 ~; 24 |; 10 &; 105 @)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 49 ( 16 ^; 26 !; 7 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
hF_Mirabelle_hf: $tType ).
thf(decl_33,type,
hF_Mirabelle_HBex: hF_Mirabelle_hf > ( hF_Mirabelle_hf > $o ) > $o ).
thf(decl_46,type,
hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).
thf(decl_73,type,
a: hF_Mirabelle_hf ).
thf(decl_74,type,
p: $o ).
thf(decl_75,type,
esk1_0: hF_Mirabelle_hf ).
thf(decl_88,type,
esk14_2: hF_Mirabelle_hf > ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
thf(decl_94,type,
esk20_2: hF_Mirabelle_hf > ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
thf(conj_0,conjecture,
( ( hF_Mirabelle_HBex @ a
@ ^ [X11: hF_Mirabelle_hf] : p )
<=> ( ? [X11: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ X11 @ a )
& p ) ),
file('/export/starexec/sandbox2/tmp/tmp.TrYGpIR62O/E---3.1_1747769.p',conj_0) ).
thf(fact_2_hbexE,axiom,
! [X6: hF_Mirabelle_hf,X4: hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_HBex @ X6 @ X4 )
=> ~ ! [X3: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X3 @ X6 )
=> ~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TrYGpIR62O/E---3.1_1747769.p',fact_2_hbexE) ).
thf(fact_1_hbexI,axiom,
! [X4: hF_Mirabelle_hf > $o,X5: hF_Mirabelle_hf,X6: hF_Mirabelle_hf] :
( ( X4 @ X5 )
=> ( ( hF_Mirabelle_hmem @ X5 @ X6 )
=> ( hF_Mirabelle_HBex @ X6 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TrYGpIR62O/E---3.1_1747769.p',fact_1_hbexI) ).
thf(fact_5_HBex__def,axiom,
( hF_Mirabelle_HBex
= ( ^ [X13: hF_Mirabelle_hf,X14: hF_Mirabelle_hf > $o] :
? [X11: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X11 @ X13 )
& ( X14 @ X11 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TrYGpIR62O/E---3.1_1747769.p',fact_5_HBex__def) ).
thf(c_0_4,negated_conjecture,
~ ( ( hF_Mirabelle_HBex @ a
@ ^ [X11: hF_Mirabelle_hf] : p )
<=> ( ? [X11: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ X11 @ a )
& p ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_5,negated_conjecture,
~ ( ( hF_Mirabelle_HBex @ a
@ ^ [Z0: hF_Mirabelle_hf] : p )
<=> ( ? [X11: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ X11 @ a )
& p ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
thf(c_0_6,negated_conjecture,
! [X505: hF_Mirabelle_hf] :
( ( ~ ( hF_Mirabelle_HBex @ a
@ ^ [Z0: hF_Mirabelle_hf] : p )
| ~ ( hF_Mirabelle_hmem @ X505 @ a )
| ~ p )
& ( ( hF_Mirabelle_hmem @ esk1_0 @ a )
| ( hF_Mirabelle_HBex @ a
@ ^ [Z0: hF_Mirabelle_hf] : p ) )
& ( p
| ( hF_Mirabelle_HBex @ a
@ ^ [Z0: hF_Mirabelle_hf] : p ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])])]) ).
thf(c_0_7,negated_conjecture,
! [X1: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_HBex @ a
@ ^ [Z0: hF_Mirabelle_hf] : p )
| ~ ( hF_Mirabelle_hmem @ X1 @ a )
| ~ p ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
( ( hF_Mirabelle_hmem @ esk1_0 @ a )
| ( hF_Mirabelle_HBex @ a
@ ^ [Z0: hF_Mirabelle_hf] : p ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
! [X551: hF_Mirabelle_hf,X552: hF_Mirabelle_hf > $o] :
( ( ( hF_Mirabelle_hmem @ ( esk14_2 @ X551 @ X552 ) @ X551 )
| ~ ( hF_Mirabelle_HBex @ X551 @ X552 ) )
& ( ( X552 @ ( esk14_2 @ X551 @ X552 ) )
| ~ ( hF_Mirabelle_HBex @ X551 @ X552 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2_hbexE])])])])]) ).
thf(c_0_10,negated_conjecture,
! [X1: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ esk1_0 @ a )
| ~ ( hF_Mirabelle_hmem @ X1 @ a )
| ~ p ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_11,plain,
! [X1: hF_Mirabelle_hf,X4: hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_hmem @ ( esk14_2 @ X1 @ X4 ) @ X1 )
| ~ ( hF_Mirabelle_HBex @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,plain,
! [X548: hF_Mirabelle_hf > $o,X549: hF_Mirabelle_hf,X550: hF_Mirabelle_hf] :
( ~ ( X548 @ X549 )
| ~ ( hF_Mirabelle_hmem @ X549 @ X550 )
| ( hF_Mirabelle_HBex @ X550 @ X548 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1_hbexI])])]) ).
thf(c_0_13,negated_conjecture,
! [X4: hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_hmem @ esk1_0 @ a )
| ~ ( hF_Mirabelle_HBex @ a @ X4 )
| ~ p ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_14,plain,
! [X1: hF_Mirabelle_hf,X4: hF_Mirabelle_hf > $o,X2: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HBex @ X2 @ X4 )
| ~ ( X4 @ X1 )
| ~ ( hF_Mirabelle_hmem @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_15,negated_conjecture,
( ( hF_Mirabelle_hmem @ esk1_0 @ a )
| ~ p ),
inference(spm,[status(thm)],[c_0_13,c_0_8]) ).
thf(c_0_16,plain,
( hF_Mirabelle_HBex
= ( ^ [Z0: hF_Mirabelle_hf,Z1: hF_Mirabelle_hf > $o] :
? [X11: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X11 @ Z0 )
& ( Z1 @ X11 ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_5_HBex__def]) ).
thf(c_0_17,negated_conjecture,
! [X4: hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_HBex @ a @ X4 )
| ~ ( X4 @ esk1_0 )
| ~ p ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_18,plain,
( hF_Mirabelle_HBex
= ( ^ [Z0: hF_Mirabelle_hf,Z1: hF_Mirabelle_hf > $o] :
? [X607: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X607 @ Z0 )
& ( Z1 @ X607 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_19,negated_conjecture,
! [X1: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ X1 @ a )
| ~ p ),
inference(spm,[status(thm)],[c_0_7,c_0_17]) ).
thf(c_0_20,plain,
! [X587: hF_Mirabelle_hf,X588: hF_Mirabelle_hf > $o] :
( ? [X608: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X608 @ X587 )
& ( X588 @ X608 ) )
<=> ( hF_Mirabelle_HBex @ X587 @ X588 ) ),
inference(arg_cong,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
( p
| ( hF_Mirabelle_HBex @ a
@ ^ [Z0: hF_Mirabelle_hf] : p ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_22,negated_conjecture,
~ p,
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
thf(c_0_23,plain,
! [X1: hF_Mirabelle_hf,X4: hF_Mirabelle_hf > $o] :
( ( X4 @ ( esk20_2 @ X1 @ X4 ) )
| ~ ( hF_Mirabelle_HBex @ X1 @ X4 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_20]) ).
thf(c_0_24,negated_conjecture,
( hF_Mirabelle_HBex @ a
@ ^ [Z0: hF_Mirabelle_hf] : p ),
inference(sr,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_25,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP075^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n004.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 19:47:37 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.20/0.27 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.TrYGpIR62O/E---3.1_1747769.p
% 0.20/0.32 % Version: 3.5.1-ho
% 0.20/0.32 % Preprocessing class: HSLSSLSSSSLCHSA.
% 0.20/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.32 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.32 % Starting sh5l with 300s (1) cores
% 0.20/0.32 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.32 % Starting new_bool_2 with 300s (1) cores
% 0.20/0.32 % new_bool_1 with pid 1747784 completed with status 0
% 0.20/0.32 % Result found by new_bool_1
% 0.20/0.32 % Preprocessing class: HSLSSLSSSSLCHSA.
% 0.20/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.32 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.32 % Starting sh5l with 300s (1) cores
% 0.20/0.32 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.32 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.20/0.32 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.32 % Search class: HGHSF-FFMS32-DHSFFSBN
% 0.20/0.32 % partial match(4): HGHSM-FSLM32-DHSFFSBN
% 0.20/0.32 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.32 % Starting SubtermCWHack with 28s (1) cores
% 0.20/0.32 % SubtermCWHack with pid 1747786 completed with status 0
% 0.20/0.32 % Result found by SubtermCWHack
% 0.20/0.32 % Preprocessing class: HSLSSLSSSSLCHSA.
% 0.20/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.32 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.32 % Starting sh5l with 300s (1) cores
% 0.20/0.32 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.32 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.20/0.32 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.32 % Search class: HGHSF-FFMS32-DHSFFSBN
% 0.20/0.32 % partial match(4): HGHSM-FSLM32-DHSFFSBN
% 0.20/0.32 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.32 % Starting SubtermCWHack with 28s (1) cores
% 0.20/0.32 % Preprocessing time : 0.003 s
% 0.20/0.32
% 0.20/0.32 % Proof found!
% 0.20/0.32 % SZS status Theorem
% 0.20/0.32 % SZS output start CNFRefutation
% See solution above
% 0.20/0.32 % Parsed axioms : 411
% 0.20/0.32 % Removed by relevancy pruning/SinE : 388
% 0.20/0.32 % Initial clauses : 60
% 0.20/0.32 % Removed in clause preprocessing : 0
% 0.20/0.32 % Initial clauses in saturation : 60
% 0.20/0.32 % Processed clauses : 155
% 0.20/0.32 % ...of these trivial : 0
% 0.20/0.32 % ...subsumed : 34
% 0.20/0.32 % ...remaining for further processing : 121
% 0.20/0.32 % Other redundant clauses eliminated : 2
% 0.20/0.32 % Clauses deleted for lack of memory : 0
% 0.20/0.32 % Backward-subsumed : 10
% 0.20/0.32 % Backward-rewritten : 0
% 0.20/0.32 % Generated clauses : 587
% 0.20/0.32 % ...of the previous two non-redundant : 574
% 0.20/0.32 % ...aggressively subsumed : 0
% 0.20/0.32 % Contextual simplify-reflections : 0
% 0.20/0.32 % Paramodulations : 568
% 0.20/0.32 % Factorizations : 2
% 0.20/0.32 % NegExts : 0
% 0.20/0.32 % Equation resolutions : 2
% 0.20/0.32 % Disequality decompositions : 0
% 0.20/0.32 % Total rewrite steps : 2
% 0.20/0.32 % ...of those cached : 0
% 0.20/0.32 % Propositional unsat checks : 0
% 0.20/0.32 % Propositional check models : 0
% 0.20/0.32 % Propositional check unsatisfiable : 0
% 0.20/0.32 % Propositional clauses : 0
% 0.20/0.32 % Propositional clauses after purity: 0
% 0.20/0.32 % Propositional unsat core size : 0
% 0.20/0.32 % Propositional preprocessing time : 0.000
% 0.20/0.32 % Propositional encoding time : 0.000
% 0.20/0.32 % Propositional solver time : 0.000
% 0.20/0.32 % Success case prop preproc time : 0.000
% 0.20/0.32 % Success case prop encoding time : 0.000
% 0.20/0.32 % Success case prop solver time : 0.000
% 0.20/0.32 % Current number of processed clauses : 106
% 0.20/0.32 % Positive orientable unit clauses : 8
% 0.20/0.32 % Positive unorientable unit clauses: 0
% 0.20/0.32 % Negative unit clauses : 27
% 0.20/0.32 % Non-unit-clauses : 71
% 0.20/0.32 % Current number of unprocessed clauses: 473
% 0.20/0.32 % ...number of literals in the above : 1332
% 0.20/0.32 % Current number of archived formulas : 0
% 0.20/0.32 % Current number of archived clauses : 13
% 0.20/0.32 % Clause-clause subsumption calls (NU) : 1585
% 0.20/0.32 % Rec. Clause-clause subsumption calls : 1327
% 0.20/0.32 % Non-unit clause-clause subsumptions : 34
% 0.20/0.32 % Unit Clause-clause subsumption calls : 429
% 0.20/0.32 % Rewrite failures with RHS unbound : 0
% 0.20/0.32 % BW rewrite match attempts : 7
% 0.20/0.32 % BW rewrite match successes : 1
% 0.20/0.32 % Condensation attempts : 0
% 0.20/0.32 % Condensation successes : 0
% 0.20/0.32 % Termbank termtop insertions : 17177
% 0.20/0.32 % Search garbage collected termcells : 3667
% 0.20/0.32
% 0.20/0.32 % -------------------------------------------------
% 0.20/0.32 % User time : 0.023 s
% 0.20/0.32 % System time : 0.003 s
% 0.20/0.32 % Total time : 0.027 s
% 0.20/0.32 % Maximum resident set size: 4772 pages
% 0.20/0.32
% 0.20/0.32 % -------------------------------------------------
% 0.20/0.32 % User time : 0.033 s
% 0.20/0.32 % System time : 0.010 s
% 0.20/0.32 % Total time : 0.043 s
% 0.20/0.32 % Maximum resident set size: 5376 pages
% 0.20/0.32 % E exiting
%------------------------------------------------------------------------------