TSTP Solution File: NUM683^4 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM683^4 : TPTP v8.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n016.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 01:15:33 EDT 2024
% Result : Theorem 0.62s 0.56s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 25
% Syntax : Number of formulae : 50 ( 20 unt; 15 typ; 0 def)
% Number of atoms : 127 ( 23 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 280 ( 15 ~; 12 |; 4 &; 234 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 69 ( 48 ^ 21 !; 0 ?; 69 :)
% 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_72,type,
l_some: $i > ( $i > $o ) > $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_127,type,
n_some: ( $i > $o ) > $o ).
thf(decl_142,type,
n_pl: $i > $i > $i ).
thf(decl_147,type,
diffprop: $i > $i > $i > $o ).
thf(decl_148,type,
d_29_ii: $i > $i > $o ).
thf(decl_149,type,
iii: $i > $i > $o ).
thf(decl_155,type,
esk1_0: $i ).
thf(decl_156,type,
esk2_0: $i ).
thf(decl_157,type,
esk3_0: $i ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_d_29_ii) ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X3: $i > $o,X2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ X3 )
=> ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_is_of) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_e_is) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_n_some) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_n_is) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_iii) ).
thf(satz20d,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X301: $i] : ( in @ X301 @ nat )
@ ^ [X302: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( d_29_ii @ ( n_pl @ X4 @ X1 ) @ ( n_pl @ X4 @ X302 ) )
=> ( d_29_ii @ X1 @ X302 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz20d) ).
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/sandbox/benchmark/theBenchmark.p',satz6) ).
thf(satz20c,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X299: $i] : ( in @ X299 @ nat )
@ ^ [X300: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( iii @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X300 @ X4 ) )
=> ( iii @ X1 @ X300 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz20c) ).
thf(c_0_10,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_11,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_12,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_13,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_14,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_10,def_n_some]) ).
thf(c_0_15,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_13]) ).
thf(c_0_17,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_18,negated_conjecture,
~ ! [X372: $i] :
( ( in @ X372 @ nat )
=> ! [X371: $i] :
( ( in @ X371 @ nat )
=> ! [X370: $i] :
( ( in @ X370 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ ( n_pl @ X370 @ X372 ) @ ( n_pl @ X370 @ X371 ) ) )
=> ( l_some @ nat @ ( diffprop @ X372 @ X371 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz20d])]),c_0_14]),c_0_15]) ).
thf(c_0_19,plain,
! [X387: $i] :
( ( in @ X387 @ nat )
=> ! [X386: $i] :
( ( in @ X386 @ nat )
=> ( ( n_pl @ X387 @ X386 )
= ( n_pl @ X386 @ X387 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz6]),c_0_15]),c_0_16]) ).
thf(c_0_20,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_17,def_n_some]) ).
thf(c_0_21,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( in @ esk3_0 @ nat )
& ( l_some @ nat @ ( diffprop @ ( n_pl @ esk3_0 @ esk1_0 ) @ ( n_pl @ esk3_0 @ esk2_0 ) ) )
& ~ ( l_some @ nat @ ( diffprop @ 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_18])])])]) ).
thf(c_0_22,plain,
! [X555: $i,X556: $i] :
( ~ ( in @ X555 @ nat )
| ~ ( in @ X556 @ nat )
| ( ( n_pl @ X555 @ X556 )
= ( n_pl @ X556 @ X555 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
thf(c_0_23,plain,
! [X477: $i] :
( ( in @ X477 @ nat )
=> ! [X476: $i] :
( ( in @ X476 @ nat )
=> ! [X475: $i] :
( ( in @ X475 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ ( n_pl @ X476 @ X475 ) @ ( n_pl @ X477 @ X475 ) ) )
=> ( l_some @ nat @ ( diffprop @ X476 @ X477 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz20c]),c_0_20]),c_0_15]) ).
thf(c_0_24,negated_conjecture,
l_some @ nat @ ( diffprop @ ( n_pl @ esk3_0 @ esk1_0 ) @ ( n_pl @ esk3_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_25,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_22]) ).
thf(c_0_26,negated_conjecture,
in @ esk3_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_27,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_28,plain,
! [X640: $i,X641: $i,X642: $i] :
( ~ ( in @ X640 @ nat )
| ~ ( in @ X641 @ nat )
| ~ ( in @ X642 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ X641 @ X642 ) @ ( n_pl @ X640 @ X642 ) ) )
| ( l_some @ nat @ ( diffprop @ X641 @ X640 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).
thf(c_0_29,negated_conjecture,
l_some @ nat @ ( diffprop @ ( 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_24,c_0_25]),c_0_26]),c_0_27])]) ).
thf(c_0_30,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_31,plain,
! [X1: $i,X4: $i,X5: $i] :
( ( l_some @ nat @ ( diffprop @ X4 @ X1 ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ X4 @ X5 ) @ ( n_pl @ X1 @ X5 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_32,negated_conjecture,
l_some @ nat @ ( diffprop @ ( n_pl @ esk1_0 @ esk3_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_29,c_0_25]),c_0_30]),c_0_26])]) ).
thf(c_0_33,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_26]),c_0_30]),c_0_27])]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM683^4 : TPTP v8.2.0. Released v7.1.0.
% 0.06/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon May 20 05:35:53 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.20/0.47 Running higher-order theorem proving
% 0.20/0.47 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
% 0.62/0.56 # Version: 3.1.0-ho
% 0.62/0.56 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.62/0.56 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.62/0.56 # Starting lpo1_fix with 900s (3) cores
% 0.62/0.56 # Starting full_lambda_9 with 300s (1) cores
% 0.62/0.56 # Starting almost_fo_4 with 300s (1) cores
% 0.62/0.56 # Starting new_ho_9 with 300s (1) cores
% 0.62/0.56 # Starting pre_casc_4 with 300s (1) cores
% 0.62/0.56 # Starting ho_unfolding_6 with 300s (1) cores
% 0.62/0.56 # full_lambda_9 with pid 20687 completed with status 0
% 0.62/0.56 # Result found by full_lambda_9
% 0.62/0.56 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.62/0.56 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.62/0.56 # Starting lpo1_fix with 900s (3) cores
% 0.62/0.56 # Starting full_lambda_9 with 300s (1) cores
% 0.62/0.56 # SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.62/0.56 # Search class: HGHSM-FSLM32-DHSMMSBN
% 0.62/0.56 # partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.62/0.56 # Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.62/0.56 # Starting full_lambda_5 with 25s (1) cores
% 0.62/0.56 # full_lambda_5 with pid 20692 completed with status 0
% 0.62/0.56 # Result found by full_lambda_5
% 0.62/0.56 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.62/0.56 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.62/0.56 # Starting lpo1_fix with 900s (3) cores
% 0.62/0.56 # Starting full_lambda_9 with 300s (1) cores
% 0.62/0.56 # SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.62/0.56 # Search class: HGHSM-FSLM32-DHSMMSBN
% 0.62/0.56 # partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.62/0.56 # Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.62/0.56 # Starting full_lambda_5 with 25s (1) cores
% 0.62/0.56 # Preprocessing time : 0.005 s
% 0.62/0.56 # Presaturation interreduction done
% 0.62/0.56
% 0.62/0.56 # Proof found!
% 0.62/0.56 # SZS status Theorem
% 0.62/0.56 # SZS output start CNFRefutation
% See solution above
% 0.62/0.56 # Parsed axioms : 386
% 0.62/0.56 # Removed by relevancy pruning/SinE : 263
% 0.62/0.56 # Initial clauses : 332
% 0.62/0.56 # Removed in clause preprocessing : 174
% 0.62/0.56 # Initial clauses in saturation : 158
% 0.62/0.56 # Processed clauses : 303
% 0.62/0.56 # ...of these trivial : 10
% 0.62/0.56 # ...subsumed : 64
% 0.62/0.56 # ...remaining for further processing : 229
% 0.62/0.56 # Other redundant clauses eliminated : 20
% 0.62/0.56 # Clauses deleted for lack of memory : 0
% 0.62/0.56 # Backward-subsumed : 0
% 0.62/0.56 # Backward-rewritten : 0
% 0.62/0.56 # Generated clauses : 412
% 0.62/0.56 # ...of the previous two non-redundant : 390
% 0.62/0.56 # ...aggressively subsumed : 0
% 0.62/0.56 # Contextual simplify-reflections : 1
% 0.62/0.56 # Paramodulations : 310
% 0.62/0.56 # Factorizations : 2
% 0.62/0.56 # NegExts : 2
% 0.62/0.56 # Equation resolutions : 24
% 0.62/0.56 # Disequality decompositions : 0
% 0.62/0.56 # Total rewrite steps : 107
% 0.62/0.56 # ...of those cached : 90
% 0.62/0.56 # Propositional unsat checks : 0
% 0.62/0.56 # Propositional check models : 0
% 0.62/0.56 # Propositional check unsatisfiable : 0
% 0.62/0.56 # Propositional clauses : 0
% 0.62/0.56 # Propositional clauses after purity: 0
% 0.62/0.56 # Propositional unsat core size : 0
% 0.62/0.56 # Propositional preprocessing time : 0.000
% 0.62/0.56 # Propositional encoding time : 0.000
% 0.62/0.56 # Propositional solver time : 0.000
% 0.62/0.56 # Success case prop preproc time : 0.000
% 0.62/0.56 # Success case prop encoding time : 0.000
% 0.62/0.56 # Success case prop solver time : 0.000
% 0.62/0.56 # Current number of processed clauses : 110
% 0.62/0.56 # Positive orientable unit clauses : 22
% 0.62/0.56 # Positive unorientable unit clauses: 0
% 0.62/0.56 # Negative unit clauses : 7
% 0.62/0.56 # Non-unit-clauses : 81
% 0.62/0.56 # Current number of unprocessed clauses: 333
% 0.62/0.56 # ...number of literals in the above : 1348
% 0.62/0.56 # Current number of archived formulas : 0
% 0.62/0.56 # Current number of archived clauses : 107
% 0.62/0.56 # Clause-clause subsumption calls (NU) : 2891
% 0.62/0.56 # Rec. Clause-clause subsumption calls : 820
% 0.62/0.56 # Non-unit clause-clause subsumptions : 62
% 0.62/0.56 # Unit Clause-clause subsumption calls : 30
% 0.62/0.56 # Rewrite failures with RHS unbound : 0
% 0.62/0.56 # BW rewrite match attempts : 13
% 0.62/0.56 # BW rewrite match successes : 0
% 0.62/0.56 # Condensation attempts : 0
% 0.62/0.56 # Condensation successes : 0
% 0.62/0.56 # Termbank termtop insertions : 52305
% 0.62/0.56 # Search garbage collected termcells : 15367
% 0.62/0.56
% 0.62/0.56 # -------------------------------------------------
% 0.62/0.56 # User time : 0.058 s
% 0.62/0.56 # System time : 0.013 s
% 0.62/0.56 # Total time : 0.071 s
% 0.62/0.56 # Maximum resident set size: 4612 pages
% 0.62/0.56
% 0.62/0.56 # -------------------------------------------------
% 0.62/0.56 # User time : 0.070 s
% 0.62/0.56 # System time : 0.015 s
% 0.62/0.56 # Total time : 0.085 s
% 0.62/0.56 # Maximum resident set size: 2344 pages
% 0.62/0.56 % E---3.1 exiting
% 0.62/0.57 % E exiting
%------------------------------------------------------------------------------