TSTP Solution File: NUM669^4 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM669^4 : TPTP v8.1.2. 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 : Sat May 4 08:56:08 EDT 2024
% Result : Theorem 0.40s 0.66s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 31
% Syntax : Number of formulae : 60 ( 32 unt; 17 typ; 0 def)
% Number of atoms : 132 ( 44 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 198 ( 32 ~; 8 |; 2 &; 124 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 5 con; 0-3 aty)
% Number of variables : 83 ( 65 ^ 18 !; 0 ?; 83 :)
% 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_47,type,
ordsucc: $i > $i ).
thf(decl_61,type,
imp: $o > $o > $o ).
thf(decl_62,type,
d_not: $o > $o ).
thf(decl_71,type,
non: $i > ( $i > $o ) > $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_130,type,
n_1: $i ).
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_218,type,
esk62_0: $i ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AiTPR9ALZB/E---3.1_16259.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AiTPR9ALZB/E---3.1_16259.p',def_imp) ).
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.AiTPR9ALZB/E---3.1_16259.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AiTPR9ALZB/E---3.1_16259.p',def_is_of) ).
thf(def_non,axiom,
( non
= ( ^ [X1: $i,X2: $i > $o,X4: $i] : ( d_not @ ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AiTPR9ALZB/E---3.1_16259.p',def_non) ).
thf(def_l_some,axiom,
( l_some
= ( ^ [X1: $i,X2: $i > $o] :
( d_not
@ ( all_of
@ ^ [X4: $i] : ( in @ X4 @ X1 )
@ ( non @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AiTPR9ALZB/E---3.1_16259.p',def_l_some) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AiTPR9ALZB/E---3.1_16259.p',def_e_is) ).
thf(def_diffprop,axiom,
( diffprop
= ( ^ [X1: $i,X207: $i,X4: $i] : ( n_is @ X1 @ ( n_pl @ X207 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AiTPR9ALZB/E---3.1_16259.p',def_diffprop) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AiTPR9ALZB/E---3.1_16259.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.AiTPR9ALZB/E---3.1_16259.p',def_d_29_ii) ).
thf(def_n_some,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X439: $i] :
( ( in @ X439 @ nat )
=> ( ( Z0 @ X439 )
=> ~ $true ) )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AiTPR9ALZB/E---3.1_16259.p',def_n_some) ).
thf(satz18b,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( d_29_ii @ ( ordsucc @ X1 ) @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.AiTPR9ALZB/E---3.1_16259.p',satz18b) ).
thf(satz4e,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ ( ordsucc @ X1 ) @ ( n_pl @ X1 @ n_1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AiTPR9ALZB/E---3.1_16259.p',satz4e) ).
thf(n_1_p,axiom,
( is_of @ n_1
@ ^ [X1: $i] : ( in @ X1 @ nat ) ),
file('/export/starexec/sandbox/tmp/tmp.AiTPR9ALZB/E---3.1_16259.p',n_1_p) ).
thf(c_0_14,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_15,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_16,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_17,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_18,plain,
( non
= ( ^ [Z0: $i,Z1: $i > $o,Z2: $i] :
( ( Z1 @ Z2 )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_non]) ).
thf(c_0_19,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_20,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X412: $i] :
( ( in @ X412 @ Z0 )
=> ( ( Z1 @ X412 )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_l_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_16,c_0_17]) ).
thf(c_0_22,plain,
( non
= ( ^ [Z0: $i,Z1: $i > $o,Z2: $i] :
( ( Z1 @ Z2 )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_23,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_24,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X412: $i] :
( ( in @ X412 @ Z0 )
=> ( ( Z1 @ X412 )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_20,c_0_21]),c_0_19]),c_0_22]) ).
thf(c_0_25,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_diffprop]) ).
thf(c_0_26,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_23]) ).
thf(c_0_27,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X450: $i] :
( ( in @ X450 @ nat )
=> ( ( Z0
= ( n_pl @ Z1 @ X450 ) )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_28,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X439: $i] :
( ( in @ X439 @ nat )
=> ( ( Z0 @ X439 )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[def_n_some,c_0_24]) ).
thf(c_0_29,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_30,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X450: $i] :
( ( in @ X450 @ nat )
=> ( ( Z0
= ( n_pl @ Z1 @ X450 ) )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
thf(c_0_31,negated_conjecture,
~ ! [X695: $i] :
( ( in @ X695 @ nat )
=> ( ! [X694: $i] :
( ( in @ X694 @ nat )
=> ( ( ( ordsucc @ X695 )
= ( n_pl @ X695 @ X694 ) )
=> ~ $true ) )
=> ~ $true ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz18b])]),c_0_21]),c_0_30]) ).
thf(c_0_32,negated_conjecture,
! [X1317: $i] :
( ( in @ esk62_0 @ nat )
& ( ~ ( in @ X1317 @ nat )
| ( ( ordsucc @ esk62_0 )
!= ( n_pl @ esk62_0 @ X1317 ) )
| ~ $true )
& $true ),
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_31])])])])]) ).
thf(c_0_33,plain,
! [X557: $i] :
( ( in @ X557 @ nat )
=> ( ( ordsucc @ X557 )
= ( n_pl @ X557 @ n_1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz4e]),c_0_21]),c_0_26]) ).
thf(c_0_34,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ nat )
| ( ( ordsucc @ esk62_0 )
!= ( n_pl @ esk62_0 @ X1 ) )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_35,plain,
! [X1167: $i] :
( ~ ( in @ X1167 @ nat )
| ( ( ordsucc @ X1167 )
= ( n_pl @ X1167 @ n_1 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])]) ).
thf(c_0_36,negated_conjecture,
! [X1: $i] :
( ( ( ordsucc @ esk62_0 )
!= ( n_pl @ esk62_0 @ X1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_34]) ).
thf(c_0_37,plain,
! [X1: $i] :
( ( ( ordsucc @ X1 )
= ( n_pl @ X1 @ n_1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_38,negated_conjecture,
in @ esk62_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_39,plain,
in @ n_1 @ nat,
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[n_1_p]),c_0_17]) ).
thf(c_0_40,negated_conjecture,
! [X1: $i] :
( ( ( n_pl @ esk62_0 @ n_1 )
!= ( n_pl @ esk62_0 @ X1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
thf(c_0_41,plain,
in @ n_1 @ nat,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_40]),c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.16 % Problem : NUM669^4 : TPTP v8.1.2. Released v7.1.0.
% 0.12/0.17 % Command : run_E %s %d THM
% 0.17/0.38 % Computer : n016.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39 % CPULimit : 300
% 0.17/0.39 % WCLimit : 300
% 0.17/0.39 % DateTime : Fri May 3 10:06:30 EDT 2024
% 0.17/0.39 % CPUTime :
% 0.23/0.55 Running higher-order theorem proving
% 0.23/0.55 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.AiTPR9ALZB/E---3.1_16259.p
% 0.40/0.63 # Type mismatch in argument #1 of prop2 @ ($not @ db(4)) @ ($db_lam @ db(0) @ ($db_lam @ db(0) @ ($@_var @ db(6) @ db(1) @ db(0)))) @ db(3) @ db(2) @ db(1) @ db(0): expected $i but got $o
% 0.40/0.63 eprover: Type error
% 0.40/0.65 # Type mismatch in argument #1 of prop2 @ ($not @ db(4)) @ ($db_lam @ db(0) @ ($db_lam @ db(0) @ ($@_var @ db(6) @ db(1) @ db(0)))) @ db(3) @ db(2) @ db(1) @ db(0): expected $i but got $o
% 0.40/0.65 eprover: Type error
% 0.40/0.66 # Version: 3.1.0-ho
% 0.40/0.66 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.40/0.66 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.40/0.66 # Starting lpo1_fix with 900s (3) cores
% 0.40/0.66 # Starting full_lambda_9 with 300s (1) cores
% 0.40/0.66 # Starting almost_fo_4 with 300s (1) cores
% 0.40/0.66 # Starting new_ho_9 with 300s (1) cores
% 0.40/0.66 # Starting pre_casc_4 with 300s (1) cores
% 0.40/0.66 # Starting ho_unfolding_6 with 300s (1) cores
% 0.40/0.66 # lpo1_fix with pid 16417 completed with status 0
% 0.40/0.66 # Result found by lpo1_fix
% 0.40/0.66 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.40/0.66 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.40/0.66 # Starting lpo1_fix with 900s (3) cores
% 0.40/0.66 # No SInE strategy applied
% 0.40/0.66 # Search class: HGHSM-FSLM32-MHSMMSBN
% 0.40/0.66 # Scheduled 11 strats onto 3 cores with 900 seconds (900 total)
% 0.40/0.66 # Starting full_lambda_5 with 82s (1) cores
% 0.40/0.66 # Starting new_ho_6 with 82s (1) cores
% 0.40/0.66 # Starting pre_casc_4 with 82s (1) cores
% 0.40/0.66 # new_ho_6 with pid 16430 completed with status 0
% 0.40/0.66 # Result found by new_ho_6
% 0.40/0.66 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.40/0.66 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.40/0.66 # Starting lpo1_fix with 900s (3) cores
% 0.40/0.66 # No SInE strategy applied
% 0.40/0.66 # Search class: HGHSM-FSLM32-MHSMMSBN
% 0.40/0.66 # Scheduled 11 strats onto 3 cores with 900 seconds (900 total)
% 0.40/0.66 # Starting full_lambda_5 with 82s (1) cores
% 0.40/0.66 # Starting new_ho_6 with 82s (1) cores
% 0.40/0.66 # Preprocessing time : 0.011 s
% 0.40/0.66
% 0.40/0.66 # Proof found!
% 0.40/0.66 # SZS status Theorem
% 0.40/0.66 # SZS output start CNFRefutation
% See solution above
% 0.40/0.66 # Parsed axioms : 367
% 0.40/0.66 # Removed by relevancy pruning/SinE : 0
% 0.40/0.66 # Initial clauses : 859
% 0.40/0.66 # Removed in clause preprocessing : 486
% 0.40/0.66 # Initial clauses in saturation : 373
% 0.40/0.66 # Processed clauses : 94
% 0.40/0.66 # ...of these trivial : 2
% 0.40/0.66 # ...subsumed : 9
% 0.40/0.66 # ...remaining for further processing : 83
% 0.40/0.66 # Other redundant clauses eliminated : 2
% 0.40/0.66 # Clauses deleted for lack of memory : 0
% 0.40/0.66 # Backward-subsumed : 0
% 0.40/0.66 # Backward-rewritten : 0
% 0.40/0.66 # Generated clauses : 73
% 0.40/0.66 # ...of the previous two non-redundant : 61
% 0.40/0.66 # ...aggressively subsumed : 0
% 0.40/0.66 # Contextual simplify-reflections : 0
% 0.40/0.66 # Paramodulations : 57
% 0.40/0.66 # Factorizations : 0
% 0.40/0.66 # NegExts : 0
% 0.40/0.66 # Equation resolutions : 6
% 0.40/0.66 # Disequality decompositions : 0
% 0.40/0.66 # Total rewrite steps : 7
% 0.40/0.66 # ...of those cached : 2
% 0.40/0.66 # Propositional unsat checks : 0
% 0.40/0.66 # Propositional check models : 0
% 0.40/0.66 # Propositional check unsatisfiable : 0
% 0.40/0.66 # Propositional clauses : 0
% 0.40/0.66 # Propositional clauses after purity: 0
% 0.40/0.66 # Propositional unsat core size : 0
% 0.40/0.66 # Propositional preprocessing time : 0.000
% 0.40/0.66 # Propositional encoding time : 0.000
% 0.40/0.66 # Propositional solver time : 0.000
% 0.40/0.66 # Success case prop preproc time : 0.000
% 0.40/0.66 # Success case prop encoding time : 0.000
% 0.40/0.66 # Success case prop solver time : 0.000
% 0.40/0.66 # Current number of processed clauses : 83
% 0.40/0.66 # Positive orientable unit clauses : 39
% 0.40/0.66 # Positive unorientable unit clauses: 0
% 0.40/0.66 # Negative unit clauses : 5
% 0.40/0.66 # Non-unit-clauses : 39
% 0.40/0.66 # Current number of unprocessed clauses: 340
% 0.40/0.66 # ...number of literals in the above : 1238
% 0.40/0.66 # Current number of archived formulas : 0
% 0.40/0.66 # Current number of archived clauses : 0
% 0.40/0.66 # Clause-clause subsumption calls (NU) : 259
% 0.40/0.66 # Rec. Clause-clause subsumption calls : 228
% 0.40/0.66 # Non-unit clause-clause subsumptions : 5
% 0.40/0.66 # Unit Clause-clause subsumption calls : 95
% 0.40/0.66 # Rewrite failures with RHS unbound : 0
% 0.40/0.66 # BW rewrite match attempts : 3
% 0.40/0.66 # BW rewrite match successes : 0
% 0.40/0.66 # Condensation attempts : 94
% 0.40/0.66 # Condensation successes : 0
% 0.40/0.66 # Termbank termtop insertions : 79186
% 0.40/0.66 # Search garbage collected termcells : 29557
% 0.40/0.66
% 0.40/0.66 # -------------------------------------------------
% 0.40/0.66 # User time : 0.070 s
% 0.40/0.66 # System time : 0.014 s
% 0.40/0.66 # Total time : 0.084 s
% 0.40/0.66 # Maximum resident set size: 6624 pages
% 0.40/0.66
% 0.40/0.66 # -------------------------------------------------
% 0.40/0.66 # User time : 0.106 s
% 0.40/0.66 # System time : 0.033 s
% 0.40/0.66 # Total time : 0.140 s
% 0.40/0.66 # Maximum resident set size: 2272 pages
% 0.40/0.66 % E---3.1 exiting
% 0.40/0.66 % E exiting
%------------------------------------------------------------------------------