%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET027^3 : 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 : n004.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 08:21:52 AM UTC 2026
% Result : Theorem 0.23s 0.28s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 82 ( 10 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 214 ( 14 ~; 12 |; 7 &; 174 @)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 57 ( 33 ^; 24 !; 0 ?; 57 :)
% 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,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(decl_35,type,
member: $i > $i > mworld > $o ).
thf(decl_36,type,
subset: $i > $i > mworld > $o ).
thf(decl_37,type,
esk1_0: $i ).
thf(decl_38,type,
esk2_0: $i ).
thf(decl_39,type,
esk3_0: $i ).
thf(decl_40,type,
esk4_2: $i > $i > $i ).
thf(mequiv_def,axiom,
( mequiv
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
<=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4403G5h3Jm/E---3.1_1285662.p',mequiv_def) ).
thf(mimplies_def,axiom,
( mimplies
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4403G5h3Jm/E---3.1_1285662.p',mimplies_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.4403G5h3Jm/E---3.1_1285662.p',mforall_di_def) ).
thf(mlocal_def,axiom,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4403G5h3Jm/E---3.1_1285662.p',mlocal_def) ).
thf(prove_transitivity_of_subset,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X13: $i] :
( mforall_di
@ ^ [X10: $i] :
( mforall_di
@ ^ [X11: $i] : ( mimplies @ ( mand @ ( subset @ X13 @ X10 ) @ ( subset @ X10 @ X11 ) ) @ ( subset @ X13 @ X11 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4403G5h3Jm/E---3.1_1285662.p',prove_transitivity_of_subset) ).
thf(mand_def,axiom,
( mand
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
& ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4403G5h3Jm/E---3.1_1285662.p',mand_def) ).
thf(subset_defn,axiom,
( mlocal
@ ( mforall_di
@ ^ [X9: $i] :
( mforall_di
@ ^ [X10: $i] :
( mequiv @ ( subset @ X9 @ X10 )
@ ( mforall_di
@ ^ [X11: $i] : ( mimplies @ ( member @ X11 @ X9 ) @ ( member @ X11 @ X10 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4403G5h3Jm/E---3.1_1285662.p',subset_defn) ).
thf(c_0_7,plain,
( mequiv
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
<=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mequiv_def]) ).
thf(c_0_8,plain,
( mimplies
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies_def]) ).
thf(c_0_9,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_10,plain,
( mlocal
= ( ^ [Z0: mworld > $o] : ( Z0 @ mactual ) ) ),
inference(fof_simplification,[status(thm)],[mlocal_def]) ).
thf(c_0_11,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X13: $i] :
( mforall_di
@ ^ [X10: $i] :
( mforall_di
@ ^ [X11: $i] : ( mimplies @ ( mand @ ( subset @ X13 @ X10 ) @ ( subset @ X10 @ X11 ) ) @ ( subset @ X13 @ X11 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_transitivity_of_subset]) ).
thf(c_0_12,plain,
( mand
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand_def]) ).
thf(c_0_13,plain,
! [X19: $i,X18: $i] :
( ( subset @ X19 @ X18 @ mactual )
<=> ! [X17: $i] :
( ( member @ X17 @ X19 @ mactual )
=> ( member @ X17 @ X18 @ 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)],[subset_defn]),c_0_7]),c_0_8]),c_0_9]),c_0_10]) ).
thf(c_0_14,negated_conjecture,
~ ! [X16: $i,X15: $i,X14: $i] :
( ( ( subset @ X16 @ X15 @ mactual )
& ( subset @ X15 @ X14 @ mactual ) )
=> ( subset @ X16 @ X14 @ 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_11]),c_0_12]),c_0_8]),c_0_9]),c_0_10]) ).
thf(c_0_15,plain,
! [X24: $i,X25: $i,X26: $i,X27: $i,X28: $i] :
( ( ~ ( subset @ X24 @ X25 @ mactual )
| ~ ( member @ X26 @ X24 @ mactual )
| ( member @ X26 @ X25 @ mactual ) )
& ( ( member @ ( esk4_2 @ X27 @ X28 ) @ X27 @ mactual )
| ( subset @ X27 @ X28 @ mactual ) )
& ( ~ ( member @ ( esk4_2 @ X27 @ X28 ) @ X28 @ mactual )
| ( subset @ X27 @ X28 @ 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(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])])])])]) ).
thf(c_0_16,negated_conjecture,
( ( subset @ esk1_0 @ esk2_0 @ mactual )
& ( subset @ esk2_0 @ esk3_0 @ mactual )
& ~ ( subset @ esk1_0 @ esk3_0 @ mactual ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
thf(c_0_17,plain,
! [X10: $i,X9: $i,X7: $i] :
( ( member @ X10 @ X9 @ mactual )
| ~ ( subset @ X7 @ X9 @ mactual )
| ~ ( member @ X10 @ X7 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_18,negated_conjecture,
subset @ esk2_0 @ esk3_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_19,plain,
! [X7: $i,X9: $i] :
( ( subset @ X7 @ X9 @ mactual )
| ~ ( member @ ( esk4_2 @ X7 @ X9 ) @ X9 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_20,negated_conjecture,
! [X7: $i] :
( ( member @ X7 @ esk3_0 @ mactual )
| ~ ( member @ X7 @ esk2_0 @ mactual ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_21,negated_conjecture,
subset @ esk1_0 @ esk2_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_22,negated_conjecture,
! [X7: $i] :
( ( subset @ X7 @ esk3_0 @ mactual )
| ~ ( member @ ( esk4_2 @ X7 @ esk3_0 ) @ esk2_0 @ mactual ) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_23,negated_conjecture,
! [X7: $i] :
( ( member @ X7 @ esk2_0 @ mactual )
| ~ ( member @ X7 @ esk1_0 @ mactual ) ),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
thf(c_0_24,negated_conjecture,
! [X7: $i] :
( ( subset @ X7 @ esk3_0 @ mactual )
| ~ ( member @ ( esk4_2 @ X7 @ esk3_0 ) @ esk1_0 @ mactual ) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_25,plain,
! [X7: $i,X9: $i] :
( ( member @ ( esk4_2 @ X7 @ X9 ) @ X7 @ mactual )
| ( subset @ X7 @ X9 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_26,negated_conjecture,
~ ( subset @ esk1_0 @ esk3_0 @ mactual ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET027^3 : 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 : n004.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
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:35:22 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.26 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.4403G5h3Jm/E---3.1_1285662.p
% 0.23/0.28 % Version: 3.5.1-ho
% 0.23/0.28 % Preprocessing class: HSSSSMSSMLMNHSN.
% 0.23/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.28 % Starting sh5l with 300s (1) cores
% 0.23/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.28 % Starting new_bool_2 with 300s (1) cores
% 0.23/0.28 % sh5l with pid 1285686 completed with status 0
% 0.23/0.28 % Result found by sh5l
% 0.23/0.28 % Preprocessing class: HSSSSMSSMLMNHSN.
% 0.23/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.28 % Starting sh5l with 300s (1) cores
% 0.23/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.23/0.28 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.23/0.28 % Search class: HGUNF-FFSF22-SHSSMFNN
% 0.23/0.28 % partial match(1): HGHNF-FFSF22-SHSSMFNN
% 0.23/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.28 % SubtermCWHack with pid 1285692 completed with status 0
% 0.23/0.28 % Result found by SubtermCWHack
% 0.23/0.28 % Preprocessing class: HSSSSMSSMLMNHSN.
% 0.23/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.28 % Starting sh5l with 300s (1) cores
% 0.23/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.23/0.28 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.23/0.28 % Search class: HGUNF-FFSF22-SHSSMFNN
% 0.23/0.28 % partial match(1): HGHNF-FFSF22-SHSSMFNN
% 0.23/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.28 % Preprocessing time : 0.001 s
% 0.23/0.28
% 0.23/0.28 % Proof found!
% 0.23/0.28 % SZS status Theorem
% 0.23/0.28 % SZS output start CNFRefutation
% See solution above
% 0.23/0.28 % Parsed axioms : 29
% 0.23/0.28 % Removed by relevancy pruning/SinE : 21
% 0.23/0.28 % Initial clauses : 7
% 0.23/0.28 % Removed in clause preprocessing : 0
% 0.23/0.28 % Initial clauses in saturation : 7
% 0.23/0.28 % Processed clauses : 12
% 0.23/0.28 % ...of these trivial : 0
% 0.23/0.28 % ...subsumed : 0
% 0.23/0.28 % ...remaining for further processing : 12
% 0.23/0.28 % Other redundant clauses eliminated : 0
% 0.23/0.28 % Clauses deleted for lack of memory : 0
% 0.23/0.28 % Backward-subsumed : 0
% 0.23/0.28 % Backward-rewritten : 0
% 0.23/0.28 % Generated clauses : 10
% 0.23/0.28 % ...of the previous two non-redundant : 5
% 0.23/0.28 % ...aggressively subsumed : 0
% 0.23/0.28 % Contextual simplify-reflections : 0
% 0.23/0.28 % Paramodulations : 10
% 0.23/0.28 % Factorizations : 0
% 0.23/0.28 % NegExts : 0
% 0.23/0.28 % Equation resolutions : 0
% 0.23/0.28 % Disequality decompositions : 0
% 0.23/0.28 % Total rewrite steps : 3
% 0.23/0.28 % ...of those cached : 0
% 0.23/0.28 % Propositional unsat checks : 0
% 0.23/0.28 % Propositional check models : 0
% 0.23/0.28 % Propositional check unsatisfiable : 0
% 0.23/0.28 % Propositional clauses : 0
% 0.23/0.28 % Propositional clauses after purity: 0
% 0.23/0.28 % Propositional unsat core size : 0
% 0.23/0.28 % Propositional preprocessing time : 0.000
% 0.23/0.28 % Propositional encoding time : 0.000
% 0.23/0.28 % Propositional solver time : 0.000
% 0.23/0.28 % Success case prop preproc time : 0.000
% 0.23/0.28 % Success case prop encoding time : 0.000
% 0.23/0.28 % Success case prop solver time : 0.000
% 0.23/0.28 % Current number of processed clauses : 12
% 0.23/0.28 % Positive orientable unit clauses : 3
% 0.23/0.28 % Positive unorientable unit clauses: 0
% 0.23/0.28 % Negative unit clauses : 1
% 0.23/0.28 % Non-unit-clauses : 8
% 0.23/0.28 % Current number of unprocessed clauses: 0
% 0.23/0.28 % ...number of literals in the above : 0
% 0.23/0.28 % Current number of archived formulas : 0
% 0.23/0.28 % Current number of archived clauses : 0
% 0.23/0.28 % Clause-clause subsumption calls (NU) : 8
% 0.23/0.28 % Rec. Clause-clause subsumption calls : 8
% 0.23/0.28 % Non-unit clause-clause subsumptions : 0
% 0.23/0.28 % Unit Clause-clause subsumption calls : 0
% 0.23/0.28 % Rewrite failures with RHS unbound : 0
% 0.23/0.28 % BW rewrite match attempts : 2
% 0.23/0.28 % BW rewrite match successes : 0
% 0.23/0.28 % Condensation attempts : 0
% 0.23/0.28 % Condensation successes : 0
% 0.23/0.28 % Termbank termtop insertions : 1236
% 0.23/0.28 % Search garbage collected termcells : 452
% 0.23/0.28
% 0.23/0.28 % -------------------------------------------------
% 0.23/0.28 % User time : 0.003 s
% 0.23/0.28 % System time : 0.004 s
% 0.23/0.28 % Total time : 0.007 s
% 0.23/0.28 % Maximum resident set size: 3912 pages
% 0.23/0.28
% 0.23/0.28 % -------------------------------------------------
% 0.23/0.28 % User time : 0.004 s
% 0.23/0.28 % System time : 0.010 s
% 0.23/0.28 % Total time : 0.014 s
% 0.23/0.28 % Maximum resident set size: 4608 pages
% 0.23/0.28 % E exiting
%------------------------------------------------------------------------------