TSTP Solution File: SEU706^2 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU706^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n021.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 03:29:19 EDT 2024
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 20
% Syntax : Number of formulae : 32 ( 9 unt; 13 typ; 0 def)
% Number of atoms : 80 ( 45 equ; 0 cnn)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 169 ( 16 ~; 12 |; 12 &; 96 @)
% ( 7 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 52 ( 2 ^ 47 !; 3 ?; 52 :)
% 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,
uniqinunit: $o ).
thf(decl_27,type,
in__Cong: $o ).
thf(decl_28,type,
setadjoin__Cong: $o ).
thf(decl_29,type,
setunion__Cong: $o ).
thf(decl_30,type,
setunionsingleton: $o ).
thf(decl_31,type,
singleton: $i > $o ).
thf(decl_32,type,
esk1_0: $i ).
thf(decl_33,type,
esk2_0: $i ).
thf(decl_34,type,
esk3_0: $i ).
thf(singleton,axiom,
( singleton
= ( ^ [X3: $i] :
? [X1: $i] :
( ( in @ X1 @ X3 )
& ( X3
= ( setadjoin @ X1 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(theeq,conjecture,
( uniqinunit
=> ( in__Cong
=> ( setadjoin__Cong
=> ( setunion__Cong
=> ( setunionsingleton
=> ! [X7: $i] :
( ( singleton @ X7 )
=> ! [X1: $i] :
( ( in @ X1 @ X7 )
=> ( ( setunion @ X7 )
= X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theeq) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( setunion @ X3 )
= ( setunion @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( in @ X1 @ X3 )
<=> ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
= X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X5: $i,X6: $i] :
( ( X5 = X6 )
=> ( ( setadjoin @ X1 @ X5 )
= ( setadjoin @ X2 @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(c_0_7,plain,
( singleton
= ( ^ [Z0: $i] :
? [X1: $i] :
( ( in @ X1 @ Z0 )
& ( Z0
= ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_8,negated_conjecture,
~ ( ! [X23: $i,X24: $i] :
( ( in @ X23 @ ( setadjoin @ X24 @ emptyset ) )
=> ( X23 = X24 ) )
=> ( ! [X25: $i,X26: $i] :
( ( X25 = X26 )
=> ! [X27: $i,X28: $i] :
( ( X27 = X28 )
=> ( ( in @ X27 @ X25 )
<=> ( in @ X28 @ X26 ) ) ) )
=> ( ! [X29: $i,X30: $i] :
( ( X29 = X30 )
=> ! [X31: $i,X32: $i] :
( ( X31 = X32 )
=> ( ( setadjoin @ X29 @ X31 )
= ( setadjoin @ X30 @ X32 ) ) ) )
=> ( ! [X33: $i,X34: $i] :
( ( X33 = X34 )
=> ( ( setunion @ X33 )
= ( setunion @ X34 ) ) )
=> ( ! [X35: $i] :
( ( setunion @ ( setadjoin @ X35 @ emptyset ) )
= X35 )
=> ! [X7: $i] :
( ? [X36: $i] :
( ( in @ X36 @ X7 )
& ( X7
= ( setadjoin @ X36 @ emptyset ) ) )
=> ! [X1: $i] :
( ( in @ X1 @ X7 )
=> ( ( setunion @ X7 )
= X1 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[theeq]),setunion__Cong]),c_0_7]),in__Cong]),uniqinunit]),setunionsingleton]),setadjoin__Cong]) ).
thf(c_0_9,negated_conjecture,
! [X37: $i,X38: $i,X39: $i,X40: $i,X41: $i,X42: $i,X43: $i,X44: $i,X45: $i,X46: $i,X47: $i,X48: $i,X49: $i] :
( ( ~ ( in @ X37 @ ( setadjoin @ X38 @ emptyset ) )
| ( X37 = X38 ) )
& ( ~ ( in @ X41 @ X39 )
| ( in @ X42 @ X40 )
| ( X41 != X42 )
| ( X39 != X40 ) )
& ( ~ ( in @ X42 @ X40 )
| ( in @ X41 @ X39 )
| ( X41 != X42 )
| ( X39 != X40 ) )
& ( ( X43 != X44 )
| ( X45 != X46 )
| ( ( setadjoin @ X43 @ X45 )
= ( setadjoin @ X44 @ X46 ) ) )
& ( ( X47 != X48 )
| ( ( setunion @ X47 )
= ( setunion @ X48 ) ) )
& ( ( setunion @ ( setadjoin @ X49 @ emptyset ) )
= X49 )
& ( in @ esk2_0 @ esk1_0 )
& ( esk1_0
= ( setadjoin @ esk2_0 @ emptyset ) )
& ( in @ esk3_0 @ esk1_0 )
& ( ( setunion @ 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_8])])])])])]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
( esk1_0
= ( setadjoin @ esk2_0 @ emptyset ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i] :
( ( X1 = esk2_0 )
| ~ ( in @ X1 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_13,negated_conjecture,
in @ esk3_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,negated_conjecture,
( ( setunion @ esk1_0 )
!= esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_15,negated_conjecture,
esk3_0 = esk2_0,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_17,negated_conjecture,
( ( setunion @ esk1_0 )
!= esk2_0 ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_18,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_11]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07 % Problem : SEU706^2 : TPTP v8.2.0. Released v3.7.0.
% 0.02/0.07 % Command : run_E %s %d THM
% 0.07/0.28 % Computer : n021.cluster.edu
% 0.07/0.28 % Model : x86_64 x86_64
% 0.07/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28 % Memory : 8042.1875MB
% 0.07/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28 % CPULimit : 300
% 0.07/0.28 % WCLimit : 300
% 0.07/0.28 % DateTime : Sun May 19 17:37:22 EDT 2024
% 0.07/0.28 % CPUTime :
% 0.12/0.36 Running higher-order theorem proving
% 0.12/0.36 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
% 0.12/0.36 # Version: 3.1.0-ho
% 0.12/0.36 # Preprocessing class: HSSSSLSSSLSNSFN.
% 0.12/0.36 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.36 # Starting new_ho_10 with 1500s (5) cores
% 0.12/0.36 # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.12/0.36 # Starting lpo1_def_fix with 300s (1) cores
% 0.12/0.36 # Starting ehoh_best8_lambda with 300s (1) cores
% 0.12/0.36 # ehoh_best_sine_rwall with pid 14426 completed with status 0
% 0.12/0.36 # Result found by ehoh_best_sine_rwall
% 0.12/0.36 # Preprocessing class: HSSSSLSSSLSNSFN.
% 0.12/0.36 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.36 # Starting new_ho_10 with 1500s (5) cores
% 0.12/0.36 # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.12/0.36 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.12/0.36 # Search class: HHUSF-FFSS21-SSFFMFNN
% 0.12/0.36 # partial match(1): HHUSF-FFSF21-SSFFMFNN
% 0.12/0.36 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.36 # Starting new_ho_10 with 163s (1) cores
% 0.12/0.36 # new_ho_10 with pid 14429 completed with status 0
% 0.12/0.36 # Result found by new_ho_10
% 0.12/0.36 # Preprocessing class: HSSSSLSSSLSNSFN.
% 0.12/0.36 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.36 # Starting new_ho_10 with 1500s (5) cores
% 0.12/0.36 # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.12/0.36 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.12/0.36 # Search class: HHUSF-FFSS21-SSFFMFNN
% 0.12/0.36 # partial match(1): HHUSF-FFSF21-SSFFMFNN
% 0.12/0.36 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.36 # Starting new_ho_10 with 163s (1) cores
% 0.12/0.36 # Preprocessing time : 0.001 s
% 0.12/0.36 # Presaturation interreduction done
% 0.12/0.36
% 0.12/0.36 # Proof found!
% 0.12/0.36 # SZS status Theorem
% 0.12/0.36 # SZS output start CNFRefutation
% See solution above
% 0.12/0.36 # Parsed axioms : 17
% 0.12/0.36 # Removed by relevancy pruning/SinE : 10
% 0.12/0.36 # Initial clauses : 10
% 0.12/0.36 # Removed in clause preprocessing : 4
% 0.12/0.36 # Initial clauses in saturation : 6
% 0.12/0.36 # Processed clauses : 15
% 0.12/0.36 # ...of these trivial : 0
% 0.12/0.36 # ...subsumed : 0
% 0.12/0.36 # ...remaining for further processing : 15
% 0.12/0.36 # Other redundant clauses eliminated : 0
% 0.12/0.36 # Clauses deleted for lack of memory : 0
% 0.12/0.36 # Backward-subsumed : 0
% 0.12/0.36 # Backward-rewritten : 2
% 0.12/0.36 # Generated clauses : 3
% 0.12/0.36 # ...of the previous two non-redundant : 3
% 0.12/0.36 # ...aggressively subsumed : 0
% 0.12/0.36 # Contextual simplify-reflections : 0
% 0.12/0.36 # Paramodulations : 3
% 0.12/0.36 # Factorizations : 0
% 0.12/0.36 # NegExts : 0
% 0.12/0.36 # Equation resolutions : 0
% 0.12/0.36 # Disequality decompositions : 0
% 0.12/0.36 # Total rewrite steps : 3
% 0.12/0.36 # ...of those cached : 1
% 0.12/0.36 # Propositional unsat checks : 0
% 0.12/0.36 # Propositional check models : 0
% 0.12/0.36 # Propositional check unsatisfiable : 0
% 0.12/0.36 # Propositional clauses : 0
% 0.12/0.36 # Propositional clauses after purity: 0
% 0.12/0.36 # Propositional unsat core size : 0
% 0.12/0.36 # Propositional preprocessing time : 0.000
% 0.12/0.36 # Propositional encoding time : 0.000
% 0.12/0.36 # Propositional solver time : 0.000
% 0.12/0.36 # Success case prop preproc time : 0.000
% 0.12/0.36 # Success case prop encoding time : 0.000
% 0.12/0.36 # Success case prop solver time : 0.000
% 0.12/0.36 # Current number of processed clauses : 7
% 0.12/0.36 # Positive orientable unit clauses : 4
% 0.12/0.36 # Positive unorientable unit clauses: 0
% 0.12/0.36 # Negative unit clauses : 1
% 0.12/0.36 # Non-unit-clauses : 2
% 0.12/0.36 # Current number of unprocessed clauses: 0
% 0.12/0.36 # ...number of literals in the above : 0
% 0.12/0.36 # Current number of archived formulas : 0
% 0.12/0.36 # Current number of archived clauses : 8
% 0.12/0.36 # Clause-clause subsumption calls (NU) : 0
% 0.12/0.36 # Rec. Clause-clause subsumption calls : 0
% 0.12/0.36 # Non-unit clause-clause subsumptions : 0
% 0.12/0.36 # Unit Clause-clause subsumption calls : 0
% 0.12/0.36 # Rewrite failures with RHS unbound : 0
% 0.12/0.36 # BW rewrite match attempts : 1
% 0.12/0.36 # BW rewrite match successes : 1
% 0.12/0.36 # Condensation attempts : 15
% 0.12/0.36 # Condensation successes : 0
% 0.12/0.36 # Termbank termtop insertions : 1063
% 0.12/0.36 # Search garbage collected termcells : 439
% 0.12/0.36
% 0.12/0.36 # -------------------------------------------------
% 0.12/0.36 # User time : 0.001 s
% 0.12/0.36 # System time : 0.002 s
% 0.12/0.36 # Total time : 0.003 s
% 0.12/0.36 # Maximum resident set size: 1912 pages
% 0.12/0.36
% 0.12/0.36 # -------------------------------------------------
% 0.12/0.36 # User time : 0.001 s
% 0.12/0.36 # System time : 0.004 s
% 0.12/0.36 # Total time : 0.005 s
% 0.12/0.36 # Maximum resident set size: 1708 pages
% 0.12/0.36 % E---3.1 exiting
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------