%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET002^3 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:21:50 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 6 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 96 ( 6 ~; 2 |; 0 &; 85 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 29 ( 17 ^; 12 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mworld: $tType ).
thf(decl_24,type,
mactual: mworld ).
thf(decl_25,type,
mlocal: ( mworld > $o ) > $o ).
thf(decl_29,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(decl_33,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(decl_35,type,
qmltpeq: $i > $i > mworld > $o ).
thf(decl_37,type,
subset: $i > $i > mworld > $o ).
thf(decl_38,type,
union: $i > $i > $i ).
thf(decl_42,type,
esk4_0: $i ).
thf(prove_idempotency_of_union,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X32: $i] : ( qmltpeq @ ( union @ X32 @ X32 ) @ X32 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.reGkNdpNZE/E---3.1_3359375.p',prove_idempotency_of_union) ).
thf(mlocal_def,axiom,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ),
file('/export/starexec/sandbox/tmp/tmp.reGkNdpNZE/E---3.1_3359375.p',mlocal_def) ).
thf(mforall_di_def,axiom,
( mforall_di
= ( ^ [X6: $i > mworld > $o,X3: mworld] :
! [X7: $i] : ( X6 @ X7 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.reGkNdpNZE/E---3.1_3359375.p',mforall_di_def) ).
thf(mimplies_def,axiom,
( mimplies
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.reGkNdpNZE/E---3.1_3359375.p',mimplies_def) ).
thf(subset_union,axiom,
( mlocal
@ ( mforall_di
@ ^ [X24: $i] :
( mforall_di
@ ^ [X13: $i] : ( mimplies @ ( subset @ X24 @ X13 ) @ ( qmltpeq @ ( union @ X24 @ X13 ) @ X13 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.reGkNdpNZE/E---3.1_3359375.p',subset_union) ).
thf(reflexivity_of_subset,axiom,
( mlocal
@ ( mforall_di
@ ^ [X30: $i] : ( subset @ X30 @ X30 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.reGkNdpNZE/E---3.1_3359375.p',reflexivity_of_subset) ).
thf(c_0_6,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X32: $i] : ( qmltpeq @ ( union @ X32 @ X32 ) @ X32 ) ) ),
inference(assume_negation,[status(cth)],[prove_idempotency_of_union]) ).
thf(c_0_7,plain,
( mlocal
= ( ^ [Z0: mworld > $o] : ( Z0 @ mactual ) ) ),
inference(fof_simplification,[status(thm)],[mlocal_def]) ).
thf(c_0_8,plain,
( mforall_di
= ( ^ [Z0: $i > mworld > $o,Z1: mworld] :
! [X7: $i] : ( Z0 @ X7 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mforall_di_def]) ).
thf(c_0_9,plain,
( mimplies
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies_def]) ).
thf(c_0_10,negated_conjecture,
~ ! [X75: $i] : ( qmltpeq @ ( union @ X75 @ X75 ) @ X75 @ mactual ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_6]),c_0_7]),c_0_8]) ).
thf(c_0_11,plain,
! [X60: $i,X59: $i] :
( ( subset @ X60 @ X59 @ mactual )
=> ( qmltpeq @ ( union @ X60 @ X59 ) @ X59 @ mactual ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[subset_union]),c_0_7]),c_0_9]),c_0_8]) ).
thf(c_0_12,plain,
! [X71: $i] : ( subset @ X71 @ X71 @ mactual ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_of_subset]),c_0_7]),c_0_8]) ).
thf(c_0_13,negated_conjecture,
~ ( qmltpeq @ ( union @ esk4_0 @ esk4_0 ) @ esk4_0 @ mactual ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
thf(c_0_14,plain,
! [X102: $i,X103: $i] :
( ~ ( subset @ X102 @ X103 @ mactual )
| ( qmltpeq @ ( union @ X102 @ X103 ) @ X103 @ mactual ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
thf(c_0_15,plain,
! [X117: $i] : ( subset @ X117 @ X117 @ mactual ),
inference(variable_rename,[status(thm)],[c_0_12]) ).
thf(c_0_16,negated_conjecture,
~ ( qmltpeq @ ( union @ esk4_0 @ esk4_0 ) @ esk4_0 @ mactual ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,plain,
! [X7: $i,X9: $i] :
( ( qmltpeq @ ( union @ X7 @ X9 ) @ X9 @ mactual )
| ~ ( subset @ X7 @ X9 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_18,plain,
! [X7: $i] : ( subset @ X7 @ X7 @ mactual ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET002^3 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n007.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
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 13:33:40 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.reGkNdpNZE/E---3.1_3359375.p
% 0.09/0.25 % Version: 3.5.1-ho
% 0.09/0.25 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.09/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.25 % Starting new_ho_12 with 300s (1) cores
% 0.09/0.25 % Starting new_bool_2 with 300s (1) cores
% 0.09/0.25 % new_ho_12 with pid 3359390 completed with status 0
% 0.09/0.25 % Result found by new_ho_12
% 0.09/0.25 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.09/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.25 % Starting new_ho_12 with 300s (1) cores
% 0.09/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.25 % No SInE strategy applied
% 0.09/0.25 % Search class: HGUNM-FFMF21-SHSSMFNN
% 0.09/0.25 % partial match(1): HGUNS-FFMF21-SHSSMFNN
% 0.09/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.25 % SubtermCWHack with pid 3359392 completed with status 0
% 0.09/0.25 % Result found by SubtermCWHack
% 0.09/0.25 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.09/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.25 % Starting new_ho_12 with 300s (1) cores
% 0.09/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.25 % No SInE strategy applied
% 0.09/0.25 % Search class: HGUNM-FFMF21-SHSSMFNN
% 0.09/0.25 % partial match(1): HGUNS-FFMF21-SHSSMFNN
% 0.09/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.25 % Preprocessing time : 0.002 s
% 0.09/0.25
% 0.09/0.25 % Proof found!
% 0.09/0.25 % SZS status Theorem
% 0.09/0.25 % SZS output start CNFRefutation
% See solution above
% 0.09/0.25 % Parsed axioms : 45
% 0.09/0.25 % Removed by relevancy pruning/SinE : 0
% 0.09/0.25 % Initial clauses : 44
% 0.09/0.25 % Removed in clause preprocessing : 17
% 0.09/0.25 % Initial clauses in saturation : 27
% 0.09/0.25 % Processed clauses : 12
% 0.09/0.25 % ...of these trivial : 0
% 0.09/0.25 % ...subsumed : 0
% 0.09/0.25 % ...remaining for further processing : 12
% 0.09/0.25 % Other redundant clauses eliminated : 0
% 0.09/0.25 % Clauses deleted for lack of memory : 0
% 0.09/0.25 % Backward-subsumed : 0
% 0.09/0.25 % Backward-rewritten : 0
% 0.09/0.25 % Generated clauses : 4
% 0.09/0.25 % ...of the previous two non-redundant : 1
% 0.09/0.25 % ...aggressively subsumed : 0
% 0.09/0.25 % Contextual simplify-reflections : 0
% 0.09/0.25 % Paramodulations : 4
% 0.09/0.25 % Factorizations : 0
% 0.09/0.25 % NegExts : 0
% 0.09/0.25 % Equation resolutions : 0
% 0.09/0.25 % Disequality decompositions : 0
% 0.09/0.25 % Total rewrite steps : 3
% 0.09/0.25 % ...of those cached : 0
% 0.09/0.25 % Propositional unsat checks : 0
% 0.09/0.25 % Propositional check models : 0
% 0.09/0.25 % Propositional check unsatisfiable : 0
% 0.09/0.25 % Propositional clauses : 0
% 0.09/0.25 % Propositional clauses after purity: 0
% 0.09/0.25 % Propositional unsat core size : 0
% 0.09/0.25 % Propositional preprocessing time : 0.000
% 0.09/0.25 % Propositional encoding time : 0.000
% 0.09/0.25 % Propositional solver time : 0.000
% 0.09/0.25 % Success case prop preproc time : 0.000
% 0.09/0.25 % Success case prop encoding time : 0.000
% 0.09/0.25 % Success case prop solver time : 0.000
% 0.09/0.25 % Current number of processed clauses : 12
% 0.09/0.25 % Positive orientable unit clauses : 4
% 0.09/0.25 % Positive unorientable unit clauses: 0
% 0.09/0.25 % Negative unit clauses : 1
% 0.09/0.25 % Non-unit-clauses : 7
% 0.09/0.25 % Current number of unprocessed clauses: 15
% 0.09/0.25 % ...number of literals in the above : 42
% 0.09/0.25 % Current number of archived formulas : 0
% 0.09/0.25 % Current number of archived clauses : 0
% 0.09/0.25 % Clause-clause subsumption calls (NU) : 4
% 0.09/0.25 % Rec. Clause-clause subsumption calls : 4
% 0.09/0.25 % Non-unit clause-clause subsumptions : 0
% 0.09/0.25 % Unit Clause-clause subsumption calls : 0
% 0.09/0.25 % Rewrite failures with RHS unbound : 0
% 0.09/0.25 % BW rewrite match attempts : 0
% 0.09/0.25 % BW rewrite match successes : 0
% 0.09/0.25 % Condensation attempts : 0
% 0.09/0.25 % Condensation successes : 0
% 0.09/0.25 % Termbank termtop insertions : 4965
% 0.09/0.25 % Search garbage collected termcells : 2076
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.006 s
% 0.09/0.25 % System time : 0.001 s
% 0.09/0.25 % Total time : 0.007 s
% 0.09/0.25 % Maximum resident set size: 3948 pages
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.009 s
% 0.09/0.25 % System time : 0.005 s
% 0.09/0.25 % Total time : 0.014 s
% 0.09/0.25 % Maximum resident set size: 4864 pages
% 0.09/0.25 % E exiting
%------------------------------------------------------------------------------