TSTP Solution File: KLE137+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : KLE137+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n032.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 01:56:09 EDT 2022

% Result   : Theorem 0.15s 1.33s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   75 (  47 unt;   0 def)
%            Number of atoms       :  105 (  50 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   58 (  28   ~;  25   |;   1   &)
%                                         (   1 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :  102 (   6 sgn  52   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(star_induction2,axiom,
    ! [X1,X2,X3] :
      ( leq(addition(multiplication(X3,X1),X2),X3)
     => leq(multiplication(X2,star(X1)),X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_induction2) ).

fof(multiplicative_left_identity,axiom,
    ! [X1] : multiplication(one,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).

fof(additive_associativity,axiom,
    ! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).

fof(idempotence,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).

fof(infty_unfold1,axiom,
    ! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).

fof(additive_commutativity,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).

fof(order,axiom,
    ! [X1,X2] :
      ( leq(X1,X2)
    <=> addition(X1,X2) = X2 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).

fof(star_unfold2,axiom,
    ! [X1] : addition(one,multiplication(star(X1),X1)) = star(X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).

fof(left_annihilation,axiom,
    ! [X1] : multiplication(zero,X1) = zero,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).

fof(additive_identity,axiom,
    ! [X1] : addition(X1,zero) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_identity) ).

fof(star_unfold1,axiom,
    ! [X1] : addition(one,multiplication(X1,star(X1))) = star(X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_unfold1) ).

fof(star_induction1,axiom,
    ! [X1,X2,X3] :
      ( leq(addition(multiplication(X1,X3),X2),X3)
     => leq(multiplication(star(X1),X2),X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_induction1) ).

fof(isolation,axiom,
    ! [X1] : strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',isolation) ).

fof(infty_coinduction,axiom,
    ! [X1,X2,X3] :
      ( leq(X3,addition(multiplication(X1,X3),X2))
     => leq(X3,multiplication(strong_iteration(X1),X2)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).

fof(goals,conjecture,
    ! [X4] : leq(X4,strong_iteration(one)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).

fof(c_0_15,plain,
    ! [X4,X5,X6] :
      ( ~ leq(addition(multiplication(X6,X4),X5),X6)
      | leq(multiplication(X5,star(X4)),X6) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction2])]) ).

fof(c_0_16,plain,
    ! [X2] : multiplication(one,X2) = X2,
    inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).

fof(c_0_17,plain,
    ! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
    inference(variable_rename,[status(thm)],[additive_associativity]) ).

fof(c_0_18,plain,
    ! [X2] : addition(X2,X2) = X2,
    inference(variable_rename,[status(thm)],[idempotence]) ).

fof(c_0_19,plain,
    ! [X2] : strong_iteration(X2) = addition(multiplication(X2,strong_iteration(X2)),one),
    inference(variable_rename,[status(thm)],[infty_unfold1]) ).

fof(c_0_20,plain,
    ! [X3,X4] : addition(X3,X4) = addition(X4,X3),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

cnf(c_0_21,plain,
    ( leq(multiplication(X1,star(X2)),X3)
    | ~ leq(addition(multiplication(X3,X2),X1),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22,plain,
    multiplication(one,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_23,plain,
    addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

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

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

cnf(c_0_26,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_27,plain,
    ( leq(multiplication(X1,star(X2)),one)
    | ~ leq(addition(X2,X1),one) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_28,plain,
    addition(X1,addition(X1,X2)) = addition(X1,X2),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_29,plain,
    addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
    inference(rw,[status(thm)],[c_0_25,c_0_26]) ).

fof(c_0_30,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])])])]) ).

cnf(c_0_31,plain,
    ( leq(multiplication(X1,star(X2)),one)
    | ~ leq(addition(X1,X2),one) ),
    inference(spm,[status(thm)],[c_0_27,c_0_26]) ).

cnf(c_0_32,plain,
    addition(one,strong_iteration(X1)) = strong_iteration(X1),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

fof(c_0_33,plain,
    ! [X2] : addition(one,multiplication(star(X2),X2)) = star(X2),
    inference(variable_rename,[status(thm)],[star_unfold2]) ).

cnf(c_0_34,plain,
    ( addition(X1,X2) = X2
    | ~ leq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_35,plain,
    ( leq(star(strong_iteration(X1)),one)
    | ~ leq(strong_iteration(X1),one) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_22]) ).

cnf(c_0_36,plain,
    addition(one,multiplication(star(X1),X1)) = star(X1),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

fof(c_0_37,plain,
    ! [X2] : multiplication(zero,X2) = zero,
    inference(variable_rename,[status(thm)],[left_annihilation]) ).

fof(c_0_38,plain,
    ! [X2] : addition(X2,zero) = X2,
    inference(variable_rename,[status(thm)],[additive_identity]) ).

cnf(c_0_39,plain,
    ( addition(one,star(strong_iteration(X1))) = one
    | ~ leq(strong_iteration(X1),one) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_26]) ).

cnf(c_0_40,plain,
    addition(one,star(X1)) = star(X1),
    inference(spm,[status(thm)],[c_0_28,c_0_36]) ).

cnf(c_0_41,plain,
    multiplication(zero,X1) = zero,
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_42,plain,
    addition(X1,zero) = X1,
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

fof(c_0_43,plain,
    ! [X2] : addition(one,multiplication(X2,star(X2))) = star(X2),
    inference(variable_rename,[status(thm)],[star_unfold1]) ).

cnf(c_0_44,plain,
    ( star(strong_iteration(X1)) = one
    | ~ leq(strong_iteration(X1),one) ),
    inference(rw,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_45,plain,
    strong_iteration(zero) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_41]),c_0_42]) ).

cnf(c_0_46,plain,
    addition(one,multiplication(X1,star(X1))) = star(X1),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_47,plain,
    ( leq(one,one)
    | ~ leq(strong_iteration(X1),one) ),
    inference(spm,[status(thm)],[c_0_35,c_0_44]) ).

cnf(c_0_48,plain,
    ( leq(X1,X2)
    | addition(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

fof(c_0_49,plain,
    ! [X4,X5,X6] :
      ( ~ leq(addition(multiplication(X4,X6),X5),X6)
      | leq(multiplication(star(X4),X5),X6) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction1])]) ).

cnf(c_0_50,plain,
    ( leq(star(one),one)
    | ~ leq(one,one) ),
    inference(spm,[status(thm)],[c_0_35,c_0_45]) ).

cnf(c_0_51,plain,
    addition(one,star(one)) = star(one),
    inference(spm,[status(thm)],[c_0_46,c_0_22]) ).

cnf(c_0_52,plain,
    ( leq(one,one)
    | strong_iteration(X1) != one ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_26]),c_0_32]) ).

cnf(c_0_53,plain,
    ( leq(multiplication(star(X1),X2),X3)
    | ~ leq(addition(multiplication(X1,X3),X2),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_54,plain,
    ( star(one) = one
    | ~ leq(one,one) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_50]),c_0_26]),c_0_51]) ).

cnf(c_0_55,plain,
    leq(one,one),
    inference(spm,[status(thm)],[c_0_52,c_0_45]) ).

fof(c_0_56,plain,
    ! [X2] : strong_iteration(X2) = addition(star(X2),multiplication(strong_iteration(X2),zero)),
    inference(variable_rename,[status(thm)],[isolation]) ).

cnf(c_0_57,plain,
    ( leq(multiplication(star(one),X1),X2)
    | ~ leq(addition(X2,X1),X2) ),
    inference(spm,[status(thm)],[c_0_53,c_0_22]) ).

cnf(c_0_58,plain,
    star(one) = one,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).

cnf(c_0_59,plain,
    strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

cnf(c_0_60,plain,
    ( leq(X1,X2)
    | ~ leq(addition(X2,X1),X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58]),c_0_22]) ).

cnf(c_0_61,plain,
    ( addition(one,multiplication(strong_iteration(one),zero)) = strong_iteration(one)
    | ~ leq(one,one) ),
    inference(spm,[status(thm)],[c_0_59,c_0_54]) ).

fof(c_0_62,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])]) ).

cnf(c_0_63,plain,
    ( leq(X1,X2)
    | ~ leq(addition(X1,X2),X2) ),
    inference(spm,[status(thm)],[c_0_60,c_0_26]) ).

cnf(c_0_64,plain,
    addition(one,multiplication(strong_iteration(one),zero)) = strong_iteration(one),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_55])]) ).

cnf(c_0_65,plain,
    ( leq(X1,multiplication(strong_iteration(X2),X3))
    | ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_66,plain,
    ( leq(one,multiplication(strong_iteration(one),zero))
    | ~ leq(strong_iteration(one),multiplication(strong_iteration(one),zero)) ),
    inference(spm,[status(thm)],[c_0_63,c_0_64]) ).

cnf(c_0_67,plain,
    ( leq(X1,multiplication(strong_iteration(X2),X3))
    | addition(X1,addition(multiplication(X2,X1),X3)) != addition(multiplication(X2,X1),X3) ),
    inference(spm,[status(thm)],[c_0_65,c_0_48]) ).

fof(c_0_68,negated_conjecture,
    ~ ! [X4] : leq(X4,strong_iteration(one)),
    inference(assume_negation,[status(cth)],[goals]) ).

cnf(c_0_69,plain,
    leq(one,multiplication(strong_iteration(one),zero)),
    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_66,c_0_67]),c_0_22]),c_0_42]),c_0_24]),c_0_22]),c_0_42])]) ).

fof(c_0_70,negated_conjecture,
    ~ leq(esk1_0,strong_iteration(one)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_68])])]) ).

cnf(c_0_71,plain,
    multiplication(strong_iteration(one),zero) = strong_iteration(one),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_69]),c_0_64]) ).

cnf(c_0_72,negated_conjecture,
    ~ leq(esk1_0,strong_iteration(one)),
    inference(split_conjunct,[status(thm)],[c_0_70]) ).

cnf(c_0_73,plain,
    leq(X1,strong_iteration(one)),
    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_67,c_0_71]),c_0_22]),c_0_42]),c_0_24]),c_0_22]),c_0_42])]) ).

cnf(c_0_74,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : KLE137+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.08  % Command  : run_ET %s %d
% 0.07/0.27  % Computer : n032.cluster.edu
% 0.07/0.27  % Model    : x86_64 x86_64
% 0.07/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27  % Memory   : 8042.1875MB
% 0.07/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27  % CPULimit : 300
% 0.07/0.27  % WCLimit  : 600
% 0.07/0.27  % DateTime : Thu Jun 16 08:38:14 EDT 2022
% 0.07/0.27  % CPUTime  : 
% 0.15/1.33  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.15/1.33  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.15/1.33  # Preprocessing time       : 0.009 s
% 0.15/1.33  
% 0.15/1.33  # Proof found!
% 0.15/1.33  # SZS status Theorem
% 0.15/1.33  # SZS output start CNFRefutation
% See solution above
% 0.15/1.33  # Proof object total steps             : 75
% 0.15/1.33  # Proof object clause steps            : 44
% 0.15/1.33  # Proof object formula steps           : 31
% 0.15/1.33  # Proof object conjectures             : 5
% 0.15/1.33  # Proof object clause conjectures      : 2
% 0.15/1.33  # Proof object formula conjectures     : 3
% 0.15/1.33  # Proof object initial clauses used    : 16
% 0.15/1.33  # Proof object initial formulas used   : 15
% 0.15/1.33  # Proof object generating inferences   : 22
% 0.15/1.33  # Proof object simplifying inferences  : 30
% 0.15/1.33  # Training examples: 0 positive, 0 negative
% 0.15/1.33  # Parsed axioms                        : 19
% 0.15/1.33  # Removed by relevancy pruning/SinE    : 0
% 0.15/1.33  # Initial clauses                      : 20
% 0.15/1.33  # Removed in clause preprocessing      : 0
% 0.15/1.33  # Initial clauses in saturation        : 20
% 0.15/1.33  # Processed clauses                    : 732
% 0.15/1.33  # ...of these trivial                  : 71
% 0.15/1.33  # ...subsumed                          : 369
% 0.15/1.33  # ...remaining for further processing  : 292
% 0.15/1.33  # Other redundant clauses eliminated   : 0
% 0.15/1.33  # Clauses deleted for lack of memory   : 0
% 0.15/1.33  # Backward-subsumed                    : 46
% 0.15/1.33  # Backward-rewritten                   : 81
% 0.15/1.33  # Generated clauses                    : 7217
% 0.15/1.33  # ...of the previous two non-trivial   : 6124
% 0.15/1.33  # Contextual simplify-reflections      : 164
% 0.15/1.33  # Paramodulations                      : 7217
% 0.15/1.33  # Factorizations                       : 0
% 0.15/1.33  # Equation resolutions                 : 0
% 0.15/1.33  # Current number of processed clauses  : 165
% 0.15/1.33  #    Positive orientable unit clauses  : 47
% 0.15/1.33  #    Positive unorientable unit clauses: 13
% 0.15/1.33  #    Negative unit clauses             : 5
% 0.15/1.33  #    Non-unit-clauses                  : 100
% 0.15/1.33  # Current number of unprocessed clauses: 4666
% 0.15/1.33  # ...number of literals in the above   : 7834
% 0.15/1.33  # Current number of archived formulas  : 0
% 0.15/1.33  # Current number of archived clauses   : 127
% 0.15/1.33  # Clause-clause subsumption calls (NU) : 4769
% 0.15/1.33  # Rec. Clause-clause subsumption calls : 4463
% 0.15/1.33  # Non-unit clause-clause subsumptions  : 430
% 0.15/1.33  # Unit Clause-clause subsumption calls : 193
% 0.15/1.33  # Rewrite failures with RHS unbound    : 0
% 0.15/1.33  # BW rewrite match attempts            : 203
% 0.15/1.33  # BW rewrite match successes           : 109
% 0.15/1.33  # Condensation attempts                : 0
% 0.15/1.33  # Condensation successes               : 0
% 0.15/1.33  # Termbank termtop insertions          : 89183
% 0.15/1.33  
% 0.15/1.33  # -------------------------------------------------
% 0.15/1.33  # User time                : 0.086 s
% 0.15/1.33  # System time              : 0.002 s
% 0.15/1.33  # Total time               : 0.088 s
% 0.15/1.33  # Maximum resident set size: 8092 pages
%------------------------------------------------------------------------------