TSTP Solution File: SYO462^5 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SYO462^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n027.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 08:46:14 EDT 2024
% Result : Theorem 0.20s 0.49s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of formulae : 48 ( 21 unt; 13 typ; 0 def)
% Number of atoms : 131 ( 17 equ; 0 cnn)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 306 ( 72 ~; 62 |; 10 &; 162 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 61 ( 40 ^ 21 !; 0 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_24,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_25,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_27,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_29,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_49,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_53,type,
rel_s4: $i > $i > $o ).
thf(decl_54,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(decl_56,type,
p: $i > $o ).
thf(decl_57,type,
q: $i > $o ).
thf(decl_58,type,
esk1_0: $i ).
thf(decl_59,type,
esk2_0: $i ).
thf(decl_60,type,
esk3_0: $i ).
thf(mand,axiom,
( mand
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mnot @ ( mor @ ( mnot @ X6 ) @ ( mnot @ X7 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(mequiv,axiom,
( mequiv
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mand @ ( mimplies @ X6 @ X7 ) @ ( mimplies @ X7 @ X6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( rel_s4 @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(prove,conjecture,
mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(c_0_8,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_9,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_10,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_11,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_12,plain,
( mequiv
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) )
| ~ ( ~ ( Z1 @ Z2 )
| ( Z0 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[mequiv]) ).
thf(c_0_13,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
thf(c_0_14,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_11,c_0_9]),c_0_10]) ).
thf(c_0_15,plain,
( mequiv
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) )
| ~ ( ~ ( Z1 @ Z2 )
| ( Z0 @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
thf(c_0_16,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_17,plain,
( mbox_s4
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X14: $i] :
( ~ ( rel_s4 @ Z1 @ X14 )
| ( Z0 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_s4]) ).
thf(c_0_18,negated_conjecture,
~ ! [X29: $i] :
( ~ ! [X26: $i] :
( ~ ( rel_s4 @ X29 @ X26 )
| ~ ( ~ ( ~ ( p @ X26 )
| ( q @ X26 ) )
| ~ ( ~ ( q @ X26 )
| ( p @ X26 ) ) ) )
| ~ ( ~ ( ~ ! [X27: $i] :
( ~ ( rel_s4 @ X29 @ X27 )
| ( p @ X27 ) )
| ! [X28: $i] :
( ~ ( rel_s4 @ X29 @ X28 )
| ( q @ X28 ) ) )
| ~ ( ~ ! [X28: $i] :
( ~ ( rel_s4 @ X29 @ X28 )
| ( q @ X28 ) )
| ! [X27: $i] :
( ~ ( rel_s4 @ X29 @ X27 )
| ( p @ X27 ) ) ) ) ),
inference(fof_simplification,[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)],[prove]),c_0_14]),c_0_15]),c_0_16]),c_0_17])]) ).
thf(c_0_19,negated_conjecture,
! [X35: $i,X36: $i,X38: $i] :
( ( ~ ( p @ X35 )
| ( q @ X35 )
| ~ ( rel_s4 @ esk1_0 @ X35 ) )
& ( ~ ( q @ X35 )
| ( p @ X35 )
| ~ ( rel_s4 @ esk1_0 @ X35 ) )
& ( ~ ( rel_s4 @ esk1_0 @ X38 )
| ( q @ X38 )
| ~ ( rel_s4 @ esk1_0 @ X36 )
| ( p @ X36 ) )
& ( ( rel_s4 @ esk1_0 @ esk3_0 )
| ~ ( rel_s4 @ esk1_0 @ X36 )
| ( p @ X36 ) )
& ( ~ ( p @ esk3_0 )
| ~ ( rel_s4 @ esk1_0 @ X36 )
| ( p @ X36 ) )
& ( ~ ( rel_s4 @ esk1_0 @ X38 )
| ( q @ X38 )
| ( rel_s4 @ esk1_0 @ esk2_0 ) )
& ( ( rel_s4 @ esk1_0 @ esk3_0 )
| ( rel_s4 @ esk1_0 @ esk2_0 ) )
& ( ~ ( p @ esk3_0 )
| ( rel_s4 @ esk1_0 @ esk2_0 ) )
& ( ~ ( rel_s4 @ esk1_0 @ X38 )
| ( q @ X38 )
| ~ ( q @ esk2_0 ) )
& ( ( rel_s4 @ esk1_0 @ esk3_0 )
| ~ ( q @ esk2_0 ) )
& ( ~ ( p @ esk3_0 )
| ~ ( q @ esk2_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_18])])])])])]) ).
thf(c_0_20,negated_conjecture,
! [X3: $i] :
( ( q @ X3 )
| ~ ( rel_s4 @ esk1_0 @ X3 )
| ~ ( q @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_21,negated_conjecture,
! [X3: $i] :
( ( q @ X3 )
| ~ ( p @ X3 )
| ~ ( rel_s4 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_22,negated_conjecture,
! [X3: $i,X14: $i] :
( ( q @ X3 )
| ( p @ X14 )
| ~ ( rel_s4 @ esk1_0 @ X3 )
| ~ ( rel_s4 @ esk1_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_23,negated_conjecture,
! [X3: $i] :
( ( q @ X3 )
| ( rel_s4 @ esk1_0 @ esk2_0 )
| ~ ( rel_s4 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_24,negated_conjecture,
! [X3: $i] :
( ( p @ X3 )
| ~ ( q @ X3 )
| ~ ( rel_s4 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_25,negated_conjecture,
! [X3: $i] :
( ( q @ X3 )
| ~ ( rel_s4 @ esk1_0 @ X3 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23]) ).
thf(c_0_26,negated_conjecture,
( ~ ( p @ esk3_0 )
| ~ ( q @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_27,negated_conjecture,
! [X3: $i] :
( ( p @ X3 )
| ~ ( rel_s4 @ esk1_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_28,negated_conjecture,
( ( rel_s4 @ esk1_0 @ esk3_0 )
| ~ ( q @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_29,negated_conjecture,
~ ( q @ esk2_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
thf(c_0_30,negated_conjecture,
( ( rel_s4 @ esk1_0 @ esk3_0 )
| ( rel_s4 @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_31,negated_conjecture,
~ ( rel_s4 @ esk1_0 @ esk2_0 ),
inference(spm,[status(thm)],[c_0_29,c_0_25]) ).
thf(c_0_32,negated_conjecture,
( ( rel_s4 @ esk1_0 @ esk2_0 )
| ~ ( p @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_33,negated_conjecture,
rel_s4 @ esk1_0 @ esk3_0,
inference(sr,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_27]),c_0_33])]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO462^5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % 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 : Mon May 20 09:57:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.48 Running higher-order theorem proving
% 0.20/0.48 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
% 0.20/0.49 # Version: 3.1.0-ho
% 0.20/0.49 # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.20/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.49 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.20/0.49 # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.20/0.49 # Starting almost_fo_3_lam with 300s (1) cores
% 0.20/0.49 # Starting post_as_ho1 with 300s (1) cores
% 0.20/0.49 # ho_unfolding_3 with pid 10529 completed with status 0
% 0.20/0.49 # Result found by ho_unfolding_3
% 0.20/0.49 # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.20/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.49 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.20/0.49 # No SInE strategy applied
% 0.20/0.49 # Search class: HGHNF-FFSF00-SHSSMFNN
% 0.20/0.49 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.49 # Starting new_ho_10 with 811s (1) cores
% 0.20/0.49 # Starting ho_unfolding_3 with 151s (1) cores
% 0.20/0.49 # Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.20/0.49 # Starting lpo1_def_fix with 136s (1) cores
% 0.20/0.49 # Starting ehoh_best8_lambda with 136s (1) cores
% 0.20/0.49 # ho_unfolding_3 with pid 10536 completed with status 0
% 0.20/0.49 # Result found by ho_unfolding_3
% 0.20/0.49 # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.20/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.49 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.20/0.49 # No SInE strategy applied
% 0.20/0.49 # Search class: HGHNF-FFSF00-SHSSMFNN
% 0.20/0.49 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.49 # Starting new_ho_10 with 811s (1) cores
% 0.20/0.49 # Starting ho_unfolding_3 with 151s (1) cores
% 0.20/0.49 # Preprocessing time : 0.001 s
% 0.20/0.49 # Presaturation interreduction done
% 0.20/0.49
% 0.20/0.49 # Proof found!
% 0.20/0.49 # SZS status Theorem
% 0.20/0.49 # SZS output start CNFRefutation
% See solution above
% 0.20/0.49 # Parsed axioms : 73
% 0.20/0.49 # Removed by relevancy pruning/SinE : 0
% 0.20/0.49 # Initial clauses : 50
% 0.20/0.49 # Removed in clause preprocessing : 37
% 0.20/0.49 # Initial clauses in saturation : 13
% 0.20/0.49 # Processed clauses : 46
% 0.20/0.49 # ...of these trivial : 0
% 0.20/0.49 # ...subsumed : 5
% 0.20/0.49 # ...remaining for further processing : 40
% 0.20/0.49 # Other redundant clauses eliminated : 0
% 0.20/0.49 # Clauses deleted for lack of memory : 0
% 0.20/0.49 # Backward-subsumed : 10
% 0.20/0.49 # Backward-rewritten : 3
% 0.20/0.49 # Generated clauses : 41
% 0.20/0.49 # ...of the previous two non-redundant : 39
% 0.20/0.49 # ...aggressively subsumed : 0
% 0.20/0.49 # Contextual simplify-reflections : 3
% 0.20/0.49 # Paramodulations : 38
% 0.20/0.49 # Factorizations : 0
% 0.20/0.49 # NegExts : 0
% 0.20/0.49 # Equation resolutions : 0
% 0.20/0.49 # Disequality decompositions : 0
% 0.20/0.49 # Total rewrite steps : 9
% 0.20/0.49 # ...of those cached : 6
% 0.20/0.49 # Propositional unsat checks : 0
% 0.20/0.49 # Propositional check models : 0
% 0.20/0.49 # Propositional check unsatisfiable : 0
% 0.20/0.49 # Propositional clauses : 0
% 0.20/0.49 # Propositional clauses after purity: 0
% 0.20/0.49 # Propositional unsat core size : 0
% 0.20/0.49 # Propositional preprocessing time : 0.000
% 0.20/0.49 # Propositional encoding time : 0.000
% 0.20/0.49 # Propositional solver time : 0.000
% 0.20/0.49 # Success case prop preproc time : 0.000
% 0.20/0.49 # Success case prop encoding time : 0.000
% 0.20/0.49 # Success case prop solver time : 0.000
% 0.20/0.49 # Current number of processed clauses : 11
% 0.20/0.49 # Positive orientable unit clauses : 5
% 0.20/0.49 # Positive unorientable unit clauses: 0
% 0.20/0.49 # Negative unit clauses : 2
% 0.20/0.49 # Non-unit-clauses : 4
% 0.20/0.49 # Current number of unprocessed clauses: 16
% 0.20/0.49 # ...number of literals in the above : 53
% 0.20/0.49 # Current number of archived formulas : 0
% 0.20/0.49 # Current number of archived clauses : 29
% 0.20/0.49 # Clause-clause subsumption calls (NU) : 30
% 0.20/0.49 # Rec. Clause-clause subsumption calls : 28
% 0.20/0.49 # Non-unit clause-clause subsumptions : 15
% 0.20/0.49 # Unit Clause-clause subsumption calls : 9
% 0.20/0.49 # Rewrite failures with RHS unbound : 0
% 0.20/0.49 # BW rewrite match attempts : 6
% 0.20/0.49 # BW rewrite match successes : 1
% 0.20/0.49 # Condensation attempts : 46
% 0.20/0.49 # Condensation successes : 0
% 0.20/0.49 # Termbank termtop insertions : 3375
% 0.20/0.49 # Search garbage collected termcells : 610
% 0.20/0.49
% 0.20/0.49 # -------------------------------------------------
% 0.20/0.49 # User time : 0.007 s
% 0.20/0.49 # System time : 0.002 s
% 0.20/0.49 # Total time : 0.010 s
% 0.20/0.49 # Maximum resident set size: 1960 pages
% 0.20/0.49
% 0.20/0.49 # -------------------------------------------------
% 0.20/0.49 # User time : 0.024 s
% 0.20/0.49 # System time : 0.008 s
% 0.20/0.49 # Total time : 0.032 s
% 0.20/0.49 # Maximum resident set size: 1800 pages
% 0.20/0.49 % E---3.1 exiting
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------