%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET047^1 : 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 08:21:53 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 93 ( 6 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 319 ( 24 ~; 31 |; 4 &; 255 @)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 47 ( 19 ^; 28 !; 0 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mworld: $tType ).
thf(decl_24,type,
mactual: mworld ).
thf(decl_25,type,
mlocal: ( mworld > $o ) > $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,
set_equal: $i > $i > mworld > $o ).
thf(decl_36,type,
element: $i > $i > mworld > $o ).
thf(decl_37,type,
esk1_0: $i ).
thf(decl_38,type,
esk2_0: $i ).
thf(decl_39,type,
esk3_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.ZR3DLKXCH6/E---3.1_1288534.p',mequiv_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.ZR3DLKXCH6/E---3.1_1288534.p',mforall_di_def) ).
thf(mlocal_def,axiom,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZR3DLKXCH6/E---3.1_1288534.p',mlocal_def) ).
thf(pel43,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X7: $i] :
( mforall_di
@ ^ [X9: $i] : ( mequiv @ ( set_equal @ X7 @ X9 ) @ ( set_equal @ X9 @ X7 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZR3DLKXCH6/E---3.1_1288534.p',pel43) ).
thf(pel43_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [X7: $i] :
( mforall_di
@ ^ [X9: $i] :
( mequiv @ ( set_equal @ X7 @ X9 )
@ ( mforall_di
@ ^ [X10: $i] : ( mequiv @ ( element @ X10 @ X7 ) @ ( element @ X10 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZR3DLKXCH6/E---3.1_1288534.p',pel43_1) ).
thf(c_0_5,plain,
( mequiv
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
<=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mequiv_def]) ).
thf(c_0_6,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_7,plain,
( mlocal
= ( ^ [Z0: mworld > $o] : ( Z0 @ mactual ) ) ),
inference(fof_simplification,[status(thm)],[mlocal_def]) ).
thf(c_0_8,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X7: $i] :
( mforall_di
@ ^ [X9: $i] : ( mequiv @ ( set_equal @ X7 @ X9 ) @ ( set_equal @ X9 @ X7 ) ) ) ) ),
inference(assume_negation,[status(cth)],[pel43]) ).
thf(c_0_9,plain,
! [X15: $i,X14: $i] :
( ( set_equal @ X15 @ X14 @ mactual )
<=> ! [X13: $i] :
( ( element @ X13 @ X15 @ mactual )
<=> ( element @ X13 @ X14 @ mactual ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[pel43_1]),c_0_5]),c_0_6]),c_0_7]) ).
thf(c_0_10,negated_conjecture,
~ ! [X12: $i,X11: $i] :
( ( set_equal @ X12 @ X11 @ mactual )
<=> ( set_equal @ X11 @ X12 @ mactual ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_8]),c_0_5]),c_0_6]),c_0_7]) ).
thf(c_0_11,plain,
! [X18: $i,X19: $i,X20: $i,X21: $i,X22: $i,X23: $i] :
( ( ~ ( element @ X20 @ X18 @ mactual )
| ( element @ X20 @ X19 @ mactual )
| ~ ( set_equal @ X18 @ X19 @ mactual ) )
& ( ~ ( element @ X21 @ X19 @ mactual )
| ( element @ X21 @ X18 @ mactual )
| ~ ( set_equal @ X18 @ X19 @ mactual ) )
& ( ~ ( element @ ( esk3_2 @ X22 @ X23 ) @ X22 @ mactual )
| ~ ( element @ ( esk3_2 @ X22 @ X23 ) @ X23 @ mactual )
| ( set_equal @ X22 @ X23 @ mactual ) )
& ( ( element @ ( esk3_2 @ X22 @ X23 ) @ X22 @ mactual )
| ( element @ ( esk3_2 @ X22 @ X23 ) @ X23 @ mactual )
| ( set_equal @ X22 @ X23 @ 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_9])])])])])])]) ).
thf(c_0_12,negated_conjecture,
( ( ~ ( set_equal @ esk1_0 @ esk2_0 @ mactual )
| ~ ( set_equal @ esk2_0 @ esk1_0 @ mactual ) )
& ( ( set_equal @ esk1_0 @ esk2_0 @ mactual )
| ( set_equal @ esk2_0 @ esk1_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_13,plain,
! [X7: $i,X9: $i,X10: $i] :
( ( element @ X7 @ X10 @ mactual )
| ~ ( element @ X7 @ X9 @ mactual )
| ~ ( set_equal @ X9 @ X10 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_14,negated_conjecture,
( ( set_equal @ esk1_0 @ esk2_0 @ mactual )
| ( set_equal @ esk2_0 @ esk1_0 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_15,plain,
! [X7: $i,X10: $i,X9: $i] :
( ( element @ X7 @ X10 @ mactual )
| ~ ( element @ X7 @ X9 @ mactual )
| ~ ( set_equal @ X10 @ X9 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,negated_conjecture,
! [X7: $i] :
( ( element @ X7 @ esk2_0 @ mactual )
| ~ ( element @ X7 @ esk1_0 @ mactual ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
thf(c_0_17,plain,
! [X7: $i,X9: $i] :
( ( element @ ( esk3_2 @ X7 @ X9 ) @ X7 @ mactual )
| ( element @ ( esk3_2 @ X7 @ X9 ) @ X9 @ mactual )
| ( set_equal @ X7 @ X9 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_18,negated_conjecture,
! [X7: $i] :
( ( element @ ( esk3_2 @ esk1_0 @ X7 ) @ esk2_0 @ mactual )
| ( element @ ( esk3_2 @ esk1_0 @ X7 ) @ X7 @ mactual )
| ( set_equal @ esk1_0 @ X7 @ mactual ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_19,plain,
! [X7: $i,X9: $i] :
( ( set_equal @ X7 @ X9 @ mactual )
| ~ ( element @ ( esk3_2 @ X7 @ X9 ) @ X7 @ mactual )
| ~ ( element @ ( esk3_2 @ X7 @ X9 ) @ X9 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_20,negated_conjecture,
( ( element @ ( esk3_2 @ esk1_0 @ esk2_0 ) @ esk2_0 @ mactual )
| ( set_equal @ esk1_0 @ esk2_0 @ mactual ) ),
inference(ef,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
( ( set_equal @ esk1_0 @ esk2_0 @ mactual )
| ~ ( element @ ( esk3_2 @ esk1_0 @ esk2_0 ) @ esk1_0 @ mactual ) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_22,negated_conjecture,
! [X7: $i] :
( ( element @ X7 @ esk1_0 @ mactual )
| ~ ( element @ X7 @ esk2_0 @ mactual ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_14]),c_0_13]) ).
thf(c_0_23,negated_conjecture,
! [X7: $i] :
( ( element @ ( esk3_2 @ X7 @ esk1_0 ) @ esk2_0 @ mactual )
| ( element @ ( esk3_2 @ X7 @ esk1_0 ) @ X7 @ mactual )
| ( set_equal @ X7 @ esk1_0 @ mactual ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_24,negated_conjecture,
( ~ ( set_equal @ esk1_0 @ esk2_0 @ mactual )
| ~ ( set_equal @ esk2_0 @ esk1_0 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_25,negated_conjecture,
set_equal @ esk1_0 @ esk2_0 @ mactual,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_20]) ).
thf(c_0_26,negated_conjecture,
( ( element @ ( esk3_2 @ esk2_0 @ esk1_0 ) @ esk2_0 @ mactual )
| ( set_equal @ esk2_0 @ esk1_0 @ mactual ) ),
inference(ef,[status(thm)],[c_0_23]) ).
thf(c_0_27,negated_conjecture,
~ ( set_equal @ esk2_0 @ esk1_0 @ mactual ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
thf(c_0_28,negated_conjecture,
! [X7: $i] :
( ( set_equal @ X7 @ esk1_0 @ mactual )
| ~ ( element @ ( esk3_2 @ X7 @ esk1_0 ) @ esk2_0 @ mactual )
| ~ ( element @ ( esk3_2 @ X7 @ esk1_0 ) @ X7 @ mactual ) ),
inference(spm,[status(thm)],[c_0_19,c_0_22]) ).
thf(c_0_29,negated_conjecture,
element @ ( esk3_2 @ esk2_0 @ esk1_0 ) @ esk2_0 @ mactual,
inference(sr,[status(thm)],[c_0_26,c_0_27]) ).
thf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_29])]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET047^1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n002.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 13:39:22 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 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.ZR3DLKXCH6/E---3.1_1288534.p
% 0.07/0.25 % Version: 3.5.1-ho
% 0.07/0.25 % Preprocessing class: HSSSSMSSMLMNHSN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.25 % Starting sh5l with 300s (1) cores
% 0.07/0.25 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.25 % Starting new_bool_2 with 300s (1) cores
% 0.07/0.25 % sh5l with pid 1288548 completed with status 0
% 0.07/0.25 % Result found by sh5l
% 0.07/0.25 % Preprocessing class: HSSSSMSSMLMNHSN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.25 % Starting sh5l with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.07/0.25 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.07/0.25 % Search class: HGHNF-FFSF22-SHSSMFNN
% 0.07/0.25 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.25 % SubtermCWHack with pid 1288553 completed with status 0
% 0.07/0.25 % Result found by SubtermCWHack
% 0.07/0.25 % Preprocessing class: HSSSSMSSMLMNHSN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.25 % Starting sh5l with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.07/0.25 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.07/0.25 % Search class: HGHNF-FFSF22-SHSSMFNN
% 0.07/0.25 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.25 % Preprocessing time : 0.001 s
% 0.07/0.25
% 0.07/0.25 % Proof found!
% 0.07/0.25 % SZS status Theorem
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25 % Parsed axioms : 27
% 0.07/0.25 % Removed by relevancy pruning/SinE : 22
% 0.07/0.25 % Initial clauses : 6
% 0.07/0.25 % Removed in clause preprocessing : 0
% 0.07/0.25 % Initial clauses in saturation : 6
% 0.07/0.25 % Processed clauses : 23
% 0.07/0.25 % ...of these trivial : 0
% 0.07/0.25 % ...subsumed : 3
% 0.07/0.25 % ...remaining for further processing : 20
% 0.07/0.25 % Other redundant clauses eliminated : 0
% 0.07/0.25 % Clauses deleted for lack of memory : 0
% 0.07/0.25 % Backward-subsumed : 1
% 0.07/0.25 % Backward-rewritten : 5
% 0.07/0.25 % Generated clauses : 30
% 0.07/0.25 % ...of the previous two non-redundant : 21
% 0.07/0.25 % ...aggressively subsumed : 0
% 0.07/0.25 % Contextual simplify-reflections : 4
% 0.07/0.25 % Paramodulations : 23
% 0.07/0.25 % Factorizations : 6
% 0.07/0.25 % NegExts : 0
% 0.07/0.25 % Equation resolutions : 0
% 0.07/0.25 % Disequality decompositions : 0
% 0.07/0.25 % Total rewrite steps : 9
% 0.07/0.25 % ...of those cached : 5
% 0.07/0.25 % Propositional unsat checks : 0
% 0.07/0.25 % Propositional check models : 0
% 0.07/0.25 % Propositional check unsatisfiable : 0
% 0.07/0.25 % Propositional clauses : 0
% 0.07/0.25 % Propositional clauses after purity: 0
% 0.07/0.25 % Propositional unsat core size : 0
% 0.07/0.25 % Propositional preprocessing time : 0.000
% 0.07/0.25 % Propositional encoding time : 0.000
% 0.07/0.25 % Propositional solver time : 0.000
% 0.07/0.25 % Success case prop preproc time : 0.000
% 0.07/0.25 % Success case prop encoding time : 0.000
% 0.07/0.25 % Success case prop solver time : 0.000
% 0.07/0.25 % Current number of processed clauses : 13
% 0.07/0.25 % Positive orientable unit clauses : 3
% 0.07/0.25 % Positive unorientable unit clauses: 0
% 0.07/0.25 % Negative unit clauses : 1
% 0.07/0.25 % Non-unit-clauses : 9
% 0.07/0.25 % Current number of unprocessed clauses: 4
% 0.07/0.25 % ...number of literals in the above : 9
% 0.07/0.25 % Current number of archived formulas : 0
% 0.07/0.25 % Current number of archived clauses : 7
% 0.07/0.25 % Clause-clause subsumption calls (NU) : 29
% 0.07/0.25 % Rec. Clause-clause subsumption calls : 22
% 0.07/0.25 % Non-unit clause-clause subsumptions : 7
% 0.07/0.25 % Unit Clause-clause subsumption calls : 7
% 0.07/0.25 % Rewrite failures with RHS unbound : 0
% 0.07/0.25 % BW rewrite match attempts : 8
% 0.07/0.25 % BW rewrite match successes : 3
% 0.07/0.25 % Condensation attempts : 0
% 0.07/0.25 % Condensation successes : 0
% 0.07/0.25 % Termbank termtop insertions : 1473
% 0.07/0.25 % Search garbage collected termcells : 414
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.005 s
% 0.07/0.25 % System time : 0.001 s
% 0.07/0.25 % Total time : 0.006 s
% 0.07/0.25 % Maximum resident set size: 3652 pages
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.005 s
% 0.07/0.25 % System time : 0.005 s
% 0.07/0.25 % Total time : 0.010 s
% 0.07/0.25 % Maximum resident set size: 4864 pages
% 0.07/0.25 % E exiting
%------------------------------------------------------------------------------