TSTP Solution File: PHI004^4 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : PHI004^4 : TPTP v8.2.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n027.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 02:18:06 EDT 2024
% Result : Theorem 0.20s 0.53s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 41 ( 7 unt; 11 typ; 0 def)
% Number of atoms : 73 ( 2 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 328 ( 35 ~; 32 |; 9 &; 241 @)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 78 ( 78 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 3 con; 0-5 aty)
% Number of variables : 80 ( 13 ^ 67 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
qML_mu: $tType ).
thf(decl_sort2,type,
qML_i: $tType ).
thf(decl_22,type,
scott_G: qML_mu > qML_i > $o ).
thf(decl_24,type,
scott_P: ( qML_mu > qML_i > $o ) > qML_i > $o ).
thf(decl_25,type,
scott_ess_QML_mu: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > $o ).
thf(decl_26,type,
epred1_2: qML_mu > qML_i > qML_mu > qML_i > $o ).
thf(decl_28,type,
epred2_3: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > qML_mu > qML_i > $o ).
thf(decl_29,type,
esk2_3: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > qML_i ).
thf(decl_30,type,
esk3_3: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > qML_mu ).
thf(decl_36,type,
esk8_0: qML_i ).
thf(decl_37,type,
esk9_0: qML_mu ).
thf(fact_0_G__def,axiom,
( scott_G
= ( ^ [X1: qML_mu,X2: qML_i] :
! [X3: qML_mu > qML_i > $o] :
( ( scott_P @ X3 @ X2 )
=> ( X3 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_G__def) ).
thf(fact_5_A1b,axiom,
! [X4: qML_i,X7: qML_mu > qML_i > $o] :
( ~ ( scott_P @ X7 @ X4 )
=> ( scott_P
@ ^ [X12: qML_mu,X13: qML_i] :
~ ( X7 @ X12 @ X13 )
@ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_A1b) ).
thf(conj_0,conjecture,
! [X19: qML_i,X6: qML_mu] :
( ~ ( scott_G @ X6 @ X19 )
| ( scott_ess_QML_mu @ scott_G @ X6 @ X19 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(fact_4_ess__def,axiom,
( scott_ess_QML_mu
= ( ^ [X9: qML_mu > qML_i > $o,X1: qML_mu,X2: qML_i] :
( ( X9 @ X1 @ X2 )
& ! [X3: qML_mu > qML_i > $o] :
( ( X3 @ X1 @ X2 )
=> ! [X10: qML_i,X11: qML_mu] :
( ( X9 @ X11 @ X10 )
=> ( X3 @ X11 @ X10 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_ess__def) ).
thf(fact_2_A4,axiom,
! [X4: qML_i,X7: qML_mu > qML_i > $o] :
( ( scott_P @ X7 @ X4 )
=> ! [X8: qML_i] : ( scott_P @ X7 @ X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_A4) ).
thf(c_0_5,plain,
! [X39: qML_mu,X40: qML_i] :
( ( scott_G @ X39 @ X40 )
<=> ! [X3: qML_mu > qML_i > $o] :
( ( scott_P @ X3 @ X40 )
=> ( X3 @ X39 @ X40 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_0_G__def])]) ).
thf(c_0_6,plain,
! [X4: qML_i,X7: qML_mu > qML_i > $o] :
( ~ ( scott_P @ X7 @ X4 )
=> ( scott_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X7 @ Z0 @ Z1 )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_5_A1b])]) ).
thf(c_0_7,plain,
! [X46: qML_mu,X47: qML_i,X48: qML_mu > qML_i > $o,X49: qML_mu,X50: qML_i] :
( ( ~ ( scott_G @ X46 @ X47 )
| ~ ( scott_P @ X48 @ X47 )
| ( X48 @ X46 @ X47 ) )
& ( ( scott_P @ ( epred1_2 @ X49 @ X50 ) @ X50 )
| ( scott_G @ X49 @ X50 ) )
& ( ~ ( epred1_2 @ X49 @ X50 @ X49 @ X50 )
| ( scott_G @ X49 @ X50 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])])])]) ).
thf(c_0_8,plain,
! [X70: qML_i,X71: qML_mu > qML_i > $o] :
( ( scott_P @ X71 @ X70 )
| ( scott_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X71 @ Z0 @ Z1 )
@ X70 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).
thf(c_0_9,negated_conjecture,
~ ! [X19: qML_i,X6: qML_mu] :
( ~ ( scott_G @ X6 @ X19 )
| ( scott_ess_QML_mu @ scott_G @ X6 @ X19 ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
thf(c_0_10,plain,
! [X41: qML_mu > qML_i > $o,X42: qML_mu,X43: qML_i] :
( ( scott_ess_QML_mu @ X41 @ X42 @ X43 )
<=> ( ( X41 @ X42 @ X43 )
& ! [X3: qML_mu > qML_i > $o] :
( ( X3 @ X42 @ X43 )
=> ! [X10: qML_i,X11: qML_mu] :
( ( X41 @ X11 @ X10 )
=> ( X3 @ X11 @ X10 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_4_ess__def])]) ).
thf(c_0_11,plain,
! [X1: qML_mu,X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( X3 @ X1 @ X2 )
| ~ ( scott_G @ X1 @ X2 )
| ~ ( scott_P @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,plain,
! [X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( scott_P @ X3 @ X2 )
| ( scott_P
@ ^ [Z0: qML_mu,Z1: qML_i] :
~ ( X3 @ Z0 @ Z1 )
@ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,negated_conjecture,
( ( scott_G @ esk9_0 @ esk8_0 )
& ~ ( scott_ess_QML_mu @ scott_G @ esk9_0 @ esk8_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
thf(c_0_14,plain,
! [X58: qML_mu > qML_i > $o,X59: qML_mu,X60: qML_i,X61: qML_mu > qML_i > $o,X62: qML_i,X63: qML_mu,X64: qML_mu > qML_i > $o,X65: qML_mu,X66: qML_i] :
( ( ( X58 @ X59 @ X60 )
| ~ ( scott_ess_QML_mu @ X58 @ X59 @ X60 ) )
& ( ~ ( X61 @ X59 @ X60 )
| ~ ( X58 @ X63 @ X62 )
| ( X61 @ X63 @ X62 )
| ~ ( scott_ess_QML_mu @ X58 @ X59 @ X60 ) )
& ( ( epred2_3 @ X64 @ X65 @ X66 @ X65 @ X66 )
| ~ ( X64 @ X65 @ X66 )
| ( scott_ess_QML_mu @ X64 @ X65 @ X66 ) )
& ( ( X64 @ ( esk3_3 @ X64 @ X65 @ X66 ) @ ( esk2_3 @ X64 @ X65 @ X66 ) )
| ~ ( X64 @ X65 @ X66 )
| ( scott_ess_QML_mu @ X64 @ X65 @ X66 ) )
& ( ~ ( epred2_3 @ X64 @ X65 @ X66 @ ( esk3_3 @ X64 @ X65 @ X66 ) @ ( esk2_3 @ X64 @ X65 @ X66 ) )
| ~ ( X64 @ X65 @ X66 )
| ( scott_ess_QML_mu @ X64 @ X65 @ X66 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])])])]) ).
thf(c_0_15,plain,
! [X1: qML_mu,X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( scott_P @ X3 @ X2 )
| ~ ( scott_G @ X1 @ X2 )
| ~ ( X3 @ X1 @ X2 ) ),
inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12])]) ).
thf(c_0_16,negated_conjecture,
scott_G @ esk9_0 @ esk8_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,plain,
! [X1: qML_mu,X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( epred2_3 @ X3 @ X1 @ X2 @ X1 @ X2 )
| ( scott_ess_QML_mu @ X3 @ X1 @ X2 )
| ~ ( X3 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_18,negated_conjecture,
~ ( scott_ess_QML_mu @ scott_G @ esk9_0 @ esk8_0 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_19,plain,
! [X54: qML_i,X55: qML_mu > qML_i > $o,X56: qML_i] :
( ~ ( scott_P @ X55 @ X54 )
| ( scott_P @ X55 @ X56 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2_A4])])])]) ).
thf(c_0_20,negated_conjecture,
! [X3: qML_mu > qML_i > $o] :
( ( scott_P @ X3 @ esk8_0 )
| ~ ( X3 @ esk9_0 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_21,negated_conjecture,
epred2_3 @ scott_G @ esk9_0 @ esk8_0 @ esk9_0 @ esk8_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_16]),c_0_18]) ).
thf(c_0_22,plain,
! [X4: qML_i,X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( scott_P @ X3 @ X4 )
| ~ ( scott_P @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_23,negated_conjecture,
scott_P @ ( epred2_3 @ scott_G @ esk9_0 @ esk8_0 ) @ esk8_0,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_24,negated_conjecture,
! [X2: qML_i] : ( scott_P @ ( epred2_3 @ scott_G @ esk9_0 @ esk8_0 ) @ X2 ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_25,plain,
! [X1: qML_mu,X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( scott_ess_QML_mu @ X3 @ X1 @ X2 )
| ~ ( epred2_3 @ X3 @ X1 @ X2 @ ( esk3_3 @ X3 @ X1 @ X2 ) @ ( esk2_3 @ X3 @ X1 @ X2 ) )
| ~ ( X3 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_26,negated_conjecture,
! [X1: qML_mu,X2: qML_i] :
( ( epred2_3 @ scott_G @ esk9_0 @ esk8_0 @ X1 @ X2 )
| ~ ( scott_G @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_24]) ).
thf(c_0_27,plain,
! [X1: qML_mu,X3: qML_mu > qML_i > $o,X2: qML_i] :
( ( X3 @ ( esk3_3 @ X3 @ X1 @ X2 ) @ ( esk2_3 @ X3 @ X1 @ X2 ) )
| ( scott_ess_QML_mu @ X3 @ X1 @ X2 )
| ~ ( X3 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_28,negated_conjecture,
~ ( scott_G @ ( esk3_3 @ scott_G @ esk9_0 @ esk8_0 ) @ ( esk2_3 @ scott_G @ esk9_0 @ esk8_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_16])]),c_0_18]) ).
thf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_16]),c_0_28]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PHI004^4 : TPTP v8.2.0. Released v6.4.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat May 18 14:43:52 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.49 Running higher-order theorem proving
% 0.20/0.49 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
% 0.20/0.53 # Version: 3.1.0-ho
% 0.20/0.53 # Preprocessing class: HSMSSMSSSSMNHSA.
% 0.20/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.20/0.53 # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.20/0.53 # Starting ehoh_best_nonlift_nonlambdatoforall with 300s (1) cores
% 0.20/0.53 # Starting ehoh_best8_lambda with 300s (1) cores
% 0.20/0.53 # ehoh_best_nonlift_rwall with pid 10659 completed with status 0
% 0.20/0.53 # Result found by ehoh_best_nonlift_rwall
% 0.20/0.53 # Preprocessing class: HSMSSMSSSSMNHSA.
% 0.20/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.20/0.53 # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.20/0.53 # No SInE strategy applied
% 0.20/0.53 # Search class: HGHNS-FFSF32-MHSFFSBN
% 0.20/0.53 # partial match(2): HGHNS-FFMF32-SHSFFSBN
% 0.20/0.53 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.53 # Starting ho_unfolding_3 with 181s (1) cores
% 0.20/0.53 # ho_unfolding_3 with pid 10664 completed with status 0
% 0.20/0.53 # Result found by ho_unfolding_3
% 0.20/0.53 # Preprocessing class: HSMSSMSSSSMNHSA.
% 0.20/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.20/0.53 # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.20/0.53 # No SInE strategy applied
% 0.20/0.53 # Search class: HGHNS-FFSF32-MHSFFSBN
% 0.20/0.53 # partial match(2): HGHNS-FFMF32-SHSFFSBN
% 0.20/0.53 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.53 # Starting ho_unfolding_3 with 181s (1) cores
% 0.20/0.53 # Preprocessing time : 0.001 s
% 0.20/0.53 # Presaturation interreduction done
% 0.20/0.53
% 0.20/0.53 # Proof found!
% 0.20/0.53 # SZS status Theorem
% 0.20/0.53 # SZS output start CNFRefutation
% See solution above
% 0.20/0.53 # Parsed axioms : 17
% 0.20/0.53 # Removed by relevancy pruning/SinE : 0
% 0.20/0.53 # Initial clauses : 27
% 0.20/0.53 # Removed in clause preprocessing : 6
% 0.20/0.53 # Initial clauses in saturation : 21
% 0.20/0.53 # Processed clauses : 138
% 0.20/0.53 # ...of these trivial : 0
% 0.20/0.53 # ...subsumed : 7
% 0.20/0.53 # ...remaining for further processing : 131
% 0.20/0.53 # Other redundant clauses eliminated : 9
% 0.20/0.53 # Clauses deleted for lack of memory : 0
% 0.20/0.53 # Backward-subsumed : 6
% 0.20/0.53 # Backward-rewritten : 1
% 0.20/0.53 # Generated clauses : 266
% 0.20/0.53 # ...of the previous two non-redundant : 217
% 0.20/0.53 # ...aggressively subsumed : 0
% 0.20/0.53 # Contextual simplify-reflections : 0
% 0.20/0.53 # Paramodulations : 162
% 0.20/0.53 # Factorizations : 0
% 0.20/0.53 # NegExts : 51
% 0.20/0.53 # Equation resolutions : 11
% 0.20/0.53 # Disequality decompositions : 0
% 0.20/0.53 # Total rewrite steps : 21
% 0.20/0.53 # ...of those cached : 12
% 0.20/0.53 # Propositional unsat checks : 0
% 0.20/0.53 # Propositional check models : 0
% 0.20/0.53 # Propositional check unsatisfiable : 0
% 0.20/0.53 # Propositional clauses : 0
% 0.20/0.53 # Propositional clauses after purity: 0
% 0.20/0.53 # Propositional unsat core size : 0
% 0.20/0.53 # Propositional preprocessing time : 0.000
% 0.20/0.53 # Propositional encoding time : 0.000
% 0.20/0.53 # Propositional solver time : 0.000
% 0.20/0.53 # Success case prop preproc time : 0.000
% 0.20/0.53 # Success case prop encoding time : 0.000
% 0.20/0.53 # Success case prop solver time : 0.000
% 0.20/0.53 # Current number of processed clauses : 88
% 0.20/0.53 # Positive orientable unit clauses : 6
% 0.20/0.53 # Positive unorientable unit clauses: 0
% 0.20/0.53 # Negative unit clauses : 12
% 0.20/0.53 # Non-unit-clauses : 70
% 0.20/0.53 # Current number of unprocessed clauses: 97
% 0.20/0.53 # ...number of literals in the above : 248
% 0.20/0.53 # Current number of archived formulas : 0
% 0.20/0.53 # Current number of archived clauses : 43
% 0.20/0.53 # Clause-clause subsumption calls (NU) : 392
% 0.20/0.53 # Rec. Clause-clause subsumption calls : 301
% 0.20/0.53 # Non-unit clause-clause subsumptions : 13
% 0.20/0.53 # Unit Clause-clause subsumption calls : 27
% 0.20/0.53 # Rewrite failures with RHS unbound : 0
% 0.20/0.53 # BW rewrite match attempts : 1
% 0.20/0.53 # BW rewrite match successes : 1
% 0.20/0.53 # Condensation attempts : 138
% 0.20/0.53 # Condensation successes : 0
% 0.20/0.53 # Termbank termtop insertions : 8598
% 0.20/0.53 # Search garbage collected termcells : 601
% 0.20/0.53
% 0.20/0.53 # -------------------------------------------------
% 0.20/0.53 # User time : 0.019 s
% 0.20/0.53 # System time : 0.001 s
% 0.20/0.53 # Total time : 0.020 s
% 0.20/0.53 # Maximum resident set size: 1888 pages
% 0.20/0.53
% 0.20/0.53 # -------------------------------------------------
% 0.20/0.53 # User time : 0.020 s
% 0.20/0.53 # System time : 0.004 s
% 0.20/0.53 # Total time : 0.024 s
% 0.20/0.53 # Maximum resident set size: 1744 pages
% 0.20/0.53 % E---3.1 exiting
% 0.20/0.53 % E exiting
%------------------------------------------------------------------------------