%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : LCL453+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n005.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 : 600s
% DateTime : Sun Jul 17 10:11:18 EDT 2022
% Result : Theorem 0.22s 1.41s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 62 ( 33 unt; 0 def)
% Number of atoms : 116 ( 5 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 91 ( 37 ~; 35 |; 10 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 14 con; 0-2 aty)
% Number of variables : 85 ( 5 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(implies(X1,X2)) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(implies_2,axiom,
( implies_2
<=> ! [X1,X2] : is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_2) ).
fof(implies_3,axiom,
( implies_3
<=> ! [X1,X2,X3] : is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_3) ).
fof(hilbert_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(hilbert_implies_2,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
fof(and_3,axiom,
( and_3
<=> ! [X1,X2] : is_a_theorem(implies(X1,implies(X2,and(X1,X2)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_3) ).
fof(hilbert_implies_3,axiom,
implies_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_3) ).
fof(hilbert_and_3,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(implies_1,axiom,
( implies_1
<=> ! [X1,X2] : is_a_theorem(implies(X1,implies(X2,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_1) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
fof(modus_tollens,axiom,
( modus_tollens
<=> ! [X1,X2] : is_a_theorem(implies(implies(not(X2),not(X1)),implies(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
fof(hilbert_implies_1,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_1) ).
fof(hilbert_modus_tollens,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_tollens) ).
fof(luka_cn3,conjecture,
cn3,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',luka_cn3) ).
fof(cn3,axiom,
( cn3
<=> ! [X4] : is_a_theorem(implies(implies(not(X4),X4),X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',cn3) ).
fof(c_0_16,plain,
! [X3,X4] :
( ( ~ modus_ponens
| ~ is_a_theorem(X3)
| ~ is_a_theorem(implies(X3,X4))
| is_a_theorem(X4) )
& ( is_a_theorem(esk1_0)
| modus_ponens )
& ( is_a_theorem(implies(esk1_0,esk2_0))
| modus_ponens )
& ( ~ is_a_theorem(esk2_0)
| modus_ponens ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens])])])])])])]) ).
fof(c_0_17,plain,
! [X3,X4] :
( ( ~ implies_2
| is_a_theorem(implies(implies(X3,implies(X3,X4)),implies(X3,X4))) )
& ( ~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0)))
| implies_2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_2])])])])])]) ).
fof(c_0_18,plain,
! [X4,X5,X6] :
( ( ~ implies_3
| is_a_theorem(implies(implies(X4,X5),implies(implies(X5,X6),implies(X4,X6)))) )
& ( ~ is_a_theorem(implies(implies(esk11_0,esk12_0),implies(implies(esk12_0,esk13_0),implies(esk11_0,esk13_0))))
| implies_3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_3])])])])])]) ).
cnf(c_0_19,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2)
| ~ modus_ponens ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[hilbert_modus_ponens]) ).
cnf(c_0_21,plain,
( is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))
| ~ implies_2 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
implies_2,
inference(split_conjunct,[status(thm)],[hilbert_implies_2]) ).
fof(c_0_23,plain,
! [X3,X4] :
( ( ~ and_3
| is_a_theorem(implies(X3,implies(X4,and(X3,X4)))) )
& ( ~ is_a_theorem(implies(esk18_0,implies(esk19_0,and(esk18_0,esk19_0))))
| and_3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_3])])])])])]) ).
cnf(c_0_24,plain,
( is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))
| ~ implies_3 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
implies_3,
inference(split_conjunct,[status(thm)],[hilbert_implies_3]) ).
cnf(c_0_26,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]) ).
cnf(c_0_27,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).
cnf(c_0_28,plain,
( is_a_theorem(implies(X1,implies(X2,and(X1,X2))))
| ~ and_3 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
and_3,
inference(split_conjunct,[status(thm)],[hilbert_and_3]) ).
fof(c_0_30,plain,
! [X3,X4] :
( ~ op_implies_and
| implies(X3,X4) = not(and(X3,not(X4))) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])])])]) ).
cnf(c_0_31,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
cnf(c_0_32,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
is_a_theorem(implies(X1,implies(X2,and(X1,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
fof(c_0_34,plain,
! [X3,X4] :
( ( ~ implies_1
| is_a_theorem(implies(X3,implies(X4,X3))) )
& ( ~ is_a_theorem(implies(esk7_0,implies(esk8_0,esk7_0)))
| implies_1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_1])])])])])]) ).
cnf(c_0_35,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
fof(c_0_37,plain,
! [X3,X4] :
( ( ~ modus_tollens
| is_a_theorem(implies(implies(not(X4),not(X3)),implies(X3,X4))) )
& ( ~ is_a_theorem(implies(implies(not(esk6_0),not(esk5_0)),implies(esk5_0,esk6_0)))
| modus_tollens ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_tollens])])])])])]) ).
cnf(c_0_38,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_26,c_0_31]) ).
cnf(c_0_39,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,plain,
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ implies_1 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
implies_1,
inference(split_conjunct,[status(thm)],[hilbert_implies_1]) ).
cnf(c_0_42,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
cnf(c_0_43,plain,
( is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))
| ~ modus_tollens ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_44,plain,
modus_tollens,
inference(split_conjunct,[status(thm)],[hilbert_modus_tollens]) ).
cnf(c_0_45,plain,
is_a_theorem(implies(implies(and(X1,X1),X2),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]) ).
cnf(c_0_47,plain,
not(and(X1,implies(X2,X3))) = implies(X1,and(X2,not(X3))),
inference(spm,[status(thm)],[c_0_42,c_0_42]) ).
fof(c_0_48,negated_conjecture,
~ cn3,
inference(assume_negation,[status(cth)],[luka_cn3]) ).
cnf(c_0_49,plain,
is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
cnf(c_0_50,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(and(X1,X1),X2)) ),
inference(spm,[status(thm)],[c_0_26,c_0_45]) ).
cnf(c_0_51,plain,
is_a_theorem(implies(and(X1,not(X2)),not(and(X3,implies(X1,X2))))),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
fof(c_0_52,plain,
! [X5] :
( ( ~ cn3
| is_a_theorem(implies(implies(not(X5),X5),X5)) )
& ( ~ is_a_theorem(implies(implies(not(esk44_0),esk44_0),esk44_0))
| cn3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn3])])])])])]) ).
fof(c_0_53,negated_conjecture,
~ cn3,
inference(fof_simplification,[status(thm)],[c_0_48]) ).
cnf(c_0_54,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(not(X2),not(X1))) ),
inference(spm,[status(thm)],[c_0_26,c_0_49]) ).
cnf(c_0_55,plain,
is_a_theorem(implies(not(X1),not(and(X2,implies(not(X1),X1))))),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,plain,
( cn3
| ~ is_a_theorem(implies(implies(not(esk44_0),esk44_0),esk44_0)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_57,negated_conjecture,
~ cn3,
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_58,plain,
is_a_theorem(implies(and(X1,implies(not(X2),X2)),X2)),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,plain,
~ is_a_theorem(implies(implies(not(esk44_0),esk44_0),esk44_0)),
inference(sr,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_60,plain,
is_a_theorem(implies(implies(not(X1),X1),X1)),
inference(spm,[status(thm)],[c_0_50,c_0_58]) ).
cnf(c_0_61,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL453+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 4 13:29:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.22/1.41 # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.22/1.41 # Preprocessing time : 0.019 s
% 0.22/1.41
% 0.22/1.41 # Proof found!
% 0.22/1.41 # SZS status Theorem
% 0.22/1.41 # SZS output start CNFRefutation
% See solution above
% 0.22/1.41 # Proof object total steps : 62
% 0.22/1.41 # Proof object clause steps : 36
% 0.22/1.41 # Proof object formula steps : 26
% 0.22/1.41 # Proof object conjectures : 4
% 0.22/1.41 # Proof object clause conjectures : 1
% 0.22/1.41 # Proof object formula conjectures : 3
% 0.22/1.41 # Proof object initial clauses used : 16
% 0.22/1.41 # Proof object initial formulas used : 16
% 0.22/1.41 # Proof object generating inferences : 11
% 0.22/1.41 # Proof object simplifying inferences : 17
% 0.22/1.41 # Training examples: 0 positive, 0 negative
% 0.22/1.41 # Parsed axioms : 53
% 0.22/1.41 # Removed by relevancy pruning/SinE : 0
% 0.22/1.41 # Initial clauses : 82
% 0.22/1.41 # Removed in clause preprocessing : 0
% 0.22/1.41 # Initial clauses in saturation : 82
% 0.22/1.41 # Processed clauses : 952
% 0.22/1.41 # ...of these trivial : 90
% 0.22/1.41 # ...subsumed : 321
% 0.22/1.41 # ...remaining for further processing : 541
% 0.22/1.41 # Other redundant clauses eliminated : 0
% 0.22/1.41 # Clauses deleted for lack of memory : 0
% 0.22/1.41 # Backward-subsumed : 9
% 0.22/1.41 # Backward-rewritten : 26
% 0.22/1.41 # Generated clauses : 36836
% 0.22/1.41 # ...of the previous two non-trivial : 34413
% 0.22/1.41 # Contextual simplify-reflections : 130
% 0.22/1.41 # Paramodulations : 36824
% 0.22/1.41 # Factorizations : 0
% 0.22/1.42 # Equation resolutions : 0
% 0.22/1.42 # Current number of processed clauses : 502
% 0.22/1.42 # Positive orientable unit clauses : 161
% 0.22/1.42 # Positive unorientable unit clauses: 7
% 0.22/1.42 # Negative unit clauses : 32
% 0.22/1.42 # Non-unit-clauses : 302
% 0.22/1.42 # Current number of unprocessed clauses: 32910
% 0.22/1.42 # ...number of literals in the above : 73671
% 0.22/1.42 # Current number of archived formulas : 0
% 0.22/1.42 # Current number of archived clauses : 35
% 0.22/1.42 # Clause-clause subsumption calls (NU) : 10087
% 0.22/1.42 # Rec. Clause-clause subsumption calls : 9379
% 0.22/1.42 # Non-unit clause-clause subsumptions : 388
% 0.22/1.42 # Unit Clause-clause subsumption calls : 2240
% 0.22/1.42 # Rewrite failures with RHS unbound : 0
% 0.22/1.42 # BW rewrite match attempts : 2839
% 0.22/1.42 # BW rewrite match successes : 26
% 0.22/1.42 # Condensation attempts : 0
% 0.22/1.42 # Condensation successes : 0
% 0.22/1.42 # Termbank termtop insertions : 825927
% 0.22/1.42
% 0.22/1.42 # -------------------------------------------------
% 0.22/1.42 # User time : 0.447 s
% 0.22/1.42 # System time : 0.019 s
% 0.22/1.42 # Total time : 0.466 s
% 0.22/1.42 # Maximum resident set size: 39228 pages
%------------------------------------------------------------------------------