TSTP Solution File: SEU779^2 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU779^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n007.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 03:30:10 EDT 2024
% Result : Theorem 0.21s 0.51s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 24
% Syntax : Number of formulae : 43 ( 15 unt; 17 typ; 0 def)
% Number of atoms : 104 ( 8 equ; 0 cnn)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 397 ( 21 ~; 16 |; 21 &; 311 @)
% ( 3 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 9 con; 0-3 aty)
% Number of variables : 81 ( 30 ^ 46 !; 5 ?; 81 :)
% 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,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_28,type,
dpsetconstrI: $o ).
thf(decl_29,type,
breln1: $i > $i > $o ).
thf(decl_30,type,
breln1compset: $i > $i > $i > $i ).
thf(decl_31,type,
esk1_0: $i ).
thf(decl_32,type,
esk2_0: $i ).
thf(decl_33,type,
esk3_0: $i ).
thf(decl_34,type,
esk4_0: $i ).
thf(decl_35,type,
esk5_0: $i ).
thf(decl_36,type,
esk6_0: $i ).
thf(decl_37,type,
epred1_0: $i > $i > $o ).
thf(decl_38,type,
esk7_2: $i > $i > $i ).
thf(breln1,axiom,
( breln1
= ( ^ [X1: $i,X9: $i] : ( breln @ X1 @ X1 @ X9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1) ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X1: $i,X2: $i,X4: $i > $i > $o,X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( ( X4 @ X5 @ X6 )
=> ( in @ ( kpair @ X5 @ X6 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [X7: $i,X8: $i] : ( X4 @ X7 @ X8 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(breln1compset,axiom,
( breln1compset
= ( ^ [X1: $i,X9: $i,X10: $i] :
( dpsetconstr @ X1 @ X1
@ ^ [X5: $i,X6: $i] :
? [X7: $i] :
( ( in @ X7 @ X1 )
& ( in @ ( kpair @ X5 @ X7 ) @ X9 )
& ( in @ ( kpair @ X7 @ X6 ) @ X10 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compset) ).
thf(breln1compI,conjecture,
( dpsetconstrI
=> ! [X1: $i,X9: $i] :
( ( breln1 @ X1 @ X9 )
=> ! [X10: $i] :
( ( breln1 @ X1 @ X10 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X7 ) @ X9 )
=> ( ( in @ ( kpair @ X7 @ X6 ) @ X10 )
=> ( in @ ( kpair @ X5 @ X6 ) @ ( breln1compset @ X1 @ X9 @ X10 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compI) ).
thf(c_0_5,plain,
( breln1
= ( ^ [Z0: $i,Z1: $i] : ( subset @ Z1 @ ( cartprod @ Z0 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln1]) ).
thf(c_0_6,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_7,plain,
( dpsetconstrI
<=> ! [X1: $i,X2: $i,X4: $i > $i > $o,X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( ( X4 @ X5 @ X6 )
=> ( in @ ( kpair @ X5 @ X6 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [Z0: $i,Z1: $i] : ( X4 @ Z0 @ Z1 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrI]) ).
thf(c_0_8,plain,
( breln1
= ( ^ [Z0: $i,Z1: $i] : ( subset @ Z1 @ ( cartprod @ Z0 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_9,plain,
( breln1compset
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( dpsetconstr @ Z0 @ Z0
@ ^ [Z3: $i,Z4: $i] :
? [X7: $i] :
( ( in @ X7 @ Z0 )
& ( in @ ( kpair @ Z3 @ X7 ) @ Z1 )
& ( in @ ( kpair @ X7 @ Z4 ) @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[breln1compset]) ).
thf(c_0_10,negated_conjecture,
~ ( ! [X22: $i,X23: $i,X24: $i > $i > $o,X25: $i] :
( ( in @ X25 @ X22 )
=> ! [X26: $i] :
( ( in @ X26 @ X23 )
=> ( ( X24 @ X25 @ X26 )
=> ( in @ ( kpair @ X25 @ X26 ) @ ( dpsetconstr @ X22 @ X23 @ X24 ) ) ) ) )
=> ! [X1: $i,X9: $i] :
( ( subset @ X9 @ ( cartprod @ X1 @ X1 ) )
=> ! [X10: $i] :
( ( subset @ X10 @ ( cartprod @ X1 @ X1 ) )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X7 ) @ X9 )
=> ( ( in @ ( kpair @ X7 @ X6 ) @ X10 )
=> ( in @ ( kpair @ X5 @ X6 )
@ ( dpsetconstr @ X1 @ X1
@ ^ [Z0: $i,Z1: $i] :
? [X27: $i] :
( ( in @ X27 @ X1 )
& ( in @ ( kpair @ Z0 @ X27 ) @ X9 )
& ( in @ ( kpair @ X27 @ Z1 ) @ X10 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[breln1compI]),c_0_7]),c_0_8]),c_0_9])]) ).
thf(c_0_11,negated_conjecture,
! [X28: $i,X29: $i,X30: $i > $i > $o,X31: $i,X32: $i] :
( ( ~ ( in @ X31 @ X28 )
| ~ ( in @ X32 @ X29 )
| ~ ( X30 @ X31 @ X32 )
| ( in @ ( kpair @ X31 @ X32 ) @ ( dpsetconstr @ X28 @ X29 @ X30 ) ) )
& ( subset @ esk2_0 @ ( cartprod @ esk1_0 @ esk1_0 ) )
& ( subset @ esk3_0 @ ( cartprod @ esk1_0 @ esk1_0 ) )
& ( in @ esk4_0 @ esk1_0 )
& ( in @ esk5_0 @ esk1_0 )
& ( in @ esk6_0 @ esk1_0 )
& ( in @ ( kpair @ esk4_0 @ esk6_0 ) @ esk2_0 )
& ( in @ ( kpair @ esk6_0 @ esk5_0 ) @ esk3_0 )
& ~ ( in @ ( kpair @ esk4_0 @ esk5_0 )
@ ( dpsetconstr @ esk1_0 @ esk1_0
@ ^ [Z0: $i,Z1: $i] :
? [X27: $i] :
( ( in @ X27 @ esk1_0 )
& ( in @ ( kpair @ Z0 @ X27 ) @ esk2_0 )
& ( in @ ( kpair @ X27 @ Z1 ) @ esk3_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_10])])])])]) ).
thf(c_0_12,plain,
! [X41: $i,X40: $i] :
( ( epred1_0 @ X40 @ X41 )
<=> ? [X39: $i] :
( ( in @ X39 @ esk1_0 )
& ( in @ ( kpair @ X40 @ X39 ) @ esk2_0 )
& ( in @ ( kpair @ X39 @ X41 ) @ esk3_0 ) ) ),
introduced(definition) ).
thf(c_0_13,plain,
! [X42: $i,X43: $i,X45: $i] :
( ( ( in @ ( esk7_2 @ X42 @ X43 ) @ esk1_0 )
| ~ ( epred1_0 @ X43 @ X42 ) )
& ( ( in @ ( kpair @ X43 @ ( esk7_2 @ X42 @ X43 ) ) @ esk2_0 )
| ~ ( epred1_0 @ X43 @ X42 ) )
& ( ( in @ ( kpair @ ( esk7_2 @ X42 @ X43 ) @ X42 ) @ esk3_0 )
| ~ ( epred1_0 @ X43 @ X42 ) )
& ( ~ ( in @ X45 @ esk1_0 )
| ~ ( in @ ( kpair @ X43 @ X45 ) @ esk2_0 )
| ~ ( in @ ( kpair @ X45 @ X42 ) @ esk3_0 )
| ( epred1_0 @ X43 @ X42 ) ) ),
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)],[])])])])])]) ).
thf(c_0_14,negated_conjecture,
( ( in @ ( kpair @ esk4_0 @ esk5_0 ) @ ( dpsetconstr @ esk1_0 @ esk1_0 @ epred1_0 ) )
!= $true ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_11]),c_0_12]) ).
thf(c_0_15,plain,
! [X1: $i,X2: $i,X3: $i] :
( ( epred1_0 @ X2 @ X3 )
| ~ ( in @ X1 @ esk1_0 )
| ~ ( in @ ( kpair @ X2 @ X1 ) @ esk2_0 )
| ~ ( in @ ( kpair @ X1 @ X3 ) @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_16,negated_conjecture,
in @ ( kpair @ esk4_0 @ esk6_0 ) @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_17,negated_conjecture,
in @ esk6_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_18,negated_conjecture,
~ ( in @ ( kpair @ esk4_0 @ esk5_0 ) @ ( dpsetconstr @ esk1_0 @ esk1_0 @ epred1_0 ) ),
inference(cn,[status(thm)],[c_0_14]) ).
thf(c_0_19,negated_conjecture,
! [X2: $i,X1: $i,X5: $i,X4: $i > $i > $o,X3: $i] :
( ( in @ ( kpair @ X1 @ X3 ) @ ( dpsetconstr @ X2 @ X5 @ X4 ) )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X3 @ X5 )
| ~ ( X4 @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_20,negated_conjecture,
in @ esk5_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_21,negated_conjecture,
in @ esk4_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_22,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ esk4_0 @ X1 )
| ~ ( in @ ( kpair @ esk6_0 @ X1 ) @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
thf(c_0_23,negated_conjecture,
in @ ( kpair @ esk6_0 @ esk5_0 ) @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_24,negated_conjecture,
~ ( epred1_0 @ esk4_0 @ esk5_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]) ).
thf(c_0_25,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU779^2 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n007.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
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sun May 19 16:24:53 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.21/0.49 Running higher-order theorem proving
% 0.21/0.49 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
% 0.21/0.51 # Version: 3.1.0-ho
% 0.21/0.51 # Preprocessing class: HSSSSMSSSLMNSFA.
% 0.21/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51 # Starting new_ho_10 with 1500s (5) cores
% 0.21/0.51 # Starting ho_unfolding_6 with 300s (1) cores
% 0.21/0.51 # Starting sh4l with 300s (1) cores
% 0.21/0.51 # Starting lpo8_s with 300s (1) cores
% 0.21/0.51 # lpo8_s with pid 19726 completed with status 0
% 0.21/0.51 # Result found by lpo8_s
% 0.21/0.51 # Preprocessing class: HSSSSMSSSLMNSFA.
% 0.21/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51 # Starting new_ho_10 with 1500s (5) cores
% 0.21/0.51 # Starting ho_unfolding_6 with 300s (1) cores
% 0.21/0.51 # Starting sh4l with 300s (1) cores
% 0.21/0.51 # Starting lpo8_s with 300s (1) cores
% 0.21/0.51 # SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
% 0.21/0.51 # Search class: HHUNF-FFSM32-SSFFMFBN
% 0.21/0.51 # partial match(3): HHUSF-FFSF22-SSFFMFBN
% 0.21/0.51 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51 # Starting new_ho_10 with 163s (1) cores
% 0.21/0.51 # new_ho_10 with pid 19729 completed with status 0
% 0.21/0.51 # Result found by new_ho_10
% 0.21/0.51 # Preprocessing class: HSSSSMSSSLMNSFA.
% 0.21/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51 # Starting new_ho_10 with 1500s (5) cores
% 0.21/0.51 # Starting ho_unfolding_6 with 300s (1) cores
% 0.21/0.51 # Starting sh4l with 300s (1) cores
% 0.21/0.51 # Starting lpo8_s with 300s (1) cores
% 0.21/0.51 # SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
% 0.21/0.51 # Search class: HHUNF-FFSM32-SSFFMFBN
% 0.21/0.51 # partial match(3): HHUSF-FFSF22-SSFFMFBN
% 0.21/0.51 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51 # Starting new_ho_10 with 163s (1) cores
% 0.21/0.51 # Preprocessing time : 0.001 s
% 0.21/0.51 # Presaturation interreduction done
% 0.21/0.51
% 0.21/0.51 # Proof found!
% 0.21/0.51 # SZS status Theorem
% 0.21/0.51 # SZS output start CNFRefutation
% See solution above
% 0.21/0.51 # Parsed axioms : 14
% 0.21/0.51 # Removed by relevancy pruning/SinE : 9
% 0.21/0.51 # Initial clauses : 13
% 0.21/0.51 # Removed in clause preprocessing : 0
% 0.21/0.51 # Initial clauses in saturation : 13
% 0.21/0.51 # Processed clauses : 30
% 0.21/0.51 # ...of these trivial : 0
% 0.21/0.51 # ...subsumed : 0
% 0.21/0.51 # ...remaining for further processing : 29
% 0.21/0.51 # Other redundant clauses eliminated : 0
% 0.21/0.51 # Clauses deleted for lack of memory : 0
% 0.21/0.51 # Backward-subsumed : 0
% 0.21/0.51 # Backward-rewritten : 0
% 0.21/0.51 # Generated clauses : 5
% 0.21/0.51 # ...of the previous two non-redundant : 4
% 0.21/0.51 # ...aggressively subsumed : 0
% 0.21/0.51 # Contextual simplify-reflections : 1
% 0.21/0.51 # Paramodulations : 5
% 0.21/0.51 # Factorizations : 0
% 0.21/0.51 # NegExts : 0
% 0.21/0.51 # Equation resolutions : 0
% 0.21/0.51 # Disequality decompositions : 0
% 0.21/0.51 # Total rewrite steps : 3
% 0.21/0.51 # ...of those cached : 0
% 0.21/0.51 # Propositional unsat checks : 0
% 0.21/0.51 # Propositional check models : 0
% 0.21/0.51 # Propositional check unsatisfiable : 0
% 0.21/0.51 # Propositional clauses : 0
% 0.21/0.51 # Propositional clauses after purity: 0
% 0.21/0.51 # Propositional unsat core size : 0
% 0.21/0.51 # Propositional preprocessing time : 0.000
% 0.21/0.51 # Propositional encoding time : 0.000
% 0.21/0.51 # Propositional solver time : 0.000
% 0.21/0.51 # Success case prop preproc time : 0.000
% 0.21/0.51 # Success case prop encoding time : 0.000
% 0.21/0.51 # Success case prop solver time : 0.000
% 0.21/0.51 # Current number of processed clauses : 16
% 0.21/0.51 # Positive orientable unit clauses : 7
% 0.21/0.51 # Positive unorientable unit clauses: 0
% 0.21/0.51 # Negative unit clauses : 2
% 0.21/0.51 # Non-unit-clauses : 7
% 0.21/0.51 # Current number of unprocessed clauses: 0
% 0.21/0.51 # ...number of literals in the above : 0
% 0.21/0.51 # Current number of archived formulas : 0
% 0.21/0.51 # Current number of archived clauses : 13
% 0.21/0.51 # Clause-clause subsumption calls (NU) : 8
% 0.21/0.51 # Rec. Clause-clause subsumption calls : 2
% 0.21/0.51 # Non-unit clause-clause subsumptions : 1
% 0.21/0.51 # Unit Clause-clause subsumption calls : 1
% 0.21/0.51 # Rewrite failures with RHS unbound : 0
% 0.21/0.51 # BW rewrite match attempts : 0
% 0.21/0.51 # BW rewrite match successes : 0
% 0.21/0.51 # Condensation attempts : 30
% 0.21/0.51 # Condensation successes : 0
% 0.21/0.51 # Termbank termtop insertions : 1592
% 0.21/0.51 # Search garbage collected termcells : 485
% 0.21/0.51
% 0.21/0.51 # -------------------------------------------------
% 0.21/0.51 # User time : 0.002 s
% 0.21/0.51 # System time : 0.004 s
% 0.21/0.51 # Total time : 0.006 s
% 0.21/0.51 # Maximum resident set size: 1996 pages
% 0.21/0.51
% 0.21/0.51 # -------------------------------------------------
% 0.21/0.51 # User time : 0.002 s
% 0.21/0.51 # System time : 0.007 s
% 0.21/0.51 # Total time : 0.010 s
% 0.21/0.51 # Maximum resident set size: 1732 pages
% 0.21/0.51 % E---3.1 exiting
% 0.21/0.51 % E exiting
%------------------------------------------------------------------------------