TSTP Solution File: SEU673^2 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU673^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n012.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 03:29:01 EDT 2024
% Result : Theorem 0.22s 0.50s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 25
% Syntax : Number of formulae : 42 ( 10 unt; 18 typ; 0 def)
% Number of atoms : 120 ( 8 equ; 0 cnn)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 383 ( 16 ~; 13 |; 13 &; 307 @)
% ( 5 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 8 con; 0-3 aty)
% Number of variables : 100 ( 43 ^ 57 !; 0 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_25,type,
setunion: $i > $i ).
thf(decl_26,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_27,type,
dsetconstrEL: $o ).
thf(decl_28,type,
subset: $i > $i > $o ).
thf(decl_29,type,
kpair: $i > $i > $i ).
thf(decl_30,type,
cartprod: $i > $i > $i ).
thf(decl_31,type,
singleton: $i > $o ).
thf(decl_32,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_33,type,
theprop: $o ).
thf(decl_34,type,
breln: $i > $i > $i > $o ).
thf(decl_35,type,
func: $i > $i > $i > $o ).
thf(decl_36,type,
funcImageSingleton: $o ).
thf(decl_37,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_38,type,
esk2_0: $i ).
thf(decl_39,type,
esk3_0: $i ).
thf(decl_40,type,
esk4_0: $i ).
thf(decl_41,type,
esk5_0: $i ).
thf(func,axiom,
( func
= ( ^ [X1: $i,X6: $i,X8: $i] :
( ( breln @ X1 @ X6 @ X8 )
& ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ex1 @ X6
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X8 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',func) ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X6: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X1 @ X6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(ex1,axiom,
( ex1
= ( ^ [X1: $i,X2: $i > $o] :
( singleton
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
<=> ! [X1: $i,X6: $i,X9: $i] :
( ( func @ X1 @ X6 @ X9 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( singleton
@ ( dsetconstr @ X6
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X9 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
=> ( in @ X3 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(apProp,conjecture,
( dsetconstrEL
=> ( theprop
=> ( funcImageSingleton
=> ! [X1: $i,X6: $i,X9: $i] :
( ( func @ X1 @ X6 @ X9 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X6
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X9 ) ) )
@ X6 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
thf(theprop,axiom,
( theprop
<=> ! [X5: $i] :
( ( singleton @ X5 )
=> ( in @ ( setunion @ X5 ) @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).
thf(c_0_7,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X3: $i] :
( ( in @ X3 @ Z0 )
=> ( singleton
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X3 @ Z3 ) @ Z2 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[func]) ).
thf(c_0_8,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_9,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
( singleton
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_10,plain,
( funcImageSingleton
<=> ! [X1: $i,X6: $i,X9: $i] :
( ( func @ X1 @ X6 @ X9 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( singleton
@ ( dsetconstr @ X6
@ ^ [Z0: $i] : ( in @ ( kpair @ X3 @ Z0 ) @ X9 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[funcImageSingleton]) ).
thf(c_0_11,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X3: $i] :
( ( in @ X3 @ Z0 )
=> ( singleton
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X3 @ Z3 ) @ Z2 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
thf(c_0_12,plain,
( dsetconstrEL
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) )
=> ( in @ X3 @ X1 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrEL]) ).
thf(c_0_13,plain,
( funcImageSingleton
= ( ! [X1: $i,X6: $i,X9: $i] :
( ( ( subset @ X9 @ ( cartprod @ X1 @ X6 ) )
& ! [X22: $i] :
( ( in @ X22 @ X1 )
=> ( singleton
@ ( dsetconstr @ X6
@ ^ [Z0: $i] : ( in @ ( kpair @ X22 @ Z0 ) @ X9 ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( singleton
@ ( dsetconstr @ X6
@ ^ [Z0: $i] : ( in @ ( kpair @ X3 @ Z0 ) @ X9 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_14,negated_conjecture,
~ ( ! [X23: $i,X24: $i > $o,X25: $i] :
( ( in @ X25 @ ( dsetconstr @ X23 @ X24 ) )
=> ( in @ X25 @ X23 ) )
=> ( ! [X26: $i] :
( ( singleton @ X26 )
=> ( in @ ( setunion @ X26 ) @ X26 ) )
=> ( ! [X27: $i,X28: $i,X29: $i] :
( ( ( subset @ X29 @ ( cartprod @ X27 @ X28 ) )
& ! [X30: $i] :
( ( in @ X30 @ X27 )
=> ( singleton
@ ( dsetconstr @ X28
@ ^ [Z0: $i] : ( in @ ( kpair @ X30 @ Z0 ) @ X29 ) ) ) ) )
=> ! [X31: $i] :
( ( in @ X31 @ X27 )
=> ( singleton
@ ( dsetconstr @ X28
@ ^ [Z0: $i] : ( in @ ( kpair @ X31 @ Z0 ) @ X29 ) ) ) ) )
=> ! [X1: $i,X6: $i,X9: $i] :
( ( ( subset @ X9 @ ( cartprod @ X1 @ X6 ) )
& ! [X32: $i] :
( ( in @ X32 @ X1 )
=> ( singleton
@ ( dsetconstr @ X6
@ ^ [Z0: $i] : ( in @ ( kpair @ X32 @ Z0 ) @ X9 ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X6
@ ^ [Z0: $i] : ( in @ ( kpair @ X3 @ Z0 ) @ X9 ) ) )
@ X6 ) ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[apProp])]),c_0_12]),c_0_13]),c_0_11]),theprop])]) ).
thf(c_0_15,negated_conjecture,
! [X33: $i,X34: $i > $o,X35: $i,X36: $i,X37: $i,X38: $i,X39: $i,X41: $i,X45: $i] :
( ( ~ ( in @ X35 @ ( dsetconstr @ X33 @ X34 ) )
| ( in @ X35 @ X33 ) )
& ( ~ ( singleton @ X36 )
| ( in @ ( setunion @ X36 ) @ X36 ) )
& ( ( in @ ( esk1_3 @ X37 @ X38 @ X39 ) @ X37 )
| ~ ( subset @ X39 @ ( cartprod @ X37 @ X38 ) )
| ~ ( in @ X41 @ X37 )
| ( singleton
@ ( dsetconstr @ X38
@ ^ [Z0: $i] : ( in @ ( kpair @ X41 @ Z0 ) @ X39 ) ) ) )
& ( ~ ( singleton
@ ( dsetconstr @ X38
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X37 @ X38 @ X39 ) @ Z0 ) @ X39 ) ) )
| ~ ( subset @ X39 @ ( cartprod @ X37 @ X38 ) )
| ~ ( in @ X41 @ X37 )
| ( singleton
@ ( dsetconstr @ X38
@ ^ [Z0: $i] : ( in @ ( kpair @ X41 @ Z0 ) @ X39 ) ) ) )
& ( subset @ esk4_0 @ ( cartprod @ esk2_0 @ esk3_0 ) )
& ( ~ ( in @ X45 @ esk2_0 )
| ( singleton
@ ( dsetconstr @ esk3_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X45 @ Z0 ) @ esk4_0 ) ) ) )
& ( in @ esk5_0 @ esk2_0 )
& ~ ( in
@ ( setunion
@ ( dsetconstr @ esk3_0
@ ^ [Z0: $i] : ( in @ ( kpair @ esk5_0 @ Z0 ) @ esk4_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_14])])])])])]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( in @ X1 @ X3 )
| ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i] :
( ( in @ ( setunion @ X1 ) @ X1 )
| ~ ( singleton @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_18,negated_conjecture,
~ ( in
@ ( setunion
@ ( dsetconstr @ esk3_0
@ ^ [Z0: $i] : ( in @ ( kpair @ esk5_0 @ Z0 ) @ esk4_0 ) ) )
@ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i,X2: $i > $o] :
( ( in @ ( setunion @ ( dsetconstr @ X1 @ X2 ) ) @ X1 )
| ~ ( singleton @ ( dsetconstr @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_20,negated_conjecture,
~ ( singleton
@ ( dsetconstr @ esk3_0
@ ^ [Z0: $i] : ( in @ ( kpair @ esk5_0 @ Z0 ) @ esk4_0 ) ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_21,negated_conjecture,
! [X1: $i] :
( ( singleton
@ ( dsetconstr @ esk3_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X1 @ Z0 ) @ esk4_0 ) ) )
| ~ ( in @ X1 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_22,negated_conjecture,
in @ esk5_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU673^2 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n012.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 18:13:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.22/0.48 Running higher-order theorem proving
% 0.22/0.49 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: HSSSSLSSSLMNHSN.
% 0.22/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50 # Starting ho_unfolding_6 with 1500s (5) cores
% 0.22/0.50 # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.22/0.50 # Starting pre_casc_5 with 300s (1) cores
% 0.22/0.50 # Starting additional_ho_6 with 300s (1) cores
% 0.22/0.50 # pre_casc_5 with pid 6790 completed with status 0
% 0.22/0.50 # Result found by pre_casc_5
% 0.22/0.50 # Preprocessing class: HSSSSLSSSLMNHSN.
% 0.22/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50 # Starting ho_unfolding_6 with 1500s (5) cores
% 0.22/0.50 # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.22/0.50 # Starting pre_casc_5 with 300s (1) cores
% 0.22/0.50 # SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 0.22/0.50 # Search class: HGUNF-FFSF32-MHSFMFBN
% 0.22/0.50 # partial match(3): HGUNF-FFSF32-MSSFFSBN
% 0.22/0.50 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.50 # Starting new_ho_10 with 55s (1) cores
% 0.22/0.50 # new_ho_10 with pid 6792 completed with status 0
% 0.22/0.50 # Result found by new_ho_10
% 0.22/0.50 # Preprocessing class: HSSSSLSSSLMNHSN.
% 0.22/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50 # Starting ho_unfolding_6 with 1500s (5) cores
% 0.22/0.50 # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.22/0.50 # Starting pre_casc_5 with 300s (1) cores
% 0.22/0.50 # SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 0.22/0.50 # Search class: HGUNF-FFSF32-MHSFMFBN
% 0.22/0.50 # partial match(3): HGUNF-FFSF32-MSSFFSBN
% 0.22/0.50 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.50 # Starting new_ho_10 with 55s (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 : 23
% 0.22/0.50 # Removed by relevancy pruning/SinE : 16
% 0.22/0.50 # Initial clauses : 8
% 0.22/0.50 # Removed in clause preprocessing : 0
% 0.22/0.50 # Initial clauses in saturation : 8
% 0.22/0.50 # Processed clauses : 20
% 0.22/0.50 # ...of these trivial : 0
% 0.22/0.50 # ...subsumed : 1
% 0.22/0.50 # ...remaining for further processing : 19
% 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 : 7
% 0.22/0.50 # ...of the previous two non-redundant : 6
% 0.22/0.50 # ...aggressively subsumed : 0
% 0.22/0.50 # Contextual simplify-reflections : 0
% 0.22/0.50 # Paramodulations : 7
% 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 : 1
% 0.22/0.50 # ...of those cached : 0
% 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 : 11
% 0.22/0.50 # Positive orientable unit clauses : 2
% 0.22/0.50 # Positive unorientable unit clauses: 0
% 0.22/0.50 # Negative unit clauses : 2
% 0.22/0.50 # Non-unit-clauses : 7
% 0.22/0.50 # Current number of unprocessed clauses: 2
% 0.22/0.50 # ...number of literals in the above : 5
% 0.22/0.50 # Current number of archived formulas : 0
% 0.22/0.50 # Current number of archived clauses : 8
% 0.22/0.50 # Clause-clause subsumption calls (NU) : 51
% 0.22/0.50 # Rec. Clause-clause subsumption calls : 34
% 0.22/0.50 # Non-unit clause-clause subsumptions : 1
% 0.22/0.50 # Unit Clause-clause subsumption calls : 2
% 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 : 20
% 0.22/0.50 # Condensation successes : 0
% 0.22/0.50 # Termbank termtop insertions : 1726
% 0.22/0.50 # Search garbage collected termcells : 535
% 0.22/0.50
% 0.22/0.50 # -------------------------------------------------
% 0.22/0.50 # User time : 0.004 s
% 0.22/0.50 # System time : 0.003 s
% 0.22/0.50 # Total time : 0.006 s
% 0.22/0.50 # Maximum resident set size: 1864 pages
% 0.22/0.50
% 0.22/0.50 # -------------------------------------------------
% 0.22/0.50 # User time : 0.007 s
% 0.22/0.50 # System time : 0.003 s
% 0.22/0.50 # Total time : 0.010 s
% 0.22/0.50 # Maximum resident set size: 1728 pages
% 0.22/0.50 % E---3.1 exiting
% 0.22/0.50 % E exiting
%------------------------------------------------------------------------------