TSTP Solution File: SEU620^2 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU620^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n025.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 03:28:37 EDT 2024
% Result : Theorem 0.22s 0.50s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 32 ( 14 unt; 11 typ; 0 def)
% Number of atoms : 50 ( 19 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 444 ( 12 ~; 7 |; 13 &; 409 @)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 51 ( 4 ^ 37 !; 10 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
emptyset: $i ).
thf(decl_24,type,
setadjoin: $i > $i > $i ).
thf(decl_25,type,
setunion: $i > $i ).
thf(decl_26,type,
iskpair: $i > $o ).
thf(decl_27,type,
kpairiskpair: $o ).
thf(decl_28,type,
kpair: $i > $i > $i ).
thf(decl_29,type,
esk1_2: $i > $i > $i ).
thf(decl_30,type,
esk2_2: $i > $i > $i ).
thf(decl_31,type,
esk3_0: $i ).
thf(decl_32,type,
esk4_0: $i ).
thf(iskpair,axiom,
( iskpair
= ( ^ [X1: $i] :
? [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
& ? [X3: $i] :
( ( in @ X3 @ ( setunion @ X1 ) )
& ( X1
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iskpair) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,conjecture,
( kpairiskpair
=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(kpair,axiom,
( kpair
= ( ^ [X2: $i,X3: $i] : ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpair) ).
thf(c_0_4,plain,
( iskpair
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ ( setunion @ Z0 ) )
& ? [X3: $i] :
( ( in @ X3 @ ( setunion @ Z0 ) )
& ( Z0
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iskpair]) ).
thf(c_0_5,axiom,
( kpairiskpair
= ( ! [X2: $i,X3: $i] :
? [X8: $i] :
( ( in @ X8 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X9: $i] :
( ( in @ X9 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X8 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X8 @ ( setadjoin @ X9 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[kpairiskpair,c_0_4]) ).
thf(c_0_6,negated_conjecture,
~ ( ! [X10: $i,X11: $i] :
? [X12: $i] :
( ( in @ X12 @ ( setunion @ ( setadjoin @ ( setadjoin @ X10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X10 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X13: $i] :
( ( in @ X13 @ ( setunion @ ( setadjoin @ ( setadjoin @ X10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X10 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X10 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X12 @ ( setadjoin @ X13 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ! [X2: $i,X3: $i] :
? [X14: $i] :
( ( in @ X14 @ ( setunion @ ( kpair @ X2 @ X3 ) ) )
& ? [X15: $i] :
( ( in @ X15 @ ( setunion @ ( kpair @ X2 @ X3 ) ) )
& ( ( kpair @ X2 @ X3 )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X15 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[kpairp]),c_0_4]),c_0_5]) ).
thf(c_0_7,plain,
! [X16: $i,X17: $i] :
( ( kpair @ X16 @ X17 )
= ( setadjoin @ ( setadjoin @ X16 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X16 @ ( setadjoin @ X17 @ emptyset ) ) @ emptyset ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kpair])]) ).
thf(c_0_8,negated_conjecture,
! [X18: $i,X19: $i,X24: $i,X25: $i] :
( ( in @ ( esk1_2 @ X18 @ X19 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X18 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X18 @ ( setadjoin @ X19 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ ( esk2_2 @ X18 @ X19 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X18 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X18 @ ( setadjoin @ X19 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X18 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X18 @ ( setadjoin @ X19 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( esk1_2 @ X18 @ X19 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk1_2 @ X18 @ X19 ) @ ( setadjoin @ ( esk2_2 @ X18 @ X19 ) @ emptyset ) ) @ emptyset ) ) )
& ( ~ ( in @ X24 @ ( setunion @ ( kpair @ esk3_0 @ esk4_0 ) ) )
| ~ ( in @ X25 @ ( setunion @ ( kpair @ esk3_0 @ esk4_0 ) ) )
| ( ( kpair @ esk3_0 @ esk4_0 )
!= ( setadjoin @ ( setadjoin @ X24 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X24 @ ( setadjoin @ X25 @ emptyset ) ) @ emptyset ) ) ) ) ),
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_6])])])])]) ).
thf(c_0_9,plain,
! [X26: $i,X27: $i] :
( ( kpair @ X26 @ X27 )
= ( setadjoin @ ( setadjoin @ X26 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X26 @ ( setadjoin @ X27 @ emptyset ) ) @ emptyset ) ) ),
inference(variable_rename,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X2: $i] :
( ~ ( in @ X1 @ ( setunion @ ( kpair @ esk3_0 @ esk4_0 ) ) )
| ~ ( in @ X2 @ ( setunion @ ( kpair @ esk3_0 @ esk4_0 ) ) )
| ( ( kpair @ esk3_0 @ esk4_0 )
!= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,plain,
! [X1: $i,X2: $i] :
( ( kpair @ X1 @ X2 )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X2: $i] : ( in @ ( esk2_2 @ X1 @ X2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( kpair @ X1 @ X2 )
!= ( kpair @ esk3_0 @ esk4_0 ) )
| ~ ( in @ X2 @ ( setunion @ ( kpair @ esk3_0 @ esk4_0 ) ) )
| ~ ( in @ X1 @ ( setunion @ ( kpair @ esk3_0 @ esk4_0 ) ) ) ),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X2: $i] : ( in @ ( esk2_2 @ X1 @ X2 ) @ ( setunion @ ( kpair @ X1 @ X2 ) ) ),
inference(rw,[status(thm)],[c_0_12,c_0_11]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X2: $i] :
( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( esk1_2 @ X1 @ X2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk1_2 @ X1 @ X2 ) @ ( setadjoin @ ( esk2_2 @ X1 @ X2 ) @ emptyset ) ) @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X2: $i] : ( in @ ( esk1_2 @ X1 @ X2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i] :
( ( ( kpair @ X1 @ ( esk2_2 @ esk3_0 @ esk4_0 ) )
!= ( kpair @ esk3_0 @ esk4_0 ) )
| ~ ( in @ X1 @ ( setunion @ ( kpair @ esk3_0 @ esk4_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i,X2: $i] :
( ( kpair @ ( esk1_2 @ X1 @ X2 ) @ ( esk2_2 @ X1 @ X2 ) )
= ( kpair @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_11]),c_0_11]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i,X2: $i] : ( in @ ( esk1_2 @ X1 @ X2 ) @ ( setunion @ ( kpair @ X1 @ X2 ) ) ),
inference(rw,[status(thm)],[c_0_16,c_0_11]) ).
thf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU620^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n025.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 : Sun May 19 17:52:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.22/0.48 Running higher-order theorem proving
% 0.22/0.48 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
% 0.22/0.50 # Version: 3.1.0-ho
% 0.22/0.50 # Preprocessing class: HSSSSMSSSLSNSFN.
% 0.22/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.50 # Starting post_as_ho5 with 300s (1) cores
% 0.22/0.50 # Starting sh4l with 300s (1) cores
% 0.22/0.50 # Starting ho_unfolding_2 with 300s (1) cores
% 0.22/0.50 # post_as_ho5 with pid 24007 completed with status 0
% 0.22/0.50 # Result found by post_as_ho5
% 0.22/0.50 # Preprocessing class: HSSSSMSSSLSNSFN.
% 0.22/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.50 # Starting post_as_ho5 with 300s (1) cores
% 0.22/0.50 # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.22/0.50 # Search class: HUHSM-FFSF21-MSFFMFNN
% 0.22/0.50 # partial match(3): HGHSF-FFSF21-SSFFMFNN
% 0.22/0.50 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.50 # Starting new_ho_10 with 163s (1) cores
% 0.22/0.50 # new_ho_10 with pid 24012 completed with status 0
% 0.22/0.50 # Result found by new_ho_10
% 0.22/0.50 # Preprocessing class: HSSSSMSSSLSNSFN.
% 0.22/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.50 # Starting post_as_ho5 with 300s (1) cores
% 0.22/0.50 # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.22/0.50 # Search class: HUHSM-FFSF21-MSFFMFNN
% 0.22/0.50 # partial match(3): HGHSF-FFSF21-SSFFMFNN
% 0.22/0.50 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.50 # Starting new_ho_10 with 163s (1) cores
% 0.22/0.50 # Preprocessing time : 0.001 s
% 0.22/0.50 # Presaturation interreduction done
% 0.22/0.50
% 0.22/0.50 # Proof found!
% 0.22/0.50 # SZS status Theorem
% 0.22/0.50 # SZS output start CNFRefutation
% See solution above
% 0.22/0.50 # Parsed axioms : 11
% 0.22/0.50 # Removed by relevancy pruning/SinE : 7
% 0.22/0.50 # Initial clauses : 5
% 0.22/0.50 # Removed in clause preprocessing : 0
% 0.22/0.50 # Initial clauses in saturation : 5
% 0.22/0.50 # Processed clauses : 12
% 0.22/0.50 # ...of these trivial : 0
% 0.22/0.50 # ...subsumed : 0
% 0.22/0.50 # ...remaining for further processing : 12
% 0.22/0.50 # Other redundant clauses eliminated : 0
% 0.22/0.50 # Clauses deleted for lack of memory : 0
% 0.22/0.50 # Backward-subsumed : 0
% 0.22/0.50 # Backward-rewritten : 0
% 0.22/0.50 # Generated clauses : 6
% 0.22/0.50 # ...of the previous two non-redundant : 5
% 0.22/0.50 # ...aggressively subsumed : 0
% 0.22/0.50 # Contextual simplify-reflections : 0
% 0.22/0.50 # Paramodulations : 6
% 0.22/0.50 # Factorizations : 0
% 0.22/0.50 # NegExts : 0
% 0.22/0.50 # Equation resolutions : 0
% 0.22/0.50 # Disequality decompositions : 0
% 0.22/0.50 # Total rewrite steps : 6
% 0.22/0.50 # ...of those cached : 3
% 0.22/0.50 # Propositional unsat checks : 0
% 0.22/0.50 # Propositional check models : 0
% 0.22/0.50 # Propositional check unsatisfiable : 0
% 0.22/0.50 # Propositional clauses : 0
% 0.22/0.50 # Propositional clauses after purity: 0
% 0.22/0.50 # Propositional unsat core size : 0
% 0.22/0.50 # Propositional preprocessing time : 0.000
% 0.22/0.50 # Propositional encoding time : 0.000
% 0.22/0.50 # Propositional solver time : 0.000
% 0.22/0.50 # Success case prop preproc time : 0.000
% 0.22/0.50 # Success case prop encoding time : 0.000
% 0.22/0.50 # Success case prop solver time : 0.000
% 0.22/0.50 # Current number of processed clauses : 7
% 0.22/0.50 # Positive orientable unit clauses : 4
% 0.22/0.50 # Positive unorientable unit clauses: 0
% 0.22/0.50 # Negative unit clauses : 0
% 0.22/0.50 # Non-unit-clauses : 3
% 0.22/0.50 # Current number of unprocessed clauses: 3
% 0.22/0.50 # ...number of literals in the above : 3
% 0.22/0.50 # Current number of archived formulas : 0
% 0.22/0.50 # Current number of archived clauses : 5
% 0.22/0.50 # Clause-clause subsumption calls (NU) : 6
% 0.22/0.50 # Rec. Clause-clause subsumption calls : 2
% 0.22/0.50 # Non-unit clause-clause subsumptions : 0
% 0.22/0.50 # Unit Clause-clause subsumption calls : 0
% 0.22/0.50 # Rewrite failures with RHS unbound : 0
% 0.22/0.50 # BW rewrite match attempts : 0
% 0.22/0.50 # BW rewrite match successes : 0
% 0.22/0.50 # Condensation attempts : 12
% 0.22/0.50 # Condensation successes : 0
% 0.22/0.50 # Termbank termtop insertions : 1047
% 0.22/0.50 # Search garbage collected termcells : 179
% 0.22/0.50
% 0.22/0.50 # -------------------------------------------------
% 0.22/0.50 # User time : 0.004 s
% 0.22/0.50 # System time : 0.002 s
% 0.22/0.50 # Total time : 0.006 s
% 0.22/0.50 # Maximum resident set size: 1740 pages
% 0.22/0.50
% 0.22/0.50 # -------------------------------------------------
% 0.22/0.50 # User time : 0.005 s
% 0.22/0.50 # System time : 0.005 s
% 0.22/0.50 # Total time : 0.009 s
% 0.22/0.50 # Maximum resident set size: 1696 pages
% 0.22/0.50 % E---3.1 exiting
% 0.22/0.50 % E exiting
%------------------------------------------------------------------------------