TSTP Solution File: SET648^3 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SET648^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n017.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 02:55:09 EDT 2024
% Result : Theorem 0.21s 0.52s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of formulae : 27 ( 13 unt; 9 typ; 0 def)
% Number of atoms : 37 ( 10 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 82 ( 8 ~; 4 |; 5 &; 57 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 57 ( 57 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 49 ( 24 ^ 19 !; 6 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_33,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_36,type,
cartesian_product: ( $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(decl_39,type,
sub_rel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(decl_49,type,
rel_codomain: ( $i > $i > $o ) > $i > $o ).
thf(decl_50,type,
rel_domain: ( $i > $i > $o ) > $i > $o ).
thf(decl_57,type,
epred1_0: $i > $i > $o ).
thf(decl_58,type,
epred2_0: $i > $o ).
thf(decl_59,type,
esk1_0: $i ).
thf(decl_60,type,
esk2_0: $i ).
thf(subset,axiom,
( subset
= ( ^ [X16: $i > $o,X17: $i > $o] :
! [X4: $i] :
( ( X16 @ X4 )
=> ( X17 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',subset) ).
thf(cartesian_product,axiom,
( cartesian_product
= ( ^ [X22: $i > $o,X23: $i > $o,X4: $i,X24: $i] :
( ( X22 @ X4 )
& ( X23 @ X24 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',cartesian_product) ).
thf(sub_rel,axiom,
( sub_rel
= ( ^ [X26: $i > $i > $o,X27: $i > $i > $o] :
! [X1: $i,X3: $i] :
( ( X26 @ X1 @ X3 )
=> ( X27 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',sub_rel) ).
thf(rel_codomain,axiom,
( rel_codomain
= ( ^ [X28: $i > $i > $o,X3: $i] :
? [X1: $i] : ( X28 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',rel_codomain) ).
thf(rel_domain,axiom,
( rel_domain
= ( ^ [X28: $i > $i > $o,X1: $i] :
? [X3: $i] : ( X28 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',rel_domain) ).
thf(thm,conjecture,
! [X28: $i > $i > $o,X36: $i > $o] :
( ( subset @ ( rel_codomain @ X28 ) @ X36 )
=> ( sub_rel @ X28 @ ( cartesian_product @ ( rel_domain @ X28 ) @ X36 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(c_0_6,plain,
( subset
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[subset]) ).
thf(c_0_7,plain,
( cartesian_product
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i,Z3: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z3 ) ) ) ),
inference(fof_simplification,[status(thm)],[cartesian_product]) ).
thf(c_0_8,plain,
( sub_rel
= ( ^ [Z0: $i > $i > $o,Z1: $i > $i > $o] :
! [X1: $i,X3: $i] :
( ( Z0 @ X1 @ X3 )
=> ( Z1 @ X1 @ X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[sub_rel]) ).
thf(c_0_9,plain,
( rel_codomain
= ( ^ [Z0: $i > $i > $o,Z1: $i] :
? [X1: $i] : ( Z0 @ X1 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[rel_codomain]) ).
thf(c_0_10,plain,
( rel_domain
= ( ^ [Z0: $i > $i > $o,Z1: $i] :
? [X3: $i] : ( Z0 @ Z1 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[rel_domain]) ).
thf(c_0_11,negated_conjecture,
~ ! [X28: $i > $i > $o,X36: $i > $o] :
( ! [X48: $i] :
( ? [X47: $i] : ( X28 @ X47 @ X48 )
=> ( X36 @ X48 ) )
=> ! [X50: $i,X51: $i] :
( ( X28 @ X50 @ X51 )
=> ( ? [X49: $i] : ( X28 @ X50 @ X49 )
& ( X36 @ X51 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]),c_0_6]),c_0_7]),c_0_8]),c_0_9]),c_0_10]) ).
thf(c_0_12,negated_conjecture,
! [X54: $i,X55: $i,X58: $i] :
( ( ~ ( epred1_0 @ X55 @ X54 )
| ( epred2_0 @ X54 ) )
& ( epred1_0 @ esk1_0 @ esk2_0 )
& ( ~ ( epred1_0 @ esk1_0 @ X58 )
| ~ ( epred2_0 @ esk2_0 ) ) ),
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_11])])])])]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i] :
( ~ ( epred1_0 @ esk1_0 @ X1 )
| ~ ( epred2_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_14,negated_conjecture,
epred1_0 @ esk1_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X3: $i] :
( ( epred2_0 @ X3 )
| ~ ( epred1_0 @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16,negated_conjecture,
~ ( epred2_0 @ esk2_0 ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_14]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET648^3 : TPTP v8.2.0. Released v3.6.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon May 20 11:10:23 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.21/0.51 Running higher-order theorem proving
% 0.21/0.51 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/benchmark/theBenchmark.p
% 0.21/0.52 # Version: 3.1.0-ho
% 0.21/0.52 # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.21/0.52 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.21/0.52 # Starting post_as_ho3 with 300s (1) cores
% 0.21/0.52 # Starting post_as_ho11 with 300s (1) cores
% 0.21/0.52 # Starting full_lambda_8 with 300s (1) cores
% 0.21/0.52 # post_as_ho3 with pid 9895 completed with status 0
% 0.21/0.52 # Result found by post_as_ho3
% 0.21/0.52 # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.21/0.52 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.21/0.52 # Starting post_as_ho3 with 300s (1) cores
% 0.21/0.52 # No SInE strategy applied
% 0.21/0.52 # Search class: HHHNF-FFSF00-SHSSMFNN
% 0.21/0.52 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.52 # Starting new_ho_10 with 163s (1) cores
% 0.21/0.52 # new_ho_10 with pid 9899 completed with status 0
% 0.21/0.52 # Result found by new_ho_10
% 0.21/0.52 # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.21/0.52 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.21/0.52 # Starting post_as_ho3 with 300s (1) cores
% 0.21/0.52 # No SInE strategy applied
% 0.21/0.52 # Search class: HHHNF-FFSF00-SHSSMFNN
% 0.21/0.52 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.52 # Starting new_ho_10 with 163s (1) cores
% 0.21/0.52 # Preprocessing time : 0.001 s
% 0.21/0.52 # Presaturation interreduction done
% 0.21/0.52
% 0.21/0.52 # Proof found!
% 0.21/0.52 # SZS status Theorem
% 0.21/0.52 # SZS output start CNFRefutation
% See solution above
% 0.21/0.52 # Parsed axioms : 71
% 0.21/0.52 # Removed by relevancy pruning/SinE : 0
% 0.21/0.52 # Initial clauses : 38
% 0.21/0.52 # Removed in clause preprocessing : 35
% 0.21/0.52 # Initial clauses in saturation : 3
% 0.21/0.52 # Processed clauses : 8
% 0.21/0.52 # ...of these trivial : 0
% 0.21/0.52 # ...subsumed : 0
% 0.21/0.52 # ...remaining for further processing : 7
% 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 : 1
% 0.21/0.52 # Backward-rewritten : 0
% 0.21/0.52 # Generated clauses : 2
% 0.21/0.52 # ...of the previous two non-redundant : 2
% 0.21/0.52 # ...aggressively subsumed : 0
% 0.21/0.52 # Contextual simplify-reflections : 0
% 0.21/0.52 # Paramodulations : 2
% 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 : 0
% 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 : 3
% 0.21/0.52 # Positive orientable unit clauses : 1
% 0.21/0.52 # Positive unorientable unit clauses: 0
% 0.21/0.52 # Negative unit clauses : 1
% 0.21/0.52 # Non-unit-clauses : 1
% 0.21/0.52 # Current number of unprocessed clauses: 0
% 0.21/0.52 # ...number of literals in the above : 0
% 0.21/0.52 # Current number of archived formulas : 0
% 0.21/0.52 # Current number of archived clauses : 4
% 0.21/0.52 # Clause-clause subsumption calls (NU) : 0
% 0.21/0.52 # Rec. Clause-clause subsumption calls : 0
% 0.21/0.52 # Non-unit clause-clause subsumptions : 0
% 0.21/0.52 # Unit Clause-clause subsumption calls : 1
% 0.21/0.52 # Rewrite failures with RHS unbound : 0
% 0.21/0.52 # BW rewrite match attempts : 0
% 0.21/0.52 # BW rewrite match successes : 0
% 0.21/0.52 # Condensation attempts : 8
% 0.21/0.52 # Condensation successes : 0
% 0.21/0.52 # Termbank termtop insertions : 1981
% 0.21/0.52 # Search garbage collected termcells : 263
% 0.21/0.52
% 0.21/0.52 # -------------------------------------------------
% 0.21/0.52 # User time : 0.002 s
% 0.21/0.52 # System time : 0.003 s
% 0.21/0.52 # Total time : 0.005 s
% 0.21/0.52 # Maximum resident set size: 1912 pages
% 0.21/0.52
% 0.21/0.52 # -------------------------------------------------
% 0.21/0.52 # User time : 0.005 s
% 0.21/0.52 # System time : 0.005 s
% 0.21/0.52 # Total time : 0.010 s
% 0.21/0.52 # Maximum resident set size: 1804 pages
% 0.21/0.52 % E---3.1 exiting
% 0.21/0.53 % E exiting
%------------------------------------------------------------------------------