TSTP Solution File: NUM816^5 by E---3.2.0
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%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : NUM816^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n018.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 : Mon Jun 24 12:38:37 EDT 2024
% Result : Theorem 0.22s 0.53s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 20 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 121 ( 17 ~; 8 |; 10 &; 72 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 6 ^ 25 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
c0: $i ).
thf(decl_23,type,
cS: $i > $i ).
thf(decl_24,type,
cEVEN1: $i > $o ).
thf(decl_25,type,
cODD1: $i > $o ).
thf(decl_26,type,
esk1_1: ( $i > $o ) > $i ).
thf(decl_27,type,
esk2_1: $i > $i ).
thf(cODD1_def,axiom,
( cODD1
= ( ^ [X1: $i] :
~ ( cEVEN1 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.5Jpb87VF1h/E---3.1_31780.p',cODD1_def) ).
thf(cEVEN1_def,axiom,
( cEVEN1
= ( ^ [X1: $i] :
! [X2: $i > $o] :
( ( ( X2 @ c0 )
& ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( cS @ ( cS @ X3 ) ) ) ) )
=> ( X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.5Jpb87VF1h/E---3.1_31780.p',cEVEN1_def) ).
thf(cTHM406,conjecture,
( ( ! [X4: $i] :
( ( cS @ X4 )
!= c0 )
& ! [X5: $i,X6: $i] :
( ( ( cS @ X5 )
= ( cS @ X6 ) )
=> ( X5 = X6 ) ) )
=> ( cODD1 @ ( cS @ c0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.5Jpb87VF1h/E---3.1_31780.p',cTHM406) ).
thf(c_0_3,plain,
( cODD1
= ( ^ [Z0: $i] :
~ ! [X10: $i > $o] :
( ( ( X10 @ c0 )
& ! [X11: $i] :
( ( X10 @ X11 )
=> ( X10 @ ( cS @ ( cS @ X11 ) ) ) ) )
=> ( X10 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[cODD1_def]) ).
thf(c_0_4,plain,
( cEVEN1
= ( ^ [Z0: $i] :
! [X2: $i > $o] :
( ( ( X2 @ c0 )
& ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( cS @ ( cS @ X3 ) ) ) ) )
=> ( X2 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[cEVEN1_def]) ).
thf(c_0_5,plain,
( cODD1
= ( ^ [Z0: $i] :
~ ! [X10: $i > $o] :
( ( ( X10 @ c0 )
& ! [X11: $i] :
( ( X10 @ X11 )
=> ( X10 @ ( cS @ ( cS @ X11 ) ) ) ) )
=> ( X10 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_3,c_0_4]) ).
thf(c_0_6,negated_conjecture,
~ ( ( ! [X4: $i] :
( ( cS @ X4 )
!= c0 )
& ! [X5: $i,X6: $i] :
( ( ( cS @ X5 )
= ( cS @ X6 ) )
=> ( X5 = X6 ) ) )
=> ~ ! [X12: $i > $o] :
( ( ( X12 @ c0 )
& ! [X13: $i] :
( ( X12 @ X13 )
=> ( X12 @ ( cS @ ( cS @ X13 ) ) ) ) )
=> ( X12 @ ( cS @ c0 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[cTHM406]),c_0_5])]) ).
thf(c_0_7,negated_conjecture,
! [X14: $i,X15: $i,X16: $i,X17: $i > $o] :
( ( ( cS @ X14 )
!= c0 )
& ( ( ( cS @ X15 )
!= ( cS @ X16 ) )
| ( X15 = X16 ) )
& ( ( X17 @ ( esk1_1 @ X17 ) )
| ~ ( X17 @ c0 )
| ( X17 @ ( cS @ c0 ) ) )
& ( ~ ( X17 @ ( cS @ ( cS @ ( esk1_1 @ X17 ) ) ) )
| ~ ( X17 @ c0 )
| ( X17 @ ( cS @ c0 ) ) ) ),
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_6])])])])])]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i,X3: $i] :
( ( X1 = X3 )
| ( ( cS @ X1 )
!= ( cS @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X2: $i > $o] :
( ( X2 @ ( cS @ c0 ) )
| ~ ( X2 @ ( cS @ ( cS @ ( esk1_1 @ X2 ) ) ) )
| ~ ( X2 @ c0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i] :
( ( cS @ X1 )
!= c0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i] :
( ( esk2_1 @ ( cS @ X1 ) )
= X1 ),
inference(recognize_injectivity,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
( ( cS
@ ( cS
@ ( esk1_1
@ ^ [Z0: $i] :
( Z0
!= ( cS @ c0 ) ) ) ) )
= ( cS @ c0 ) ),
inference(sr,[status(thm)],[inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_9]),c_0_10]) ).
thf(c_0_13,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_11]),c_0_10]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : NUM816^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n018.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 : Sat Jun 22 20:41:54 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.22/0.51 Running higher-order theorem proving
% 0.22/0.51 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/tmp/tmp.5Jpb87VF1h/E---3.1_31780.p
% 0.22/0.53 # Version: 3.2.0-ho
% 0.22/0.53 # Preprocessing class: HSSSSMSSSLSNSFN.
% 0.22/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.53 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.53 # Starting post_as_ho5 with 300s (1) cores
% 0.22/0.53 # Starting sh4l with 300s (1) cores
% 0.22/0.53 # Starting ho_unfolding_2 with 300s (1) cores
% 0.22/0.53 # post_as_ho5 with pid 31859 completed with status 0
% 0.22/0.53 # Result found by post_as_ho5
% 0.22/0.53 # Preprocessing class: HSSSSMSSSLSNSFN.
% 0.22/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.53 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.53 # Starting post_as_ho5 with 300s (1) cores
% 0.22/0.53 # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.22/0.53 # Search class: HGUSF-FFSF11-MSFFMMBN
% 0.22/0.53 # partial match(1): HGUSF-FFSF21-MSFFMMBN
% 0.22/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.53 # Starting ho_unfolding_3 with 163s (1) cores
% 0.22/0.53 # ho_unfolding_3 with pid 31862 completed with status 0
% 0.22/0.53 # Result found by ho_unfolding_3
% 0.22/0.53 # Preprocessing class: HSSSSMSSSLSNSFN.
% 0.22/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.53 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.53 # Starting post_as_ho5 with 300s (1) cores
% 0.22/0.53 # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.22/0.53 # Search class: HGUSF-FFSF11-MSFFMMBN
% 0.22/0.53 # partial match(1): HGUSF-FFSF21-MSFFMMBN
% 0.22/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.53 # Starting ho_unfolding_3 with 163s (1) cores
% 0.22/0.53 # Preprocessing time : 0.001 s
% 0.22/0.53 # Presaturation interreduction done
% 0.22/0.53
% 0.22/0.53 # Proof found!
% 0.22/0.53 # SZS status Theorem
% 0.22/0.53 # SZS output start CNFRefutation
% See solution above
% 0.22/0.53 # Parsed axioms : 7
% 0.22/0.53 # Removed by relevancy pruning/SinE : 4
% 0.22/0.53 # Initial clauses : 4
% 0.22/0.53 # Removed in clause preprocessing : 0
% 0.22/0.53 # Initial clauses in saturation : 4
% 0.22/0.53 # Processed clauses : 14
% 0.22/0.53 # ...of these trivial : 0
% 0.22/0.53 # ...subsumed : 2
% 0.22/0.53 # ...remaining for further processing : 12
% 0.22/0.53 # Other redundant clauses eliminated : 0
% 0.22/0.53 # Clauses deleted for lack of memory : 0
% 0.22/0.53 # Backward-subsumed : 0
% 0.22/0.53 # Backward-rewritten : 0
% 0.22/0.53 # Generated clauses : 14
% 0.22/0.53 # ...of the previous two non-redundant : 10
% 0.22/0.53 # ...aggressively subsumed : 0
% 0.22/0.53 # Contextual simplify-reflections : 0
% 0.22/0.53 # Paramodulations : 6
% 0.22/0.53 # Factorizations : 0
% 0.22/0.53 # NegExts : 0
% 0.22/0.53 # Equation resolutions : 1
% 0.22/0.53 # Disequality decompositions : 0
% 0.22/0.53 # Total rewrite steps : 1
% 0.22/0.53 # ...of those cached : 0
% 0.22/0.53 # Propositional unsat checks : 0
% 0.22/0.53 # Propositional check models : 0
% 0.22/0.53 # Propositional check unsatisfiable : 0
% 0.22/0.53 # Propositional clauses : 0
% 0.22/0.53 # Propositional clauses after purity: 0
% 0.22/0.53 # Propositional unsat core size : 0
% 0.22/0.53 # Propositional preprocessing time : 0.000
% 0.22/0.53 # Propositional encoding time : 0.000
% 0.22/0.53 # Propositional solver time : 0.000
% 0.22/0.53 # Success case prop preproc time : 0.000
% 0.22/0.53 # Success case prop encoding time : 0.000
% 0.22/0.53 # Success case prop solver time : 0.000
% 0.22/0.53 # Current number of processed clauses : 8
% 0.22/0.53 # Positive orientable unit clauses : 3
% 0.22/0.53 # Positive unorientable unit clauses: 0
% 0.22/0.53 # Negative unit clauses : 2
% 0.22/0.53 # Non-unit-clauses : 3
% 0.22/0.53 # Current number of unprocessed clauses: 1
% 0.22/0.53 # ...number of literals in the above : 2
% 0.22/0.53 # Current number of archived formulas : 0
% 0.22/0.53 # Current number of archived clauses : 4
% 0.22/0.53 # Clause-clause subsumption calls (NU) : 4
% 0.22/0.53 # Rec. Clause-clause subsumption calls : 4
% 0.22/0.53 # Non-unit clause-clause subsumptions : 0
% 0.22/0.53 # Unit Clause-clause subsumption calls : 0
% 0.22/0.53 # Rewrite failures with RHS unbound : 0
% 0.22/0.53 # BW rewrite match attempts : 1
% 0.22/0.53 # BW rewrite match successes : 0
% 0.22/0.53 # Condensation attempts : 14
% 0.22/0.53 # Condensation successes : 0
% 0.22/0.53 # Termbank termtop insertions : 772
% 0.22/0.53 # Search garbage collected termcells : 201
% 0.22/0.53
% 0.22/0.53 # -------------------------------------------------
% 0.22/0.53 # User time : 0.004 s
% 0.22/0.53 # System time : 0.001 s
% 0.22/0.53 # Total time : 0.006 s
% 0.22/0.53 # Maximum resident set size: 1752 pages
% 0.22/0.53
% 0.22/0.53 # -------------------------------------------------
% 0.22/0.53 # User time : 0.005 s
% 0.22/0.53 # System time : 0.004 s
% 0.22/0.53 # Total time : 0.009 s
% 0.22/0.53 # Maximum resident set size: 1708 pages
% 0.22/0.53 % E---3.1 exiting
% 0.22/0.53 % E exiting
%------------------------------------------------------------------------------