TSTP Solution File: SEU627^2 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU627^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:28:40 EDT 2024
% Result : Theorem 0.22s 0.50s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 20
% Syntax : Number of formulae : 36 ( 5 unt; 15 typ; 0 def)
% Number of atoms : 79 ( 11 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 366 ( 19 ~; 23 |; 7 &; 289 @)
% ( 4 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 69 ( 0 ^ 69 !; 0 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
emptyset: $i ).
thf(decl_24,type,
setadjoin: $i > $i > $i ).
thf(decl_25,type,
powerset: $i > $i ).
thf(decl_26,type,
subset: $i > $i > $o ).
thf(decl_27,type,
subsetI2: $o ).
thf(decl_28,type,
binunion: $i > $i > $i ).
thf(decl_29,type,
singletoninpowunion: $o ).
thf(decl_30,type,
upairset2E: $o ).
thf(decl_31,type,
upairinpowunion: $o ).
thf(decl_32,type,
esk1_2: $i > $i > $i ).
thf(decl_33,type,
esk2_0: $i ).
thf(decl_34,type,
esk3_0: $i ).
thf(decl_35,type,
esk4_0: $i ).
thf(decl_36,type,
esk5_0: $i ).
thf(ubforcartprodlem1,conjecture,
( subsetI2
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairinpowunion
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
thf(singletoninpowunion,axiom,
( singletoninpowunion
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(upairset2E,axiom,
( upairset2E
<=> ! [X3: $i,X4: $i,X5: $i] :
( ( in @ X5 @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) )
=> ( ( X5 = X3 )
| ( X5 = X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2E) ).
thf(upairinpowunion,axiom,
( upairinpowunion
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairinpowunion) ).
thf(c_0_5,negated_conjecture,
~ ( ! [X23: $i,X24: $i] :
( ! [X25: $i] :
( ( in @ X25 @ X23 )
=> ( in @ X25 @ X24 ) )
=> ( subset @ X23 @ X24 ) )
=> ( ! [X26: $i,X27: $i,X28: $i] :
( ( in @ X28 @ X26 )
=> ( in @ ( setadjoin @ X28 @ emptyset ) @ ( powerset @ ( binunion @ X26 @ X27 ) ) ) )
=> ( ! [X29: $i,X30: $i,X31: $i] :
( ( in @ X31 @ ( setadjoin @ X29 @ ( setadjoin @ X30 @ emptyset ) ) )
=> ( ( X31 = X29 )
| ( X31 = X30 ) ) )
=> ( ! [X32: $i,X33: $i,X34: $i] :
( ( in @ X34 @ X32 )
=> ! [X35: $i] :
( ( in @ X35 @ X33 )
=> ( in @ ( setadjoin @ X34 @ ( setadjoin @ X35 @ emptyset ) ) @ ( powerset @ ( binunion @ X32 @ X33 ) ) ) ) )
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[ubforcartprodlem1]),subsetI2]),singletoninpowunion]),upairset2E]),upairinpowunion]) ).
thf(c_0_6,negated_conjecture,
! [X36: $i,X37: $i,X39: $i,X40: $i,X41: $i,X42: $i,X43: $i,X44: $i,X45: $i,X46: $i,X47: $i,X48: $i] :
( ( ( in @ ( esk1_2 @ X36 @ X37 ) @ X36 )
| ( subset @ X36 @ X37 ) )
& ( ~ ( in @ ( esk1_2 @ X36 @ X37 ) @ X37 )
| ( subset @ X36 @ X37 ) )
& ( ~ ( in @ X41 @ X39 )
| ( in @ ( setadjoin @ X41 @ emptyset ) @ ( powerset @ ( binunion @ X39 @ X40 ) ) ) )
& ( ~ ( in @ X44 @ ( setadjoin @ X42 @ ( setadjoin @ X43 @ emptyset ) ) )
| ( X44 = X42 )
| ( X44 = X43 ) )
& ( ~ ( in @ X47 @ X45 )
| ~ ( in @ X48 @ X46 )
| ( in @ ( setadjoin @ X47 @ ( setadjoin @ X48 @ emptyset ) ) @ ( powerset @ ( binunion @ X45 @ X46 ) ) ) )
& ( in @ esk4_0 @ esk2_0 )
& ( in @ esk5_0 @ esk3_0 )
& ~ ( subset @ ( setadjoin @ ( setadjoin @ esk4_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk4_0 @ ( setadjoin @ esk5_0 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ esk2_0 @ esk3_0 ) ) ) ),
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_5])])])])])]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( X1 = X3 )
| ~ ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk1_2 @ X1 @ X2 ) @ X1 )
| ( subset @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
| ~ ( in @ ( esk1_2 @ X1 @ X2 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( ( esk1_2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ X3 )
= X1 )
| ( ( esk1_2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ X3 )
= X2 )
| ( subset @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ X3 ) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( ( esk1_2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ X3 )
= X1 )
| ( subset @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ X3 )
| ~ ( in @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_12,negated_conjecture,
~ ( subset @ ( setadjoin @ ( setadjoin @ esk4_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk4_0 @ ( setadjoin @ esk5_0 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ esk2_0 @ esk3_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( subset @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ X3 )
| ~ ( in @ X1 @ X3 )
| ~ ( in @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
thf(c_0_14,negated_conjecture,
( ~ ( in @ ( setadjoin @ esk4_0 @ ( setadjoin @ esk5_0 @ emptyset ) ) @ ( powerset @ ( binunion @ esk2_0 @ esk3_0 ) ) )
| ~ ( in @ ( setadjoin @ esk4_0 @ emptyset ) @ ( powerset @ ( binunion @ esk2_0 @ esk3_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( in @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X2 @ X4 ) ) )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_16,negated_conjecture,
in @ esk5_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_17,negated_conjecture,
in @ esk4_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_18,negated_conjecture,
~ ( in @ ( setadjoin @ esk4_0 @ emptyset ) @ ( powerset @ ( binunion @ esk2_0 @ esk3_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( powerset @ ( binunion @ X2 @ X3 ) ) )
| ~ ( in @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SEU627^2 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 16:39:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.22/0.49 Running higher-order theorem proving
% 0.22/0.49 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.22/0.50 # Version: 3.1.0-ho
% 0.22/0.50 # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.22/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50 # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.22/0.50 # Starting post_as_ho8 with 300s (1) cores
% 0.22/0.50 # Starting post_as_ho3 with 300s (1) cores
% 0.22/0.50 # Starting post_as_ho2 with 300s (1) cores
% 0.22/0.50 # post_as_ho8 with pid 30863 completed with status 0
% 0.22/0.50 # Result found by post_as_ho8
% 0.22/0.50 # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.22/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50 # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.22/0.50 # Starting post_as_ho8 with 300s (1) cores
% 0.22/0.50 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.22/0.50 # Search class: HGUSF-FFSF21-MFFFMFNN
% 0.22/0.50 # partial match(1): HGUSF-FFSF21-SFFFMFNN
% 0.22/0.50 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.50 # Starting new_ho_10 with 163s (1) cores
% 0.22/0.50 # new_ho_10 with pid 30866 completed with status 0
% 0.22/0.50 # Result found by new_ho_10
% 0.22/0.50 # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.22/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50 # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.22/0.50 # Starting post_as_ho8 with 300s (1) cores
% 0.22/0.50 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.22/0.50 # Search class: HGUSF-FFSF21-MFFFMFNN
% 0.22/0.50 # partial match(1): HGUSF-FFSF21-SFFFMFNN
% 0.22/0.50 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.50 # Starting new_ho_10 with 163s (1) cores
% 0.22/0.50 # Preprocessing time : 0.001 s
% 0.22/0.50 # Presaturation interreduction done
% 0.22/0.50
% 0.22/0.50 # Proof found!
% 0.22/0.50 # SZS status Theorem
% 0.22/0.50 # SZS output start CNFRefutation
% See solution above
% 0.22/0.50 # Parsed axioms : 15
% 0.22/0.50 # Removed by relevancy pruning/SinE : 10
% 0.22/0.50 # Initial clauses : 8
% 0.22/0.50 # Removed in clause preprocessing : 0
% 0.22/0.50 # Initial clauses in saturation : 8
% 0.22/0.50 # Processed clauses : 24
% 0.22/0.50 # ...of these trivial : 0
% 0.22/0.50 # ...subsumed : 0
% 0.22/0.50 # ...remaining for further processing : 24
% 0.22/0.50 # Other redundant clauses eliminated : 2
% 0.22/0.50 # Clauses deleted for lack of memory : 0
% 0.22/0.50 # Backward-subsumed : 1
% 0.22/0.50 # Backward-rewritten : 0
% 0.22/0.50 # Generated clauses : 21
% 0.22/0.50 # ...of the previous two non-redundant : 18
% 0.22/0.50 # ...aggressively subsumed : 0
% 0.22/0.50 # Contextual simplify-reflections : 0
% 0.22/0.50 # Paramodulations : 17
% 0.22/0.50 # Factorizations : 2
% 0.22/0.50 # NegExts : 0
% 0.22/0.50 # Equation resolutions : 2
% 0.22/0.50 # Disequality decompositions : 0
% 0.22/0.50 # Total rewrite steps : 3
% 0.22/0.50 # ...of those cached : 1
% 0.22/0.50 # Propositional unsat checks : 0
% 0.22/0.50 # Propositional check models : 0
% 0.22/0.50 # Propositional check unsatisfiable : 0
% 0.22/0.50 # Propositional clauses : 0
% 0.22/0.50 # Propositional clauses after purity: 0
% 0.22/0.50 # Propositional unsat core size : 0
% 0.22/0.50 # Propositional preprocessing time : 0.000
% 0.22/0.50 # Propositional encoding time : 0.000
% 0.22/0.50 # Propositional solver time : 0.000
% 0.22/0.50 # Success case prop preproc time : 0.000
% 0.22/0.50 # Success case prop encoding time : 0.000
% 0.22/0.50 # Success case prop solver time : 0.000
% 0.22/0.50 # Current number of processed clauses : 15
% 0.22/0.50 # Positive orientable unit clauses : 3
% 0.22/0.50 # Positive unorientable unit clauses: 0
% 0.22/0.50 # Negative unit clauses : 2
% 0.22/0.50 # Non-unit-clauses : 10
% 0.22/0.50 # Current number of unprocessed clauses: 10
% 0.22/0.50 # ...number of literals in the above : 30
% 0.22/0.50 # Current number of archived formulas : 0
% 0.22/0.50 # Current number of archived clauses : 9
% 0.22/0.50 # Clause-clause subsumption calls (NU) : 34
% 0.22/0.50 # Rec. Clause-clause subsumption calls : 30
% 0.22/0.50 # Non-unit clause-clause subsumptions : 0
% 0.22/0.50 # Unit Clause-clause subsumption calls : 3
% 0.22/0.50 # Rewrite failures with RHS unbound : 0
% 0.22/0.50 # BW rewrite match attempts : 2
% 0.22/0.50 # BW rewrite match successes : 0
% 0.22/0.50 # Condensation attempts : 24
% 0.22/0.50 # Condensation successes : 0
% 0.22/0.50 # Termbank termtop insertions : 1665
% 0.22/0.50 # Search garbage collected termcells : 412
% 0.22/0.50
% 0.22/0.50 # -------------------------------------------------
% 0.22/0.50 # User time : 0.004 s
% 0.22/0.50 # System time : 0.003 s
% 0.22/0.50 # Total time : 0.007 s
% 0.22/0.50 # Maximum resident set size: 1912 pages
% 0.22/0.50
% 0.22/0.50 # -------------------------------------------------
% 0.22/0.50 # User time : 0.005 s
% 0.22/0.50 # System time : 0.005 s
% 0.22/0.50 # Total time : 0.010 s
% 0.22/0.50 # Maximum resident set size: 1704 pages
% 0.22/0.50 % E---3.1 exiting
% 0.22/0.50 % E exiting
%------------------------------------------------------------------------------