TSTP Solution File: ALG277^5 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ALG277^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% 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 May 20 18:06:00 EDT 2024
% Result : Theorem 0.19s 0.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 31 ( 19 unt; 9 typ; 0 def)
% Number of atoms : 53 ( 39 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 142 ( 3 ~; 0 |; 11 &; 126 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 70 ( 16 ^ 49 !; 5 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
g: $tType ).
thf(decl_22,type,
cGROUP3: ( g > g > g ) > g > $o ).
thf(decl_23,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf(decl_24,type,
cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
thf(decl_25,type,
cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
thf(decl_26,type,
esk1_0: g > g > g ).
thf(decl_27,type,
esk2_0: g ).
thf(decl_28,type,
esk3_1: g > g ).
thf(decl_29,type,
esk4_0: g ).
thf(cGROUP3_def,axiom,
( cGROUP3
= ( ^ [X1: g > g > g,X5: g] :
( ( cGRP_ASSOC @ X1 )
& ( cGRP_RIGHT_UNIT @ X1 @ X5 )
& ( cGRP_RIGHT_INVERSE @ X1 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGROUP3_def) ).
thf(cGRP_ASSOC_def,axiom,
( cGRP_ASSOC
= ( ^ [X1: g > g > g] :
! [X2: g,X3: g,X4: g] :
( ( X1 @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ X2 @ ( X1 @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_ASSOC_def) ).
thf(cGRP_RIGHT_INVERSE_def,axiom,
( cGRP_RIGHT_INVERSE
= ( ^ [X1: g > g > g,X5: g] :
! [X2: g] :
? [X3: g] :
( ( X1 @ X2 @ X3 )
= X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_RIGHT_INVERSE_def) ).
thf(cGRP_RIGHT_UNIT_def,axiom,
( cGRP_RIGHT_UNIT
= ( ^ [X1: g > g > g,X5: g] :
! [X2: g] :
( ( X1 @ X2 @ X5 )
= X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_RIGHT_UNIT_def) ).
thf(cE13A2,conjecture,
! [X1: g > g > g,X5: g] :
( ( cGROUP3 @ X1 @ X5 )
=> ! [X2: g] :
( ( X1 @ X5 @ X2 )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cE13A2) ).
thf(c_0_5,plain,
( cGROUP3
= ( ^ [Z0: g > g > g,Z1: g] :
( ! [X9: g,X10: g,X11: g] :
( ( Z0 @ ( Z0 @ X9 @ X10 ) @ X11 )
= ( Z0 @ X9 @ ( Z0 @ X10 @ X11 ) ) )
& ! [X12: g] :
( ( Z0 @ X12 @ Z1 )
= X12 )
& ! [X13: g] :
? [X14: g] :
( ( Z0 @ X13 @ X14 )
= Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[cGROUP3_def]) ).
thf(c_0_6,plain,
( cGRP_ASSOC
= ( ^ [Z0: g > g > g] :
! [X2: g,X3: g,X4: g] :
( ( Z0 @ ( Z0 @ X2 @ X3 ) @ X4 )
= ( Z0 @ X2 @ ( Z0 @ X3 @ X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cGRP_ASSOC_def]) ).
thf(c_0_7,plain,
( cGRP_RIGHT_INVERSE
= ( ^ [Z0: g > g > g,Z1: g] :
! [X2: g] :
? [X3: g] :
( ( Z0 @ X2 @ X3 )
= Z1 ) ) ),
inference(fof_simplification,[status(thm)],[cGRP_RIGHT_INVERSE_def]) ).
thf(c_0_8,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Z0: g > g > g,Z1: g] :
! [X2: g] :
( ( Z0 @ X2 @ Z1 )
= X2 ) ) ),
inference(fof_simplification,[status(thm)],[cGRP_RIGHT_UNIT_def]) ).
thf(c_0_9,plain,
( cGROUP3
= ( ^ [Z0: g > g > g,Z1: g] :
( ! [X9: g,X10: g,X11: g] :
( ( Z0 @ ( Z0 @ X9 @ X10 ) @ X11 )
= ( Z0 @ X9 @ ( Z0 @ X10 @ X11 ) ) )
& ! [X12: g] :
( ( Z0 @ X12 @ Z1 )
= X12 )
& ! [X13: g] :
? [X14: g] :
( ( Z0 @ X13 @ X14 )
= Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,c_0_6]),c_0_7]),c_0_8]) ).
thf(c_0_10,negated_conjecture,
~ ! [X1: g > g > g,X5: g] :
( ( ! [X15: g,X16: g,X17: g] :
( ( X1 @ ( X1 @ X15 @ X16 ) @ X17 )
= ( X1 @ X15 @ ( X1 @ X16 @ X17 ) ) )
& ! [X18: g] :
( ( X1 @ X18 @ X5 )
= X18 )
& ! [X19: g] :
? [X20: g] :
( ( X1 @ X19 @ X20 )
= X5 ) )
=> ! [X2: g] :
( ( X1 @ X5 @ X2 )
= X2 ) ),
inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[cE13A2]),c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X23: g,X24: g,X25: g,X26: g,X27: g] :
( ( ( esk1_0 @ ( esk1_0 @ X23 @ X24 ) @ X25 )
= ( esk1_0 @ X23 @ ( esk1_0 @ X24 @ X25 ) ) )
& ( ( esk1_0 @ X26 @ esk2_0 )
= X26 )
& ( ( esk1_0 @ X27 @ ( esk3_1 @ X27 ) )
= esk2_0 )
& ( ( esk1_0 @ esk2_0 @ esk4_0 )
!= esk4_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_10])])])])]) ).
thf(c_0_12,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( esk1_0 @ ( esk1_0 @ X2 @ X3 ) @ X4 )
= ( esk1_0 @ X2 @ ( esk1_0 @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_13,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ X2 @ ( esk3_1 @ X2 ) )
= esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ X2 @ esk2_0 )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,negated_conjecture,
! [X2: g,X3: g] :
( ( esk1_0 @ X2 @ ( esk1_0 @ ( esk3_1 @ X2 ) @ X3 ) )
= ( esk1_0 @ esk2_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,negated_conjecture,
! [X2: g,X3: g] :
( ( esk1_0 @ X2 @ ( esk1_0 @ esk2_0 @ X3 ) )
= ( esk1_0 @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
thf(c_0_17,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ esk2_0 @ ( esk3_1 @ ( esk3_1 @ X2 ) ) )
= X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_13]),c_0_14]) ).
thf(c_0_18,negated_conjecture,
! [X2: g,X3: g] :
( ( esk1_0 @ X2 @ ( esk3_1 @ ( esk3_1 @ X3 ) ) )
= ( esk1_0 @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_19,negated_conjecture,
( ( esk1_0 @ esk2_0 @ esk4_0 )
!= esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_20,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ esk2_0 @ X2 )
= X2 ),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ALG277^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n018.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 : Sat May 18 23:51:38 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running higher-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.19/0.49 # Version: 3.1.0-ho
% 0.19/0.49 # Preprocessing class: HSSSSMSSSLSNHSA.
% 0.19/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49 # Starting post_as_ho12 with 1500s (5) cores
% 0.19/0.49 # Starting post_as_ho4 with 300s (1) cores
% 0.19/0.49 # Starting lpo8_s with 300s (1) cores
% 0.19/0.49 # Starting sh5l with 300s (1) cores
% 0.19/0.49 # post_as_ho12 with pid 24319 completed with status 0
% 0.19/0.49 # Result found by post_as_ho12
% 0.19/0.49 # Preprocessing class: HSSSSMSSSLSNHSA.
% 0.19/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49 # Starting post_as_ho12 with 1500s (5) cores
% 0.19/0.49 # No SInE strategy applied
% 0.19/0.49 # Search class: HUUPS-FFSF11-SHSFMFNN
% 0.19/0.49 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.49 # Starting new_ho_10 with 811s (1) cores
% 0.19/0.49 # Starting post_as_ho12 with 151s (1) cores
% 0.19/0.49 # Starting new_bool_1 with 136s (1) cores
% 0.19/0.49 # Starting new_bool_2 with 136s (1) cores
% 0.19/0.49 # Starting new_bool_9 with 136s (1) cores
% 0.19/0.49 # post_as_ho12 with pid 24327 completed with status 0
% 0.19/0.49 # Result found by post_as_ho12
% 0.19/0.49 # Preprocessing class: HSSSSMSSSLSNHSA.
% 0.19/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49 # Starting post_as_ho12 with 1500s (5) cores
% 0.19/0.49 # No SInE strategy applied
% 0.19/0.49 # Search class: HUUPS-FFSF11-SHSFMFNN
% 0.19/0.49 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.49 # Starting new_ho_10 with 811s (1) cores
% 0.19/0.49 # Starting post_as_ho12 with 151s (1) cores
% 0.19/0.49 # Preprocessing time : 0.001 s
% 0.19/0.49 # Presaturation interreduction done
% 0.19/0.49
% 0.19/0.49 # Proof found!
% 0.19/0.49 # SZS status Theorem
% 0.19/0.49 # SZS output start CNFRefutation
% See solution above
% 0.19/0.49 # Parsed axioms : 10
% 0.19/0.49 # Removed by relevancy pruning/SinE : 0
% 0.19/0.49 # Initial clauses : 9
% 0.19/0.49 # Removed in clause preprocessing : 5
% 0.19/0.49 # Initial clauses in saturation : 4
% 0.19/0.49 # Processed clauses : 14
% 0.19/0.49 # ...of these trivial : 0
% 0.19/0.49 # ...subsumed : 0
% 0.19/0.49 # ...remaining for further processing : 14
% 0.19/0.49 # Other redundant clauses eliminated : 0
% 0.19/0.49 # Clauses deleted for lack of memory : 0
% 0.19/0.49 # Backward-subsumed : 0
% 0.19/0.49 # Backward-rewritten : 4
% 0.19/0.49 # Generated clauses : 30
% 0.19/0.49 # ...of the previous two non-redundant : 15
% 0.19/0.49 # ...aggressively subsumed : 0
% 0.19/0.49 # Contextual simplify-reflections : 0
% 0.19/0.49 # Paramodulations : 30
% 0.19/0.49 # Factorizations : 0
% 0.19/0.49 # NegExts : 0
% 0.19/0.49 # Equation resolutions : 0
% 0.19/0.49 # Disequality decompositions : 0
% 0.19/0.49 # Total rewrite steps : 36
% 0.19/0.49 # ...of those cached : 11
% 0.19/0.49 # Propositional unsat checks : 0
% 0.19/0.49 # Propositional check models : 0
% 0.19/0.49 # Propositional check unsatisfiable : 0
% 0.19/0.49 # Propositional clauses : 0
% 0.19/0.49 # Propositional clauses after purity: 0
% 0.19/0.49 # Propositional unsat core size : 0
% 0.19/0.49 # Propositional preprocessing time : 0.000
% 0.19/0.49 # Propositional encoding time : 0.000
% 0.19/0.49 # Propositional solver time : 0.000
% 0.19/0.49 # Success case prop preproc time : 0.000
% 0.19/0.49 # Success case prop encoding time : 0.000
% 0.19/0.49 # Success case prop solver time : 0.000
% 0.19/0.49 # Current number of processed clauses : 6
% 0.19/0.49 # Positive orientable unit clauses : 6
% 0.19/0.49 # Positive unorientable unit clauses: 0
% 0.19/0.49 # Negative unit clauses : 0
% 0.19/0.49 # Non-unit-clauses : 0
% 0.19/0.49 # Current number of unprocessed clauses: 8
% 0.19/0.49 # ...number of literals in the above : 8
% 0.19/0.49 # Current number of archived formulas : 0
% 0.19/0.49 # Current number of archived clauses : 8
% 0.19/0.49 # Clause-clause subsumption calls (NU) : 0
% 0.19/0.49 # Rec. Clause-clause subsumption calls : 0
% 0.19/0.49 # Non-unit clause-clause subsumptions : 0
% 0.19/0.49 # Unit Clause-clause subsumption calls : 0
% 0.19/0.49 # Rewrite failures with RHS unbound : 0
% 0.19/0.49 # BW rewrite match attempts : 3
% 0.19/0.49 # BW rewrite match successes : 3
% 0.19/0.49 # Condensation attempts : 0
% 0.19/0.49 # Condensation successes : 0
% 0.19/0.49 # Termbank termtop insertions : 877
% 0.19/0.49 # Search garbage collected termcells : 180
% 0.19/0.49
% 0.19/0.49 # -------------------------------------------------
% 0.19/0.49 # User time : 0.004 s
% 0.19/0.49 # System time : 0.002 s
% 0.19/0.49 # Total time : 0.006 s
% 0.19/0.49 # Maximum resident set size: 1764 pages
% 0.19/0.49
% 0.19/0.49 # -------------------------------------------------
% 0.19/0.49 # User time : 0.012 s
% 0.19/0.49 # System time : 0.007 s
% 0.19/0.49 # Total time : 0.020 s
% 0.19/0.49 # Maximum resident set size: 1728 pages
% 0.19/0.49 % E---3.1 exiting
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------