TSTP Solution File: NUM684^4 by E---3.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : NUM684^4 : TPTP v8.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n028.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 12:36:41 EDT 2024
% Result : Theorem 0.53s 0.57s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 92 ( 35 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 223 ( 17 ~; 14 |; 4 &; 173 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 58 ( 36 ^ 22 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
is_of: $i > ( $i > $o ) > $o ).
thf(decl_23,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_25,type,
in: $i > $i > $o ).
thf(decl_77,type,
e_is: $i > $i > $i > $o ).
thf(decl_123,type,
nat: $i ).
thf(decl_124,type,
n_is: $i > $i > $o ).
thf(decl_142,type,
n_pl: $i > $i > $i ).
thf(decl_153,type,
esk1_0: $i ).
thf(decl_154,type,
esk2_0: $i ).
thf(decl_155,type,
esk3_0: $i ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X3: $i > $o,X2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ X3 )
=> ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LM0G12S5lG/E---3.1_15840.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LM0G12S5lG/E---3.1_15840.p',def_is_of) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LM0G12S5lG/E---3.1_15840.p',def_e_is) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LM0G12S5lG/E---3.1_15840.p',def_n_is) ).
thf(satz20e,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X303: $i] : ( in @ X303 @ nat )
@ ^ [X304: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( n_is @ ( n_pl @ X4 @ X1 ) @ ( n_pl @ X4 @ X304 ) )
=> ( n_is @ X1 @ X304 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LM0G12S5lG/E---3.1_15840.p',satz20e) ).
thf(satz6,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X197: $i] : ( in @ X197 @ nat )
@ ^ [X198: $i] : ( n_is @ ( n_pl @ X1 @ X198 ) @ ( n_pl @ X198 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LM0G12S5lG/E---3.1_15840.p',satz6) ).
thf(satz8a,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X205: $i] : ( in @ X205 @ nat )
@ ^ [X206: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( n_is @ ( n_pl @ X1 @ X206 ) @ ( n_pl @ X1 @ X4 ) )
=> ( n_is @ X206 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LM0G12S5lG/E---3.1_15840.p',satz8a) ).
thf(c_0_7,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_all_of]) ).
thf(c_0_8,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_9,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_10,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_11,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_9]) ).
thf(c_0_12,negated_conjecture,
~ ! [X392: $i] :
( ( in @ X392 @ nat )
=> ! [X391: $i] :
( ( in @ X391 @ nat )
=> ! [X390: $i] :
( ( in @ X390 @ nat )
=> ( ( ( n_pl @ X390 @ X392 )
= ( n_pl @ X390 @ X391 ) )
=> ( X392 = X391 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz20e])]),c_0_10]),c_0_11]) ).
thf(c_0_13,plain,
! [X397: $i] :
( ( in @ X397 @ nat )
=> ! [X396: $i] :
( ( in @ X396 @ nat )
=> ( ( n_pl @ X397 @ X396 )
= ( n_pl @ X396 @ X397 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz6]),c_0_10]),c_0_11]) ).
thf(c_0_14,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( in @ esk3_0 @ nat )
& ( ( n_pl @ esk3_0 @ esk1_0 )
= ( n_pl @ esk3_0 @ esk2_0 ) )
& ( esk1_0 != esk2_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
thf(c_0_15,plain,
! [X476: $i,X477: $i] :
( ~ ( in @ X476 @ nat )
| ~ ( in @ X477 @ nat )
| ( ( n_pl @ X476 @ X477 )
= ( n_pl @ X477 @ X476 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
thf(c_0_16,negated_conjecture,
( ( n_pl @ esk3_0 @ esk1_0 )
= ( n_pl @ esk3_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_17,plain,
! [X1: $i,X4: $i] :
( ( ( n_pl @ X1 @ X4 )
= ( n_pl @ X4 @ X1 ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_18,negated_conjecture,
in @ esk3_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_19,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_20,plain,
! [X400: $i] :
( ( in @ X400 @ nat )
=> ! [X399: $i] :
( ( in @ X399 @ nat )
=> ! [X398: $i] :
( ( in @ X398 @ nat )
=> ( ( ( n_pl @ X400 @ X399 )
= ( n_pl @ X400 @ X398 ) )
=> ( X399 = X398 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz8a]),c_0_10]),c_0_11]) ).
thf(c_0_21,negated_conjecture,
( ( n_pl @ esk3_0 @ esk1_0 )
= ( n_pl @ esk2_0 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19])]) ).
thf(c_0_22,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_23,plain,
! [X478: $i,X479: $i,X480: $i] :
( ~ ( in @ X478 @ nat )
| ~ ( in @ X479 @ nat )
| ~ ( in @ X480 @ nat )
| ( ( n_pl @ X478 @ X479 )
!= ( n_pl @ X478 @ X480 ) )
| ( X479 = X480 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
thf(c_0_24,negated_conjecture,
( ( n_pl @ esk3_0 @ esk2_0 )
= ( n_pl @ esk2_0 @ esk3_0 ) ),
inference(rw,[status(thm)],[c_0_16,c_0_21]) ).
thf(c_0_25,negated_conjecture,
( ( n_pl @ esk2_0 @ esk3_0 )
= ( n_pl @ esk1_0 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_21]),c_0_22]),c_0_18])]) ).
thf(c_0_26,plain,
! [X1: $i,X4: $i,X5: $i] :
( ( X4 = X5 )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat )
| ( ( n_pl @ X1 @ X4 )
!= ( n_pl @ X1 @ X5 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_27,negated_conjecture,
( ( n_pl @ esk3_0 @ esk2_0 )
= ( n_pl @ esk1_0 @ esk3_0 ) ),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_28,negated_conjecture,
! [X1: $i] :
( ( X1 = esk2_0 )
| ( ( n_pl @ esk3_0 @ X1 )
!= ( n_pl @ esk1_0 @ esk3_0 ) )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_19]),c_0_18])]) ).
thf(c_0_29,negated_conjecture,
( ( n_pl @ esk3_0 @ esk1_0 )
= ( n_pl @ esk1_0 @ esk3_0 ) ),
inference(rw,[status(thm)],[c_0_21,c_0_25]) ).
thf(c_0_30,negated_conjecture,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_22])]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM684^4 : TPTP v8.2.0. Released v7.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Jun 22 23:56:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.21/0.51 Running higher-order theorem proving
% 0.21/0.51 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.LM0G12S5lG/E---3.1_15840.p
% 0.53/0.57 # Version: 3.2.0-ho
% 0.53/0.57 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.53/0.57 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.57 # Starting lpo1_fix with 900s (3) cores
% 0.53/0.57 # Starting full_lambda_9 with 300s (1) cores
% 0.53/0.57 # Starting almost_fo_4 with 300s (1) cores
% 0.53/0.57 # Starting new_ho_9 with 300s (1) cores
% 0.53/0.57 # Starting pre_casc_4 with 300s (1) cores
% 0.53/0.57 # Starting ho_unfolding_6 with 300s (1) cores
% 0.53/0.57 # pre_casc_4 with pid 15922 completed with status 0
% 0.53/0.57 # Result found by pre_casc_4
% 0.53/0.57 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.53/0.57 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.57 # Starting lpo1_fix with 900s (3) cores
% 0.53/0.57 # Starting full_lambda_9 with 300s (1) cores
% 0.53/0.57 # Starting almost_fo_4 with 300s (1) cores
% 0.53/0.57 # Starting new_ho_9 with 300s (1) cores
% 0.53/0.57 # Starting pre_casc_4 with 300s (1) cores
% 0.53/0.57 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.53/0.57 # Search class: HGUSM-FFMM31-DHSMMSBN
% 0.53/0.57 # partial match(3): HGHSM-FFMM31-SHSSMSBN
% 0.53/0.57 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.53/0.57 # Starting new_ho_10 with 163s (1) cores
% 0.53/0.57 # new_ho_10 with pid 15924 completed with status 0
% 0.53/0.57 # Result found by new_ho_10
% 0.53/0.57 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.53/0.57 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.57 # Starting lpo1_fix with 900s (3) cores
% 0.53/0.57 # Starting full_lambda_9 with 300s (1) cores
% 0.53/0.57 # Starting almost_fo_4 with 300s (1) cores
% 0.53/0.57 # Starting new_ho_9 with 300s (1) cores
% 0.53/0.57 # Starting pre_casc_4 with 300s (1) cores
% 0.53/0.57 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.53/0.57 # Search class: HGUSM-FFMM31-DHSMMSBN
% 0.53/0.57 # partial match(3): HGHSM-FFMM31-SHSSMSBN
% 0.53/0.57 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.53/0.57 # Starting new_ho_10 with 163s (1) cores
% 0.53/0.57 # Preprocessing time : 0.005 s
% 0.53/0.57 # Presaturation interreduction done
% 0.53/0.57
% 0.53/0.57 # Proof found!
% 0.53/0.57 # SZS status Theorem
% 0.53/0.57 # SZS output start CNFRefutation
% See solution above
% 0.53/0.57 # Parsed axioms : 387
% 0.53/0.57 # Removed by relevancy pruning/SinE : 314
% 0.53/0.57 # Initial clauses : 113
% 0.53/0.57 # Removed in clause preprocessing : 5
% 0.53/0.57 # Initial clauses in saturation : 108
% 0.53/0.57 # Processed clauses : 193
% 0.53/0.57 # ...of these trivial : 4
% 0.53/0.57 # ...subsumed : 14
% 0.53/0.57 # ...remaining for further processing : 175
% 0.53/0.57 # Other redundant clauses eliminated : 9
% 0.53/0.57 # Clauses deleted for lack of memory : 0
% 0.53/0.57 # Backward-subsumed : 0
% 0.53/0.57 # Backward-rewritten : 3
% 0.53/0.57 # Generated clauses : 169
% 0.53/0.57 # ...of the previous two non-redundant : 148
% 0.53/0.57 # ...aggressively subsumed : 0
% 0.53/0.57 # Contextual simplify-reflections : 0
% 0.53/0.57 # Paramodulations : 153
% 0.53/0.57 # Factorizations : 0
% 0.53/0.57 # NegExts : 0
% 0.53/0.57 # Equation resolutions : 12
% 0.53/0.57 # Disequality decompositions : 0
% 0.53/0.57 # Total rewrite steps : 90
% 0.53/0.57 # ...of those cached : 72
% 0.53/0.57 # Propositional unsat checks : 0
% 0.53/0.57 # Propositional check models : 0
% 0.53/0.57 # Propositional check unsatisfiable : 0
% 0.53/0.57 # Propositional clauses : 0
% 0.53/0.57 # Propositional clauses after purity: 0
% 0.53/0.57 # Propositional unsat core size : 0
% 0.53/0.57 # Propositional preprocessing time : 0.000
% 0.53/0.57 # Propositional encoding time : 0.000
% 0.53/0.57 # Propositional solver time : 0.000
% 0.53/0.57 # Success case prop preproc time : 0.000
% 0.53/0.57 # Success case prop encoding time : 0.000
% 0.53/0.57 # Success case prop solver time : 0.000
% 0.53/0.57 # Current number of processed clauses : 75
% 0.53/0.57 # Positive orientable unit clauses : 30
% 0.53/0.57 # Positive unorientable unit clauses: 0
% 0.53/0.57 # Negative unit clauses : 9
% 0.53/0.57 # Non-unit-clauses : 36
% 0.53/0.57 # Current number of unprocessed clauses: 153
% 0.53/0.57 # ...number of literals in the above : 571
% 0.53/0.57 # Current number of archived formulas : 0
% 0.53/0.57 # Current number of archived clauses : 99
% 0.53/0.57 # Clause-clause subsumption calls (NU) : 1108
% 0.53/0.57 # Rec. Clause-clause subsumption calls : 401
% 0.53/0.57 # Non-unit clause-clause subsumptions : 13
% 0.53/0.57 # Unit Clause-clause subsumption calls : 19
% 0.53/0.57 # Rewrite failures with RHS unbound : 0
% 0.53/0.57 # BW rewrite match attempts : 7
% 0.53/0.57 # BW rewrite match successes : 2
% 0.53/0.57 # Condensation attempts : 193
% 0.53/0.57 # Condensation successes : 0
% 0.53/0.57 # Termbank termtop insertions : 21748
% 0.53/0.57 # Search garbage collected termcells : 6420
% 0.53/0.57
% 0.53/0.57 # -------------------------------------------------
% 0.53/0.57 # User time : 0.027 s
% 0.53/0.57 # System time : 0.008 s
% 0.53/0.57 # Total time : 0.035 s
% 0.53/0.57 # Maximum resident set size: 3328 pages
% 0.53/0.57
% 0.53/0.57 # -------------------------------------------------
% 0.53/0.57 # User time : 0.036 s
% 0.53/0.57 # System time : 0.011 s
% 0.53/0.57 # Total time : 0.048 s
% 0.53/0.57 # Maximum resident set size: 2344 pages
% 0.53/0.57 % E---3.1 exiting
% 0.53/0.57 % E exiting
%------------------------------------------------------------------------------