%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET574^20 : 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 : n002.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 08:21:57 AM UTC 2026
% Result : Theorem 0.28s 0.26s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 107 ( 12 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 279 ( 25 ~; 21 |; 15 &; 205 @)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 54 ( 37 ^; 14 !; 3 ?; 54 :)
% 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_35,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(decl_36,type,
intersect: $i > $i > mworld > $o ).
thf(decl_37,type,
member: $i > $i > mworld > $o ).
thf(decl_39,type,
esk2_2: $i > $i > $i ).
thf(decl_40,type,
esk3_0: $i ).
thf(decl_41,type,
esk4_0: $i ).
thf(decl_42,type,
esk5_0: $i ).
thf(mlocal_def,axiom,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0M0Tr3rJ9r/E---3.1_1291581.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.0M0Tr3rJ9r/E---3.1_1291581.p',mand_def) ).
thf(mequiv_def,axiom,
( mequiv
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
<=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0M0Tr3rJ9r/E---3.1_1291581.p',mequiv_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.0M0Tr3rJ9r/E---3.1_1291581.p',mforall_di_def) ).
thf(mexists_di_def,axiom,
( mexists_di
= ( ^ [X8: $i > mworld > $o,X3: mworld] :
? [X6: $i] :
( ( eiw_di @ X6 @ X3 )
& ( X8 @ X6 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0M0Tr3rJ9r/E---3.1_1291581.p',mexists_di_def) ).
thf(prove_th13,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X13: $i] :
( mforall_di
@ ^ [X10: $i] :
( mforall_di
@ ^ [X11: $i] : ( mimplies @ ( mand @ ( member @ X13 @ X10 ) @ ( member @ X13 @ X11 ) ) @ ( intersect @ X10 @ X11 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0M0Tr3rJ9r/E---3.1_1291581.p',prove_th13) ).
thf(mimplies_def,axiom,
( mimplies
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0M0Tr3rJ9r/E---3.1_1291581.p',mimplies_def) ).
thf(intersect_defn,axiom,
( mlocal
@ ( mforall_di
@ ^ [X9: $i] :
( mforall_di
@ ^ [X10: $i] :
( mequiv @ ( intersect @ X9 @ X10 )
@ ( mexists_di
@ ^ [X11: $i] : ( mand @ ( member @ X11 @ X9 ) @ ( member @ X11 @ X10 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0M0Tr3rJ9r/E---3.1_1291581.p',intersect_defn) ).
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,
( mequiv
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
<=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mequiv_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,
( mexists_di
= ( ^ [Z0: $i > mworld > $o,Z1: mworld] :
? [X6: $i] :
( ( eiw_di @ X6 @ Z1 )
& ( Z0 @ X6 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mexists_di_def]) ).
thf(c_0_13,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X13: $i] :
( mforall_di
@ ^ [X10: $i] :
( mforall_di
@ ^ [X11: $i] : ( mimplies @ ( mand @ ( member @ X13 @ X10 ) @ ( member @ X13 @ X11 ) ) @ ( intersect @ X10 @ X11 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_th13]) ).
thf(c_0_14,plain,
( mimplies
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies_def]) ).
thf(c_0_15,plain,
! [X22: $i] :
( ( eiw_di @ X22 @ mactual )
=> ! [X21: $i] :
( ( eiw_di @ X21 @ mactual )
=> ( ( intersect @ X22 @ X21 @ mactual )
<=> ? [X20: $i] :
( ( eiw_di @ X20 @ mactual )
& ( member @ X20 @ X22 @ mactual )
& ( member @ X20 @ X21 @ mactual ) ) ) ) ),
inference(apply_def,[status(thm)],[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)],[intersect_defn]),c_0_8]),c_0_9]),c_0_10]),c_0_11]),c_0_12]) ).
thf(c_0_16,negated_conjecture,
~ ! [X27: $i] :
( ( eiw_di @ X27 @ mactual )
=> ! [X26: $i] :
( ( eiw_di @ X26 @ mactual )
=> ! [X25: $i] :
( ( eiw_di @ X25 @ mactual )
=> ( ( ( member @ X27 @ X26 @ mactual )
& ( member @ X27 @ X25 @ mactual ) )
=> ( intersect @ X26 @ X25 @ 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_13]),c_0_8]),c_0_9]),c_0_14]),c_0_11]) ).
thf(c_0_17,plain,
! [X34: $i,X35: $i,X37: $i] :
( ( ( eiw_di @ ( esk2_2 @ X34 @ X35 ) @ mactual )
| ~ ( intersect @ X34 @ X35 @ mactual )
| ~ ( eiw_di @ X35 @ mactual )
| ~ ( eiw_di @ X34 @ mactual ) )
& ( ( member @ ( esk2_2 @ X34 @ X35 ) @ X34 @ mactual )
| ~ ( intersect @ X34 @ X35 @ mactual )
| ~ ( eiw_di @ X35 @ mactual )
| ~ ( eiw_di @ X34 @ mactual ) )
& ( ( member @ ( esk2_2 @ X34 @ X35 ) @ X35 @ mactual )
| ~ ( intersect @ X34 @ X35 @ mactual )
| ~ ( eiw_di @ X35 @ mactual )
| ~ ( eiw_di @ X34 @ mactual ) )
& ( ~ ( eiw_di @ X37 @ mactual )
| ~ ( member @ X37 @ X34 @ mactual )
| ~ ( member @ X37 @ X35 @ mactual )
| ( intersect @ X34 @ X35 @ mactual )
| ~ ( eiw_di @ X35 @ mactual )
| ~ ( eiw_di @ X34 @ mactual ) ) ),
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_15])])])])])]) ).
thf(c_0_18,negated_conjecture,
( ( eiw_di @ esk3_0 @ mactual )
& ( eiw_di @ esk4_0 @ mactual )
& ( eiw_di @ esk5_0 @ mactual )
& ( member @ esk3_0 @ esk4_0 @ mactual )
& ( member @ esk3_0 @ esk5_0 @ mactual )
& ~ ( intersect @ esk4_0 @ esk5_0 @ mactual ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
thf(c_0_19,plain,
! [X6: $i,X10: $i,X9: $i] :
( ( intersect @ X9 @ X10 @ mactual )
| ~ ( eiw_di @ X6 @ mactual )
| ~ ( member @ X6 @ X9 @ mactual )
| ~ ( member @ X6 @ X10 @ mactual )
| ~ ( eiw_di @ X10 @ mactual )
| ~ ( eiw_di @ X9 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
member @ esk3_0 @ esk5_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
eiw_di @ esk5_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_22,negated_conjecture,
eiw_di @ esk3_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_23,negated_conjecture,
! [X6: $i] :
( ( intersect @ X6 @ esk5_0 @ mactual )
| ~ ( member @ esk3_0 @ X6 @ mactual )
| ~ ( eiw_di @ X6 @ mactual ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]) ).
thf(c_0_24,negated_conjecture,
member @ esk3_0 @ esk4_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_25,negated_conjecture,
eiw_di @ esk4_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_26,negated_conjecture,
~ ( intersect @ esk4_0 @ esk5_0 @ mactual ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET574^20 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n002.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 13:40:22 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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.0M0Tr3rJ9r/E---3.1_1291581.p
% 0.28/0.26 % Version: 3.5.1-ho
% 0.28/0.26 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.28/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.26 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.28/0.26 % Starting post_as_ho3 with 300s (1) cores
% 0.28/0.26 % Starting new_ho_12 with 300s (1) cores
% 0.28/0.26 % Starting new_bool_2 with 300s (1) cores
% 0.28/0.26 % post_as_ho3 with pid 1291609 completed with status 0
% 0.28/0.26 % Result found by post_as_ho3
% 0.28/0.26 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.28/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.26 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.28/0.26 % Starting post_as_ho3 with 300s (1) cores
% 0.28/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.28/0.26 % No SInE strategy applied
% 0.28/0.26 % Search class: HHUNS-FFSS21-SHSSMFNN
% 0.28/0.26 % partial match(3): HHHNS-FFSF11-SHSSMFNN
% 0.28/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.26 % SubtermCWHack with pid 1291612 completed with status 0
% 0.28/0.26 % Result found by SubtermCWHack
% 0.28/0.26 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.28/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.26 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.28/0.26 % Starting post_as_ho3 with 300s (1) cores
% 0.28/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.28/0.26 % No SInE strategy applied
% 0.28/0.26 % Search class: HHUNS-FFSS21-SHSSMFNN
% 0.28/0.26 % partial match(3): HHHNS-FFSF11-SHSSMFNN
% 0.28/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.26 % Preprocessing time : 0.002 s
% 0.28/0.26
% 0.28/0.26 % Proof found!
% 0.28/0.26 % SZS status Theorem
% 0.28/0.26 % SZS output start CNFRefutation
% See solution above
% 0.28/0.26 % Parsed axioms : 32
% 0.28/0.26 % Removed by relevancy pruning/SinE : 0
% 0.28/0.26 % Initial clauses : 30
% 0.28/0.26 % Removed in clause preprocessing : 16
% 0.28/0.26 % Initial clauses in saturation : 14
% 0.28/0.26 % Processed clauses : 15
% 0.28/0.26 % ...of these trivial : 0
% 0.28/0.26 % ...subsumed : 0
% 0.28/0.26 % ...remaining for further processing : 15
% 0.28/0.26 % Other redundant clauses eliminated : 0
% 0.28/0.26 % Clauses deleted for lack of memory : 0
% 0.28/0.26 % Backward-subsumed : 0
% 0.28/0.26 % Backward-rewritten : 0
% 0.28/0.26 % Generated clauses : 7
% 0.28/0.26 % ...of the previous two non-redundant : 5
% 0.28/0.26 % ...aggressively subsumed : 0
% 0.28/0.26 % Contextual simplify-reflections : 0
% 0.28/0.26 % Paramodulations : 7
% 0.28/0.26 % Factorizations : 0
% 0.28/0.26 % NegExts : 0
% 0.28/0.26 % Equation resolutions : 0
% 0.28/0.26 % Disequality decompositions : 0
% 0.28/0.26 % Total rewrite steps : 6
% 0.28/0.26 % ...of those cached : 3
% 0.28/0.26 % Propositional unsat checks : 0
% 0.28/0.26 % Propositional check models : 0
% 0.28/0.26 % Propositional check unsatisfiable : 0
% 0.28/0.26 % Propositional clauses : 0
% 0.28/0.26 % Propositional clauses after purity: 0
% 0.28/0.26 % Propositional unsat core size : 0
% 0.28/0.26 % Propositional preprocessing time : 0.000
% 0.28/0.26 % Propositional encoding time : 0.000
% 0.28/0.26 % Propositional solver time : 0.000
% 0.28/0.26 % Success case prop preproc time : 0.000
% 0.28/0.26 % Success case prop encoding time : 0.000
% 0.28/0.26 % Success case prop solver time : 0.000
% 0.28/0.26 % Current number of processed clauses : 15
% 0.28/0.26 % Positive orientable unit clauses : 7
% 0.28/0.26 % Positive unorientable unit clauses: 0
% 0.28/0.26 % Negative unit clauses : 1
% 0.28/0.26 % Non-unit-clauses : 7
% 0.28/0.26 % Current number of unprocessed clauses: 3
% 0.28/0.26 % ...number of literals in the above : 17
% 0.28/0.26 % Current number of archived formulas : 0
% 0.28/0.26 % Current number of archived clauses : 0
% 0.28/0.26 % Clause-clause subsumption calls (NU) : 2
% 0.28/0.26 % Rec. Clause-clause subsumption calls : 0
% 0.28/0.26 % Non-unit clause-clause subsumptions : 0
% 0.28/0.26 % Unit Clause-clause subsumption calls : 0
% 0.28/0.26 % Rewrite failures with RHS unbound : 0
% 0.28/0.26 % BW rewrite match attempts : 0
% 0.28/0.26 % BW rewrite match successes : 0
% 0.28/0.26 % Condensation attempts : 0
% 0.28/0.26 % Condensation successes : 0
% 0.28/0.26 % Termbank termtop insertions : 2236
% 0.28/0.26 % Search garbage collected termcells : 667
% 0.28/0.26
% 0.28/0.26 % -------------------------------------------------
% 0.28/0.26 % User time : 0.004 s
% 0.28/0.26 % System time : 0.003 s
% 0.28/0.26 % Total time : 0.007 s
% 0.28/0.26 % Maximum resident set size: 3660 pages
% 0.28/0.26
% 0.28/0.26 % -------------------------------------------------
% 0.28/0.26 % User time : 0.005 s
% 0.28/0.26 % System time : 0.008 s
% 0.28/0.26 % Total time : 0.013 s
% 0.28/0.26 % Maximum resident set size: 4608 pages
% 0.28/0.26 % E exiting
%------------------------------------------------------------------------------