%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET019^4 : 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 : n006.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 08:21:51 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 85 ( 10 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 213 ( 18 ~; 14 |; 10 &; 159 @)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 40 ( 30 ^; 10 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mworld: $tType ).
thf(decl_24,type,
mactual: mworld ).
thf(decl_25,type,
mlocal: ( mworld > $o ) > $o ).
thf(decl_27,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(decl_29,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(decl_30,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(decl_33,type,
eiw_di: $i > mworld > $o ).
thf(decl_34,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(decl_38,type,
equal_set: $i > $i > mworld > $o ).
thf(decl_40,type,
subset: $i > $i > mworld > $o ).
thf(decl_53,type,
esk5_0: $i ).
thf(decl_54,type,
esk6_0: $i ).
thf(thI02,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X65: $i] :
( mforall_di
@ ^ [X66: $i] : ( mimplies @ ( mand @ ( subset @ X65 @ X66 ) @ ( subset @ X66 @ X65 ) ) @ ( equal_set @ X65 @ X66 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0JHcUILfbm/E---3.1_714541.p',thI02) ).
thf(mlocal_def,axiom,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0JHcUILfbm/E---3.1_714541.p',mlocal_def) ).
thf(mand_def,axiom,
( mand
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
& ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0JHcUILfbm/E---3.1_714541.p',mand_def) ).
thf(mimplies_def,axiom,
( mimplies
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0JHcUILfbm/E---3.1_714541.p',mimplies_def) ).
thf(mforall_di_def,axiom,
( mforall_di
= ( ^ [X7: $i > mworld > $o,X3: mworld] :
! [X6: $i] :
( ( eiw_di @ X6 @ X3 )
=> ( X7 @ X6 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0JHcUILfbm/E---3.1_714541.p',mforall_di_def) ).
thf(mequiv_def,axiom,
( mequiv
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
<=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0JHcUILfbm/E---3.1_714541.p',mequiv_def) ).
thf(equal_set_0,axiom,
( mlocal
@ ( mforall_di
@ ^ [X50: $i] :
( mforall_di
@ ^ [X51: $i] : ( mequiv @ ( equal_set @ X50 @ X51 ) @ ( mand @ ( subset @ X50 @ X51 ) @ ( subset @ X51 @ X50 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0JHcUILfbm/E---3.1_714541.p',equal_set_0) ).
thf(c_0_7,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X65: $i] :
( mforall_di
@ ^ [X66: $i] : ( mimplies @ ( mand @ ( subset @ X65 @ X66 ) @ ( subset @ X66 @ X65 ) ) @ ( equal_set @ X65 @ X66 ) ) ) ) ),
inference(assume_negation,[status(cth)],[thI02]) ).
thf(c_0_8,plain,
( mlocal
= ( ^ [Z0: mworld > $o] : ( Z0 @ mactual ) ) ),
inference(fof_simplification,[status(thm)],[mlocal_def]) ).
thf(c_0_9,plain,
( mand
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand_def]) ).
thf(c_0_10,plain,
( mimplies
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies_def]) ).
thf(c_0_11,plain,
( mforall_di
= ( ^ [Z0: $i > mworld > $o,Z1: mworld] :
! [X6: $i] :
( ( eiw_di @ X6 @ Z1 )
=> ( Z0 @ X6 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mforall_di_def]) ).
thf(c_0_12,plain,
( mequiv
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
<=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mequiv_def]) ).
thf(c_0_13,negated_conjecture,
~ ! [X158: $i] :
( ( eiw_di @ X158 @ mactual )
=> ! [X157: $i] :
( ( eiw_di @ X157 @ mactual )
=> ( ( ( subset @ X158 @ X157 @ mactual )
& ( subset @ X157 @ X158 @ mactual ) )
=> ( equal_set @ X158 @ X157 @ mactual ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_7]),c_0_8]),c_0_9]),c_0_10]),c_0_11]) ).
thf(c_0_14,plain,
! [X133: $i] :
( ( eiw_di @ X133 @ mactual )
=> ! [X132: $i] :
( ( eiw_di @ X132 @ mactual )
=> ( ( equal_set @ X133 @ X132 @ mactual )
<=> ( ( subset @ X133 @ X132 @ mactual )
& ( subset @ X132 @ X133 @ mactual ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[equal_set_0]),c_0_8]),c_0_9]),c_0_12]),c_0_11]) ).
thf(c_0_15,negated_conjecture,
( ( eiw_di @ esk5_0 @ mactual )
& ( eiw_di @ esk6_0 @ mactual )
& ( subset @ esk5_0 @ esk6_0 @ mactual )
& ( subset @ esk6_0 @ esk5_0 @ mactual )
& ~ ( equal_set @ esk5_0 @ esk6_0 @ mactual ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
thf(c_0_16,plain,
! [X225: $i,X226: $i] :
( ( ( subset @ X225 @ X226 @ mactual )
| ~ ( equal_set @ X225 @ X226 @ mactual )
| ~ ( eiw_di @ X226 @ mactual )
| ~ ( eiw_di @ X225 @ mactual ) )
& ( ( subset @ X226 @ X225 @ mactual )
| ~ ( equal_set @ X225 @ X226 @ mactual )
| ~ ( eiw_di @ X226 @ mactual )
| ~ ( eiw_di @ X225 @ mactual ) )
& ( ~ ( subset @ X225 @ X226 @ mactual )
| ~ ( subset @ X226 @ X225 @ mactual )
| ( equal_set @ X225 @ X226 @ mactual )
| ~ ( eiw_di @ X226 @ mactual )
| ~ ( eiw_di @ X225 @ mactual ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])])]) ).
thf(c_0_17,negated_conjecture,
~ ( equal_set @ esk5_0 @ esk6_0 @ mactual ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_18,plain,
! [X9: $i,X6: $i] :
( ( equal_set @ X6 @ X9 @ mactual )
| ~ ( subset @ X6 @ X9 @ mactual )
| ~ ( subset @ X9 @ X6 @ mactual )
| ~ ( eiw_di @ X9 @ mactual )
| ~ ( eiw_di @ X6 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_19,negated_conjecture,
subset @ esk6_0 @ esk5_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_20,negated_conjecture,
subset @ esk5_0 @ esk6_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_21,negated_conjecture,
eiw_di @ esk6_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_22,negated_conjecture,
eiw_di @ esk5_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET019^4 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.15 % Computer : n006.cluster.edu
% 0.09/0.15 % Model : x86_64 x86_64
% 0.09/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.15 % Memory : 8046.5625MB
% 0.09/0.15 % OS : Linux 6.8.0-71-generic
% 0.09/0.15 % CPULimit : 300
% 0.09/0.15 % WCLimit : 300
% 0.09/0.15 % DateTime : Tue Sep 29 13:35:09 UTC 2026
% 0.09/0.15 % CPUTime :
% 0.09/0.15 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 Running higher-order theorem proving
% 0.09/0.21 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.0JHcUILfbm/E---3.1_714541.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 % post_as_ho3 with pid 714555 completed with status 0
% 0.09/0.25 % Result found by post_as_ho3
% 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 % (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: HGHNS-FFMS21-SHSSMFNN
% 0.09/0.25 % partial match(2): 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 714559 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 % (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: HGHNS-FFMS21-SHSSMFNN
% 0.09/0.25 % partial match(2): 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 : 0.003 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 : 73
% 0.09/0.25 % Removed by relevancy pruning/SinE : 0
% 0.09/0.25 % Initial clauses : 88
% 0.09/0.25 % Removed in clause preprocessing : 27
% 0.09/0.25 % Initial clauses in saturation : 61
% 0.09/0.25 % Processed clauses : 36
% 0.09/0.25 % ...of these trivial : 0
% 0.09/0.25 % ...subsumed : 1
% 0.09/0.25 % ...remaining for further processing : 35
% 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 : 27
% 0.09/0.25 % ...of the previous two non-redundant : 21
% 0.09/0.25 % ...aggressively subsumed : 0
% 0.09/0.25 % Contextual simplify-reflections : 3
% 0.09/0.25 % Paramodulations : 27
% 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 : 4
% 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 : 35
% 0.09/0.25 % Positive orientable unit clauses : 6
% 0.09/0.25 % Positive unorientable unit clauses: 0
% 0.09/0.25 % Negative unit clauses : 1
% 0.09/0.25 % Non-unit-clauses : 28
% 0.09/0.25 % Current number of unprocessed clauses: 46
% 0.09/0.25 % ...number of literals in the above : 256
% 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) : 275
% 0.09/0.25 % Rec. Clause-clause subsumption calls : 89
% 0.09/0.25 % Non-unit clause-clause subsumptions : 4
% 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 : 14588
% 0.09/0.25 % Search garbage collected termcells : 5889
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.011 s
% 0.09/0.25 % System time : 0.003 s
% 0.09/0.25 % Total time : 0.014 s
% 0.09/0.25 % Maximum resident set size: 4520 pages
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.014 s
% 0.09/0.25 % System time : 0.007 s
% 0.09/0.25 % Total time : 0.021 s
% 0.09/0.25 % Maximum resident set size: 4864 pages
% 0.09/0.25 % E exiting
%------------------------------------------------------------------------------