TSTP Solution File: DAT056^2 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : DAT056^2 : TPTP v8.1.2. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n018.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 07:38:43 EDT 2024
% Result : Theorem 0.21s 0.51s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 30 ( 12 unt; 10 typ; 0 def)
% Number of atoms : 34 ( 33 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 343 ( 13 ~; 14 |; 1 &; 312 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 43 ( 12 ^ 31 !; 0 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
lst: $tType ).
thf(decl_sort2,type,
a: $tType ).
thf(decl_22,type,
ap: lst > lst > lst ).
thf(decl_23,type,
cns: a > lst > lst ).
thf(decl_24,type,
nl: lst ).
thf(decl_25,type,
xs: lst ).
thf(decl_26,type,
esk1_0: lst ).
thf(decl_27,type,
esk2_0: lst ).
thf(decl_28,type,
esk3_2: lst > ( lst > $o ) > a ).
thf(decl_29,type,
esk4_2: lst > ( lst > $o ) > lst ).
thf(conj_0,conjecture,
! [X8: lst,X9: lst] :
( ( ap @ xs @ ( ap @ X8 @ X9 ) )
= ( ap @ ( ap @ xs @ X8 ) @ X9 ) ),
file('/export/starexec/sandbox/tmp/tmp.7V1X92UL9R/E---3.1_20296.p',conj_0) ).
thf(fact_0_lst_Oinduct,axiom,
! [X1: lst,X2: lst > $o] :
( ( X2 @ nl )
=> ( ! [X3: a,X4: lst] :
( ( X2 @ X4 )
=> ( X2 @ ( cns @ X3 @ X4 ) ) )
=> ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.7V1X92UL9R/E---3.1_20296.p',fact_0_lst_Oinduct) ).
thf(fact_2p_Osimps_I1_J,axiom,
! [X5: lst] :
( ( ap @ nl @ X5 )
= X5 ),
file('/export/starexec/sandbox/tmp/tmp.7V1X92UL9R/E---3.1_20296.p',fact_2p_Osimps_I1_J) ).
thf(fact_1p_Osimps_I2_J,axiom,
! [X5: lst,X6: lst,X7: a] :
( ( ap @ ( cns @ X7 @ X6 ) @ X5 )
= ( cns @ X7 @ ( ap @ X6 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.7V1X92UL9R/E---3.1_20296.p',fact_1p_Osimps_I2_J) ).
thf(c_0_4,negated_conjecture,
~ ! [X8: lst,X9: lst] :
( ( ap @ xs @ ( ap @ X8 @ X9 ) )
= ( ap @ ( ap @ xs @ X8 ) @ X9 ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_5,plain,
! [X26: lst,X27: lst > $o] :
( ( ( X27 @ ( esk4_2 @ X26 @ X27 ) )
| ( X27 @ X26 )
| ~ ( X27 @ nl ) )
& ( ~ ( X27 @ ( cns @ ( esk3_2 @ X26 @ X27 ) @ ( esk4_2 @ X26 @ X27 ) ) )
| ( X27 @ X26 )
| ~ ( X27 @ nl ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_0_lst_Oinduct])])])])]) ).
thf(c_0_6,negated_conjecture,
( ( ap @ xs @ ( ap @ esk1_0 @ esk2_0 ) )
!= ( ap @ ( ap @ xs @ 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_4])])])]) ).
thf(c_0_7,plain,
! [X1: lst,X2: lst > $o] :
( ( X2 @ X1 )
| ~ ( X2 @ ( cns @ ( esk3_2 @ X1 @ X2 ) @ ( esk4_2 @ X1 @ X2 ) ) )
| ~ ( X2 @ nl ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
( ( ap @ xs @ ( ap @ esk1_0 @ esk2_0 ) )
!= ( ap @ ( ap @ xs @ esk1_0 ) @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
! [X25: lst] :
( ( ap @ nl @ X25 )
= X25 ),
inference(variable_rename,[status(thm)],[fact_2p_Osimps_I1_J]) ).
thf(c_0_10,plain,
! [X22: lst,X23: lst,X24: a] :
( ( ap @ ( cns @ X24 @ X23 ) @ X22 )
= ( cns @ X24 @ ( ap @ X23 @ X22 ) ) ),
inference(variable_rename,[status(thm)],[fact_1p_Osimps_I2_J]) ).
thf(c_0_11,plain,
! [X1: lst,X2: lst > $o] :
( ( X2 @ ( esk4_2 @ X1 @ X2 ) )
| ( X2 @ X1 )
| ~ ( X2 @ nl ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_12,plain,
! [X1: lst] :
( ( ( ap @ X1 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ X1 @ esk1_0 ) @ esk2_0 ) )
| ( ( ap @ nl @ ( ap @ esk1_0 @ esk2_0 ) )
!= ( ap @ ( ap @ nl @ esk1_0 ) @ esk2_0 ) )
| ( ( ap
@ ( cns
@ ( esk3_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) )
@ ( esk4_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) ) )
@ ( ap @ esk1_0 @ esk2_0 ) )
!= ( ap
@ ( ap
@ ( cns
@ ( esk3_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) )
@ ( esk4_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) ) )
@ esk1_0 )
@ esk2_0 ) ) ),
inference(trigger,[status(thm)],[inference(cn,[status(thm)],[]),c_0_7,c_0_8]) ).
thf(c_0_13,plain,
! [X1: lst] :
( ( ap @ nl @ X1 )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
! [X1: lst,X3: a,X4: lst] :
( ( ap @ ( cns @ X3 @ X1 ) @ X4 )
= ( cns @ X3 @ ( ap @ X1 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,plain,
! [X1: lst] :
( ( ( ap @ X1 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ X1 @ esk1_0 ) @ esk2_0 ) )
| ( ( ap
@ ( esk4_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) )
@ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap
@ ( ap
@ ( esk4_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) )
@ esk1_0 )
@ esk2_0 ) )
| ( ( ap @ nl @ ( ap @ esk1_0 @ esk2_0 ) )
!= ( ap @ ( ap @ nl @ esk1_0 ) @ esk2_0 ) ) ),
inference(trigger,[status(thm)],[inference(cn,[status(thm)],[]),c_0_11,c_0_8]) ).
thf(c_0_16,plain,
! [X1: lst] :
( ( ( ap @ ( ap @ X1 @ esk1_0 ) @ esk2_0 )
= ( ap @ X1 @ ( ap @ esk1_0 @ esk2_0 ) ) )
| ( ( cns
@ ( esk3_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) )
@ ( ap
@ ( ap
@ ( esk4_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) )
@ esk1_0 )
@ esk2_0 ) )
!= ( cns
@ ( esk3_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) )
@ ( ap
@ ( esk4_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) )
@ ( ap @ esk1_0 @ esk2_0 ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_13]),c_0_14]),c_0_14]),c_0_14])]) ).
thf(c_0_17,plain,
! [X1: lst] :
( ( ( ap
@ ( ap
@ ( esk4_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) )
@ esk1_0 )
@ esk2_0 )
= ( ap
@ ( esk4_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) )
@ ( ap @ esk1_0 @ esk2_0 ) ) )
| ( ( ap @ ( ap @ X1 @ esk1_0 ) @ esk2_0 )
= ( ap @ X1 @ ( ap @ esk1_0 @ esk2_0 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_13]),c_0_13])]) ).
thf(c_0_18,plain,
! [X1: lst] :
( ( ap @ ( ap @ X1 @ esk1_0 ) @ esk2_0 )
= ( ap @ X1 @ ( ap @ esk1_0 @ esk2_0 ) ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : DAT056^2 : TPTP v8.1.2. Released v5.4.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 08:56:01 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.21/0.50 Running higher-order theorem proving
% 0.21/0.50 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.7V1X92UL9R/E---3.1_20296.p
% 0.21/0.51 # Version: 3.1.0-ho
% 0.21/0.51 # Preprocessing class: HSSSSMSSSSSNSFA.
% 0.21/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51 # Starting new_ho_14 with 1500s (5) cores
% 0.21/0.51 # Starting full_lambda_8 with 300s (1) cores
% 0.21/0.51 # Starting new_ho_13 with 300s (1) cores
% 0.21/0.51 # Starting ho_unfolding_3 with 300s (1) cores
% 0.21/0.51 # new_ho_14 with pid 20449 completed with status 0
% 0.21/0.51 # Result found by new_ho_14
% 0.21/0.51 # Preprocessing class: HSSSSMSSSSSNSFA.
% 0.21/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51 # Starting new_ho_14 with 1500s (5) cores
% 0.21/0.51 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.51 # Search class: HGUSS-FFMF22-DSFFFSBN
% 0.21/0.51 # partial match(3): HGUSS-FFSF21-SSFFFSBN
% 0.21/0.51 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.51 # Starting new_ho_14 with 901s (1) cores
% 0.21/0.51 # Starting new_ho_13 with 151s (1) cores
% 0.21/0.51 # Starting new_bool_3 with 151s (1) cores
% 0.21/0.51 # Starting new_bool_1 with 151s (1) cores
% 0.21/0.51 # Starting ho_unfolding_6 with 146s (1) cores
% 0.21/0.51 # ho_unfolding_6 with pid 20461 completed with status 0
% 0.21/0.51 # Result found by ho_unfolding_6
% 0.21/0.51 # Preprocessing class: HSSSSMSSSSSNSFA.
% 0.21/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51 # Starting new_ho_14 with 1500s (5) cores
% 0.21/0.51 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.51 # Search class: HGUSS-FFMF22-DSFFFSBN
% 0.21/0.51 # partial match(3): HGUSS-FFSF21-SSFFFSBN
% 0.21/0.51 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.51 # Starting new_ho_14 with 901s (1) cores
% 0.21/0.51 # Starting new_ho_13 with 151s (1) cores
% 0.21/0.51 # Starting new_bool_3 with 151s (1) cores
% 0.21/0.51 # Starting new_bool_1 with 151s (1) cores
% 0.21/0.51 # Starting ho_unfolding_6 with 146s (1) cores
% 0.21/0.51 # Preprocessing time : 0.002 s
% 0.21/0.51
% 0.21/0.51 # Proof found!
% 0.21/0.51 # SZS status Theorem
% 0.21/0.51 # SZS output start CNFRefutation
% See solution above
% 0.21/0.52 # Parsed axioms : 10
% 0.21/0.52 # Removed by relevancy pruning/SinE : 6
% 0.21/0.52 # Initial clauses : 5
% 0.21/0.52 # Removed in clause preprocessing : 0
% 0.21/0.52 # Initial clauses in saturation : 13
% 0.21/0.52 # Processed clauses : 14
% 0.21/0.52 # ...of these trivial : 0
% 0.21/0.52 # ...subsumed : 0
% 0.21/0.52 # ...remaining for further processing : 14
% 0.21/0.52 # Other redundant clauses eliminated : 0
% 0.21/0.52 # Clauses deleted for lack of memory : 0
% 0.21/0.52 # Backward-subsumed : 0
% 0.21/0.52 # Backward-rewritten : 3
% 0.21/0.52 # Generated clauses : 10
% 0.21/0.52 # ...of the previous two non-redundant : 8
% 0.21/0.52 # ...aggressively subsumed : 0
% 0.21/0.52 # Contextual simplify-reflections : 0
% 0.21/0.52 # Paramodulations : 4
% 0.21/0.52 # Factorizations : 0
% 0.21/0.52 # NegExts : 0
% 0.21/0.52 # Equation resolutions : 0
% 0.21/0.52 # Disequality decompositions : 0
% 0.21/0.52 # Total rewrite steps : 11
% 0.21/0.52 # ...of those cached : 0
% 0.21/0.52 # Propositional unsat checks : 0
% 0.21/0.52 # Propositional check models : 0
% 0.21/0.52 # Propositional check unsatisfiable : 0
% 0.21/0.52 # Propositional clauses : 0
% 0.21/0.52 # Propositional clauses after purity: 0
% 0.21/0.52 # Propositional unsat core size : 0
% 0.21/0.52 # Propositional preprocessing time : 0.000
% 0.21/0.52 # Propositional encoding time : 0.000
% 0.21/0.52 # Propositional solver time : 0.000
% 0.21/0.52 # Success case prop preproc time : 0.000
% 0.21/0.52 # Success case prop encoding time : 0.000
% 0.21/0.52 # Success case prop solver time : 0.000
% 0.21/0.52 # Current number of processed clauses : 9
% 0.21/0.52 # Positive orientable unit clauses : 3
% 0.21/0.52 # Positive unorientable unit clauses: 0
% 0.21/0.52 # Negative unit clauses : 0
% 0.21/0.52 # Non-unit-clauses : 6
% 0.21/0.52 # Current number of unprocessed clauses: 7
% 0.21/0.52 # ...number of literals in the above : 17
% 0.21/0.52 # Current number of archived formulas : 0
% 0.21/0.52 # Current number of archived clauses : 6
% 0.21/0.52 # Clause-clause subsumption calls (NU) : 21
% 0.21/0.52 # Rec. Clause-clause subsumption calls : 21
% 0.21/0.52 # Non-unit clause-clause subsumptions : 0
% 0.21/0.52 # Unit Clause-clause subsumption calls : 0
% 0.21/0.52 # Rewrite failures with RHS unbound : 0
% 0.21/0.52 # BW rewrite match attempts : 3
% 0.21/0.52 # BW rewrite match successes : 3
% 0.21/0.52 # Condensation attempts : 14
% 0.21/0.52 # Condensation successes : 0
% 0.21/0.52 # Termbank termtop insertions : 3542
% 0.21/0.52 # Search garbage collected termcells : 114
% 0.21/0.52
% 0.21/0.52 # -------------------------------------------------
% 0.21/0.52 # User time : 0.005 s
% 0.21/0.52 # System time : 0.004 s
% 0.21/0.52 # Total time : 0.009 s
% 0.21/0.52 # Maximum resident set size: 1888 pages
% 0.21/0.52
% 0.21/0.52 # -------------------------------------------------
% 0.21/0.52 # User time : 0.026 s
% 0.21/0.52 # System time : 0.014 s
% 0.21/0.52 # Total time : 0.040 s
% 0.21/0.52 # Maximum resident set size: 1732 pages
% 0.21/0.52 % E---3.1 exiting
% 0.21/0.52 % E exiting
%------------------------------------------------------------------------------