TSTP Solution File: SEU707^2 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU707^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n003.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 03:29:20 EDT 2024
% Result : Theorem 0.20s 0.51s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of formulae : 35 ( 8 unt; 12 typ; 0 def)
% Number of atoms : 133 ( 57 equ; 0 cnn)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 332 ( 47 ~; 43 |; 46 &; 160 @)
% ( 5 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 9 con; 0-4 aty)
% Number of variables : 100 ( 32 ^ 68 !; 0 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
setunion: $i > $i ).
thf(decl_24,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_25,type,
singleton: $i > $o ).
thf(decl_26,type,
iftrueProp1: $o ).
thf(decl_27,type,
ifSingleton: $o ).
thf(decl_28,type,
if: $i > $o > $i > $i > $i ).
thf(decl_29,type,
theeq: $o ).
thf(decl_30,type,
esk1_0: $i ).
thf(decl_31,type,
epred1_0: $o ).
thf(decl_32,type,
esk2_0: $i ).
thf(decl_33,type,
esk3_0: $i ).
thf(if,axiom,
( if
= ( ^ [X1: $i,X2: $o,X3: $i,X4: $i] :
( setunion
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
& ( X5 = X3 ) )
| ( ~ X2
& ( X5 = X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',if) ).
thf(ifSingleton,axiom,
( ifSingleton
<=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( singleton
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
& ( X5 = X3 ) )
| ( ~ X2
& ( X5 = X4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifSingleton) ).
thf(iftrueProp1,axiom,
( iftrueProp1
<=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X2
=> ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
& ( X5 = X3 ) )
| ( ~ X2
& ( X5 = X4 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueProp1) ).
thf(iftrue,conjecture,
( iftrueProp1
=> ( ifSingleton
=> ( theeq
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X2
=> ( ( if @ X1 @ X2 @ X3 @ X4 )
= X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrue) ).
thf(theeq,axiom,
( theeq
<=> ! [X6: $i] :
( ( singleton @ X6 )
=> ! [X3: $i] :
( ( in @ X3 @ X6 )
=> ( ( setunion @ X6 )
= X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theeq) ).
thf(c_0_5,plain,
( if
= ( ^ [Z0: $i,Z1: $o,Z2: $i,Z3: $i] :
( setunion
@ ( dsetconstr @ Z0
@ ^ [Z4: $i] :
( ( Z1
& ( Z4 = Z2 ) )
| ( ~ Z1
& Z4 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[if]) ).
thf(c_0_6,plain,
( ifSingleton
<=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( singleton
@ ( dsetconstr @ X1
@ ^ [Z0: $i] :
( ( X2
& ( Z0 = X3 ) )
| ( ~ X2
& ( Z0 = X4 ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ifSingleton]) ).
thf(c_0_7,plain,
( iftrueProp1
<=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X2
=> ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] :
( ( X2
& ( Z0 = X3 ) )
| ( ~ X2
& ( Z0 = X4 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iftrueProp1]) ).
thf(c_0_8,negated_conjecture,
~ ( ! [X21: $i,X22: $o,X23: $i] :
( ( in @ X23 @ X21 )
=> ! [X24: $i] :
( ( in @ X24 @ X21 )
=> ( X22
=> ( in @ X23
@ ( dsetconstr @ X21
@ ^ [Z0: $i] :
( ( X22
& ( Z0 = X23 ) )
| ( ~ X22
& ( Z0 = X24 ) ) ) ) ) ) ) )
=> ( ! [X25: $i,X26: $o,X27: $i] :
( ( in @ X27 @ X25 )
=> ! [X28: $i] :
( ( in @ X28 @ X25 )
=> ( singleton
@ ( dsetconstr @ X25
@ ^ [Z0: $i] :
( ( X26
& ( Z0 = X27 ) )
| ( ~ X26
& ( Z0 = X28 ) ) ) ) ) ) )
=> ( ! [X29: $i] :
( ( singleton @ X29 )
=> ! [X30: $i] :
( ( in @ X30 @ X29 )
=> ( ( setunion @ X29 )
= X30 ) ) )
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X2
=> ( ( setunion
@ ( dsetconstr @ X1
@ ^ [Z0: $i] :
( ( X2
& ( Z0 = X3 ) )
| ( ~ X2
& ( Z0 = X4 ) ) ) ) )
= 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)],[iftrue]),c_0_5]),theeq]),c_0_6]),c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X31: $i,X32: $o,X33: $i,X34: $i,X35: $i,X36: $o,X37: $i,X38: $i,X39: $i,X40: $i] :
( ( ~ ( in @ X33 @ X31 )
| ~ ( in @ X34 @ X31 )
| ~ X32
| ( in @ X33
@ ( dsetconstr @ X31
@ ^ [Z0: $i] :
( ( X32
& ( Z0 = X33 ) )
| ( ~ X32
& ( Z0 = X34 ) ) ) ) ) )
& ( ~ ( in @ X37 @ X35 )
| ~ ( in @ X38 @ X35 )
| ( singleton
@ ( dsetconstr @ X35
@ ^ [Z0: $i] :
( ( X36
& ( Z0 = X37 ) )
| ( ~ X36
& ( Z0 = X38 ) ) ) ) ) )
& ( ~ ( singleton @ X39 )
| ~ ( in @ X40 @ X39 )
| ( ( setunion @ X39 )
= X40 ) )
& ( in @ esk2_0 @ esk1_0 )
& ( in @ esk3_0 @ esk1_0 )
& epred1_0
& ( ( setunion
@ ( dsetconstr @ esk1_0
@ ^ [Z0: $i] :
( ( epred1_0
& ( Z0 = esk2_0 ) )
| ( ~ epred1_0
& ( Z0 = esk3_0 ) ) ) ) )
!= esk2_0 ) ),
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_8])])])])]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X4: $i,X3: $i] :
( ( in @ X1
@ ( dsetconstr @ X3
@ ^ [Z0: $i] :
( ( $true
& ( Z0 = X1 ) )
| ( ~ $true
& ( Z0 = X4 ) ) ) ) )
| ~ ( in @ X1 @ X3 )
| ~ ( in @ X4 @ X3 ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_9])])]) ).
thf(c_0_11,negated_conjecture,
! [X3: $i,X1: $i] :
( ( ( setunion @ X1 )
= X3 )
| ~ ( singleton @ X1 )
| ~ ( in @ X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X2: $o,X1: $i,X4: $i,X3: $i] :
( ( singleton
@ ( dsetconstr @ X3
@ ^ [Z0: $i] :
( ( X2
& ( Z0 = X1 ) )
| ( ~ X2
& ( Z0 = X4 ) ) ) ) )
| ~ ( in @ X1 @ X3 )
| ~ ( in @ X4 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X4: $i,X3: $i] :
( ( in @ X1
@ ( dsetconstr @ X3
@ ^ [Z0: $i] : ( Z0 = X1 ) ) )
| ~ ( in @ X4 @ X3 )
| ~ ( in @ X1 @ X3 ) ),
inference(cn,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
in @ esk3_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_15,negated_conjecture,
! [X2: $o,X5: $i,X4: $i,X3: $i,X1: $i] :
( ( ( setunion
@ ( dsetconstr @ X1
@ ^ [Z0: $i] :
( ( X2
& ( Z0 = X3 ) )
| ( ~ X2
& ( Z0 = X4 ) ) ) ) )
= X5 )
| ~ ( in @ X5
@ ( dsetconstr @ X1
@ ^ [Z0: $i] :
( ( X2
& ( Z0 = X3 ) )
| ( ~ X2
& ( Z0 = X4 ) ) ) ) )
| ~ ( in @ X4 @ X1 )
| ~ ( in @ X3 @ X1 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ esk1_0
@ ^ [Z0: $i] : ( Z0 = X1 ) ) )
| ~ ( in @ X1 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,negated_conjecture,
( ( setunion
@ ( dsetconstr @ esk1_0
@ ^ [Z0: $i] :
( ( epred1_0
& ( Z0 = esk2_0 ) )
| ( ~ epred1_0
& ( Z0 = esk3_0 ) ) ) ) )
!= esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_18,plain,
! [X1: $i,X3: $i,X2: $o,X4: $i] :
( ( ( setunion
@ ( dsetconstr @ esk1_0
@ ^ [Z0: $i] :
( ( X2
& ( Z0 = X1 ) )
| ( ~ X2
& ( Z0 = X3 ) ) ) ) )
= X4 )
| ( ( ^ [Z0: $i] :
( ( X2
& ( Z0 = X1 ) )
| ( ~ X2
& ( Z0 = X3 ) ) ) )
!= ( ^ [Z0: $i] : ( Z0 = X4 ) ) )
| ~ ( in @ X3 @ esk1_0 )
| ~ ( in @ X1 @ esk1_0 )
| ~ ( in @ X4 @ esk1_0 ) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_15,c_0_16])])]) ).
thf(c_0_19,negated_conjecture,
in @ esk2_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_20,negated_conjecture,
( ( ^ [Z0: $i] :
( ( epred1_0
& ( Z0 = esk2_0 ) )
| ( ~ epred1_0
& ( Z0 = esk3_0 ) ) ) )
!= ( ^ [Z0: $i] : ( Z0 = esk2_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_14]),c_0_19])])]),c_0_19])]) ).
thf(c_0_21,negated_conjecture,
epred1_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_20]),c_0_21]),c_0_21])])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU707^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n003.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 17:40:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.48 Running higher-order theorem proving
% 0.20/0.48 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
% 0.20/0.51 # Version: 3.1.0-ho
% 0.20/0.51 # Preprocessing class: HSSSSLSSSLMNSFN.
% 0.20/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.51 # Starting ho_unfolding_6 with 1500s (5) cores
% 0.20/0.51 # Starting pre_casc_5 with 300s (1) cores
% 0.20/0.51 # Starting sh4l with 300s (1) cores
% 0.20/0.51 # Starting full_lambda_3 with 300s (1) cores
% 0.20/0.51 # pre_casc_5 with pid 2585 completed with status 0
% 0.20/0.51 # Result found by pre_casc_5
% 0.20/0.51 # Preprocessing class: HSSSSLSSSLMNSFN.
% 0.20/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.51 # Starting ho_unfolding_6 with 1500s (5) cores
% 0.20/0.51 # Starting pre_casc_5 with 300s (1) cores
% 0.20/0.51 # SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 0.20/0.51 # Search class: HHUSF-FFSS21-DSFFMFBN
% 0.20/0.51 # partial match(3): HHUSF-FFSF21-SSFFMFNN
% 0.20/0.51 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.51 # Starting new_ho_10 with 163s (1) cores
% 0.20/0.51 # new_ho_10 with pid 2593 completed with status 9
% 0.20/0.51 # Starting pre_casc_5 with 31s (1) cores
% 0.20/0.51 # pre_casc_5 with pid 2600 completed with status 0
% 0.20/0.51 # Result found by pre_casc_5
% 0.20/0.51 # Preprocessing class: HSSSSLSSSLMNSFN.
% 0.20/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.51 # Starting ho_unfolding_6 with 1500s (5) cores
% 0.20/0.51 # Starting pre_casc_5 with 300s (1) cores
% 0.20/0.51 # SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 0.20/0.51 # Search class: HHUSF-FFSS21-DSFFMFBN
% 0.20/0.51 # partial match(3): HHUSF-FFSF21-SSFFMFNN
% 0.20/0.51 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.51 # Starting new_ho_10 with 163s (1) cores
% 0.20/0.51 # new_ho_10 with pid 2593 completed with status 9
% 0.20/0.51 # Starting pre_casc_5 with 31s (1) cores
% 0.20/0.51 # Preprocessing time : 0.001 s
% 0.20/0.51
% 0.20/0.51 # Proof found!
% 0.20/0.51 # SZS status Theorem
% 0.20/0.51 # SZS output start CNFRefutation
% See solution above
% 0.20/0.51 # Parsed axioms : 13
% 0.20/0.51 # Removed by relevancy pruning/SinE : 8
% 0.20/0.51 # Initial clauses : 7
% 0.20/0.51 # Removed in clause preprocessing : 0
% 0.20/0.51 # Initial clauses in saturation : 7
% 0.20/0.51 # Processed clauses : 27
% 0.20/0.51 # ...of these trivial : 0
% 0.20/0.51 # ...subsumed : 2
% 0.20/0.51 # ...remaining for further processing : 24
% 0.20/0.51 # Other redundant clauses eliminated : 10
% 0.20/0.51 # Clauses deleted for lack of memory : 0
% 0.20/0.51 # Backward-subsumed : 1
% 0.20/0.51 # Backward-rewritten : 0
% 0.20/0.51 # Generated clauses : 63
% 0.20/0.51 # ...of the previous two non-redundant : 53
% 0.20/0.51 # ...aggressively subsumed : 0
% 0.20/0.51 # Contextual simplify-reflections : 0
% 0.20/0.51 # Paramodulations : 46
% 0.20/0.51 # Factorizations : 0
% 0.20/0.51 # NegExts : 3
% 0.20/0.51 # Equation resolutions : 10
% 0.20/0.51 # Disequality decompositions : 0
% 0.20/0.51 # Total rewrite steps : 11
% 0.20/0.51 # ...of those cached : 8
% 0.20/0.51 # Propositional unsat checks : 0
% 0.20/0.51 # Propositional check models : 0
% 0.20/0.51 # Propositional check unsatisfiable : 0
% 0.20/0.51 # Propositional clauses : 0
% 0.20/0.51 # Propositional clauses after purity: 0
% 0.20/0.51 # Propositional unsat core size : 0
% 0.20/0.51 # Propositional preprocessing time : 0.000
% 0.20/0.51 # Propositional encoding time : 0.000
% 0.20/0.51 # Propositional solver time : 0.000
% 0.20/0.51 # Success case prop preproc time : 0.000
% 0.20/0.51 # Success case prop encoding time : 0.000
% 0.20/0.51 # Success case prop solver time : 0.000
% 0.20/0.51 # Current number of processed clauses : 23
% 0.20/0.51 # Positive orientable unit clauses : 3
% 0.20/0.51 # Positive unorientable unit clauses: 0
% 0.20/0.51 # Negative unit clauses : 3
% 0.20/0.51 # Non-unit-clauses : 17
% 0.20/0.51 # Current number of unprocessed clauses: 33
% 0.20/0.51 # ...number of literals in the above : 235
% 0.20/0.51 # Current number of archived formulas : 0
% 0.20/0.51 # Current number of archived clauses : 1
% 0.20/0.51 # Clause-clause subsumption calls (NU) : 182
% 0.20/0.51 # Rec. Clause-clause subsumption calls : 61
% 0.20/0.51 # Non-unit clause-clause subsumptions : 1
% 0.20/0.51 # Unit Clause-clause subsumption calls : 2
% 0.20/0.51 # Rewrite failures with RHS unbound : 0
% 0.20/0.51 # BW rewrite match attempts : 0
% 0.20/0.51 # BW rewrite match successes : 0
% 0.20/0.51 # Condensation attempts : 27
% 0.20/0.51 # Condensation successes : 0
% 0.20/0.51 # Termbank termtop insertions : 3982
% 0.20/0.51 # Search garbage collected termcells : 392
% 0.20/0.51
% 0.20/0.51 # -------------------------------------------------
% 0.20/0.51 # User time : 0.009 s
% 0.20/0.51 # System time : 0.005 s
% 0.20/0.51 # Total time : 0.014 s
% 0.20/0.51 # Maximum resident set size: 1872 pages
% 0.20/0.51
% 0.20/0.51 # -------------------------------------------------
% 0.20/0.51 # User time : 0.010 s
% 0.20/0.51 # System time : 0.007 s
% 0.20/0.51 # Total time : 0.017 s
% 0.20/0.51 # Maximum resident set size: 1712 pages
% 0.20/0.51 % E---3.1 exiting
% 0.20/0.51 % E exiting
%------------------------------------------------------------------------------