TSTP Solution File: NUM749^4 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM749^4 : TPTP v8.1.2. 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 : Sat May 4 08:57:40 EDT 2024
% Result : Theorem 0.43s 0.71s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 32
% Syntax : Number of formulae : 54 ( 25 unt; 21 typ; 0 def)
% Number of atoms : 107 ( 22 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 321 ( 7 ~; 4 |; 2 &; 301 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 5 con; 0-3 aty)
% Number of variables : 76 ( 65 ^ 11 !; 0 ?; 76 :)
% 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_162,type,
n_ts: $i > $i > $i ).
thf(decl_189,type,
frac: $i ).
thf(decl_191,type,
num: $i > $i ).
thf(decl_192,type,
den: $i > $i ).
thf(decl_194,type,
moref: $i > $i > $o ).
thf(decl_195,type,
lessf: $i > $i > $o ).
thf(decl_198,type,
n_pf: $i > $i > $i ).
thf(decl_200,type,
esk1_0: $i ).
thf(decl_201,type,
esk2_0: $i ).
thf(def_diffprop,axiom,
( diffprop
= ( ^ [X1: $i,X207: $i,X4: $i] : ( n_is @ X1 @ ( n_pl @ X207 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5eoEMko9IO/E---3.1_8894.p',def_diffprop) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5eoEMko9IO/E---3.1_8894.p',def_iii) ).
thf(def_n_is,axiom,
( n_is
= ( e_is @ nat ) ),
file('/export/starexec/sandbox/tmp/tmp.5eoEMko9IO/E---3.1_8894.p',def_n_is) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5eoEMko9IO/E---3.1_8894.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/tmp/tmp.5eoEMko9IO/E---3.1_8894.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5eoEMko9IO/E---3.1_8894.p',def_is_of) ).
thf(def_lessf,axiom,
( lessf
= ( ^ [X1: $i,X450: $i] : ( iii @ ( n_ts @ ( num @ X1 ) @ ( den @ X450 ) ) @ ( n_ts @ ( num @ X450 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5eoEMko9IO/E---3.1_8894.p',def_lessf) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox/tmp/tmp.5eoEMko9IO/E---3.1_8894.p',def_n_some) ).
thf(def_moref,axiom,
( moref
= ( ^ [X1: $i,X449: $i] : ( d_29_ii @ ( n_ts @ ( num @ X1 ) @ ( den @ X449 ) ) @ ( n_ts @ ( num @ X449 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5eoEMko9IO/E---3.1_8894.p',def_moref) ).
thf(satz60a,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X520: $i] : ( in @ X520 @ frac )
@ ^ [X521: $i] : ( lessf @ X1 @ ( n_pf @ X1 @ X521 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5eoEMko9IO/E---3.1_8894.p',satz60a) ).
thf(satz60,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X518: $i] : ( in @ X518 @ frac )
@ ^ [X519: $i] : ( moref @ ( n_pf @ X1 @ X519 ) @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5eoEMko9IO/E---3.1_8894.p',satz60) ).
thf(c_0_11,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( e_is @ nat @ Z0 @ ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_diffprop]) ).
thf(c_0_12,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] : ( e_is @ nat @ Z1 @ ( n_pl @ Z0 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_13,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( e_is @ nat @ Z0 @ ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_11,def_n_is]) ).
thf(c_0_14,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] : ( e_is @ nat @ Z0 @ ( n_pl @ Z1 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_15,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_16,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_17,plain,
( lessf
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] : ( e_is @ nat @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lessf]) ).
thf(c_0_18,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] : ( e_is @ nat @ Z1 @ ( n_pl @ Z0 @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_12,c_0_13]),def_n_some]) ).
thf(c_0_19,plain,
( moref
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] : ( e_is @ nat @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_moref]) ).
thf(c_0_20,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] : ( e_is @ nat @ Z0 @ ( n_pl @ Z1 @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_14,c_0_13]),def_n_some]) ).
thf(c_0_21,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_22,plain,
( lessf
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] : ( e_is @ nat @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_23,plain,
( moref
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] : ( e_is @ nat @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_24,negated_conjecture,
~ ! [X560: $i] :
( ( in @ X560 @ frac )
=> ! [X559: $i] :
( ( in @ X559 @ frac )
=> ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ ( n_pf @ X560 @ X559 ) ) @ ( den @ X560 ) ) @ ( n_pl @ ( n_ts @ ( num @ X560 ) @ ( den @ ( n_pf @ X560 @ X559 ) ) ) @ Z0 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz60a])]),c_0_21]),c_0_22]) ).
thf(c_0_25,plain,
! [X584: $i] :
( ( in @ X584 @ frac )
=> ! [X583: $i] :
( ( in @ X583 @ frac )
=> ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ ( n_pf @ X584 @ X583 ) ) @ ( den @ X584 ) ) @ ( n_pl @ ( n_ts @ ( num @ X584 ) @ ( den @ ( n_pf @ X584 @ X583 ) ) ) @ Z0 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz60]),c_0_21]),c_0_23]) ).
thf(c_0_26,negated_conjecture,
( ( in @ esk1_0 @ frac )
& ( in @ esk2_0 @ frac )
& ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ ( n_pf @ esk1_0 @ esk2_0 ) ) @ ( den @ esk1_0 ) ) @ ( n_pl @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ ( n_pf @ esk1_0 @ esk2_0 ) ) ) @ Z0 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
thf(c_0_27,plain,
! [X832: $i,X833: $i] :
( ~ ( in @ X832 @ frac )
| ~ ( in @ X833 @ frac )
| ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ ( n_pf @ X832 @ X833 ) ) @ ( den @ X832 ) ) @ ( n_pl @ ( n_ts @ ( num @ X832 ) @ ( den @ ( n_pf @ X832 @ X833 ) ) ) @ Z0 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])]) ).
thf(c_0_28,negated_conjecture,
~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ ( n_pf @ esk1_0 @ esk2_0 ) ) @ ( den @ esk1_0 ) ) @ ( n_pl @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ ( n_pf @ esk1_0 @ esk2_0 ) ) ) @ Z0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_29,plain,
! [X1: $i,X4: $i] :
( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ ( n_pf @ X1 @ X4 ) ) @ ( den @ X1 ) ) @ ( n_pl @ ( n_ts @ ( num @ X1 ) @ ( den @ ( n_pf @ X1 @ X4 ) ) ) @ Z0 ) ) )
| ~ ( in @ X1 @ frac )
| ~ ( in @ X4 @ frac ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_30,negated_conjecture,
in @ esk2_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_31,negated_conjecture,
in @ esk1_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.18 % Problem : NUM749^4 : TPTP v8.1.2. Released v7.1.0.
% 0.12/0.19 % Command : run_E %s %d THM
% 0.19/0.40 % Computer : n028.cluster.edu
% 0.19/0.40 % Model : x86_64 x86_64
% 0.19/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.40 % Memory : 8042.1875MB
% 0.19/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.40 % CPULimit : 300
% 0.19/0.40 % WCLimit : 300
% 0.19/0.40 % DateTime : Fri May 3 09:49:03 EDT 2024
% 0.19/0.40 % CPUTime :
% 0.36/0.59 Running higher-order theorem proving
% 0.36/0.59 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/tmp/tmp.5eoEMko9IO/E---3.1_8894.p
% 0.43/0.71 # Version: 3.1.0-ho
% 0.43/0.71 # Preprocessing class: HSLMSMSMLLLCHSA.
% 0.43/0.71 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.71 # Starting pre_casc_4 with 1200s (4) cores
% 0.43/0.71 # Starting full_lambda_6 with 300s (1) cores
% 0.43/0.71 # Starting sh10 with 300s (1) cores
% 0.43/0.71 # Starting post_as_ho9 with 300s (1) cores
% 0.43/0.71 # Starting post_as_ho8 with 300s (1) cores
% 0.43/0.71 # pre_casc_4 with pid 9062 completed with status 0
% 0.43/0.71 # Result found by pre_casc_4
% 0.43/0.71 # Preprocessing class: HSLMSMSMLLLCHSA.
% 0.43/0.71 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.71 # Starting pre_casc_4 with 1200s (4) cores
% 0.43/0.71 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.43/0.71 # Search class: HGUSM-FSLM31-DHSMMFBN
% 0.43/0.71 # partial match(2): HGUSM-FSLM31-DHSFFFBN
% 0.43/0.71 # Scheduled 6 strats onto 4 cores with 1200 seconds (1200 total)
% 0.43/0.71 # Starting new_bool_5 with 540s (1) cores
% 0.43/0.71 # Starting pre_casc_4 with 121s (1) cores
% 0.43/0.71 # Starting ehoh_best8_lambda with 135s (1) cores
% 0.43/0.71 # Starting new_bool_1 with 135s (1) cores
% 0.43/0.71 # new_bool_5 with pid 9080 completed with status 0
% 0.43/0.71 # Result found by new_bool_5
% 0.43/0.71 # Preprocessing class: HSLMSMSMLLLCHSA.
% 0.43/0.71 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.71 # Starting pre_casc_4 with 1200s (4) cores
% 0.43/0.71 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.43/0.71 # Search class: HGUSM-FSLM31-DHSMMFBN
% 0.43/0.71 # partial match(2): HGUSM-FSLM31-DHSFFFBN
% 0.43/0.71 # Scheduled 6 strats onto 4 cores with 1200 seconds (1200 total)
% 0.43/0.71 # Starting new_bool_5 with 540s (1) cores
% 0.43/0.71 # Preprocessing time : 0.006 s
% 0.43/0.71 # Presaturation interreduction done
% 0.43/0.71
% 0.43/0.71 # Proof found!
% 0.43/0.71 # SZS status Theorem
% 0.43/0.71 # SZS output start CNFRefutation
% See solution above
% 0.43/0.71 # Parsed axioms : 581
% 0.43/0.71 # Removed by relevancy pruning/SinE : 445
% 0.43/0.71 # Initial clauses : 142
% 0.43/0.71 # Removed in clause preprocessing : 4
% 0.43/0.71 # Initial clauses in saturation : 138
% 0.43/0.71 # Processed clauses : 282
% 0.43/0.71 # ...of these trivial : 3
% 0.43/0.71 # ...subsumed : 22
% 0.43/0.71 # ...remaining for further processing : 257
% 0.43/0.71 # Other redundant clauses eliminated : 5
% 0.43/0.71 # Clauses deleted for lack of memory : 0
% 0.43/0.71 # Backward-subsumed : 0
% 0.43/0.71 # Backward-rewritten : 6
% 0.43/0.71 # Generated clauses : 225
% 0.43/0.71 # ...of the previous two non-redundant : 203
% 0.43/0.71 # ...aggressively subsumed : 0
% 0.43/0.71 # Contextual simplify-reflections : 0
% 0.43/0.71 # Paramodulations : 120
% 0.43/0.71 # Factorizations : 0
% 0.43/0.71 # NegExts : 6
% 0.43/0.71 # Equation resolutions : 7
% 0.43/0.71 # Disequality decompositions : 0
% 0.43/0.71 # Total rewrite steps : 76
% 0.43/0.71 # ...of those cached : 45
% 0.43/0.71 # Propositional unsat checks : 0
% 0.43/0.71 # Propositional check models : 0
% 0.43/0.71 # Propositional check unsatisfiable : 0
% 0.43/0.71 # Propositional clauses : 0
% 0.43/0.71 # Propositional clauses after purity: 0
% 0.43/0.71 # Propositional unsat core size : 0
% 0.43/0.71 # Propositional preprocessing time : 0.000
% 0.43/0.71 # Propositional encoding time : 0.000
% 0.43/0.71 # Propositional solver time : 0.000
% 0.43/0.71 # Success case prop preproc time : 0.000
% 0.43/0.71 # Success case prop encoding time : 0.000
% 0.43/0.71 # Success case prop solver time : 0.000
% 0.43/0.71 # Current number of processed clauses : 123
% 0.43/0.71 # Positive orientable unit clauses : 47
% 0.43/0.71 # Positive unorientable unit clauses: 0
% 0.43/0.71 # Negative unit clauses : 5
% 0.43/0.71 # Non-unit-clauses : 71
% 0.43/0.71 # Current number of unprocessed clauses: 176
% 0.43/0.71 # ...number of literals in the above : 790
% 0.43/0.71 # Current number of archived formulas : 0
% 0.43/0.71 # Current number of archived clauses : 134
% 0.43/0.71 # Clause-clause subsumption calls (NU) : 7560
% 0.43/0.71 # Rec. Clause-clause subsumption calls : 2271
% 0.43/0.71 # Non-unit clause-clause subsumptions : 18
% 0.43/0.71 # Unit Clause-clause subsumption calls : 23
% 0.43/0.71 # Rewrite failures with RHS unbound : 0
% 0.43/0.71 # BW rewrite match attempts : 21
% 0.43/0.71 # BW rewrite match successes : 6
% 0.43/0.71 # Condensation attempts : 282
% 0.43/0.71 # Condensation successes : 0
% 0.43/0.71 # Termbank termtop insertions : 60245
% 0.43/0.71 # Search garbage collected termcells : 16468
% 0.43/0.71
% 0.43/0.71 # -------------------------------------------------
% 0.43/0.71 # User time : 0.064 s
% 0.43/0.71 # System time : 0.014 s
% 0.43/0.71 # Total time : 0.078 s
% 0.43/0.71 # Maximum resident set size: 5304 pages
% 0.43/0.71
% 0.43/0.71 # -------------------------------------------------
% 0.43/0.71 # User time : 0.206 s
% 0.43/0.71 # System time : 0.037 s
% 0.43/0.71 # Total time : 0.243 s
% 0.43/0.71 # Maximum resident set size: 2772 pages
% 0.43/0.71 % E---3.1 exiting
% 0.43/0.71 % E exiting
%------------------------------------------------------------------------------