TSTP Solution File: SEU682^2 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU682^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n020.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 03:29:06 EDT 2024
% Result : Theorem 0.16s 0.43s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 37 ( 11 unt; 13 typ; 0 def)
% Number of atoms : 84 ( 3 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 451 ( 31 ~; 41 |; 7 &; 339 @)
% ( 1 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 39 ( 39 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 84 ( 6 ^ 78 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
subset: $i > $i > $o ).
thf(decl_24,type,
kpair: $i > $i > $i ).
thf(decl_25,type,
cartprod: $i > $i > $i ).
thf(decl_26,type,
breln: $i > $i > $i > $o ).
thf(decl_27,type,
brelnall1: $o ).
thf(decl_28,type,
esk1_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_29,type,
esk2_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_30,type,
esk3_0: $i ).
thf(decl_31,type,
esk4_0: $i ).
thf(decl_32,type,
esk5_0: $i ).
thf(decl_33,type,
epred1_0: $i > $o ).
thf(decl_34,type,
esk6_0: $i ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(brelnall1,axiom,
( brelnall1
<=> ! [X1: $i,X2: $i,X4: $i] :
( ( breln @ X1 @ X2 @ X4 )
=> ! [X5: $i > $o] :
( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X2 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X4 )
=> ( X5 @ ( kpair @ X6 @ X7 ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6 @ X4 )
=> ( X5 @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).
thf(brelnall2,conjecture,
( brelnall1
=> ! [X1: $i,X2: $i,X4: $i] :
( ( breln @ X1 @ X2 @ X4 )
=> ! [X5: $i > $o] :
( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X2 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X4 )
=> ( X5 @ ( kpair @ X6 @ X7 ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6 @ X4 )
=> ( X5 @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall2) ).
thf(c_0_3,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_4,axiom,
( brelnall1
= ( ! [X1: $i,X2: $i,X4: $i] :
( ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
=> ! [X5: $i > $o] :
( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X2 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X4 )
=> ( X5 @ ( kpair @ X6 @ X7 ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6 @ X4 )
=> ( X5 @ X6 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall1,c_0_3]) ).
thf(c_0_5,negated_conjecture,
~ ( ! [X22: $i,X23: $i,X24: $i] :
( ( subset @ X24 @ ( cartprod @ X22 @ X23 ) )
=> ! [X25: $i > $o] :
( ! [X26: $i] :
( ( in @ X26 @ X22 )
=> ! [X27: $i] :
( ( in @ X27 @ X23 )
=> ( ( in @ ( kpair @ X26 @ X27 ) @ X24 )
=> ( X25 @ ( kpair @ X26 @ X27 ) ) ) ) )
=> ! [X28: $i] :
( ( in @ X28 @ X24 )
=> ( X25 @ X28 ) ) ) )
=> ! [X1: $i,X2: $i,X4: $i] :
( ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
=> ! [X5: $i > $o] :
( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X2 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X4 )
=> ( X5 @ ( kpair @ X6 @ X7 ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6 @ X4 )
=> ( X5 @ X6 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[brelnall2]),c_0_3]),c_0_4]) ).
thf(c_0_6,negated_conjecture,
! [X29: $i,X30: $i,X31: $i,X32: $i > $o,X35: $i,X40: $i,X41: $i] :
( ( ( in @ ( esk1_4 @ X29 @ X30 @ X31 @ X32 ) @ X29 )
| ~ ( in @ X35 @ X31 )
| ( X32 @ X35 )
| ~ ( subset @ X31 @ ( cartprod @ X29 @ X30 ) ) )
& ( ( in @ ( esk2_4 @ X29 @ X30 @ X31 @ X32 ) @ X30 )
| ~ ( in @ X35 @ X31 )
| ( X32 @ X35 )
| ~ ( subset @ X31 @ ( cartprod @ X29 @ X30 ) ) )
& ( ( in @ ( kpair @ ( esk1_4 @ X29 @ X30 @ X31 @ X32 ) @ ( esk2_4 @ X29 @ X30 @ X31 @ X32 ) ) @ X31 )
| ~ ( in @ X35 @ X31 )
| ( X32 @ X35 )
| ~ ( subset @ X31 @ ( cartprod @ X29 @ X30 ) ) )
& ( ~ ( X32 @ ( kpair @ ( esk1_4 @ X29 @ X30 @ X31 @ X32 ) @ ( esk2_4 @ X29 @ X30 @ X31 @ X32 ) ) )
| ~ ( in @ X35 @ X31 )
| ( X32 @ X35 )
| ~ ( subset @ X31 @ ( cartprod @ X29 @ X30 ) ) )
& ( subset @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ) )
& ( ~ ( in @ X40 @ esk3_0 )
| ~ ( in @ X41 @ esk4_0 )
| ~ ( in @ ( kpair @ X40 @ X41 ) @ esk5_0 )
| ( epred1_0 @ ( kpair @ X40 @ X41 ) ) )
& ( in @ esk6_0 @ esk5_0 )
& ~ ( epred1_0 @ esk6_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,X5: $i > $o,X4: $i,X3: $i,X2: $i] :
( ( in @ ( kpair @ ( esk1_4 @ X1 @ X2 @ X3 @ X5 ) @ ( esk2_4 @ X1 @ X2 @ X3 @ X5 ) ) @ X3 )
| ( X5 @ X4 )
| ~ ( in @ X4 @ X3 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
in @ esk6_0 @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X5: $i > $o,X4: $i,X3: $i,X2: $i] :
( ( in @ ( esk1_4 @ X1 @ X2 @ X3 @ X5 ) @ X1 )
| ( X5 @ X4 )
| ~ ( in @ X4 @ X3 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X5: $i > $o,X4: $i,X3: $i,X2: $i] :
( ( in @ ( esk2_4 @ X1 @ X2 @ X3 @ X5 ) @ X2 )
| ( X5 @ X4 )
| ~ ( in @ X4 @ X3 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X5: $i > $o,X2: $i] :
( ( in @ ( kpair @ ( esk1_4 @ X1 @ X2 @ esk5_0 @ X5 ) @ ( esk2_4 @ X1 @ X2 @ esk5_0 @ X5 ) ) @ esk5_0 )
| ( X5 @ esk6_0 )
| ~ ( subset @ esk5_0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_12,negated_conjecture,
subset @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X5: $i > $o,X2: $i] :
( ( in @ ( esk1_4 @ X1 @ X2 @ esk5_0 @ X5 ) @ X1 )
| ( X5 @ esk6_0 )
| ~ ( subset @ esk5_0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X5: $i > $o,X2: $i] :
( ( in @ ( esk2_4 @ X1 @ X2 @ esk5_0 @ X5 ) @ X2 )
| ( X5 @ esk6_0 )
| ~ ( subset @ esk5_0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_10,c_0_8]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X2: $i] :
( ( epred1_0 @ ( kpair @ X1 @ X2 ) )
| ~ ( in @ X1 @ esk3_0 )
| ~ ( in @ X2 @ esk4_0 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_16,negated_conjecture,
! [X5: $i > $o] :
( ( in @ ( kpair @ ( esk1_4 @ esk3_0 @ esk4_0 @ esk5_0 @ X5 ) @ ( esk2_4 @ esk3_0 @ esk4_0 @ esk5_0 @ X5 ) ) @ esk5_0 )
| ( X5 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_17,negated_conjecture,
! [X5: $i > $o] :
( ( in @ ( esk1_4 @ esk3_0 @ esk4_0 @ esk5_0 @ X5 ) @ esk3_0 )
| ( X5 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
thf(c_0_18,negated_conjecture,
! [X5: $i > $o] :
( ( in @ ( esk2_4 @ esk3_0 @ esk4_0 @ esk5_0 @ X5 ) @ esk4_0 )
| ( X5 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i,X5: $i > $o,X4: $i,X3: $i,X2: $i] :
( ( X5 @ X4 )
| ~ ( X5 @ ( kpair @ ( esk1_4 @ X1 @ X2 @ X3 @ X5 ) @ ( esk2_4 @ X1 @ X2 @ X3 @ X5 ) ) )
| ~ ( in @ X4 @ X3 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_20,negated_conjecture,
! [X5: $i > $o] :
( ( epred1_0 @ ( kpair @ ( esk1_4 @ esk3_0 @ esk4_0 @ esk5_0 @ X5 ) @ ( esk2_4 @ esk3_0 @ esk4_0 @ esk5_0 @ X5 ) ) )
| ( X5 @ esk6_0 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]) ).
thf(c_0_21,negated_conjecture,
~ ( epred1_0 @ esk6_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_22,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ X1 )
| ~ ( in @ X1 @ esk5_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_12])]),c_0_21]) ).
thf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_8]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU682^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.12/0.30 % Computer : n020.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Sun May 19 16:02:23 EDT 2024
% 0.16/0.30 % CPUTime :
% 0.16/0.42 Running higher-order theorem proving
% 0.16/0.42 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
% 0.16/0.43 # Version: 3.1.0-ho
% 0.16/0.43 # Preprocessing class: HSSSSMSSSLSNSSA.
% 0.16/0.43 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.43 # Starting new_ho_10 with 1500s (5) cores
% 0.16/0.43 # Starting sh5l with 300s (1) cores
% 0.16/0.43 # Starting new_bool_1 with 300s (1) cores
% 0.16/0.43 # Starting new_bool_2 with 300s (1) cores
% 0.16/0.43 # new_ho_10 with pid 14412 completed with status 0
% 0.16/0.43 # Result found by new_ho_10
% 0.16/0.43 # Preprocessing class: HSSSSMSSSLSNSSA.
% 0.16/0.43 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.43 # Starting new_ho_10 with 1500s (5) cores
% 0.16/0.43 # No SInE strategy applied
% 0.16/0.43 # Search class: HGUNF-FFSF33-SSSFMMBN
% 0.16/0.43 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.43 # Starting new_ho_10 with 901s (1) cores
% 0.16/0.43 # Starting sh5l with 151s (1) cores
% 0.16/0.43 # Starting new_bool_1 with 151s (1) cores
% 0.16/0.43 # Starting new_bool_2 with 151s (1) cores
% 0.16/0.43 # Starting new_bool_9 with 146s (1) cores
% 0.16/0.43 # sh5l with pid 14418 completed with status 0
% 0.16/0.43 # Result found by sh5l
% 0.16/0.43 # Preprocessing class: HSSSSMSSSLSNSSA.
% 0.16/0.43 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.43 # Starting new_ho_10 with 1500s (5) cores
% 0.16/0.43 # No SInE strategy applied
% 0.16/0.43 # Search class: HGUNF-FFSF33-SSSFMMBN
% 0.16/0.43 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.43 # Starting new_ho_10 with 901s (1) cores
% 0.16/0.43 # Starting sh5l with 151s (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 : 9
% 0.16/0.43 # Removed by relevancy pruning/SinE : 0
% 0.16/0.43 # Initial clauses : 14
% 0.16/0.43 # Removed in clause preprocessing : 6
% 0.16/0.43 # Initial clauses in saturation : 8
% 0.16/0.43 # Processed clauses : 26
% 0.16/0.43 # ...of these trivial : 0
% 0.16/0.43 # ...subsumed : 0
% 0.16/0.43 # ...remaining for further processing : 26
% 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 : 1
% 0.16/0.43 # Backward-rewritten : 0
% 0.16/0.43 # Generated clauses : 20
% 0.16/0.43 # ...of the previous two non-redundant : 18
% 0.16/0.43 # ...aggressively subsumed : 0
% 0.16/0.43 # Contextual simplify-reflections : 2
% 0.16/0.43 # Paramodulations : 19
% 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 : 1
% 0.16/0.43 # ...of those cached : 0
% 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 : 17
% 0.16/0.43 # Positive orientable unit clauses : 2
% 0.16/0.43 # Positive unorientable unit clauses: 0
% 0.16/0.43 # Negative unit clauses : 1
% 0.16/0.43 # Non-unit-clauses : 14
% 0.16/0.43 # Current number of unprocessed clauses: 8
% 0.16/0.43 # ...number of literals in the above : 31
% 0.16/0.43 # Current number of archived formulas : 0
% 0.16/0.43 # Current number of archived clauses : 9
% 0.16/0.43 # Clause-clause subsumption calls (NU) : 29
% 0.16/0.43 # Rec. Clause-clause subsumption calls : 15
% 0.16/0.43 # Non-unit clause-clause subsumptions : 3
% 0.16/0.43 # Unit Clause-clause subsumption calls : 0
% 0.16/0.43 # Rewrite failures with RHS unbound : 0
% 0.16/0.43 # BW rewrite match attempts : 0
% 0.16/0.43 # BW rewrite match successes : 0
% 0.16/0.43 # Condensation attempts : 26
% 0.16/0.43 # Condensation successes : 0
% 0.16/0.43 # Termbank termtop insertions : 3444
% 0.16/0.43 # Search garbage collected termcells : 427
% 0.16/0.43
% 0.16/0.43 # -------------------------------------------------
% 0.16/0.43 # User time : 0.004 s
% 0.16/0.43 # System time : 0.002 s
% 0.16/0.43 # Total time : 0.006 s
% 0.16/0.43 # Maximum resident set size: 1836 pages
% 0.16/0.43
% 0.16/0.43 # -------------------------------------------------
% 0.16/0.43 # User time : 0.017 s
% 0.16/0.43 # System time : 0.008 s
% 0.16/0.43 # Total time : 0.025 s
% 0.16/0.43 # Maximum resident set size: 1708 pages
% 0.16/0.43 % E---3.1 exiting
% 0.16/0.44 % E exiting
%------------------------------------------------------------------------------