TSTP Solution File: SET753^4 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SET753^4 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n023.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 02:55:32 EDT 2024
% Result : Theorem 0.15s 0.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 23 ( 10 unt; 8 typ; 0 def)
% Number of atoms : 40 ( 18 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 80 ( 11 ~; 7 |; 12 &; 47 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 35 ( 16 ^ 14 !; 5 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_29,type,
intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_33,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_36,type,
fun_image: ( $i > $i ) > ( $i > $o ) > $i > $o ).
thf(decl_44,type,
epred1_0: $i > $o ).
thf(decl_45,type,
epred2_0: $i > $o ).
thf(decl_46,type,
esk1_0: $i > $i ).
thf(decl_47,type,
esk2_0: $i ).
thf(decl_48,type,
esk3_0: $i ).
thf(intersection,axiom,
( intersection
= ( ^ [X9: $i > $o,X10: $i > $o,X4: $i] :
( ( X9 @ X4 )
& ( X10 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',intersection) ).
thf(subset,axiom,
( subset
= ( ^ [X16: $i > $o,X17: $i > $o] :
! [X4: $i] :
( ( X16 @ X4 )
=> ( X17 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',subset) ).
thf(fun_image,axiom,
( fun_image
= ( ^ [X22: $i > $i,X23: $i > $o,X3: $i] :
? [X1: $i] :
( ( X23 @ X1 )
& ( X3
= ( X22 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^1.ax',fun_image) ).
thf(thm,conjecture,
! [X27: $i > $o,X28: $i > $o,X22: $i > $i] : ( subset @ ( fun_image @ X22 @ ( intersection @ X27 @ X28 ) ) @ ( intersection @ ( fun_image @ X22 @ X27 ) @ ( fun_image @ X22 @ X28 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(c_0_4,plain,
( intersection
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[intersection]) ).
thf(c_0_5,plain,
( subset
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[subset]) ).
thf(c_0_6,plain,
( fun_image
= ( ^ [Z0: $i > $i,Z1: $i > $o,Z2: $i] :
? [X1: $i] :
( ( Z1 @ X1 )
& ( Z2
= ( Z0 @ X1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fun_image]) ).
thf(c_0_7,negated_conjecture,
~ ! [X27: $i > $o,X28: $i > $o,X22: $i > $i,X39: $i] :
( ? [X36: $i] :
( ( X27 @ X36 )
& ( X28 @ X36 )
& ( X39
= ( X22 @ X36 ) ) )
=> ( ? [X37: $i] :
( ( X27 @ X37 )
& ( X39
= ( X22 @ X37 ) ) )
& ? [X38: $i] :
( ( X28 @ X38 )
& ( X39
= ( X22 @ X38 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]),c_0_4]),c_0_5]),c_0_6]) ).
thf(c_0_8,negated_conjecture,
! [X51: $i,X52: $i] :
( ( epred1_0 @ esk3_0 )
& ( epred2_0 @ esk3_0 )
& ( esk2_0
= ( esk1_0 @ esk3_0 ) )
& ( ~ ( epred1_0 @ X51 )
| ( esk2_0
!= ( esk1_0 @ X51 ) )
| ~ ( epred2_0 @ X52 )
| ( esk2_0
!= ( esk1_0 @ X52 ) ) ) ),
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_7])])])])]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X3: $i] :
( ~ ( epred1_0 @ X1 )
| ( esk2_0
!= ( esk1_0 @ X1 ) )
| ~ ( epred2_0 @ X3 )
| ( esk2_0
!= ( esk1_0 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_10,negated_conjecture,
epred1_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
( esk2_0
= ( esk1_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i] :
( ( ( esk1_0 @ X1 )
!= esk2_0 )
| ~ ( epred2_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]) ).
thf(c_0_13,negated_conjecture,
epred2_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_14,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SET753^4 : TPTP v8.2.0. Released v3.6.0.
% 0.02/0.10 % Command : run_E %s %d THM
% 0.09/0.30 % Computer : n023.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon May 20 13:10:37 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.15/0.40 Running higher-order theorem proving
% 0.15/0.40 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/benchmark/theBenchmark.p
% 0.15/0.41 # Version: 3.1.0-ho
% 0.15/0.41 # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.15/0.41 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.41 # Starting new_ho_9 with 1500s (5) cores
% 0.15/0.41 # Starting post_as_ho1 with 300s (1) cores
% 0.15/0.41 # Starting sh1l with 300s (1) cores
% 0.15/0.41 # Starting post_as_ho10 with 300s (1) cores
% 0.15/0.41 # post_as_ho1 with pid 24464 completed with status 0
% 0.15/0.41 # Result found by post_as_ho1
% 0.15/0.41 # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.15/0.41 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.41 # Starting new_ho_9 with 1500s (5) cores
% 0.15/0.41 # Starting post_as_ho1 with 300s (1) cores
% 0.15/0.41 # No SInE strategy applied
% 0.15/0.41 # Search class: HUHSF-FFSS33-SHSSMSNN
% 0.15/0.41 # partial match(4): HGHNF-FFSS33-SHHSMSBN
% 0.15/0.41 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.41 # Starting new_ho_10 with 163s (1) cores
% 0.15/0.41 # new_ho_10 with pid 24467 completed with status 0
% 0.15/0.41 # Result found by new_ho_10
% 0.15/0.41 # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.15/0.41 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.41 # Starting new_ho_9 with 1500s (5) cores
% 0.15/0.41 # Starting post_as_ho1 with 300s (1) cores
% 0.15/0.41 # No SInE strategy applied
% 0.15/0.41 # Search class: HUHSF-FFSS33-SHSSMSNN
% 0.15/0.41 # partial match(4): HGHNF-FFSS33-SHHSMSBN
% 0.15/0.41 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.41 # Starting new_ho_10 with 163s (1) cores
% 0.15/0.41 # Preprocessing time : 0.001 s
% 0.15/0.41 # Presaturation interreduction done
% 0.15/0.41
% 0.15/0.41 # Proof found!
% 0.15/0.41 # SZS status Theorem
% 0.15/0.41 # SZS output start CNFRefutation
% See solution above
% 0.15/0.41 # Parsed axioms : 45
% 0.15/0.41 # Removed by relevancy pruning/SinE : 0
% 0.15/0.41 # Initial clauses : 27
% 0.15/0.41 # Removed in clause preprocessing : 22
% 0.15/0.41 # Initial clauses in saturation : 5
% 0.15/0.41 # Processed clauses : 11
% 0.15/0.41 # ...of these trivial : 0
% 0.15/0.41 # ...subsumed : 0
% 0.15/0.41 # ...remaining for further processing : 11
% 0.15/0.41 # Other redundant clauses eliminated : 0
% 0.15/0.41 # Clauses deleted for lack of memory : 0
% 0.15/0.41 # Backward-subsumed : 1
% 0.15/0.41 # Backward-rewritten : 0
% 0.15/0.41 # Generated clauses : 2
% 0.15/0.41 # ...of the previous two non-redundant : 1
% 0.15/0.41 # ...aggressively subsumed : 0
% 0.15/0.41 # Contextual simplify-reflections : 0
% 0.15/0.41 # Paramodulations : 2
% 0.15/0.41 # Factorizations : 0
% 0.15/0.41 # NegExts : 0
% 0.15/0.41 # Equation resolutions : 0
% 0.15/0.41 # Disequality decompositions : 0
% 0.15/0.41 # Total rewrite steps : 2
% 0.15/0.41 # ...of those cached : 1
% 0.15/0.41 # Propositional unsat checks : 0
% 0.15/0.41 # Propositional check models : 0
% 0.15/0.41 # Propositional check unsatisfiable : 0
% 0.15/0.41 # Propositional clauses : 0
% 0.15/0.41 # Propositional clauses after purity: 0
% 0.15/0.41 # Propositional unsat core size : 0
% 0.15/0.41 # Propositional preprocessing time : 0.000
% 0.15/0.41 # Propositional encoding time : 0.000
% 0.15/0.41 # Propositional solver time : 0.000
% 0.15/0.41 # Success case prop preproc time : 0.000
% 0.15/0.41 # Success case prop encoding time : 0.000
% 0.15/0.41 # Success case prop solver time : 0.000
% 0.15/0.41 # Current number of processed clauses : 5
% 0.15/0.41 # Positive orientable unit clauses : 4
% 0.15/0.41 # Positive unorientable unit clauses: 0
% 0.15/0.41 # Negative unit clauses : 0
% 0.15/0.41 # Non-unit-clauses : 1
% 0.15/0.41 # Current number of unprocessed clauses: 0
% 0.15/0.41 # ...number of literals in the above : 0
% 0.15/0.41 # Current number of archived formulas : 0
% 0.15/0.41 # Current number of archived clauses : 6
% 0.15/0.41 # Clause-clause subsumption calls (NU) : 3
% 0.15/0.41 # Rec. Clause-clause subsumption calls : 3
% 0.15/0.41 # Non-unit clause-clause subsumptions : 1
% 0.15/0.41 # Unit Clause-clause subsumption calls : 0
% 0.15/0.41 # Rewrite failures with RHS unbound : 0
% 0.15/0.41 # BW rewrite match attempts : 0
% 0.15/0.41 # BW rewrite match successes : 0
% 0.15/0.41 # Condensation attempts : 11
% 0.15/0.41 # Condensation successes : 0
% 0.15/0.41 # Termbank termtop insertions : 1473
% 0.15/0.41 # Search garbage collected termcells : 278
% 0.15/0.41
% 0.15/0.41 # -------------------------------------------------
% 0.15/0.41 # User time : 0.002 s
% 0.15/0.41 # System time : 0.002 s
% 0.15/0.41 # Total time : 0.004 s
% 0.15/0.41 # Maximum resident set size: 1872 pages
% 0.15/0.41
% 0.15/0.41 # -------------------------------------------------
% 0.15/0.41 # User time : 0.004 s
% 0.15/0.41 # System time : 0.003 s
% 0.15/0.41 # Total time : 0.007 s
% 0.15/0.41 # Maximum resident set size: 1780 pages
% 0.15/0.41 % E---3.1 exiting
% 0.15/0.41 % E exiting
%------------------------------------------------------------------------------