TSTP Solution File: SEU640^2 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU640^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n022.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 03:28:46 EDT 2024
% Result : Theorem 0.20s 0.49s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 37 ( 9 unt; 10 typ; 0 def)
% Number of atoms : 100 ( 17 equ; 0 cnn)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 401 ( 45 ~; 56 |; 13 &; 253 @)
% ( 2 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 64 ( 9 ^ 50 !; 5 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_25,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_26,type,
singleton: $i > $o ).
thf(decl_27,type,
singletonprop: $o ).
thf(decl_28,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_29,type,
esk1_2: $i > ( $i > $o ) > $i ).
thf(decl_30,type,
esk2_2: $i > ( $i > $o ) > $i ).
thf(decl_31,type,
esk3_0: $i ).
thf(decl_32,type,
epred1_0: $i > $o ).
thf(decl_33,type,
esk4_0: $i ).
thf(ex1,axiom,
( ex1
= ( ^ [X1: $i,X3: $i > $o] :
( singleton
@ ( dsetconstr @ X1
@ ^ [X2: $i] : ( X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1) ).
thf(singletonprop,axiom,
( singletonprop
<=> ! [X1: $i,X3: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X3 @ X2 )
=> ( ( X3 @ X4 )
=> ( X2 = X4 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X1 )
& ( X3 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X1
@ ^ [X2: $i] : ( X3 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonprop) ).
thf(ex1I2,conjecture,
( singletonprop
=> ! [X1: $i,X3: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X3 @ X2 )
=> ( ( X3 @ X4 )
=> ( X2 = X4 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X1 )
& ( X3 @ X2 ) )
=> ( ex1 @ X1
@ ^ [X2: $i] : ( X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I2) ).
thf(c_0_3,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
( singleton
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_4,plain,
( singletonprop
<=> ! [X1: $i,X3: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X3 @ X2 )
=> ( ( X3 @ X4 )
=> ( X2 = X4 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X1 )
& ( X3 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X3 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singletonprop]) ).
thf(c_0_5,negated_conjecture,
~ ( ! [X15: $i,X16: $i > $o] :
( ! [X17: $i] :
( ( in @ X17 @ X15 )
=> ! [X18: $i] :
( ( in @ X18 @ X15 )
=> ( ( X16 @ X17 )
=> ( ( X16 @ X18 )
=> ( X17 = X18 ) ) ) ) )
=> ( ? [X19: $i] :
( ( in @ X19 @ X15 )
& ( X16 @ X19 ) )
=> ( singleton @ ( dsetconstr @ X15 @ X16 ) ) ) )
=> ! [X1: $i,X3: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X3 @ X2 )
=> ( ( X3 @ X4 )
=> ( X2 = X4 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X1 )
& ( X3 @ X2 ) )
=> ( singleton @ ( dsetconstr @ X1 @ X3 ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[ex1I2])]),c_0_3]),c_0_4])]) ).
thf(c_0_6,negated_conjecture,
! [X20: $i,X21: $i > $o,X24: $i,X27: $i,X28: $i] :
( ( ( in @ ( esk1_2 @ X20 @ X21 ) @ X20 )
| ~ ( in @ X24 @ X20 )
| ~ ( X21 @ X24 )
| ( singleton @ ( dsetconstr @ X20 @ X21 ) ) )
& ( ( in @ ( esk2_2 @ X20 @ X21 ) @ X20 )
| ~ ( in @ X24 @ X20 )
| ~ ( X21 @ X24 )
| ( singleton @ ( dsetconstr @ X20 @ X21 ) ) )
& ( ( X21 @ ( esk1_2 @ X20 @ X21 ) )
| ~ ( in @ X24 @ X20 )
| ~ ( X21 @ X24 )
| ( singleton @ ( dsetconstr @ X20 @ X21 ) ) )
& ( ( X21 @ ( esk2_2 @ X20 @ X21 ) )
| ~ ( in @ X24 @ X20 )
| ~ ( X21 @ X24 )
| ( singleton @ ( dsetconstr @ X20 @ X21 ) ) )
& ( ( ( esk1_2 @ X20 @ X21 )
!= ( esk2_2 @ X20 @ X21 ) )
| ~ ( in @ X24 @ X20 )
| ~ ( X21 @ X24 )
| ( singleton @ ( dsetconstr @ X20 @ X21 ) ) )
& ( ~ ( in @ X27 @ esk3_0 )
| ~ ( in @ X28 @ esk3_0 )
| ~ ( epred1_0 @ X27 )
| ~ ( epred1_0 @ X28 )
| ( X27 = X28 ) )
& ( in @ esk4_0 @ esk3_0 )
& ( epred1_0 @ esk4_0 )
& ~ ( singleton @ ( dsetconstr @ esk3_0 @ epred1_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] :
( ( X1 = X2 )
| ~ ( in @ X1 @ esk3_0 )
| ~ ( in @ X2 @ esk3_0 )
| ~ ( epred1_0 @ X1 )
| ~ ( epred1_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
in @ esk4_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
epred1_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X3: $i > $o,X2: $i] :
( ( in @ ( esk2_2 @ X1 @ X3 ) @ X1 )
| ( singleton @ ( dsetconstr @ X1 @ X3 ) )
| ~ ( in @ X2 @ X1 )
| ~ ( X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X3: $i > $o,X2: $i] :
( ( in @ ( esk1_2 @ X1 @ X3 ) @ X1 )
| ( singleton @ ( dsetconstr @ X1 @ X3 ) )
| ~ ( in @ X2 @ X1 )
| ~ ( X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i] :
( ( X1 = esk4_0 )
| ~ ( in @ X1 @ esk3_0 )
| ~ ( epred1_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9])]) ).
thf(c_0_13,negated_conjecture,
! [X3: $i > $o] :
( ( in @ ( esk2_2 @ esk3_0 @ X3 ) @ esk3_0 )
| ( singleton @ ( dsetconstr @ esk3_0 @ X3 ) )
| ~ ( X3 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_10,c_0_8]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X3: $i > $o,X2: $i] :
( ( X3 @ ( esk2_2 @ X1 @ X3 ) )
| ( singleton @ ( dsetconstr @ X1 @ X3 ) )
| ~ ( in @ X2 @ X1 )
| ~ ( X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_15,negated_conjecture,
! [X3: $i > $o] :
( ( in @ ( esk1_2 @ esk3_0 @ X3 ) @ esk3_0 )
| ( singleton @ ( dsetconstr @ esk3_0 @ X3 ) )
| ~ ( X3 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_8]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X3: $i > $o,X2: $i] :
( ( X3 @ ( esk1_2 @ X1 @ X3 ) )
| ( singleton @ ( dsetconstr @ X1 @ X3 ) )
| ~ ( in @ X2 @ X1 )
| ~ ( X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i,X3: $i > $o,X2: $i] :
( ( singleton @ ( dsetconstr @ X1 @ X3 ) )
| ( ( esk1_2 @ X1 @ X3 )
!= ( esk2_2 @ X1 @ X3 ) )
| ~ ( in @ X2 @ X1 )
| ~ ( X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_18,negated_conjecture,
! [X3: $i > $o] :
( ( ( esk2_2 @ esk3_0 @ X3 )
= esk4_0 )
| ( singleton @ ( dsetconstr @ esk3_0 @ X3 ) )
| ~ ( epred1_0 @ ( esk2_2 @ esk3_0 @ X3 ) )
| ~ ( X3 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_19,negated_conjecture,
! [X3: $i > $o] :
( ( singleton @ ( dsetconstr @ esk3_0 @ X3 ) )
| ( X3 @ ( esk2_2 @ esk3_0 @ X3 ) )
| ~ ( X3 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_8]) ).
thf(c_0_20,negated_conjecture,
~ ( singleton @ ( dsetconstr @ esk3_0 @ epred1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_21,negated_conjecture,
! [X3: $i > $o] :
( ( ( esk1_2 @ esk3_0 @ X3 )
= esk4_0 )
| ( singleton @ ( dsetconstr @ esk3_0 @ X3 ) )
| ~ ( epred1_0 @ ( esk1_2 @ esk3_0 @ X3 ) )
| ~ ( X3 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_15]) ).
thf(c_0_22,negated_conjecture,
! [X3: $i > $o] :
( ( singleton @ ( dsetconstr @ esk3_0 @ X3 ) )
| ( X3 @ ( esk1_2 @ esk3_0 @ X3 ) )
| ~ ( X3 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_16,c_0_8]) ).
thf(c_0_23,negated_conjecture,
! [X3: $i > $o] :
( ( singleton @ ( dsetconstr @ esk3_0 @ X3 ) )
| ( ( esk2_2 @ esk3_0 @ X3 )
!= ( esk1_2 @ esk3_0 @ X3 ) )
| ~ ( X3 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_8]) ).
thf(c_0_24,negated_conjecture,
( ( esk2_2 @ esk3_0 @ epred1_0 )
= esk4_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_9])]),c_0_20]) ).
thf(c_0_25,negated_conjecture,
( ( esk1_2 @ esk3_0 @ epred1_0 )
= esk4_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_9])]),c_0_20]) ).
thf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_9])]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU640^2 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n022.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 17:03:53 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.20/0.47 Running higher-order theorem proving
% 0.20/0.47 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
% 0.20/0.49 # Version: 3.1.0-ho
% 0.20/0.49 # Preprocessing class: HSSSSMSSSLMNHSA.
% 0.20/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.49 # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.49 # Starting sh5l with 300s (1) cores
% 0.20/0.49 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.49 # Starting new_bool_2 with 300s (1) cores
% 0.20/0.49 # new_bool_1 with pid 30616 completed with status 0
% 0.20/0.49 # Result found by new_bool_1
% 0.20/0.49 # Preprocessing class: HSSSSMSSSLMNHSA.
% 0.20/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.49 # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.49 # Starting sh5l with 300s (1) cores
% 0.20/0.49 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.49 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.49 # Search class: HGUSF-FFSF22-SHSFMMBN
% 0.20/0.49 # partial match(2): HGUNF-FFSF22-SHSSMMBN
% 0.20/0.49 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.49 # Starting new_ho_10 with 163s (1) cores
% 0.20/0.49 # new_ho_10 with pid 30618 completed with status 0
% 0.20/0.49 # Result found by new_ho_10
% 0.20/0.49 # Preprocessing class: HSSSSMSSSLMNHSA.
% 0.20/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.49 # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.49 # Starting sh5l with 300s (1) cores
% 0.20/0.49 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.49 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.49 # Search class: HGUSF-FFSF22-SHSFMMBN
% 0.20/0.49 # partial match(2): HGUNF-FFSF22-SHSSMMBN
% 0.20/0.49 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.49 # Starting new_ho_10 with 163s (1) cores
% 0.20/0.49 # Preprocessing time : 0.001 s
% 0.20/0.49 # Presaturation interreduction done
% 0.20/0.49
% 0.20/0.49 # Proof found!
% 0.20/0.49 # SZS status Theorem
% 0.20/0.49 # SZS output start CNFRefutation
% See solution above
% 0.20/0.49 # Parsed axioms : 11
% 0.20/0.49 # Removed by relevancy pruning/SinE : 8
% 0.20/0.49 # Initial clauses : 9
% 0.20/0.49 # Removed in clause preprocessing : 0
% 0.20/0.49 # Initial clauses in saturation : 9
% 0.20/0.49 # Processed clauses : 34
% 0.20/0.49 # ...of these trivial : 0
% 0.20/0.49 # ...subsumed : 0
% 0.20/0.49 # ...remaining for further processing : 34
% 0.20/0.49 # Other redundant clauses eliminated : 0
% 0.20/0.49 # Clauses deleted for lack of memory : 0
% 0.20/0.49 # Backward-subsumed : 0
% 0.20/0.49 # Backward-rewritten : 0
% 0.20/0.49 # Generated clauses : 51
% 0.20/0.49 # ...of the previous two non-redundant : 45
% 0.20/0.49 # ...aggressively subsumed : 0
% 0.20/0.49 # Contextual simplify-reflections : 0
% 0.20/0.49 # Paramodulations : 51
% 0.20/0.49 # Factorizations : 0
% 0.20/0.49 # NegExts : 0
% 0.20/0.49 # Equation resolutions : 0
% 0.20/0.49 # Disequality decompositions : 0
% 0.20/0.49 # Total rewrite steps : 13
% 0.20/0.49 # ...of those cached : 10
% 0.20/0.49 # Propositional unsat checks : 0
% 0.20/0.49 # Propositional check models : 0
% 0.20/0.49 # Propositional check unsatisfiable : 0
% 0.20/0.49 # Propositional clauses : 0
% 0.20/0.49 # Propositional clauses after purity: 0
% 0.20/0.49 # Propositional unsat core size : 0
% 0.20/0.49 # Propositional preprocessing time : 0.000
% 0.20/0.49 # Propositional encoding time : 0.000
% 0.20/0.49 # Propositional solver time : 0.000
% 0.20/0.49 # Success case prop preproc time : 0.000
% 0.20/0.49 # Success case prop encoding time : 0.000
% 0.20/0.49 # Success case prop solver time : 0.000
% 0.20/0.49 # Current number of processed clauses : 25
% 0.20/0.49 # Positive orientable unit clauses : 4
% 0.20/0.49 # Positive unorientable unit clauses: 0
% 0.20/0.49 # Negative unit clauses : 1
% 0.20/0.49 # Non-unit-clauses : 20
% 0.20/0.49 # Current number of unprocessed clauses: 27
% 0.20/0.49 # ...number of literals in the above : 135
% 0.20/0.49 # Current number of archived formulas : 0
% 0.20/0.49 # Current number of archived clauses : 9
% 0.20/0.49 # Clause-clause subsumption calls (NU) : 134
% 0.20/0.49 # Rec. Clause-clause subsumption calls : 35
% 0.20/0.49 # Non-unit clause-clause subsumptions : 0
% 0.20/0.49 # Unit Clause-clause subsumption calls : 0
% 0.20/0.49 # Rewrite failures with RHS unbound : 0
% 0.20/0.49 # BW rewrite match attempts : 0
% 0.20/0.49 # BW rewrite match successes : 0
% 0.20/0.49 # Condensation attempts : 34
% 0.20/0.49 # Condensation successes : 0
% 0.20/0.49 # Termbank termtop insertions : 3183
% 0.20/0.49 # Search garbage collected termcells : 463
% 0.20/0.49
% 0.20/0.49 # -------------------------------------------------
% 0.20/0.49 # User time : 0.006 s
% 0.20/0.49 # System time : 0.003 s
% 0.20/0.49 # Total time : 0.009 s
% 0.20/0.49 # Maximum resident set size: 1916 pages
% 0.20/0.49
% 0.20/0.49 # -------------------------------------------------
% 0.20/0.49 # User time : 0.006 s
% 0.20/0.49 # System time : 0.006 s
% 0.20/0.49 # Total time : 0.012 s
% 0.20/0.49 # Maximum resident set size: 1712 pages
% 0.20/0.49 % E---3.1 exiting
% 0.20/0.49 % E exiting
%------------------------------------------------------------------------------