%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL952^12 : 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 : 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 08:12:53 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 78 ( 2 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 139 ( 3 ~; 0 |; 0 &; 130 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 12 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 1 con; 0-3 aty)
% Number of variables : 24 ( 24 ^; 0 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mworld: $tType ).
thf(decl_25,type,
mlocal: ( mworld > $o ) > $o ).
thf(decl_29,type,
mimplies: ( 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,
qmltpeq: $i > $i > mworld > $o ).
thf(decl_37,type,
in: $i > $i > mworld > $o ).
thf(decl_39,type,
set_intersection2: $i > $i > $i ).
thf(decl_40,type,
singleton: $i > $i ).
thf(t51_zfmisc_1,conjecture,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X32: $i] :
( mbox
@ ( mforall_di
@ ^ [X33: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ X32 @ ( singleton @ X33 ) ) @ ( singleton @ X33 ) ) ) @ ( mbox @ ( in @ X33 @ X32 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.AsahIK9d1y/E---3.1_2509619.p',t51_zfmisc_1) ).
thf(mimplies_def,axiom,
( mimplies
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.AsahIK9d1y/E---3.1_2509619.p',mimplies_def) ).
thf(l30_zfmisc_1,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X34: $i] :
( mbox
@ ( mforall_di
@ ^ [X35: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ X34 @ ( singleton @ X35 ) ) @ ( singleton @ X35 ) ) ) @ ( mbox @ ( in @ X35 @ X34 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.AsahIK9d1y/E---3.1_2509619.p',l30_zfmisc_1) ).
thf(c_0_3,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X32: $i] :
( mbox
@ ( mforall_di
@ ^ [X33: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ X32 @ ( singleton @ X33 ) ) @ ( singleton @ X33 ) ) ) @ ( mbox @ ( in @ X33 @ X32 ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t51_zfmisc_1]) ).
thf(c_0_4,plain,
( mimplies
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies_def]) ).
thf(c_0_5,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Z0: $i] :
( mbox
@ ( mforall_di
@ ^ [Z1: $i] :
( mbox
@ ^ [Z2: mworld] :
( ( mbox @ ( qmltpeq @ ( set_intersection2 @ Z0 @ ( singleton @ Z1 ) ) @ ( singleton @ Z1 ) ) @ Z2 )
=> ( mbox @ ( in @ Z1 @ Z0 ) @ Z2 ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_3]),c_0_4])]) ).
thf(c_0_6,plain,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Z0: $i] :
( mbox
@ ( mforall_di
@ ^ [Z1: $i] :
( mbox
@ ^ [Z2: mworld] :
( ( mbox @ ( qmltpeq @ ( set_intersection2 @ Z0 @ ( singleton @ Z1 ) ) @ ( singleton @ Z1 ) ) @ Z2 )
=> ( mbox @ ( in @ Z1 @ Z0 ) @ Z2 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[l30_zfmisc_1]),c_0_4]) ).
thf(c_0_7,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Z0: $i] :
( mbox
@ ( mforall_di
@ ^ [Z1: $i] :
( mbox
@ ^ [Z2: mworld] :
( ( mbox @ ( qmltpeq @ ( set_intersection2 @ Z0 @ ( singleton @ Z1 ) ) @ ( singleton @ Z1 ) ) @ Z2 )
=> ( mbox @ ( in @ Z1 @ Z0 ) @ Z2 ) ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,plain,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Z0: $i] :
( mbox
@ ( mforall_di
@ ^ [Z1: $i] :
( mbox
@ ^ [Z2: mworld] :
( ( mbox @ ( qmltpeq @ ( set_intersection2 @ Z0 @ ( singleton @ Z1 ) ) @ ( singleton @ Z1 ) ) @ Z2 )
=> ( mbox @ ( in @ Z1 @ Z0 ) @ Z2 ) ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL952^12 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n014.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 10:52:45 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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.AsahIK9d1y/E---3.1_2509619.p
% 0.07/0.26 % Version: 3.5.1-ho
% 0.07/0.26 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.07/0.26 % Starting post_as_ho3 with 300s (1) cores
% 0.07/0.26 % Starting new_ho_12 with 300s (1) cores
% 0.07/0.26 % Starting new_bool_2 with 300s (1) cores
% 0.07/0.26 % new_bool_2 with pid 2509635 completed with status 0
% 0.07/0.26 % Result found by new_bool_2
% 0.07/0.26 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.07/0.26 % Starting post_as_ho3 with 300s (1) cores
% 0.07/0.26 % Starting new_ho_12 with 300s (1) cores
% 0.07/0.26 % Starting new_bool_2 with 300s (1) cores
% 0.07/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.26 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.26 % Search class: HUUNF-FFMM21-DHSSMFNN
% 0.07/0.26 % partial match(4): HGUNS-FFMF21-SHSSMFNN
% 0.07/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.26 % SubtermCWHack with pid 2509636 completed with status 0
% 0.07/0.26 % Result found by SubtermCWHack
% 0.07/0.26 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.07/0.26 % Starting post_as_ho3 with 300s (1) cores
% 0.07/0.26 % Starting new_ho_12 with 300s (1) cores
% 0.07/0.26 % Starting new_bool_2 with 300s (1) cores
% 0.07/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.26 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.26 % Search class: HUUNF-FFMM21-DHSSMFNN
% 0.07/0.26 % partial match(4): HGUNS-FFMF21-SHSSMFNN
% 0.07/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.26 % Preprocessing time : 0.002 s
% 0.07/0.26
% 0.07/0.26 % Proof found!
% 0.07/0.26 % SZS status Theorem
% 0.07/0.26 % SZS output start CNFRefutation
% See solution above
% 0.07/0.26 % Parsed axioms : 47
% 0.07/0.26 % Removed by relevancy pruning/SinE : 33
% 0.07/0.26 % Initial clauses : 12
% 0.07/0.26 % Removed in clause preprocessing : 0
% 0.07/0.26 % Initial clauses in saturation : 12
% 0.07/0.26 % Processed clauses : 7
% 0.07/0.26 % ...of these trivial : 0
% 0.07/0.26 % ...subsumed : 0
% 0.07/0.26 % ...remaining for further processing : 6
% 0.07/0.26 % Other redundant clauses eliminated : 0
% 0.07/0.26 % Clauses deleted for lack of memory : 0
% 0.07/0.26 % Backward-subsumed : 0
% 0.07/0.26 % Backward-rewritten : 0
% 0.07/0.26 % Generated clauses : 0
% 0.07/0.26 % ...of the previous two non-redundant : 0
% 0.07/0.26 % ...aggressively subsumed : 0
% 0.07/0.26 % Contextual simplify-reflections : 0
% 0.07/0.26 % Paramodulations : 0
% 0.07/0.26 % Factorizations : 0
% 0.07/0.26 % NegExts : 0
% 0.07/0.26 % Equation resolutions : 0
% 0.07/0.26 % Disequality decompositions : 0
% 0.07/0.26 % Total rewrite steps : 1
% 0.07/0.26 % ...of those cached : 0
% 0.07/0.26 % Propositional unsat checks : 0
% 0.07/0.26 % Propositional check models : 0
% 0.07/0.26 % Propositional check unsatisfiable : 0
% 0.07/0.26 % Propositional clauses : 0
% 0.07/0.26 % Propositional clauses after purity: 0
% 0.07/0.26 % Propositional unsat core size : 0
% 0.07/0.26 % Propositional preprocessing time : 0.000
% 0.07/0.26 % Propositional encoding time : 0.000
% 0.07/0.26 % Propositional solver time : 0.000
% 0.07/0.26 % Success case prop preproc time : 0.000
% 0.07/0.26 % Success case prop encoding time : 0.000
% 0.07/0.26 % Success case prop solver time : 0.000
% 0.07/0.26 % Current number of processed clauses : 6
% 0.07/0.26 % Positive orientable unit clauses : 6
% 0.07/0.26 % Positive unorientable unit clauses: 0
% 0.07/0.26 % Negative unit clauses : 0
% 0.07/0.26 % Non-unit-clauses : 0
% 0.07/0.26 % Current number of unprocessed clauses: 5
% 0.07/0.26 % ...number of literals in the above : 5
% 0.07/0.26 % Current number of archived formulas : 0
% 0.07/0.26 % Current number of archived clauses : 0
% 0.07/0.26 % Clause-clause subsumption calls (NU) : 0
% 0.07/0.26 % Rec. Clause-clause subsumption calls : 0
% 0.07/0.26 % Non-unit clause-clause subsumptions : 0
% 0.07/0.26 % Unit Clause-clause subsumption calls : 0
% 0.07/0.26 % Rewrite failures with RHS unbound : 0
% 0.07/0.26 % BW rewrite match attempts : 15
% 0.07/0.26 % BW rewrite match successes : 0
% 0.07/0.26 % Condensation attempts : 0
% 0.07/0.26 % Condensation successes : 0
% 0.07/0.26 % Termbank termtop insertions : 8569
% 0.07/0.26 % Search garbage collected termcells : 343
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.006 s
% 0.07/0.26 % System time : 0.003 s
% 0.07/0.26 % Total time : 0.009 s
% 0.07/0.26 % Maximum resident set size: 3704 pages
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.011 s
% 0.07/0.26 % System time : 0.006 s
% 0.07/0.26 % Total time : 0.017 s
% 0.07/0.26 % Maximum resident set size: 4864 pages
% 0.07/0.26 % E exiting
%------------------------------------------------------------------------------