TSTP Solution File: KLE148+2 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : KLE148+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n011.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 01:56:15 EDT 2022

% Result   : Theorem 0.24s 1.43s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   48 (  38 unt;   0 def)
%            Number of atoms       :   64 (  47 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   31 (  15   ~;   9   |;   4   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :   71 (   4 sgn  42   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
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(goals,conjecture,
    ! [X4,X5] :
      ( ( multiplication(X4,X5) = zero
       => leq(multiplication(X4,strong_iteration(X5)),X4) )
      & leq(X4,multiplication(X4,strong_iteration(X5))) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).

fof(distributivity1,axiom,
    ! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity1) ).

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

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

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

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(c_0_11,plain,
    ! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
    inference(variable_rename,[status(thm)],[additive_associativity]) ).

fof(c_0_12,plain,
    ! [X2] : addition(X2,X2) = X2,
    inference(variable_rename,[status(thm)],[idempotence]) ).

fof(c_0_13,plain,
    ! [X2] : strong_iteration(X2) = addition(multiplication(X2,strong_iteration(X2)),one),
    inference(variable_rename,[status(thm)],[infty_unfold1]) ).

fof(c_0_14,plain,
    ! [X3,X4] : addition(X3,X4) = addition(X4,X3),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

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

fof(c_0_16,plain,
    ! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
    inference(variable_rename,[status(thm)],[distributivity1]) ).

fof(c_0_17,plain,
    ! [X2] : multiplication(X2,one) = X2,
    inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).

cnf(c_0_18,plain,
    addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_19,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

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

cnf(c_0_21,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_22,negated_conjecture,
    ( ( multiplication(esk1_0,esk2_0) = zero
      | ~ leq(esk3_0,multiplication(esk3_0,strong_iteration(esk4_0))) )
    & ( ~ leq(multiplication(esk1_0,strong_iteration(esk2_0)),esk1_0)
      | ~ leq(esk3_0,multiplication(esk3_0,strong_iteration(esk4_0))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])]) ).

fof(c_0_23,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_24,plain,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_25,plain,
    multiplication(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_26,plain,
    addition(X1,addition(X1,X2)) = addition(X1,X2),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_27,plain,
    addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
    inference(rw,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_28,negated_conjecture,
    ( multiplication(esk1_0,esk2_0) = zero
    | ~ leq(esk3_0,multiplication(esk3_0,strong_iteration(esk4_0))) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_29,plain,
    ( leq(X1,X2)
    | addition(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_30,plain,
    addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_31,plain,
    addition(one,strong_iteration(X1)) = strong_iteration(X1),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_32,negated_conjecture,
    ( ~ leq(esk3_0,multiplication(esk3_0,strong_iteration(esk4_0)))
    | ~ leq(multiplication(esk1_0,strong_iteration(esk2_0)),esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

fof(c_0_33,plain,
    ! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
    inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).

cnf(c_0_34,negated_conjecture,
    ( multiplication(esk1_0,esk2_0) = zero
    | addition(esk3_0,multiplication(esk3_0,strong_iteration(esk4_0))) != multiplication(esk3_0,strong_iteration(esk4_0)) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_35,plain,
    addition(X1,multiplication(X1,strong_iteration(X2))) = multiplication(X1,strong_iteration(X2)),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

fof(c_0_36,plain,
    ! [X2] : multiplication(zero,X2) = zero,
    inference(variable_rename,[status(thm)],[left_annihilation]) ).

cnf(c_0_37,negated_conjecture,
    ( addition(esk3_0,multiplication(esk3_0,strong_iteration(esk4_0))) != multiplication(esk3_0,strong_iteration(esk4_0))
    | ~ leq(multiplication(esk1_0,strong_iteration(esk2_0)),esk1_0) ),
    inference(spm,[status(thm)],[c_0_32,c_0_29]) ).

cnf(c_0_38,plain,
    multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_39,negated_conjecture,
    multiplication(esk1_0,esk2_0) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).

cnf(c_0_40,plain,
    multiplication(zero,X1) = zero,
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

fof(c_0_41,plain,
    ! [X2] : addition(X2,zero) = X2,
    inference(variable_rename,[status(thm)],[additive_identity]) ).

cnf(c_0_42,negated_conjecture,
    ~ leq(multiplication(esk1_0,strong_iteration(esk2_0)),esk1_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_35])]) ).

cnf(c_0_43,plain,
    addition(X1,multiplication(X1,multiplication(X2,strong_iteration(X2)))) = multiplication(X1,strong_iteration(X2)),
    inference(spm,[status(thm)],[c_0_30,c_0_27]) ).

cnf(c_0_44,negated_conjecture,
    multiplication(esk1_0,multiplication(esk2_0,X1)) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).

cnf(c_0_45,plain,
    addition(X1,zero) = X1,
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_46,negated_conjecture,
    multiplication(esk1_0,strong_iteration(esk2_0)) != esk1_0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_29]),c_0_21]),c_0_35]) ).

cnf(c_0_47,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : KLE148+2 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.14  % Command  : run_ET %s %d
% 0.13/0.35  % Computer : n011.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Thu Jun 16 13:36:36 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.24/1.43  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.43  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.43  # Preprocessing time       : 0.015 s
% 0.24/1.43  
% 0.24/1.43  # Proof found!
% 0.24/1.43  # SZS status Theorem
% 0.24/1.43  # SZS output start CNFRefutation
% See solution above
% 0.24/1.43  # Proof object total steps             : 48
% 0.24/1.43  # Proof object clause steps            : 25
% 0.24/1.43  # Proof object formula steps           : 23
% 0.24/1.43  # Proof object conjectures             : 12
% 0.24/1.43  # Proof object clause conjectures      : 9
% 0.24/1.43  # Proof object formula conjectures     : 3
% 0.24/1.43  # Proof object initial clauses used    : 12
% 0.24/1.43  # Proof object initial formulas used   : 11
% 0.24/1.43  # Proof object generating inferences   : 10
% 0.24/1.43  # Proof object simplifying inferences  : 10
% 0.24/1.43  # Training examples: 0 positive, 0 negative
% 0.24/1.43  # Parsed axioms                        : 19
% 0.24/1.43  # Removed by relevancy pruning/SinE    : 0
% 0.24/1.43  # Initial clauses                      : 21
% 0.24/1.43  # Removed in clause preprocessing      : 0
% 0.24/1.43  # Initial clauses in saturation        : 21
% 0.24/1.43  # Processed clauses                    : 2905
% 0.24/1.43  # ...of these trivial                  : 153
% 0.24/1.43  # ...subsumed                          : 1950
% 0.24/1.43  # ...remaining for further processing  : 802
% 0.24/1.43  # Other redundant clauses eliminated   : 0
% 0.24/1.43  # Clauses deleted for lack of memory   : 0
% 0.24/1.43  # Backward-subsumed                    : 51
% 0.24/1.43  # Backward-rewritten                   : 97
% 0.24/1.43  # Generated clauses                    : 39521
% 0.24/1.43  # ...of the previous two non-trivial   : 32718
% 0.24/1.43  # Contextual simplify-reflections      : 742
% 0.24/1.43  # Paramodulations                      : 39521
% 0.24/1.43  # Factorizations                       : 0
% 0.24/1.43  # Equation resolutions                 : 0
% 0.24/1.43  # Current number of processed clauses  : 654
% 0.24/1.43  #    Positive orientable unit clauses  : 101
% 0.24/1.43  #    Positive unorientable unit clauses: 22
% 0.24/1.43  #    Negative unit clauses             : 29
% 0.24/1.43  #    Non-unit-clauses                  : 502
% 0.24/1.43  # Current number of unprocessed clauses: 27933
% 0.24/1.43  # ...number of literals in the above   : 57662
% 0.24/1.43  # Current number of archived formulas  : 0
% 0.24/1.43  # Current number of archived clauses   : 148
% 0.24/1.43  # Clause-clause subsumption calls (NU) : 86716
% 0.24/1.43  # Rec. Clause-clause subsumption calls : 42216
% 0.24/1.43  # Non-unit clause-clause subsumptions  : 1540
% 0.24/1.43  # Unit Clause-clause subsumption calls : 1254
% 0.24/1.43  # Rewrite failures with RHS unbound    : 0
% 0.24/1.43  # BW rewrite match attempts            : 579
% 0.24/1.43  # BW rewrite match successes           : 253
% 0.24/1.43  # Condensation attempts                : 0
% 0.24/1.43  # Condensation successes               : 0
% 0.24/1.43  # Termbank termtop insertions          : 645179
% 0.24/1.43  
% 0.24/1.43  # -------------------------------------------------
% 0.24/1.43  # User time                : 0.686 s
% 0.24/1.43  # System time              : 0.016 s
% 0.24/1.43  # Total time               : 0.702 s
% 0.24/1.43  # Maximum resident set size: 36084 pages
%------------------------------------------------------------------------------