%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL951^24 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 08:12:53 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 173 ( 4 equ; 0 cnn)
% Maximal formula atoms : 28 ( 14 avg)
% Number of connectives : 285 ( 25 ~; 0 |; 14 &; 246 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 16 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 51 ( 51 ^; 0 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mworld: $tType ).
thf(decl_25,type,
mlocal: ( mworld > $o ) > $o ).
thf(decl_26,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(decl_27,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(decl_31,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(decl_34,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(decl_36,type,
empty_set: $i ).
thf(decl_37,type,
qmltpeq: $i > $i > mworld > $o ).
thf(decl_38,type,
in: $i > $i > mworld > $o ).
thf(decl_40,type,
singleton: $i > $i ).
thf(t41_zfmisc_1,conjecture,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X24: $i] :
( mbox
@ ( mforall_di
@ ^ [X25: $i] :
( mbox
@ ( mnot
@ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ X24 @ ( singleton @ X25 ) ) ) ) )
@ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ X24 @ empty_set ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X17: $i] : ( mbox @ ( mnot @ ( mand @ ( mbox @ ( in @ X17 @ X24 ) ) @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ X17 @ X25 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yqUxyFEXtg/E---3.1_185229.p',t41_zfmisc_1) ).
thf(mand_def,axiom,
( mand
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
& ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yqUxyFEXtg/E---3.1_185229.p',mand_def) ).
thf(mnot_def,axiom,
( mnot
= ( ^ [X2: mworld > $o,X3: mworld] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yqUxyFEXtg/E---3.1_185229.p',mnot_def) ).
thf(l45_zfmisc_1,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X26: $i] :
( mbox
@ ( mforall_di
@ ^ [X27: $i] :
( mbox
@ ( mnot
@ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ X26 @ ( singleton @ X27 ) ) ) ) )
@ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ X26 @ empty_set ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X17: $i] : ( mbox @ ( mnot @ ( mand @ ( mbox @ ( in @ X17 @ X26 ) ) @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ X17 @ X27 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yqUxyFEXtg/E---3.1_185229.p',l45_zfmisc_1) ).
thf(c_0_4,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X24: $i] :
( mbox
@ ( mforall_di
@ ^ [X25: $i] :
( mbox
@ ( mnot
@ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ X24 @ ( singleton @ X25 ) ) ) ) )
@ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ X24 @ empty_set ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X17: $i] : ( mbox @ ( mnot @ ( mand @ ( mbox @ ( in @ X17 @ X24 ) ) @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ X17 @ X25 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t41_zfmisc_1]) ).
thf(c_0_5,plain,
( mand
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand_def]) ).
thf(c_0_6,plain,
( mnot
= ( ^ [Z0: mworld > $o,Z1: mworld] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot_def]) ).
thf(c_0_7,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Z0: $i] :
( mbox
@ ( mforall_di
@ ^ [Z1: $i] :
( mbox
@ ^ [Z2: mworld] :
~ ( ( mbox
@ ^ [Z3: mworld] :
~ ( mbox @ ( qmltpeq @ Z0 @ ( singleton @ Z1 ) ) @ Z3 )
@ Z2 )
& ( mbox
@ ^ [Z3: mworld] :
~ ( mbox @ ( qmltpeq @ Z0 @ empty_set ) @ Z3 )
@ Z2 )
& ( mbox
@ ( mforall_di
@ ^ [Z3: $i] :
( mbox
@ ^ [Z4: mworld] :
~ ( ( mbox @ ( in @ Z3 @ Z0 ) @ Z4 )
& ( mbox
@ ^ [Z5: mworld] :
~ ( mbox @ ( qmltpeq @ Z3 @ Z1 ) @ Z5 )
@ Z4 ) ) ) )
@ Z2 ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_4]),c_0_5]),c_0_6])]) ).
thf(c_0_8,plain,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Z0: $i] :
( mbox
@ ( mforall_di
@ ^ [Z1: $i] :
( mbox
@ ^ [Z2: mworld] :
~ ( ( mbox
@ ^ [Z3: mworld] :
~ ( mbox @ ( qmltpeq @ Z0 @ ( singleton @ Z1 ) ) @ Z3 )
@ Z2 )
& ( mbox
@ ^ [Z3: mworld] :
~ ( mbox @ ( qmltpeq @ Z0 @ empty_set ) @ Z3 )
@ Z2 )
& ( mbox
@ ( mforall_di
@ ^ [Z3: $i] :
( mbox
@ ^ [Z4: mworld] :
~ ( ( mbox @ ( in @ Z3 @ Z0 ) @ Z4 )
& ( mbox
@ ^ [Z5: mworld] :
~ ( mbox @ ( qmltpeq @ Z3 @ Z1 ) @ Z5 )
@ Z4 ) ) ) )
@ Z2 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[l45_zfmisc_1]),c_0_5]),c_0_6]) ).
thf(c_0_9,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Z0: $i] :
( mbox
@ ( mforall_di
@ ^ [Z1: $i] :
( mbox
@ ^ [Z2: mworld] :
~ ( ( mbox
@ ^ [Z3: mworld] :
~ ( mbox @ ( qmltpeq @ Z0 @ ( singleton @ Z1 ) ) @ Z3 )
@ Z2 )
& ( mbox
@ ^ [Z3: mworld] :
~ ( mbox @ ( qmltpeq @ Z0 @ empty_set ) @ Z3 )
@ Z2 )
& ( mbox
@ ( mforall_di
@ ^ [Z3: $i] :
( mbox
@ ^ [Z4: mworld] :
~ ( ( mbox @ ( in @ Z3 @ Z0 ) @ Z4 )
& ( mbox
@ ^ [Z5: mworld] :
~ ( mbox @ ( qmltpeq @ Z3 @ Z1 ) @ Z5 )
@ Z4 ) ) ) )
@ Z2 ) ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,plain,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Z0: $i] :
( mbox
@ ( mforall_di
@ ^ [Z1: $i] :
( mbox
@ ^ [Z2: mworld] :
~ ( ( mbox
@ ^ [Z3: mworld] :
~ ( mbox @ ( qmltpeq @ Z0 @ ( singleton @ Z1 ) ) @ Z3 )
@ Z2 )
& ( mbox
@ ^ [Z3: mworld] :
~ ( mbox @ ( qmltpeq @ Z0 @ empty_set ) @ Z3 )
@ Z2 )
& ( mbox
@ ( mforall_di
@ ^ [Z3: $i] :
( mbox
@ ^ [Z4: mworld] :
~ ( ( mbox @ ( in @ Z3 @ Z0 ) @ Z4 )
& ( mbox
@ ^ [Z5: mworld] :
~ ( mbox @ ( qmltpeq @ Z3 @ Z1 ) @ Z5 )
@ Z4 ) ) ) )
@ Z2 ) ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL951^24 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n017.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 10:46:24 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
% 0.07/0.24 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.yqUxyFEXtg/E---3.1_185229.p
% 0.21/0.29 % Version: 3.5.1-ho
% 0.21/0.29 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.21/0.29 % Starting post_as_ho3 with 300s (1) cores
% 0.21/0.29 % Starting new_ho_12 with 300s (1) cores
% 0.21/0.29 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.29 % new_bool_2 with pid 185245 completed with status 0
% 0.21/0.29 % Result found by new_bool_2
% 0.21/0.29 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.21/0.29 % Starting post_as_ho3 with 300s (1) cores
% 0.21/0.29 % Starting new_ho_12 with 300s (1) cores
% 0.21/0.29 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.29 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.29 % Search class: HUUNF-FFMM11-DHSSMFNN
% 0.21/0.29 % partial match(4): HGHNF-FFMF11-SHSSMFNN
% 0.21/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.29 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.29 % SubtermCWHack with pid 185246 completed with status 0
% 0.21/0.29 % Result found by SubtermCWHack
% 0.21/0.29 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.21/0.29 % Starting post_as_ho3 with 300s (1) cores
% 0.21/0.29 % Starting new_ho_12 with 300s (1) cores
% 0.21/0.29 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.29 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.29 % Search class: HUUNF-FFMM11-DHSSMFNN
% 0.21/0.29 % partial match(4): HGHNF-FFMF11-SHSSMFNN
% 0.21/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.29 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.29 % Preprocessing time : 0.003 s
% 0.21/0.29
% 0.21/0.29 % Proof found!
% 0.21/0.29 % SZS status Theorem
% 0.21/0.29 % SZS output start CNFRefutation
% See solution above
% 0.21/0.29 % Parsed axioms : 45
% 0.21/0.29 % Removed by relevancy pruning/SinE : 28
% 0.21/0.29 % Initial clauses : 13
% 0.21/0.29 % Removed in clause preprocessing : 0
% 0.21/0.29 % Initial clauses in saturation : 13
% 0.21/0.29 % Processed clauses : 13
% 0.21/0.29 % ...of these trivial : 0
% 0.21/0.29 % ...subsumed : 0
% 0.21/0.29 % ...remaining for further processing : 12
% 0.21/0.29 % Other redundant clauses eliminated : 0
% 0.21/0.29 % Clauses deleted for lack of memory : 0
% 0.21/0.29 % Backward-subsumed : 0
% 0.21/0.29 % Backward-rewritten : 0
% 0.21/0.29 % Generated clauses : 0
% 0.21/0.29 % ...of the previous two non-redundant : 0
% 0.21/0.29 % ...aggressively subsumed : 0
% 0.21/0.29 % Contextual simplify-reflections : 0
% 0.21/0.29 % Paramodulations : 0
% 0.21/0.29 % Factorizations : 0
% 0.21/0.29 % NegExts : 0
% 0.21/0.29 % Equation resolutions : 0
% 0.21/0.29 % Disequality decompositions : 0
% 0.21/0.29 % Total rewrite steps : 1
% 0.21/0.29 % ...of those cached : 0
% 0.21/0.29 % Propositional unsat checks : 0
% 0.21/0.29 % Propositional check models : 0
% 0.21/0.29 % Propositional check unsatisfiable : 0
% 0.21/0.29 % Propositional clauses : 0
% 0.21/0.29 % Propositional clauses after purity: 0
% 0.21/0.29 % Propositional unsat core size : 0
% 0.21/0.29 % Propositional preprocessing time : 0.000
% 0.21/0.29 % Propositional encoding time : 0.000
% 0.21/0.29 % Propositional solver time : 0.000
% 0.21/0.29 % Success case prop preproc time : 0.000
% 0.21/0.29 % Success case prop encoding time : 0.000
% 0.21/0.29 % Success case prop solver time : 0.000
% 0.21/0.29 % Current number of processed clauses : 12
% 0.21/0.29 % Positive orientable unit clauses : 12
% 0.21/0.29 % Positive unorientable unit clauses: 0
% 0.21/0.29 % Negative unit clauses : 0
% 0.21/0.29 % Non-unit-clauses : 0
% 0.21/0.29 % Current number of unprocessed clauses: 0
% 0.21/0.29 % ...number of literals in the above : 0
% 0.21/0.29 % Current number of archived formulas : 0
% 0.21/0.29 % Current number of archived clauses : 0
% 0.21/0.29 % Clause-clause subsumption calls (NU) : 0
% 0.21/0.29 % Rec. Clause-clause subsumption calls : 0
% 0.21/0.29 % Non-unit clause-clause subsumptions : 0
% 0.21/0.29 % Unit Clause-clause subsumption calls : 0
% 0.21/0.29 % Rewrite failures with RHS unbound : 0
% 0.21/0.29 % BW rewrite match attempts : 37
% 0.21/0.29 % BW rewrite match successes : 0
% 0.21/0.29 % Condensation attempts : 0
% 0.21/0.29 % Condensation successes : 0
% 0.21/0.29 % Termbank termtop insertions : 25960
% 0.21/0.29 % Search garbage collected termcells : 526
% 0.21/0.29
% 0.21/0.29 % -------------------------------------------------
% 0.21/0.29 % User time : 0.017 s
% 0.21/0.29 % System time : 0.005 s
% 0.21/0.29 % Total time : 0.022 s
% 0.21/0.29 % Maximum resident set size: 3952 pages
% 0.21/0.29
% 0.21/0.29 % -------------------------------------------------
% 0.21/0.29 % User time : 0.018 s
% 0.21/0.29 % System time : 0.011 s
% 0.21/0.29 % Total time : 0.029 s
% 0.21/0.29 % Maximum resident set size: 4864 pages
% 0.21/0.29 % E exiting
%------------------------------------------------------------------------------