TSTP Solution File: KLE151+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : KLE151+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n026.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 01:56:16 EDT 2022

% Result   : Theorem 0.23s 1.42s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   34 (  26 unt;   0 def)
%            Number of atoms       :   44 (  26 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   20 (  10   ~;   7   |;   1   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   68 (   2 sgn  38   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(infty_unfold1,axiom,
    ! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).

fof(additive_commutativity,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).

fof(infty_coinduction,axiom,
    ! [X1,X2,X3] :
      ( leq(X3,addition(multiplication(X1,X3),X2))
     => leq(X3,multiplication(strong_iteration(X1),X2)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).

fof(multiplicative_associativity,axiom,
    ! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).

fof(goals,conjecture,
    ! [X4,X5] : leq(multiplication(X4,strong_iteration(multiplication(X5,X4))),multiplication(strong_iteration(multiplication(X4,X5)),X4)),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).

fof(order,axiom,
    ! [X1,X2] :
      ( leq(X1,X2)
    <=> addition(X1,X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).

fof(distributivity1,axiom,
    ! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity1) ).

fof(multiplicative_right_identity,axiom,
    ! [X1] : multiplication(X1,one) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).

fof(idempotence,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',idempotence) ).

fof(c_0_9,plain,
    ! [X2] : strong_iteration(X2) = addition(multiplication(X2,strong_iteration(X2)),one),
    inference(variable_rename,[status(thm)],[infty_unfold1]) ).

fof(c_0_10,plain,
    ! [X3,X4] : addition(X3,X4) = addition(X4,X3),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

fof(c_0_11,plain,
    ! [X4,X5,X6] :
      ( ~ leq(X6,addition(multiplication(X4,X6),X5))
      | leq(X6,multiplication(strong_iteration(X4),X5)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[infty_coinduction])]) ).

fof(c_0_12,plain,
    ! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
    inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).

cnf(c_0_13,plain,
    strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_15,negated_conjecture,
    ~ ! [X4,X5] : leq(multiplication(X4,strong_iteration(multiplication(X5,X4))),multiplication(strong_iteration(multiplication(X4,X5)),X4)),
    inference(assume_negation,[status(cth)],[goals]) ).

cnf(c_0_16,plain,
    ( leq(X1,multiplication(strong_iteration(X2),X3))
    | ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17,plain,
    multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_18,plain,
    ! [X3,X4,X3,X4] :
      ( ( ~ leq(X3,X4)
        | addition(X3,X4) = X4 )
      & ( addition(X3,X4) != X4
        | leq(X3,X4) ) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])])]) ).

fof(c_0_19,plain,
    ! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
    inference(variable_rename,[status(thm)],[distributivity1]) ).

cnf(c_0_20,plain,
    addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
    inference(rw,[status(thm)],[c_0_13,c_0_14]) ).

fof(c_0_21,plain,
    ! [X2] : multiplication(X2,one) = X2,
    inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).

fof(c_0_22,negated_conjecture,
    ~ leq(multiplication(esk1_0,strong_iteration(multiplication(esk2_0,esk1_0))),multiplication(strong_iteration(multiplication(esk1_0,esk2_0)),esk1_0)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).

cnf(c_0_23,plain,
    ( leq(X1,multiplication(strong_iteration(multiplication(X2,X3)),X4))
    | ~ leq(X1,addition(multiplication(X2,multiplication(X3,X1)),X4)) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_24,plain,
    ( leq(X1,X2)
    | addition(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_25,plain,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_26,plain,
    addition(one,multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2))))) = strong_iteration(multiplication(X1,X2)),
    inference(spm,[status(thm)],[c_0_20,c_0_17]) ).

cnf(c_0_27,plain,
    multiplication(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

fof(c_0_28,plain,
    ! [X2] : addition(X2,X2) = X2,
    inference(variable_rename,[status(thm)],[idempotence]) ).

cnf(c_0_29,negated_conjecture,
    ~ leq(multiplication(esk1_0,strong_iteration(multiplication(esk2_0,esk1_0))),multiplication(strong_iteration(multiplication(esk1_0,esk2_0)),esk1_0)),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_30,plain,
    ( leq(X1,multiplication(strong_iteration(multiplication(X2,X3)),X4))
    | addition(X1,addition(multiplication(X2,multiplication(X3,X1)),X4)) != addition(multiplication(X2,multiplication(X3,X1)),X4) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_31,plain,
    addition(X1,multiplication(X1,multiplication(X2,multiplication(X3,strong_iteration(multiplication(X2,X3)))))) = multiplication(X1,strong_iteration(multiplication(X2,X3))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).

cnf(c_0_32,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_33,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_14]),c_0_31]),c_0_32]),c_0_14]),c_0_31])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : KLE151+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % Command  : run_ET %s %d
% 0.12/0.34  % Computer : n026.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 : Thu Jun 16 07:27:53 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.23/1.42  # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.23/1.42  # Preprocessing time       : 0.014 s
% 0.23/1.42  
% 0.23/1.42  # Proof found!
% 0.23/1.42  # SZS status Theorem
% 0.23/1.42  # SZS output start CNFRefutation
% See solution above
% 0.23/1.42  # Proof object total steps             : 34
% 0.23/1.42  # Proof object clause steps            : 15
% 0.23/1.42  # Proof object formula steps           : 19
% 0.23/1.42  # Proof object conjectures             : 5
% 0.23/1.42  # Proof object clause conjectures      : 2
% 0.23/1.42  # Proof object formula conjectures     : 3
% 0.23/1.42  # Proof object initial clauses used    : 9
% 0.23/1.42  # Proof object initial formulas used   : 9
% 0.23/1.42  # Proof object generating inferences   : 5
% 0.23/1.42  # Proof object simplifying inferences  : 8
% 0.23/1.42  # Training examples: 0 positive, 0 negative
% 0.23/1.42  # Parsed axioms                        : 19
% 0.23/1.42  # Removed by relevancy pruning/SinE    : 0
% 0.23/1.42  # Initial clauses                      : 20
% 0.23/1.42  # Removed in clause preprocessing      : 0
% 0.23/1.42  # Initial clauses in saturation        : 20
% 0.23/1.42  # Processed clauses                    : 2242
% 0.23/1.42  # ...of these trivial                  : 207
% 0.23/1.42  # ...subsumed                          : 1385
% 0.23/1.42  # ...remaining for further processing  : 650
% 0.23/1.42  # Other redundant clauses eliminated   : 0
% 0.23/1.42  # Clauses deleted for lack of memory   : 0
% 0.23/1.42  # Backward-subsumed                    : 13
% 0.23/1.42  # Backward-rewritten                   : 121
% 0.23/1.42  # Generated clauses                    : 42601
% 0.23/1.42  # ...of the previous two non-trivial   : 31348
% 0.23/1.42  # Contextual simplify-reflections      : 159
% 0.23/1.42  # Paramodulations                      : 42599
% 0.23/1.42  # Factorizations                       : 0
% 0.23/1.42  # Equation resolutions                 : 2
% 0.23/1.42  # Current number of processed clauses  : 516
% 0.23/1.42  #    Positive orientable unit clauses  : 207
% 0.23/1.42  #    Positive unorientable unit clauses: 11
% 0.23/1.42  #    Negative unit clauses             : 11
% 0.23/1.42  #    Non-unit-clauses                  : 287
% 0.23/1.42  # Current number of unprocessed clauses: 26451
% 0.23/1.42  # ...number of literals in the above   : 48287
% 0.23/1.42  # Current number of archived formulas  : 0
% 0.23/1.42  # Current number of archived clauses   : 134
% 0.23/1.42  # Clause-clause subsumption calls (NU) : 10251
% 0.23/1.42  # Rec. Clause-clause subsumption calls : 10176
% 0.23/1.42  # Non-unit clause-clause subsumptions  : 765
% 0.23/1.42  # Unit Clause-clause subsumption calls : 603
% 0.23/1.42  # Rewrite failures with RHS unbound    : 0
% 0.23/1.42  # BW rewrite match attempts            : 1503
% 0.23/1.42  # BW rewrite match successes           : 286
% 0.23/1.42  # Condensation attempts                : 0
% 0.23/1.42  # Condensation successes               : 0
% 0.23/1.42  # Termbank termtop insertions          : 894555
% 0.23/1.42  
% 0.23/1.42  # -------------------------------------------------
% 0.23/1.42  # User time                : 0.470 s
% 0.23/1.42  # System time              : 0.020 s
% 0.23/1.42  # Total time               : 0.490 s
% 0.23/1.42  # Maximum resident set size: 37400 pages
% 0.23/23.41  eprover: CPU time limit exceeded, terminating
% 0.23/23.42  eprover: CPU time limit exceeded, terminating
% 0.23/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.43  eprover: No such file or directory
% 0.23/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.43  eprover: No such file or directory
% 0.23/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.43  eprover: No such file or directory
% 0.23/23.43  eprover: CPU time limit exceeded, terminating
% 0.23/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.44  eprover: No such file or directory
% 0.23/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.44  eprover: No such file or directory
% 0.23/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.44  eprover: No such file or directory
% 0.23/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.44  eprover: No such file or directory
% 0.23/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.45  eprover: No such file or directory
% 0.23/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.45  eprover: No such file or directory
% 0.23/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.45  eprover: No such file or directory
% 0.23/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.45  eprover: No such file or directory
% 0.23/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.45  eprover: No such file or directory
% 0.23/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46  eprover: No such file or directory
% 0.23/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46  eprover: No such file or directory
% 0.23/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.46  eprover: No such file or directory
% 0.23/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46  eprover: No such file or directory
% 0.23/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46  eprover: No such file or directory
% 0.23/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.46  eprover: No such file or directory
% 0.23/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.47  eprover: No such file or directory
% 0.23/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.47  eprover: No such file or directory
% 0.23/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.47  eprover: No such file or directory
% 0.23/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.47  eprover: No such file or directory
% 0.23/23.47  eprover: No such file or directory
% 0.23/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.47  eprover: No such file or directory
% 0.23/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.48  eprover: No such file or directory
% 0.23/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.48  eprover: No such file or directory
% 0.23/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.48  eprover: No such file or directory
% 0.23/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.48  eprover: No such file or directory
% 0.23/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.48  eprover: No such file or directory
% 0.23/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.48  eprover: No such file or directory
% 0.23/23.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.49  eprover: No such file or directory
% 0.23/23.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.49  eprover: No such file or directory
% 0.23/23.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.49  eprover: No such file or directory
%------------------------------------------------------------------------------