TSTP Solution File: SYO433^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SYO433^1 : TPTP v8.2.0. Released v4.0.0.
% 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 08:45:59 EDT 2024
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 27
% Syntax : Number of formulae : 57 ( 27 unt; 15 typ; 0 def)
% Number of atoms : 123 ( 21 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 266 ( 59 ~; 38 |; 7 &; 159 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 70 ( 70 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 3 con; 0-3 aty)
% Number of variables : 82 ( 41 ^ 41 !; 0 ?; 82 :)
% 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_39,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(decl_42,type,
mtransitive: ( $i > $i > $o ) > $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_55,type,
mdia_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_1: $i > $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(mdia_s4,axiom,
( mdia_s4
= ( ^ [X6: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mdia_s4) ).
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(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(mtransitive,axiom,
( mtransitive
= ( ^ [X13: $i > $i > $o] :
! [X15: $i,X16: $i,X17: $i] :
( ( ( X13 @ X15 @ X16 )
& ( X13 @ X16 @ X17 ) )
=> ( X13 @ X15 @ X17 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(prove,conjecture,
mvalid @ ( mimplies @ ( mand @ ( mdia_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mdia_s4 @ ( mand @ p @ ( mbox_s4 @ q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(a2,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a2) ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [X13: $i > $i > $o] :
! [X15: $i] : ( X13 @ X15 @ X15 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(a1,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a1) ).
thf(c_0_12,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_13,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_14,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_15,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_16,plain,
( mdia_s4
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ! [X21: $i] :
( ~ ( rel_s4 @ Z1 @ X21 )
| ~ ( Z0 @ X21 ) ) ) ),
inference(fof_simplification,[status(thm)],[mdia_s4]) ).
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,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_12,c_0_13]),c_0_14]) ).
thf(c_0_19,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_15,c_0_13]),c_0_14]) ).
thf(c_0_20,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_21,plain,
( mdia_s4
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ! [X21: $i] :
( ~ ( rel_s4 @ Z1 @ X21 )
| ~ ( Z0 @ X21 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_16,c_0_13]),c_0_17]) ).
thf(c_0_22,plain,
( mtransitive
= ( ^ [Z0: $i > $i > $o] :
! [X15: $i,X16: $i,X17: $i] :
( ( ( Z0 @ X15 @ X16 )
& ( Z0 @ X16 @ X17 ) )
=> ( Z0 @ X15 @ X17 ) ) ) ),
inference(fof_simplification,[status(thm)],[mtransitive]) ).
thf(c_0_23,negated_conjecture,
~ ! [X30: $i] :
( ~ ~ ( ~ ~ ! [X26: $i] :
( ~ ( rel_s4 @ X30 @ X26 )
| ~ ( p @ X26 ) )
| ~ ! [X27: $i] :
( ~ ( rel_s4 @ X30 @ X27 )
| ( q @ X27 ) ) )
| ~ ! [X29: $i] :
( ~ ( rel_s4 @ X30 @ X29 )
| ~ ~ ( ~ ( p @ X29 )
| ~ ! [X28: $i] :
( ~ ( rel_s4 @ X29 @ X28 )
| ( q @ X28 ) ) ) ) ),
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(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[prove]),c_0_18]),c_0_19]),c_0_20]),c_0_17]),c_0_21])]) ).
thf(c_0_24,plain,
! [X23: $i,X24: $i,X25: $i] :
( ( ( rel_s4 @ X23 @ X24 )
& ( rel_s4 @ X24 @ X25 ) )
=> ( rel_s4 @ X23 @ X25 ) ),
inference(apply_def,[status(thm)],[a2,c_0_22]) ).
thf(c_0_25,negated_conjecture,
! [X37: $i,X38: $i] :
( ( rel_s4 @ esk1_0 @ esk2_0 )
& ( p @ esk2_0 )
& ( ~ ( rel_s4 @ esk1_0 @ X37 )
| ( q @ X37 ) )
& ( ( rel_s4 @ X38 @ ( esk3_1 @ X38 ) )
| ~ ( p @ X38 )
| ~ ( rel_s4 @ esk1_0 @ X38 ) )
& ( ~ ( q @ ( esk3_1 @ X38 ) )
| ~ ( p @ X38 )
| ~ ( rel_s4 @ esk1_0 @ X38 ) ) ),
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_23])])])])])]) ).
thf(c_0_26,plain,
! [X32: $i,X33: $i,X34: $i] :
( ~ ( rel_s4 @ X32 @ X33 )
| ~ ( rel_s4 @ X33 @ X34 )
| ( rel_s4 @ X32 @ X34 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
thf(c_0_27,plain,
( mreflexive
= ( ^ [Z0: $i > $i > $o] :
! [X15: $i] : ( Z0 @ X15 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mreflexive]) ).
thf(c_0_28,negated_conjecture,
! [X3: $i] :
( ~ ( q @ ( esk3_1 @ X3 ) )
| ~ ( p @ X3 )
| ~ ( rel_s4 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_29,negated_conjecture,
! [X3: $i] :
( ( q @ X3 )
| ~ ( rel_s4 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_30,plain,
! [X14: $i,X3: $i,X15: $i] :
( ( rel_s4 @ X3 @ X15 )
| ~ ( rel_s4 @ X3 @ X14 )
| ~ ( rel_s4 @ X14 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_31,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ X3 @ ( esk3_1 @ X3 ) )
| ~ ( p @ X3 )
| ~ ( rel_s4 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_32,plain,
! [X22: $i] : ( rel_s4 @ X22 @ X22 ),
inference(apply_def,[status(thm)],[a1,c_0_27]) ).
thf(c_0_33,negated_conjecture,
! [X3: $i] :
( ~ ( rel_s4 @ esk1_0 @ ( esk3_1 @ X3 ) )
| ~ ( rel_s4 @ esk1_0 @ X3 )
| ~ ( p @ X3 ) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_34,negated_conjecture,
! [X3: $i,X14: $i] :
( ( rel_s4 @ X3 @ ( esk3_1 @ X14 ) )
| ~ ( rel_s4 @ esk1_0 @ X14 )
| ~ ( rel_s4 @ X3 @ X14 )
| ~ ( p @ X14 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_35,negated_conjecture,
rel_s4 @ esk1_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_36,plain,
! [X31: $i] : ( rel_s4 @ X31 @ X31 ),
inference(variable_rename,[status(thm)],[c_0_32]) ).
thf(c_0_37,negated_conjecture,
! [X3: $i] :
( ~ ( rel_s4 @ esk1_0 @ X3 )
| ~ ( p @ X3 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
thf(c_0_38,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ X3 @ esk2_0 )
| ~ ( rel_s4 @ X3 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_35]) ).
thf(c_0_39,negated_conjecture,
p @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_40,plain,
! [X3: $i] : ( rel_s4 @ X3 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO433^1 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon May 20 09:57:52 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.18/0.45 Running higher-order theorem proving
% 0.18/0.45 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
% 0.18/0.47 # Version: 3.1.0-ho
% 0.18/0.47 # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.18/0.47 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.47 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.18/0.47 # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.18/0.47 # Starting almost_fo_3_lam with 300s (1) cores
% 0.18/0.47 # Starting post_as_ho1 with 300s (1) cores
% 0.18/0.47 # ho_unfolding_3 with pid 17482 completed with status 0
% 0.18/0.47 # Result found by ho_unfolding_3
% 0.18/0.47 # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.18/0.47 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.47 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.18/0.47 # No SInE strategy applied
% 0.18/0.47 # Search class: HHHNF-FFSF11-SHSSMFNN
% 0.18/0.47 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.47 # Starting sh7 with 811s (1) cores
% 0.18/0.47 # Starting ho_unfolding_3 with 151s (1) cores
% 0.18/0.47 # Starting lpo1_lambda_fix with 136s (1) cores
% 0.18/0.47 # Starting new_ho_7 with 136s (1) cores
% 0.18/0.47 # Starting full_lambda_1 with 136s (1) cores
% 0.18/0.47 # full_lambda_1 with pid 17491 completed with status 0
% 0.18/0.47 # Result found by full_lambda_1
% 0.18/0.47 # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.18/0.47 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.47 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.18/0.47 # No SInE strategy applied
% 0.18/0.47 # Search class: HHHNF-FFSF11-SHSSMFNN
% 0.18/0.47 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.47 # Starting sh7 with 811s (1) cores
% 0.18/0.47 # Starting ho_unfolding_3 with 151s (1) cores
% 0.18/0.47 # Starting lpo1_lambda_fix with 136s (1) cores
% 0.18/0.47 # Starting new_ho_7 with 136s (1) cores
% 0.18/0.47 # Starting full_lambda_1 with 136s (1) cores
% 0.18/0.47 # Preprocessing time : 0.001 s
% 0.18/0.47
% 0.18/0.47 # Proof found!
% 0.18/0.47 # SZS status Theorem
% 0.18/0.47 # SZS output start CNFRefutation
% See solution above
% 0.18/0.47 # Parsed axioms : 73
% 0.18/0.47 # Removed by relevancy pruning/SinE : 0
% 0.18/0.47 # Initial clauses : 44
% 0.18/0.47 # Removed in clause preprocessing : 37
% 0.18/0.47 # Initial clauses in saturation : 7
% 0.18/0.47 # Processed clauses : 14
% 0.18/0.47 # ...of these trivial : 0
% 0.18/0.47 # ...subsumed : 1
% 0.18/0.47 # ...remaining for further processing : 13
% 0.18/0.47 # Other redundant clauses eliminated : 0
% 0.18/0.47 # Clauses deleted for lack of memory : 0
% 0.18/0.47 # Backward-subsumed : 4
% 0.18/0.47 # Backward-rewritten : 0
% 0.18/0.47 # Generated clauses : 12
% 0.18/0.47 # ...of the previous two non-redundant : 8
% 0.18/0.47 # ...aggressively subsumed : 0
% 0.18/0.47 # Contextual simplify-reflections : 0
% 0.18/0.47 # Paramodulations : 12
% 0.18/0.47 # Factorizations : 0
% 0.18/0.47 # NegExts : 0
% 0.18/0.47 # Equation resolutions : 0
% 0.18/0.47 # Disequality decompositions : 0
% 0.18/0.47 # Total rewrite steps : 3
% 0.18/0.47 # ...of those cached : 1
% 0.18/0.47 # Propositional unsat checks : 0
% 0.18/0.47 # Propositional check models : 0
% 0.18/0.47 # Propositional check unsatisfiable : 0
% 0.18/0.47 # Propositional clauses : 0
% 0.18/0.47 # Propositional clauses after purity: 0
% 0.18/0.47 # Propositional unsat core size : 0
% 0.18/0.47 # Propositional preprocessing time : 0.000
% 0.18/0.47 # Propositional encoding time : 0.000
% 0.18/0.47 # Propositional solver time : 0.000
% 0.18/0.47 # Success case prop preproc time : 0.000
% 0.18/0.47 # Success case prop encoding time : 0.000
% 0.18/0.47 # Success case prop solver time : 0.000
% 0.18/0.47 # Current number of processed clauses : 9
% 0.18/0.47 # Positive orientable unit clauses : 3
% 0.18/0.47 # Positive unorientable unit clauses: 0
% 0.18/0.47 # Negative unit clauses : 1
% 0.18/0.47 # Non-unit-clauses : 5
% 0.18/0.47 # Current number of unprocessed clauses: 1
% 0.18/0.47 # ...number of literals in the above : 5
% 0.18/0.47 # Current number of archived formulas : 0
% 0.18/0.47 # Current number of archived clauses : 4
% 0.18/0.47 # Clause-clause subsumption calls (NU) : 17
% 0.18/0.47 # Rec. Clause-clause subsumption calls : 15
% 0.18/0.47 # Non-unit clause-clause subsumptions : 5
% 0.18/0.47 # Unit Clause-clause subsumption calls : 3
% 0.18/0.47 # Rewrite failures with RHS unbound : 0
% 0.18/0.47 # BW rewrite match attempts : 2
% 0.18/0.47 # BW rewrite match successes : 0
% 0.18/0.47 # Condensation attempts : 14
% 0.18/0.47 # Condensation successes : 0
% 0.18/0.47 # Termbank termtop insertions : 2770
% 0.18/0.47 # Search garbage collected termcells : 580
% 0.18/0.47
% 0.18/0.47 # -------------------------------------------------
% 0.18/0.47 # User time : 0.005 s
% 0.18/0.47 # System time : 0.002 s
% 0.18/0.47 # Total time : 0.008 s
% 0.18/0.47 # Maximum resident set size: 1960 pages
% 0.18/0.47
% 0.18/0.47 # -------------------------------------------------
% 0.18/0.47 # User time : 0.019 s
% 0.18/0.47 # System time : 0.007 s
% 0.18/0.47 # Total time : 0.026 s
% 0.18/0.47 # Maximum resident set size: 1800 pages
% 0.18/0.47 % E---3.1 exiting
% 0.18/0.47 % E exiting
%------------------------------------------------------------------------------