TSTP Solution File: NUM636^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM636^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n011.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 08:55:51 EDT 2024
% Result : Theorem 0.17s 0.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 38 ( 16 unt; 8 typ; 0 def)
% Number of atoms : 57 ( 27 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 174 ( 33 ~; 18 |; 1 &; 115 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 7 ^ 39 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
set: $tType ).
thf(decl_22,type,
x: nat ).
thf(decl_23,type,
suc: nat > nat ).
thf(decl_24,type,
esti: nat > set > $o ).
thf(decl_25,type,
setof: ( nat > $o ) > set ).
thf(decl_26,type,
n_1: nat ).
thf(decl_27,type,
esk1_1: set > nat ).
thf(ax3,axiom,
! [X4: nat] :
( ( suc @ X4 )
!= n_1 ),
file('/export/starexec/sandbox2/tmp/tmp.n4KXk9dlN3/E---3.1_14593.p',ax3) ).
thf(estii,axiom,
! [X1: nat > $o,X2: nat] :
( ( X1 @ X2 )
=> ( esti @ X2 @ ( setof @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.n4KXk9dlN3/E---3.1_14593.p',estii) ).
thf(satz2,conjecture,
( ( suc @ x )
!= x ),
file('/export/starexec/sandbox2/tmp/tmp.n4KXk9dlN3/E---3.1_14593.p',satz2) ).
thf(satz1,axiom,
! [X4: nat,X5: nat] :
( ( X4 != X5 )
=> ( ( suc @ X4 )
!= ( suc @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.n4KXk9dlN3/E---3.1_14593.p',satz1) ).
thf(estie,axiom,
! [X1: nat > $o,X2: nat] :
( ( esti @ X2 @ ( setof @ X1 ) )
=> ( X1 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.n4KXk9dlN3/E---3.1_14593.p',estie) ).
thf(ax5,axiom,
! [X3: set] :
( ( esti @ n_1 @ X3 )
=> ( ! [X4: nat] :
( ( esti @ X4 @ X3 )
=> ( esti @ ( suc @ X4 ) @ X3 ) )
=> ! [X4: nat] : ( esti @ X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.n4KXk9dlN3/E---3.1_14593.p',ax5) ).
thf(c_0_6,plain,
! [X4: nat] :
( ( suc @ X4 )
!= n_1 ),
inference(fof_simplification,[status(thm)],[ax3]) ).
thf(c_0_7,plain,
! [X24: nat > $o,X25: nat] :
( ~ ( X24 @ X25 )
| ( esti @ X25 @ ( setof @ X24 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[estii])])]) ).
thf(c_0_8,negated_conjecture,
( ( suc @ x )
= x ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz2])]) ).
thf(c_0_9,plain,
! [X4: nat,X5: nat] :
( ( X4 != X5 )
=> ( ( suc @ X4 )
!= ( suc @ X5 ) ) ),
inference(fof_simplification,[status(thm)],[satz1]) ).
thf(c_0_10,plain,
! [X22: nat > $o,X23: nat] :
( ~ ( esti @ X23 @ ( setof @ X22 ) )
| ( X22 @ X23 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[estie])])]) ).
thf(c_0_11,plain,
! [X16: set,X18: nat] :
( ( ( esti @ ( esk1_1 @ X16 ) @ X16 )
| ( esti @ X18 @ X16 )
| ~ ( esti @ n_1 @ X16 ) )
& ( ~ ( esti @ ( suc @ ( esk1_1 @ X16 ) ) @ X16 )
| ( esti @ X18 @ X16 )
| ~ ( esti @ n_1 @ X16 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])])]) ).
thf(c_0_12,plain,
! [X19: nat] :
( ( suc @ X19 )
!= n_1 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_6])]) ).
thf(c_0_13,plain,
! [X1: nat > $o,X2: nat] :
( ( esti @ X2 @ ( setof @ X1 ) )
| ~ ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_14,negated_conjecture,
( ( suc @ x )
= x ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_15,plain,
! [X20: nat,X21: nat] :
( ( X20 = X21 )
| ( ( suc @ X20 )
!= ( suc @ X21 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
thf(c_0_16,plain,
! [X2: nat,X1: nat > $o] :
( ( X1 @ X2 )
| ~ ( esti @ X2 @ ( setof @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_17,plain,
! [X2: nat,X3: set] :
( ( esti @ ( esk1_1 @ X3 ) @ X3 )
| ( esti @ X2 @ X3 )
| ~ ( esti @ n_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_18,plain,
! [X2: nat] :
( ( suc @ X2 )
!= n_1 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_19,plain,
! [X2: nat] :
( ( esti @ X2
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) )
| ( X2
= ( suc @ X2 ) ) ),
inference(trigger,[status(thm)],[inference(cn,[status(thm)],[]),c_0_13,c_0_14]) ).
thf(c_0_20,plain,
! [X2: nat,X4: nat] :
( ( X2 = X4 )
| ( ( suc @ X2 )
!= ( suc @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_21,plain,
! [X2: nat] :
( ( X2
!= ( suc @ X2 ) )
| ~ ( esti @ X2
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ) ),
inference(trigger,[status(thm)],[inference(cn,[status(thm)],[]),c_0_16,c_0_14]) ).
thf(c_0_22,plain,
! [X3: set] :
( ( esti @ ( esk1_1 @ X3 ) @ X3 )
| ~ ( esti @ n_1 @ X3 ) ),
inference(condense,[status(thm)],[c_0_17]) ).
thf(c_0_23,plain,
( esti @ n_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19])]) ).
thf(c_0_24,plain,
! [X2: nat,X3: set] :
( ( esti @ X2 @ X3 )
| ~ ( esti @ ( suc @ ( esk1_1 @ X3 ) ) @ X3 )
| ~ ( esti @ n_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_25,plain,
! [X2: nat] :
( ( ( suc @ X2 )
= X2 )
| ( esti @ ( suc @ X2 )
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_19])]) ).
thf(c_0_26,plain,
( ( suc
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ) )
!= ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
thf(c_0_27,plain,
! [X2: nat] :
( esti @ X2
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( suc @ Z0 ) ) ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_23])]),c_0_26]) ).
thf(c_0_28,plain,
! [X2: nat] :
( ( suc @ X2 )
!= X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_27])]) ).
thf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_14,c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM636^1 : TPTP v8.1.2. Released v3.7.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n011.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri May 3 09:33:48 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.17/0.43 Running higher-order theorem proving
% 0.17/0.43 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.n4KXk9dlN3/E---3.1_14593.p
% 0.17/0.45 # Version: 3.1.0-ho
% 0.17/0.45 # Preprocessing class: HSSSSMSSSSSNSFA.
% 0.17/0.45 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.45 # Starting new_ho_14 with 1500s (5) cores
% 0.17/0.45 # Starting full_lambda_8 with 300s (1) cores
% 0.17/0.45 # Starting new_ho_13 with 300s (1) cores
% 0.17/0.45 # Starting ho_unfolding_3 with 300s (1) cores
% 0.17/0.45 # new_ho_14 with pid 14673 completed with status 0
% 0.17/0.45 # Result found by new_ho_14
% 0.17/0.45 # Preprocessing class: HSSSSMSSSSSNSFA.
% 0.17/0.45 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.45 # Starting new_ho_14 with 1500s (5) cores
% 0.17/0.45 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.17/0.45 # Search class: HGHSF-FFSF11-MSFFFSBN
% 0.17/0.45 # partial match(2): HGUSF-FFSF11-SSFFFSBN
% 0.17/0.45 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.45 # Starting new_ho_14 with 901s (1) cores
% 0.17/0.45 # Starting new_ho_13 with 151s (1) cores
% 0.17/0.45 # Starting ho_unfolding_6 with 151s (1) cores
% 0.17/0.45 # Starting sh4l with 151s (1) cores
% 0.17/0.45 # Starting full_lambda_8 with 146s (1) cores
% 0.17/0.45 # full_lambda_8 with pid 14684 completed with status 0
% 0.17/0.45 # Result found by full_lambda_8
% 0.17/0.45 # Preprocessing class: HSSSSMSSSSSNSFA.
% 0.17/0.45 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.45 # Starting new_ho_14 with 1500s (5) cores
% 0.17/0.45 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.17/0.45 # Search class: HGHSF-FFSF11-MSFFFSBN
% 0.17/0.45 # partial match(2): HGUSF-FFSF11-SSFFFSBN
% 0.17/0.45 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.45 # Starting new_ho_14 with 901s (1) cores
% 0.17/0.45 # Starting new_ho_13 with 151s (1) cores
% 0.17/0.45 # Starting ho_unfolding_6 with 151s (1) cores
% 0.17/0.45 # Starting sh4l with 151s (1) cores
% 0.17/0.45 # Starting full_lambda_8 with 146s (1) cores
% 0.17/0.45 # Preprocessing time : 0.001 s
% 0.17/0.45 # Presaturation interreduction done
% 0.17/0.45
% 0.17/0.45 # Proof found!
% 0.17/0.45 # SZS status Theorem
% 0.17/0.45 # SZS output start CNFRefutation
% See solution above
% 0.17/0.45 # Parsed axioms : 13
% 0.17/0.45 # Removed by relevancy pruning/SinE : 7
% 0.17/0.45 # Initial clauses : 7
% 0.17/0.45 # Removed in clause preprocessing : 0
% 0.17/0.45 # Initial clauses in saturation : 9
% 0.17/0.45 # Processed clauses : 35
% 0.17/0.45 # ...of these trivial : 0
% 0.17/0.45 # ...subsumed : 7
% 0.17/0.45 # ...remaining for further processing : 28
% 0.17/0.45 # Other redundant clauses eliminated : 3
% 0.17/0.45 # Clauses deleted for lack of memory : 0
% 0.17/0.45 # Backward-subsumed : 2
% 0.17/0.45 # Backward-rewritten : 4
% 0.17/0.45 # Generated clauses : 30
% 0.17/0.45 # ...of the previous two non-redundant : 22
% 0.17/0.45 # ...aggressively subsumed : 0
% 0.17/0.45 # Contextual simplify-reflections : 0
% 0.17/0.45 # Paramodulations : 24
% 0.17/0.45 # Factorizations : 0
% 0.17/0.45 # NegExts : 0
% 0.17/0.45 # Equation resolutions : 4
% 0.17/0.45 # Disequality decompositions : 0
% 0.17/0.45 # Total rewrite steps : 8
% 0.17/0.45 # ...of those cached : 3
% 0.17/0.45 # Propositional unsat checks : 0
% 0.17/0.45 # Propositional check models : 0
% 0.17/0.45 # Propositional check unsatisfiable : 0
% 0.17/0.45 # Propositional clauses : 0
% 0.17/0.45 # Propositional clauses after purity: 0
% 0.17/0.45 # Propositional unsat core size : 0
% 0.17/0.45 # Propositional preprocessing time : 0.000
% 0.17/0.45 # Propositional encoding time : 0.000
% 0.17/0.45 # Propositional solver time : 0.000
% 0.17/0.45 # Success case prop preproc time : 0.000
% 0.17/0.45 # Success case prop encoding time : 0.000
% 0.17/0.45 # Success case prop solver time : 0.000
% 0.17/0.45 # Current number of processed clauses : 12
% 0.17/0.45 # Positive orientable unit clauses : 3
% 0.17/0.45 # Positive unorientable unit clauses: 0
% 0.17/0.45 # Negative unit clauses : 3
% 0.17/0.45 # Non-unit-clauses : 6
% 0.17/0.45 # Current number of unprocessed clauses: 5
% 0.17/0.45 # ...number of literals in the above : 11
% 0.17/0.45 # Current number of archived formulas : 0
% 0.17/0.45 # Current number of archived clauses : 16
% 0.17/0.45 # Clause-clause subsumption calls (NU) : 7
% 0.17/0.45 # Rec. Clause-clause subsumption calls : 7
% 0.17/0.45 # Non-unit clause-clause subsumptions : 4
% 0.17/0.45 # Unit Clause-clause subsumption calls : 8
% 0.17/0.45 # Rewrite failures with RHS unbound : 0
% 0.17/0.45 # BW rewrite match attempts : 4
% 0.17/0.45 # BW rewrite match successes : 4
% 0.17/0.45 # Condensation attempts : 35
% 0.17/0.45 # Condensation successes : 1
% 0.17/0.45 # Termbank termtop insertions : 936
% 0.17/0.45 # Search garbage collected termcells : 150
% 0.17/0.45
% 0.17/0.45 # -------------------------------------------------
% 0.17/0.45 # User time : 0.005 s
% 0.17/0.45 # System time : 0.001 s
% 0.17/0.45 # Total time : 0.006 s
% 0.17/0.45 # Maximum resident set size: 1864 pages
% 0.17/0.45
% 0.17/0.45 # -------------------------------------------------
% 0.17/0.45 # User time : 0.016 s
% 0.17/0.45 # System time : 0.006 s
% 0.17/0.45 # Total time : 0.023 s
% 0.17/0.45 # Maximum resident set size: 1728 pages
% 0.17/0.45 % E---3.1 exiting
% 0.17/0.45 % E exiting
%------------------------------------------------------------------------------