TSTP Solution File: SET669^3 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SET669^3 : TPTP v8.1.2. Released v3.6.0.
% 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 09:19:51 EDT 2024
% Result : Theorem 0.21s 0.49s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 29 ( 13 unt; 9 typ; 0 def)
% Number of atoms : 63 ( 17 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 117 ( 18 ~; 16 |; 9 &; 65 @)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 57 ( 25 ^ 26 !; 6 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_33,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_38,type,
id_rel: ( $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,
esk1_0: $i ).
thf(decl_59,type,
esk2_0: $i ).
thf(decl_60,type,
esk3_0: $i ).
thf(subset,axiom,
( subset
= ( ^ [X16: $i > $o,X17: $i > $o] :
! [X4: $i] :
( ( X16 @ X4 )
=> ( X17 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LZauHkvSy1/E---3.1_8658.p',subset) ).
thf(id_rel,axiom,
( id_rel
= ( ^ [X25: $i > $o,X1: $i,X3: $i] :
( ( X25 @ X1 )
& ( X1 = X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LZauHkvSy1/E---3.1_8658.p',id_rel) ).
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/tmp/tmp.LZauHkvSy1/E---3.1_8658.p',sub_rel) ).
thf(rel_codomain,axiom,
( rel_codomain
= ( ^ [X28: $i > $i > $o,X3: $i] :
? [X1: $i] : ( X28 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LZauHkvSy1/E---3.1_8658.p',rel_codomain) ).
thf(rel_domain,axiom,
( rel_domain
= ( ^ [X28: $i > $i > $o,X1: $i] :
? [X3: $i] : ( X28 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LZauHkvSy1/E---3.1_8658.p',rel_domain) ).
thf(thm,conjecture,
! [X28: $i > $i > $o] :
( ( sub_rel
@ ( id_rel
@ ^ [X1: $i] : $true )
@ X28 )
=> ( ( subset
@ ^ [X1: $i] : $true
@ ( rel_domain @ X28 ) )
& ( ( ^ [X1: $i] : $true )
= ( rel_codomain @ X28 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LZauHkvSy1/E---3.1_8658.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,
( id_rel
= ( ^ [Z0: $i > $o,Z1: $i,Z2: $i] :
( ( Z0 @ Z1 )
& ( Z1 = Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[id_rel]) ).
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] :
( ! [X45: $i,X46: $i] :
( ( $true
& ( X45 = X46 ) )
=> ( X28 @ X45 @ X46 ) )
=> ( ! [X48: $i] :
( $true
=> ? [X47: $i] : ( X28 @ X48 @ X47 ) )
& ! [X50: $i] :
( $true
<=> ? [X49: $i] : ( X28 @ X49 @ X50 ) ) ) ),
inference(fof_simplification,[status(thm)],[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(fof_simplification,[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,
! [X52: $i,X53: $i,X55: $i,X57: $i] :
( ( ~ $true
| ( X52 != X53 )
| ( epred1_0 @ X52 @ X53 ) )
& ( ~ $true
| ~ ( epred1_0 @ X57 @ esk2_0 )
| $true )
& ( $true
| ( epred1_0 @ esk3_0 @ esk2_0 )
| $true )
& ( ~ $true
| ~ ( epred1_0 @ X57 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ X55 ) )
& ( $true
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ X55 ) ) ),
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)],[c_0_11])])])])])]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X3: $i] :
( ( epred1_0 @ X1 @ X3 )
| ~ $true
| ( X1 != X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X3: $i] :
( ~ $true
| ~ ( epred1_0 @ X1 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X3: $i] :
( ( epred1_0 @ X1 @ X3 )
| ( X1 != X3 ) ),
inference(cn,[status(thm)],[c_0_13]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X3: $i] :
( ~ ( epred1_0 @ X1 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ X3 ) ),
inference(cn,[status(thm)],[c_0_14]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i] : ( epred1_0 @ X1 @ X1 ),
inference(er,[status(thm)],[c_0_15]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i] :
~ ( epred1_0 @ esk1_0 @ X1 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_19,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_18,c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET669^3 : TPTP v8.1.2. Released v3.6.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 10:26:03 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running higher-order theorem proving
% 0.21/0.48 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.LZauHkvSy1/E---3.1_8658.p
% 0.21/0.49 # Version: 3.1.0-ho
% 0.21/0.49 # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.21/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.49 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.21/0.49 # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.21/0.49 # Starting almost_fo_3_lam with 300s (1) cores
% 0.21/0.49 # Starting post_as_ho1 with 300s (1) cores
% 0.21/0.49 # ehoh_best2_full_lfho with pid 8737 completed with status 0
% 0.21/0.49 # Result found by ehoh_best2_full_lfho
% 0.21/0.49 # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.21/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.49 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.21/0.49 # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.21/0.49 # No SInE strategy applied
% 0.21/0.49 # Search class: HHHSF-FFSF00-SHSSMFNN
% 0.21/0.49 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.49 # Starting new_ho_10 with 163s (1) cores
% 0.21/0.49 # new_ho_10 with pid 8741 completed with status 0
% 0.21/0.49 # Result found by new_ho_10
% 0.21/0.49 # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.21/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.49 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.21/0.49 # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.21/0.49 # No SInE strategy applied
% 0.21/0.49 # Search class: HHHSF-FFSF00-SHSSMFNN
% 0.21/0.49 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.49 # Starting new_ho_10 with 163s (1) cores
% 0.21/0.49 # Preprocessing time : 0.001 s
% 0.21/0.49 # Presaturation interreduction done
% 0.21/0.49
% 0.21/0.49 # Proof found!
% 0.21/0.49 # SZS status Theorem
% 0.21/0.49 # SZS output start CNFRefutation
% See solution above
% 0.21/0.49 # Parsed axioms : 71
% 0.21/0.49 # Removed by relevancy pruning/SinE : 0
% 0.21/0.49 # Initial clauses : 40
% 0.21/0.49 # Removed in clause preprocessing : 38
% 0.21/0.49 # Initial clauses in saturation : 2
% 0.21/0.49 # Processed clauses : 6
% 0.21/0.49 # ...of these trivial : 0
% 0.21/0.49 # ...subsumed : 0
% 0.21/0.49 # ...remaining for further processing : 6
% 0.21/0.49 # Other redundant clauses eliminated : 1
% 0.21/0.49 # Clauses deleted for lack of memory : 0
% 0.21/0.49 # Backward-subsumed : 1
% 0.21/0.49 # Backward-rewritten : 0
% 0.21/0.49 # Generated clauses : 3
% 0.21/0.49 # ...of the previous two non-redundant : 2
% 0.21/0.49 # ...aggressively subsumed : 0
% 0.21/0.49 # Contextual simplify-reflections : 0
% 0.21/0.49 # Paramodulations : 2
% 0.21/0.49 # Factorizations : 0
% 0.21/0.49 # NegExts : 0
% 0.21/0.49 # Equation resolutions : 1
% 0.21/0.49 # Disequality decompositions : 0
% 0.21/0.49 # Total rewrite steps : 0
% 0.21/0.49 # ...of those cached : 0
% 0.21/0.49 # Propositional unsat checks : 0
% 0.21/0.49 # Propositional check models : 0
% 0.21/0.49 # Propositional check unsatisfiable : 0
% 0.21/0.49 # Propositional clauses : 0
% 0.21/0.49 # Propositional clauses after purity: 0
% 0.21/0.49 # Propositional unsat core size : 0
% 0.21/0.49 # Propositional preprocessing time : 0.000
% 0.21/0.49 # Propositional encoding time : 0.000
% 0.21/0.49 # Propositional solver time : 0.000
% 0.21/0.49 # Success case prop preproc time : 0.000
% 0.21/0.49 # Success case prop encoding time : 0.000
% 0.21/0.49 # Success case prop solver time : 0.000
% 0.21/0.49 # Current number of processed clauses : 2
% 0.21/0.49 # Positive orientable unit clauses : 1
% 0.21/0.49 # Positive unorientable unit clauses: 0
% 0.21/0.49 # Negative unit clauses : 1
% 0.21/0.49 # Non-unit-clauses : 0
% 0.21/0.49 # Current number of unprocessed clauses: 0
% 0.21/0.49 # ...number of literals in the above : 0
% 0.21/0.49 # Current number of archived formulas : 0
% 0.21/0.49 # Current number of archived clauses : 3
% 0.21/0.49 # Clause-clause subsumption calls (NU) : 0
% 0.21/0.49 # Rec. Clause-clause subsumption calls : 0
% 0.21/0.49 # Non-unit clause-clause subsumptions : 0
% 0.21/0.49 # Unit Clause-clause subsumption calls : 3
% 0.21/0.49 # Rewrite failures with RHS unbound : 0
% 0.21/0.49 # BW rewrite match attempts : 2
% 0.21/0.49 # BW rewrite match successes : 0
% 0.21/0.49 # Condensation attempts : 6
% 0.21/0.49 # Condensation successes : 0
% 0.21/0.49 # Termbank termtop insertions : 2159
% 0.21/0.49 # Search garbage collected termcells : 319
% 0.21/0.49
% 0.21/0.49 # -------------------------------------------------
% 0.21/0.49 # User time : 0.004 s
% 0.21/0.49 # System time : 0.002 s
% 0.21/0.49 # Total time : 0.006 s
% 0.21/0.49 # Maximum resident set size: 1928 pages
% 0.21/0.49
% 0.21/0.49 # -------------------------------------------------
% 0.21/0.49 # User time : 0.008 s
% 0.21/0.49 # System time : 0.002 s
% 0.21/0.49 # Total time : 0.011 s
% 0.21/0.49 # Maximum resident set size: 1800 pages
% 0.21/0.49 % E---3.1 exiting
% 0.21/0.50 % E exiting
%------------------------------------------------------------------------------