TSTP Solution File: SEU734^2 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU734^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n013.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 03:29:39 EDT 2024
% Result : Theorem 0.21s 0.49s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 35 ( 6 unt; 13 typ; 0 def)
% Number of atoms : 116 ( 0 equ; 0 cnn)
% Maximal formula atoms : 25 ( 5 avg)
% Number of connectives : 563 ( 47 ~; 46 |; 8 &; 422 @)
% ( 4 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 74 ( 0 ^ 74 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
powerset: $i > $i ).
thf(decl_24,type,
subset: $i > $i > $o ).
thf(decl_25,type,
binintersect: $i > $i > $i ).
thf(decl_26,type,
setminus: $i > $i > $i ).
thf(decl_27,type,
binintersectT_lem: $o ).
thf(decl_28,type,
complementT_lem: $o ).
thf(decl_29,type,
subsetTI: $o ).
thf(decl_30,type,
complementImpComplementIntersect: $o ).
thf(decl_31,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_32,type,
esk2_0: $i ).
thf(decl_33,type,
esk3_0: $i ).
thf(decl_34,type,
esk4_0: $i ).
thf(complementSubsetComplementIntersect,conjecture,
( binintersectT_lem
=> ( complementT_lem
=> ( subsetTI
=> ( complementImpComplementIntersect
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( subset @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementSubsetComplementIntersect) ).
thf(subsetTI,axiom,
( subsetTI
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ X3 ) ) )
=> ( subset @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTI) ).
thf(binintersectT_lem,axiom,
( binintersectT_lem
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( in @ ( binintersect @ X2 @ X3 ) @ ( powerset @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectT_lem) ).
thf(complementT_lem,axiom,
( complementT_lem
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementT_lem) ).
thf(complementImpComplementIntersect,axiom,
( complementImpComplementIntersect
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( setminus @ X1 @ X2 ) )
=> ( in @ X4 @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementImpComplementIntersect) ).
thf(c_0_5,negated_conjecture,
~ ( ! [X21: $i,X22: $i] :
( ( in @ X22 @ ( powerset @ X21 ) )
=> ! [X23: $i] :
( ( in @ X23 @ ( powerset @ X21 ) )
=> ( in @ ( binintersect @ X22 @ X23 ) @ ( powerset @ X21 ) ) ) )
=> ( ! [X24: $i,X25: $i] :
( ( in @ X25 @ ( powerset @ X24 ) )
=> ( in @ ( setminus @ X24 @ X25 ) @ ( powerset @ X24 ) ) )
=> ( ! [X26: $i,X27: $i] :
( ( in @ X27 @ ( powerset @ X26 ) )
=> ! [X28: $i] :
( ( in @ X28 @ ( powerset @ X26 ) )
=> ( ! [X29: $i] :
( ( in @ X29 @ X26 )
=> ( ( in @ X29 @ X27 )
=> ( in @ X29 @ X28 ) ) )
=> ( subset @ X27 @ X28 ) ) ) )
=> ( ! [X30: $i,X31: $i] :
( ( in @ X31 @ ( powerset @ X30 ) )
=> ! [X32: $i] :
( ( in @ X32 @ ( powerset @ X30 ) )
=> ! [X33: $i] :
( ( in @ X33 @ X30 )
=> ( ( in @ X33 @ ( setminus @ X30 @ X31 ) )
=> ( in @ X33 @ ( setminus @ X30 @ ( binintersect @ X31 @ X32 ) ) ) ) ) ) )
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( subset @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ) ),
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)],[complementSubsetComplementIntersect]),subsetTI]),binintersectT_lem]),complementT_lem]),complementImpComplementIntersect]) ).
thf(c_0_6,negated_conjecture,
! [X34: $i,X35: $i,X36: $i,X37: $i,X38: $i,X39: $i,X40: $i,X41: $i,X43: $i,X44: $i,X45: $i,X46: $i] :
( ( ~ ( in @ X35 @ ( powerset @ X34 ) )
| ~ ( in @ X36 @ ( powerset @ X34 ) )
| ( in @ ( binintersect @ X35 @ X36 ) @ ( powerset @ X34 ) ) )
& ( ~ ( in @ X38 @ ( powerset @ X37 ) )
| ( in @ ( setminus @ X37 @ X38 ) @ ( powerset @ X37 ) ) )
& ( ( in @ ( esk1_3 @ X39 @ X40 @ X41 ) @ X39 )
| ( subset @ X40 @ X41 )
| ~ ( in @ X41 @ ( powerset @ X39 ) )
| ~ ( in @ X40 @ ( powerset @ X39 ) ) )
& ( ( in @ ( esk1_3 @ X39 @ X40 @ X41 ) @ X40 )
| ( subset @ X40 @ X41 )
| ~ ( in @ X41 @ ( powerset @ X39 ) )
| ~ ( in @ X40 @ ( powerset @ X39 ) ) )
& ( ~ ( in @ ( esk1_3 @ X39 @ X40 @ X41 ) @ X41 )
| ( subset @ X40 @ X41 )
| ~ ( in @ X41 @ ( powerset @ X39 ) )
| ~ ( in @ X40 @ ( powerset @ X39 ) ) )
& ( ~ ( in @ X44 @ ( powerset @ X43 ) )
| ~ ( in @ X45 @ ( powerset @ X43 ) )
| ~ ( in @ X46 @ X43 )
| ~ ( in @ X46 @ ( setminus @ X43 @ X44 ) )
| ( in @ X46 @ ( setminus @ X43 @ ( binintersect @ X44 @ X45 ) ) ) )
& ( in @ esk3_0 @ ( powerset @ esk2_0 ) )
& ( in @ esk4_0 @ ( powerset @ esk2_0 ) )
& ~ ( subset @ ( setminus @ esk2_0 @ esk3_0 ) @ ( setminus @ esk2_0 @ ( binintersect @ esk3_0 @ esk4_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,
! [X3: $i,X2: $i,X1: $i] :
( ( subset @ X2 @ X3 )
| ~ ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X3 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ( in @ X4 @ ( setminus @ X2 @ ( binintersect @ X1 @ X3 ) ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ X2 )
| ~ ( in @ X4 @ ( setminus @ X2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X5: $i,X4: $i,X3: $i,X2: $i] :
( ( subset @ X1 @ ( setminus @ X2 @ ( binintersect @ X3 @ X4 ) ) )
| ~ ( in @ ( esk1_3 @ X5 @ X1 @ ( setminus @ X2 @ ( binintersect @ X3 @ X4 ) ) ) @ ( setminus @ X2 @ X3 ) )
| ~ ( in @ ( esk1_3 @ X5 @ X1 @ ( setminus @ X2 @ ( binintersect @ X3 @ X4 ) ) ) @ X2 )
| ~ ( in @ ( setminus @ X2 @ ( binintersect @ X3 @ X4 ) ) @ ( powerset @ X5 ) )
| ~ ( in @ X1 @ ( powerset @ X5 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ ( powerset @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X2 )
| ( subset @ X2 @ X3 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_11,negated_conjecture,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ( subset @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) )
| ~ ( in @ ( esk1_3 @ X4 @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) @ X1 )
| ~ ( in @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) @ ( powerset @ X4 ) )
| ~ ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X4 ) )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_12,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X1 )
| ( subset @ X2 @ X3 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( setminus @ X2 @ X1 ) @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_14,negated_conjecture,
~ ( subset @ ( setminus @ esk2_0 @ esk3_0 ) @ ( setminus @ esk2_0 @ ( binintersect @ esk3_0 @ esk4_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_15,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( subset @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) )
| ~ ( in @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) @ ( powerset @ X1 ) )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
thf(c_0_16,negated_conjecture,
in @ esk4_0 @ ( powerset @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_17,negated_conjecture,
in @ esk3_0 @ ( powerset @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_18,negated_conjecture,
~ ( in @ ( setminus @ esk2_0 @ ( binintersect @ esk3_0 @ esk4_0 ) ) @ ( powerset @ esk2_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,
~ ( in @ ( binintersect @ esk3_0 @ esk4_0 ) @ ( powerset @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_18,c_0_13]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ ( binintersect @ X1 @ X3 ) @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ ( powerset @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU734^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 18:13:38 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.21/0.47 Running higher-order theorem proving
% 0.21/0.47 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
% 0.21/0.49 # Version: 3.1.0-ho
% 0.21/0.49 # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.21/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.49 # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.21/0.49 # Starting post_as_ho8 with 300s (1) cores
% 0.21/0.49 # Starting post_as_ho3 with 300s (1) cores
% 0.21/0.49 # Starting post_as_ho2 with 300s (1) cores
% 0.21/0.49 # post_as_ho8 with pid 19530 completed with status 0
% 0.21/0.49 # Result found by post_as_ho8
% 0.21/0.49 # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.21/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.49 # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.21/0.49 # Starting post_as_ho8 with 300s (1) cores
% 0.21/0.49 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.21/0.49 # Search class: HGUNF-FFSF32-SFFFMFNN
% 0.21/0.49 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.49 # Starting new_ho_10 with 163s (1) cores
% 0.21/0.49 # new_ho_10 with pid 19533 completed with status 0
% 0.21/0.49 # Result found by new_ho_10
% 0.21/0.49 # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.21/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.49 # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.21/0.49 # Starting post_as_ho8 with 300s (1) cores
% 0.21/0.49 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.21/0.49 # Search class: HGUNF-FFSF32-SFFFMFNN
% 0.21/0.49 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.49 # Starting new_ho_10 with 163s (1) cores
% 0.21/0.49 # Preprocessing time : 0.001 s
% 0.21/0.49 # Presaturation interreduction done
% 0.21/0.49
% 0.21/0.49 # Proof found!
% 0.21/0.49 # SZS status Theorem
% 0.21/0.49 # SZS output start CNFRefutation
% See solution above
% 0.21/0.49 # Parsed axioms : 14
% 0.21/0.49 # Removed by relevancy pruning/SinE : 9
% 0.21/0.49 # Initial clauses : 9
% 0.21/0.49 # Removed in clause preprocessing : 0
% 0.21/0.49 # Initial clauses in saturation : 9
% 0.21/0.49 # Processed clauses : 48
% 0.21/0.49 # ...of these trivial : 0
% 0.21/0.49 # ...subsumed : 0
% 0.21/0.49 # ...remaining for further processing : 48
% 0.21/0.49 # Other redundant clauses eliminated : 0
% 0.21/0.49 # Clauses deleted for lack of memory : 0
% 0.21/0.49 # Backward-subsumed : 0
% 0.21/0.49 # Backward-rewritten : 0
% 0.21/0.49 # Generated clauses : 49
% 0.21/0.49 # ...of the previous two non-redundant : 48
% 0.21/0.49 # ...aggressively subsumed : 0
% 0.21/0.49 # Contextual simplify-reflections : 2
% 0.21/0.49 # Paramodulations : 49
% 0.21/0.49 # Factorizations : 0
% 0.21/0.49 # NegExts : 0
% 0.21/0.49 # Equation resolutions : 0
% 0.21/0.49 # Disequality decompositions : 0
% 0.21/0.49 # Total rewrite steps : 4
% 0.21/0.49 # ...of those cached : 2
% 0.21/0.49 # Propositional unsat checks : 0
% 0.21/0.49 # Propositional check models : 0
% 0.21/0.49 # Propositional check unsatisfiable : 0
% 0.21/0.49 # Propositional clauses : 0
% 0.21/0.49 # Propositional clauses after purity: 0
% 0.21/0.49 # Propositional unsat core size : 0
% 0.21/0.49 # Propositional preprocessing time : 0.000
% 0.21/0.49 # Propositional encoding time : 0.000
% 0.21/0.49 # Propositional solver time : 0.000
% 0.21/0.49 # Success case prop preproc time : 0.000
% 0.21/0.49 # Success case prop encoding time : 0.000
% 0.21/0.49 # Success case prop solver time : 0.000
% 0.21/0.49 # Current number of processed clauses : 39
% 0.21/0.49 # Positive orientable unit clauses : 4
% 0.21/0.49 # Positive unorientable unit clauses: 0
% 0.21/0.49 # Negative unit clauses : 3
% 0.21/0.49 # Non-unit-clauses : 32
% 0.21/0.49 # Current number of unprocessed clauses: 18
% 0.21/0.49 # ...number of literals in the above : 125
% 0.21/0.49 # Current number of archived formulas : 0
% 0.21/0.49 # Current number of archived clauses : 9
% 0.21/0.49 # Clause-clause subsumption calls (NU) : 940
% 0.21/0.49 # Rec. Clause-clause subsumption calls : 142
% 0.21/0.49 # Non-unit clause-clause subsumptions : 2
% 0.21/0.49 # Unit Clause-clause subsumption calls : 7
% 0.21/0.49 # Rewrite failures with RHS unbound : 0
% 0.21/0.49 # BW rewrite match attempts : 0
% 0.21/0.49 # BW rewrite match successes : 0
% 0.21/0.49 # Condensation attempts : 48
% 0.21/0.49 # Condensation successes : 0
% 0.21/0.49 # Termbank termtop insertions : 5539
% 0.21/0.49 # Search garbage collected termcells : 511
% 0.21/0.49
% 0.21/0.49 # -------------------------------------------------
% 0.21/0.49 # User time : 0.012 s
% 0.21/0.49 # System time : 0.000 s
% 0.21/0.49 # Total time : 0.012 s
% 0.21/0.49 # Maximum resident set size: 1912 pages
% 0.21/0.49
% 0.21/0.49 # -------------------------------------------------
% 0.21/0.49 # User time : 0.014 s
% 0.21/0.49 # System time : 0.001 s
% 0.21/0.49 # Total time : 0.016 s
% 0.21/0.49 # Maximum resident set size: 1704 pages
% 0.21/0.49 % E---3.1 exiting
% 0.21/0.49 % E exiting
%------------------------------------------------------------------------------