TSTP Solution File: SEU481^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU481^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n006.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 03:27:33 EDT 2024
% Result : Theorem 0.20s 0.51s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 40 ( 17 unt; 11 typ; 0 def)
% Number of atoms : 61 ( 12 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 334 ( 28 ~; 30 |; 22 &; 214 @)
% ( 0 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 89 ( 89 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 2 con; 0-4 aty)
% Number of variables : 129 ( 23 ^ 100 !; 6 ?; 129 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(decl_34,type,
trans: ( $i > $i > $o ) > $o ).
thf(decl_35,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(decl_41,type,
term: ( $i > $i > $o ) > $o ).
thf(decl_42,type,
ind: ( $i > $i > $o ) > $o ).
thf(decl_51,type,
epred1_0: $i > $i > $o ).
thf(decl_52,type,
esk1_1: ( $i > $o ) > $i ).
thf(decl_53,type,
epred2_2: ( $i > $o ) > $i > $i > $i > $o ).
thf(decl_54,type,
epred3_0: $i > $o ).
thf(decl_55,type,
esk2_0: $i ).
thf(decl_56,type,
esk3_1: $i > $i ).
thf(transitive_closure,axiom,
( tc
= ( ^ [X1: $i > $i > $o,X3: $i,X4: $i] :
! [X2: $i > $i > $o] :
( ( ( trans @ X2 )
& ( subrel @ X1 @ X2 ) )
=> ( X2 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',transitive_closure) ).
thf(subrel,axiom,
( subrel
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',subrel) ).
thf(transitive,axiom,
( trans
= ( ^ [X1: $i > $i > $o] :
! [X3: $i,X4: $i,X6: $i] :
( ( ( X1 @ X3 @ X4 )
& ( X1 @ X4 @ X6 ) )
=> ( X1 @ X3 @ X6 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',transitive) ).
thf(satisfying_the_induction_principle,axiom,
( ind
= ( ^ [X1: $i > $i > $o] :
! [X8: $i > $o] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( tc @ X1 @ X3 @ X4 )
=> ( X8 @ X4 ) )
=> ( X8 @ X3 ) )
=> ! [X3: $i] : ( X8 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',satisfying_the_induction_principle) ).
thf(terminating,axiom,
( term
= ( ^ [X1: $i > $i > $o] :
! [X7: $i > $o] :
( ? [X3: $i] : ( X7 @ X3 )
=> ? [X3: $i] :
( ( X7 @ X3 )
& ! [X4: $i] :
( ( X7 @ X4 )
=> ~ ( X1 @ X3 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',terminating) ).
thf(induction_implies_termination,conjecture,
! [X1: $i > $i > $o] :
( ( ind @ X1 )
=> ( term @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction_implies_termination) ).
thf(c_0_6,plain,
( tc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
! [X2: $i > $i > $o] :
( ( ! [X16: $i,X17: $i,X18: $i] :
( ( ( X2 @ X16 @ X17 )
& ( X2 @ X17 @ X18 ) )
=> ( X2 @ X16 @ X18 ) )
& ! [X19: $i,X20: $i] :
( ( Z0 @ X19 @ X20 )
=> ( X2 @ X19 @ X20 ) ) )
=> ( X2 @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[transitive_closure]) ).
thf(c_0_7,plain,
( subrel
= ( ^ [Z0: $i > $i > $o,Z1: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( Z0 @ X3 @ X4 )
=> ( Z1 @ X3 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[subrel]) ).
thf(c_0_8,plain,
( trans
= ( ^ [Z0: $i > $i > $o] :
! [X3: $i,X4: $i,X6: $i] :
( ( ( Z0 @ X3 @ X4 )
& ( Z0 @ X4 @ X6 ) )
=> ( Z0 @ X3 @ X6 ) ) ) ),
inference(fof_simplification,[status(thm)],[transitive]) ).
thf(c_0_9,plain,
( ind
= ( ^ [Z0: $i > $i > $o] :
! [X8: $i > $o] :
( ! [X3: $i] :
( ! [X4: $i] :
( ! [X44: $i > $i > $o] :
( ( ! [X45: $i,X46: $i,X47: $i] :
( ( ( X44 @ X45 @ X46 )
& ( X44 @ X46 @ X47 ) )
=> ( X44 @ X45 @ X47 ) )
& ! [X48: $i,X49: $i] :
( ( Z0 @ X48 @ X49 )
=> ( X44 @ X48 @ X49 ) ) )
=> ( X44 @ X3 @ X4 ) )
=> ( X8 @ X4 ) )
=> ( X8 @ X3 ) )
=> ! [X3: $i] : ( X8 @ X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[satisfying_the_induction_principle]) ).
thf(c_0_10,plain,
( tc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
! [X2: $i > $i > $o] :
( ( ! [X16: $i,X17: $i,X18: $i] :
( ( ( X2 @ X16 @ X17 )
& ( X2 @ X17 @ X18 ) )
=> ( X2 @ X16 @ X18 ) )
& ! [X19: $i,X20: $i] :
( ( Z0 @ X19 @ X20 )
=> ( X2 @ X19 @ X20 ) ) )
=> ( X2 @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).
thf(c_0_11,plain,
( term
= ( ^ [Z0: $i > $i > $o] :
! [X7: $i > $o] :
( ? [X3: $i] : ( X7 @ X3 )
=> ? [X3: $i] :
( ( X7 @ X3 )
& ! [X4: $i] :
( ( X7 @ X4 )
=> ~ ( Z0 @ X3 @ X4 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[terminating]) ).
thf(c_0_12,plain,
( ind
= ( ^ [Z0: $i > $i > $o] :
! [X8: $i > $o] :
( ! [X3: $i] :
( ! [X4: $i] :
( ! [X44: $i > $i > $o] :
( ( ! [X45: $i,X46: $i,X47: $i] :
( ( ( X44 @ X45 @ X46 )
& ( X44 @ X46 @ X47 ) )
=> ( X44 @ X45 @ X47 ) )
& ! [X48: $i,X49: $i] :
( ( Z0 @ X48 @ X49 )
=> ( X44 @ X48 @ X49 ) ) )
=> ( X44 @ X3 @ X4 ) )
=> ( X8 @ X4 ) )
=> ( X8 @ X3 ) )
=> ! [X3: $i] : ( X8 @ X3 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_13,negated_conjecture,
~ ! [X1: $i > $i > $o] :
( ! [X158: $i > $o] :
( ! [X159: $i] :
( ! [X160: $i] :
( ! [X161: $i > $i > $o] :
( ( ! [X162: $i,X163: $i,X164: $i] :
( ( ( X161 @ X162 @ X163 )
& ( X161 @ X163 @ X164 ) )
=> ( X161 @ X162 @ X164 ) )
& ! [X165: $i,X166: $i] :
( ( X1 @ X165 @ X166 )
=> ( X161 @ X165 @ X166 ) ) )
=> ( X161 @ X159 @ X160 ) )
=> ( X158 @ X160 ) )
=> ( X158 @ X159 ) )
=> ! [X167: $i] : ( X158 @ X167 ) )
=> ! [X168: $i > $o] :
( ? [X169: $i] : ( X168 @ X169 )
=> ? [X170: $i] :
( ( X168 @ X170 )
& ! [X171: $i] :
( ( X168 @ X171 )
=> ~ ( X1 @ X170 @ X171 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[induction_implies_termination]),c_0_11]),c_0_12]) ).
thf(c_0_14,negated_conjecture,
! [X173: $i > $o,X175: $i,X177: $i,X178: $i,X179: $i,X180: $i,X181: $i,X182: $i,X185: $i] :
( ( ~ ( epred2_2 @ X173 @ X175 @ X177 @ X178 )
| ~ ( epred2_2 @ X173 @ X175 @ X178 @ X179 )
| ( epred2_2 @ X173 @ X175 @ X177 @ X179 )
| ( X173 @ X175 )
| ( X173 @ X182 ) )
& ( ~ ( epred1_0 @ X180 @ X181 )
| ( epred2_2 @ X173 @ X175 @ X180 @ X181 )
| ( X173 @ X175 )
| ( X173 @ X182 ) )
& ( ~ ( epred2_2 @ X173 @ X175 @ ( esk1_1 @ X173 ) @ X175 )
| ( X173 @ X175 )
| ( X173 @ X182 ) )
& ( ~ ( X173 @ ( esk1_1 @ X173 ) )
| ( X173 @ X182 ) )
& ( epred3_0 @ esk2_0 )
& ( ( epred3_0 @ ( esk3_1 @ X185 ) )
| ~ ( epred3_0 @ X185 ) )
& ( ( epred1_0 @ X185 @ ( esk3_1 @ X185 ) )
| ~ ( epred3_0 @ X185 ) ) ),
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_13])])])])])]) ).
thf(c_0_15,negated_conjecture,
! [X3: $i,X6: $i,X10: $i,X7: $i > $o,X4: $i] :
( ( epred2_2 @ X7 @ X6 @ X3 @ X4 )
| ( X7 @ X6 )
| ( X7 @ X10 )
| ~ ( epred1_0 @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_16,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ X3 @ ( esk3_1 @ X3 ) )
| ~ ( epred3_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_17,negated_conjecture,
! [X3: $i,X7: $i > $o] :
( ( X7 @ X3 )
| ~ ( X7 @ ( esk1_1 @ X7 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_18,negated_conjecture,
! [X7: $i > $o,X4: $i,X3: $i] :
( ( X7 @ X3 )
| ( X7 @ X4 )
| ~ ( epred2_2 @ X7 @ X3 @ ( esk1_1 @ X7 ) @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_19,negated_conjecture,
! [X3: $i,X7: $i > $o,X6: $i,X4: $i] :
( ( epred2_2 @ X7 @ X3 @ X4 @ ( esk3_1 @ X4 ) )
| ( X7 @ X6 )
| ( X7 @ X3 )
| ~ ( epred3_0 @ X4 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_20,negated_conjecture,
! [X7: $i > $o,X3: $i] :
( ( X7
@ ( esk1_1
@ ^ [Z0: $i] :
~ ( X7 @ Z0 ) ) )
| ~ ( X7 @ X3 ) ),
inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[]),c_0_17]) ).
thf(c_0_21,negated_conjecture,
epred3_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_22,negated_conjecture,
! [X3: $i,X4: $i,X7: $i > $o] :
( ( X7 @ ( esk3_1 @ ( esk1_1 @ X7 ) ) )
| ( X7 @ X3 )
| ( X7 @ X4 )
| ~ ( epred3_0 @ ( esk1_1 @ X7 ) ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_23,negated_conjecture,
( epred3_0
@ ( esk1_1
@ ^ [Z0: $i] :
~ ( epred3_0 @ Z0 ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_24,negated_conjecture,
! [X3: $i,X4: $i] :
( ~ ( epred3_0
@ ( esk3_1
@ ( esk1_1
@ ^ [Z0: $i] :
~ ( epred3_0 @ Z0 ) ) ) )
| ~ ( epred3_0 @ X3 )
| ~ ( epred3_0 @ X4 ) ),
inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23])]) ).
thf(c_0_25,negated_conjecture,
! [X3: $i] :
( ( epred3_0 @ ( esk3_1 @ X3 ) )
| ~ ( epred3_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_26,negated_conjecture,
! [X3: $i,X4: $i] :
( ~ ( epred3_0 @ X3 )
| ~ ( epred3_0 @ X4 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_23])]) ).
thf(c_0_27,negated_conjecture,
! [X3: $i] :
~ ( epred3_0 @ X3 ),
inference(spm,[status(thm)],[c_0_26,c_0_21]) ).
thf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_21,c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU481^1 : TPTP v8.2.0. Released v3.6.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 16:03:08 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.20/0.47 Running higher-order theorem proving
% 0.20/0.47 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
% 0.20/0.51 # Version: 3.1.0-ho
% 0.20/0.51 # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.20/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.51 # Starting new_ho_9 with 1500s (5) cores
% 0.20/0.51 # Starting post_as_ho1 with 300s (1) cores
% 0.20/0.51 # Starting sh1l with 300s (1) cores
% 0.20/0.51 # Starting post_as_ho10 with 300s (1) cores
% 0.20/0.51 # sh1l with pid 6387 completed with status 0
% 0.20/0.51 # Result found by sh1l
% 0.20/0.51 # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.20/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.51 # Starting new_ho_9 with 1500s (5) cores
% 0.20/0.51 # Starting post_as_ho1 with 300s (1) cores
% 0.20/0.51 # Starting sh1l with 300s (1) cores
% 0.20/0.51 # No SInE strategy applied
% 0.20/0.51 # Search class: HGUNF-FFSF11-SHSSMMBN
% 0.20/0.51 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.51 # Starting ehoh_best2_full_lfho with 181s (1) cores
% 0.20/0.51 # ehoh_best2_full_lfho with pid 6392 completed with status 0
% 0.20/0.51 # Result found by ehoh_best2_full_lfho
% 0.20/0.51 # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.20/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.51 # Starting new_ho_9 with 1500s (5) cores
% 0.20/0.51 # Starting post_as_ho1 with 300s (1) cores
% 0.20/0.51 # Starting sh1l with 300s (1) cores
% 0.20/0.51 # No SInE strategy applied
% 0.20/0.51 # Search class: HGUNF-FFSF11-SHSSMMBN
% 0.20/0.51 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.51 # Starting ehoh_best2_full_lfho with 181s (1) cores
% 0.20/0.51 # Preprocessing time : 0.001 s
% 0.20/0.51
% 0.20/0.51 # Proof found!
% 0.20/0.51 # SZS status Theorem
% 0.20/0.51 # SZS output start CNFRefutation
% See solution above
% 0.20/0.51 # Parsed axioms : 59
% 0.20/0.51 # Removed by relevancy pruning/SinE : 0
% 0.20/0.51 # Initial clauses : 36
% 0.20/0.51 # Removed in clause preprocessing : 29
% 0.20/0.51 # Initial clauses in saturation : 7
% 0.20/0.51 # Processed clauses : 40
% 0.20/0.51 # ...of these trivial : 2
% 0.20/0.51 # ...subsumed : 7
% 0.20/0.51 # ...remaining for further processing : 31
% 0.20/0.51 # Other redundant clauses eliminated : 8
% 0.20/0.51 # Clauses deleted for lack of memory : 0
% 0.20/0.51 # Backward-subsumed : 11
% 0.20/0.51 # Backward-rewritten : 0
% 0.20/0.51 # Generated clauses : 108
% 0.20/0.51 # ...of the previous two non-redundant : 86
% 0.20/0.51 # ...aggressively subsumed : 0
% 0.20/0.51 # Contextual simplify-reflections : 0
% 0.20/0.51 # Paramodulations : 47
% 0.20/0.51 # Factorizations : 0
% 0.20/0.51 # NegExts : 3
% 0.20/0.51 # Equation resolutions : 9
% 0.20/0.51 # Disequality decompositions : 0
% 0.20/0.51 # Total rewrite steps : 3
% 0.20/0.51 # ...of those cached : 1
% 0.20/0.51 # Propositional unsat checks : 0
% 0.20/0.51 # Propositional check models : 0
% 0.20/0.51 # Propositional check unsatisfiable : 0
% 0.20/0.51 # Propositional clauses : 0
% 0.20/0.51 # Propositional clauses after purity: 0
% 0.20/0.51 # Propositional unsat core size : 0
% 0.20/0.51 # Propositional preprocessing time : 0.000
% 0.20/0.51 # Propositional encoding time : 0.000
% 0.20/0.51 # Propositional solver time : 0.000
% 0.20/0.51 # Success case prop preproc time : 0.000
% 0.20/0.51 # Success case prop encoding time : 0.000
% 0.20/0.51 # Success case prop solver time : 0.000
% 0.20/0.51 # Current number of processed clauses : 15
% 0.20/0.51 # Positive orientable unit clauses : 2
% 0.20/0.51 # Positive unorientable unit clauses: 0
% 0.20/0.51 # Negative unit clauses : 3
% 0.20/0.51 # Non-unit-clauses : 10
% 0.20/0.51 # Current number of unprocessed clauses: 53
% 0.20/0.51 # ...number of literals in the above : 186
% 0.20/0.51 # Current number of archived formulas : 0
% 0.20/0.51 # Current number of archived clauses : 16
% 0.20/0.51 # Clause-clause subsumption calls (NU) : 53
% 0.20/0.51 # Rec. Clause-clause subsumption calls : 41
% 0.20/0.51 # Non-unit clause-clause subsumptions : 5
% 0.20/0.51 # Unit Clause-clause subsumption calls : 12
% 0.20/0.51 # Rewrite failures with RHS unbound : 0
% 0.20/0.51 # BW rewrite match attempts : 1
% 0.20/0.51 # BW rewrite match successes : 1
% 0.20/0.51 # Condensation attempts : 0
% 0.20/0.51 # Condensation successes : 0
% 0.20/0.51 # Termbank termtop insertions : 6061
% 0.20/0.51 # Search garbage collected termcells : 989
% 0.20/0.51
% 0.20/0.51 # -------------------------------------------------
% 0.20/0.51 # User time : 0.011 s
% 0.20/0.51 # System time : 0.002 s
% 0.20/0.51 # Total time : 0.012 s
% 0.20/0.51 # Maximum resident set size: 2144 pages
% 0.20/0.51
% 0.20/0.51 # -------------------------------------------------
% 0.20/0.51 # User time : 0.013 s
% 0.20/0.51 # System time : 0.004 s
% 0.20/0.51 # Total time : 0.017 s
% 0.20/0.51 # Maximum resident set size: 1788 pages
% 0.20/0.51 % E---3.1 exiting
% 0.20/0.52 % E exiting
%------------------------------------------------------------------------------