TSTP Solution File: SET752^4 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SET752^4 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n029.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 09:20:08 EDT 2024
% Result : Theorem 0.16s 0.43s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 38 ( 9 unt; 9 typ; 0 def)
% Number of atoms : 121 ( 55 equ; 0 cnn)
% Maximal formula atoms : 44 ( 4 avg)
% Number of connectives : 244 ( 29 ~; 72 |; 16 &; 126 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 33 ( 12 ^ 16 !; 5 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_27,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $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(decl_49,type,
esk4_0: $i ).
thf(decl_50,type,
esk5_0: $i ).
thf(union,axiom,
( union
= ( ^ [X5: $i > $o,X6: $i > $o,X4: $i] :
( ( X5 @ X4 )
| ( X6 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qC5acoxxSz/E---3.1_6069.p',union) ).
thf(fun_image,axiom,
( fun_image
= ( ^ [X22: $i > $i,X23: $i > $o,X3: $i] :
? [X1: $i] :
( ( X23 @ X1 )
& ( X3
= ( X22 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qC5acoxxSz/E---3.1_6069.p',fun_image) ).
thf(thm,conjecture,
! [X27: $i > $o,X28: $i > $o,X22: $i > $i] :
( ( fun_image @ X22 @ ( union @ X27 @ X28 ) )
= ( union @ ( fun_image @ X22 @ X27 ) @ ( fun_image @ X22 @ X28 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qC5acoxxSz/E---3.1_6069.p',thm) ).
thf(c_0_3,plain,
( union
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[union]) ).
thf(c_0_4,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_5,negated_conjecture,
~ ! [X27: $i > $o,X28: $i > $o,X22: $i > $i,X42: $i] :
( ? [X36: $i] :
( ( ( X27 @ X36 )
| ( X28 @ X36 ) )
& ( X42
= ( X22 @ X36 ) ) )
<=> ( ? [X37: $i] :
( ( X27 @ X37 )
& ( X42
= ( X22 @ X37 ) ) )
| ? [X38: $i] :
( ( X28 @ X38 )
& ( X42
= ( X22 @ X38 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]),c_0_3]),c_0_4])]) ).
thf(c_0_6,negated_conjecture,
! [X50: $i,X51: $i,X52: $i] :
( ( ~ ( epred1_0 @ X51 )
| ( esk2_0
!= ( esk1_0 @ X51 ) )
| ~ ( epred1_0 @ X50 )
| ( esk2_0
!= ( esk1_0 @ X50 ) ) )
& ( ~ ( epred2_0 @ X52 )
| ( esk2_0
!= ( esk1_0 @ X52 ) )
| ~ ( epred1_0 @ X50 )
| ( esk2_0
!= ( esk1_0 @ X50 ) ) )
& ( ~ ( epred1_0 @ X51 )
| ( esk2_0
!= ( esk1_0 @ X51 ) )
| ~ ( epred2_0 @ X50 )
| ( esk2_0
!= ( esk1_0 @ X50 ) ) )
& ( ~ ( epred2_0 @ X52 )
| ( esk2_0
!= ( esk1_0 @ X52 ) )
| ~ ( epred2_0 @ X50 )
| ( esk2_0
!= ( esk1_0 @ X50 ) ) )
& ( ( epred2_0 @ esk5_0 )
| ( epred1_0 @ esk4_0 )
| ( epred1_0 @ esk3_0 )
| ( epred2_0 @ esk3_0 ) )
& ( ( esk2_0
= ( esk1_0 @ esk5_0 ) )
| ( epred1_0 @ esk4_0 )
| ( epred1_0 @ esk3_0 )
| ( epred2_0 @ esk3_0 ) )
& ( ( epred2_0 @ esk5_0 )
| ( esk2_0
= ( esk1_0 @ esk4_0 ) )
| ( epred1_0 @ esk3_0 )
| ( epred2_0 @ esk3_0 ) )
& ( ( esk2_0
= ( esk1_0 @ esk5_0 ) )
| ( esk2_0
= ( esk1_0 @ esk4_0 ) )
| ( epred1_0 @ esk3_0 )
| ( epred2_0 @ esk3_0 ) )
& ( ( epred2_0 @ esk5_0 )
| ( epred1_0 @ esk4_0 )
| ( esk2_0
= ( esk1_0 @ esk3_0 ) ) )
& ( ( esk2_0
= ( esk1_0 @ esk5_0 ) )
| ( epred1_0 @ esk4_0 )
| ( esk2_0
= ( esk1_0 @ esk3_0 ) ) )
& ( ( epred2_0 @ esk5_0 )
| ( esk2_0
= ( esk1_0 @ esk4_0 ) )
| ( esk2_0
= ( esk1_0 @ esk3_0 ) ) )
& ( ( esk2_0
= ( esk1_0 @ esk5_0 ) )
| ( esk2_0
= ( esk1_0 @ esk4_0 ) )
| ( esk2_0
= ( esk1_0 @ esk3_0 ) ) ) ),
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_5])])])])])]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i,X3: $i] :
( ~ ( epred1_0 @ X1 )
| ( esk2_0
!= ( esk1_0 @ X1 ) )
| ~ ( epred1_0 @ X3 )
| ( esk2_0
!= ( esk1_0 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i,X3: $i] :
( ~ ( epred2_0 @ X1 )
| ( esk2_0
!= ( esk1_0 @ X1 ) )
| ~ ( epred2_0 @ X3 )
| ( esk2_0
!= ( esk1_0 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i] :
( ( ( esk1_0 @ X1 )
!= esk2_0 )
| ~ ( epred1_0 @ X1 ) ),
inference(condense,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
( ( epred2_0 @ esk5_0 )
| ( epred1_0 @ esk4_0 )
| ( esk2_0
= ( esk1_0 @ esk3_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_11,negated_conjecture,
( ( epred2_0 @ esk5_0 )
| ( esk2_0
= ( esk1_0 @ esk4_0 ) )
| ( esk2_0
= ( esk1_0 @ esk3_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_12,negated_conjecture,
( ( esk2_0
= ( esk1_0 @ esk5_0 ) )
| ( epred1_0 @ esk4_0 )
| ( esk2_0
= ( esk1_0 @ esk3_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_13,negated_conjecture,
( ( esk2_0
= ( esk1_0 @ esk5_0 ) )
| ( esk2_0
= ( esk1_0 @ esk4_0 ) )
| ( esk2_0
= ( esk1_0 @ esk3_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_14,negated_conjecture,
( ( esk2_0
= ( esk1_0 @ esk5_0 ) )
| ( epred1_0 @ esk4_0 )
| ( epred1_0 @ esk3_0 )
| ( epred2_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_15,negated_conjecture,
( ( esk2_0
= ( esk1_0 @ esk5_0 ) )
| ( esk2_0
= ( esk1_0 @ esk4_0 ) )
| ( epred1_0 @ esk3_0 )
| ( epred2_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i] :
( ( ( esk1_0 @ X1 )
!= esk2_0 )
| ~ ( epred2_0 @ X1 ) ),
inference(condense,[status(thm)],[c_0_8]) ).
thf(c_0_17,negated_conjecture,
( ( ( esk1_0 @ esk3_0 )
= esk2_0 )
| ( epred2_0 @ esk5_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
thf(c_0_18,negated_conjecture,
( ( ( esk1_0 @ esk5_0 )
= esk2_0 )
| ( ( esk1_0 @ esk3_0 )
= esk2_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_12]),c_0_13]) ).
thf(c_0_19,negated_conjecture,
( ( epred2_0 @ esk5_0 )
| ( epred1_0 @ esk4_0 )
| ( epred1_0 @ esk3_0 )
| ( epred2_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_20,negated_conjecture,
( ( epred2_0 @ esk5_0 )
| ( esk2_0
= ( esk1_0 @ esk4_0 ) )
| ( epred1_0 @ esk3_0 )
| ( epred2_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_21,negated_conjecture,
( ( ( esk1_0 @ esk5_0 )
= esk2_0 )
| ( epred2_0 @ esk3_0 )
| ( epred1_0 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_14]),c_0_15]) ).
thf(c_0_22,negated_conjecture,
( ( esk1_0 @ esk3_0 )
= esk2_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
thf(c_0_23,negated_conjecture,
( ( epred2_0 @ esk5_0 )
| ( epred2_0 @ esk3_0 )
| ( epred1_0 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_19]),c_0_20]) ).
thf(c_0_24,negated_conjecture,
( ( ( esk1_0 @ esk5_0 )
= esk2_0 )
| ( epred2_0 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_21]),c_0_22])]) ).
thf(c_0_25,negated_conjecture,
( ( epred2_0 @ esk3_0 )
| ( epred2_0 @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_23]),c_0_22])]) ).
thf(c_0_26,negated_conjecture,
( ( esk1_0 @ esk5_0 )
= esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_24]),c_0_22])]) ).
thf(c_0_27,negated_conjecture,
epred2_0 @ esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_25]),c_0_26])]) ).
thf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_27]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET752^4 : TPTP v8.1.2. Released v3.6.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n029.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri May 3 10:42:22 EDT 2024
% 0.16/0.31 % CPUTime :
% 0.16/0.41 Running higher-order theorem proving
% 0.16/0.42 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.qC5acoxxSz/E---3.1_6069.p
% 0.16/0.43 # Version: 3.1.0-ho
% 0.16/0.43 # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.16/0.43 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.43 # Starting new_ho_9 with 1500s (5) cores
% 0.16/0.43 # Starting post_as_ho1 with 300s (1) cores
% 0.16/0.43 # Starting sh1l with 300s (1) cores
% 0.16/0.43 # Starting post_as_ho10 with 300s (1) cores
% 0.16/0.43 # post_as_ho1 with pid 6151 completed with status 0
% 0.16/0.43 # Result found by post_as_ho1
% 0.16/0.43 # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.16/0.43 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.43 # Starting new_ho_9 with 1500s (5) cores
% 0.16/0.43 # Starting post_as_ho1 with 300s (1) cores
% 0.16/0.43 # No SInE strategy applied
% 0.16/0.43 # Search class: HGHSF-FFSM33-SHSSMFNN
% 0.16/0.43 # partial match(3): HGHNF-FFSM00-SHSSMFNN
% 0.16/0.43 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.43 # Starting new_ho_10 with 163s (1) cores
% 0.16/0.43 # new_ho_10 with pid 6154 completed with status 0
% 0.16/0.43 # Result found by new_ho_10
% 0.16/0.43 # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.16/0.43 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.43 # Starting new_ho_9 with 1500s (5) cores
% 0.16/0.43 # Starting post_as_ho1 with 300s (1) cores
% 0.16/0.43 # No SInE strategy applied
% 0.16/0.43 # Search class: HGHSF-FFSM33-SHSSMFNN
% 0.16/0.43 # partial match(3): HGHNF-FFSM00-SHSSMFNN
% 0.16/0.43 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.43 # Starting new_ho_10 with 163s (1) cores
% 0.16/0.43 # Preprocessing time : 0.001 s
% 0.16/0.43 # Presaturation interreduction done
% 0.16/0.43
% 0.16/0.43 # Proof found!
% 0.16/0.43 # SZS status Theorem
% 0.16/0.43 # SZS output start CNFRefutation
% See solution above
% 0.16/0.43 # Parsed axioms : 45
% 0.16/0.43 # Removed by relevancy pruning/SinE : 0
% 0.16/0.43 # Initial clauses : 35
% 0.16/0.43 # Removed in clause preprocessing : 22
% 0.16/0.43 # Initial clauses in saturation : 13
% 0.16/0.43 # Processed clauses : 33
% 0.16/0.43 # ...of these trivial : 0
% 0.16/0.43 # ...subsumed : 2
% 0.16/0.43 # ...remaining for further processing : 31
% 0.16/0.43 # Other redundant clauses eliminated : 0
% 0.16/0.43 # Clauses deleted for lack of memory : 0
% 0.16/0.43 # Backward-subsumed : 10
% 0.16/0.43 # Backward-rewritten : 4
% 0.16/0.43 # Generated clauses : 13
% 0.16/0.43 # ...of the previous two non-redundant : 12
% 0.16/0.43 # ...aggressively subsumed : 0
% 0.16/0.43 # Contextual simplify-reflections : 5
% 0.16/0.43 # Paramodulations : 13
% 0.16/0.43 # Factorizations : 0
% 0.16/0.43 # NegExts : 0
% 0.16/0.43 # Equation resolutions : 0
% 0.16/0.43 # Disequality decompositions : 0
% 0.16/0.43 # Total rewrite steps : 9
% 0.16/0.43 # ...of those cached : 6
% 0.16/0.43 # Propositional unsat checks : 0
% 0.16/0.43 # Propositional check models : 0
% 0.16/0.43 # Propositional check unsatisfiable : 0
% 0.16/0.43 # Propositional clauses : 0
% 0.16/0.43 # Propositional clauses after purity: 0
% 0.16/0.43 # Propositional unsat core size : 0
% 0.16/0.43 # Propositional preprocessing time : 0.000
% 0.16/0.43 # Propositional encoding time : 0.000
% 0.16/0.43 # Propositional solver time : 0.000
% 0.16/0.43 # Success case prop preproc time : 0.000
% 0.16/0.43 # Success case prop encoding time : 0.000
% 0.16/0.43 # Success case prop solver time : 0.000
% 0.16/0.43 # Current number of processed clauses : 6
% 0.16/0.43 # Positive orientable unit clauses : 4
% 0.16/0.43 # Positive unorientable unit clauses: 0
% 0.16/0.43 # Negative unit clauses : 0
% 0.16/0.43 # Non-unit-clauses : 2
% 0.16/0.43 # Current number of unprocessed clauses: 0
% 0.16/0.43 # ...number of literals in the above : 0
% 0.16/0.43 # Current number of archived formulas : 0
% 0.16/0.43 # Current number of archived clauses : 25
% 0.16/0.43 # Clause-clause subsumption calls (NU) : 52
% 0.16/0.43 # Rec. Clause-clause subsumption calls : 22
% 0.16/0.43 # Non-unit clause-clause subsumptions : 19
% 0.16/0.43 # Unit Clause-clause subsumption calls : 1
% 0.16/0.43 # Rewrite failures with RHS unbound : 0
% 0.16/0.43 # BW rewrite match attempts : 3
% 0.16/0.43 # BW rewrite match successes : 3
% 0.16/0.43 # Condensation attempts : 33
% 0.16/0.43 # Condensation successes : 2
% 0.16/0.43 # Termbank termtop insertions : 2034
% 0.16/0.43 # Search garbage collected termcells : 380
% 0.16/0.43
% 0.16/0.43 # -------------------------------------------------
% 0.16/0.43 # User time : 0.005 s
% 0.16/0.43 # System time : 0.001 s
% 0.16/0.43 # Total time : 0.006 s
% 0.16/0.43 # Maximum resident set size: 1908 pages
% 0.16/0.43
% 0.16/0.43 # -------------------------------------------------
% 0.16/0.43 # User time : 0.006 s
% 0.16/0.43 # System time : 0.003 s
% 0.16/0.43 # Total time : 0.009 s
% 0.16/0.43 # Maximum resident set size: 1768 pages
% 0.16/0.43 % E---3.1 exiting
% 0.16/0.43 % E exiting
%------------------------------------------------------------------------------