TSTP Solution File: KLE010+3 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : KLE010+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n004.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 01:55:16 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    :   55 (  39 unt;   0 def)
%            Number of atoms       :   93 (  58 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :   65 (  27   ~;  21   |;  11   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   82 (   4 sgn  47   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(additive_associativity,axiom,
    ! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).

fof(additive_idempotence,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).

fof(test_2,axiom,
    ! [X4,X5] :
      ( complement(X5,X4)
    <=> ( multiplication(X4,X5) = zero
        & multiplication(X5,X4) = zero
        & addition(X4,X5) = one ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).

fof(test_1,axiom,
    ! [X4] :
      ( test(X4)
    <=> ? [X5] : complement(X5,X4) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).

fof(goals,conjecture,
    ! [X4,X5] :
      ( ( test(X5)
        & test(X4) )
     => one = addition(addition(addition(addition(multiplication(X5,X4),multiplication(c(X5),X4)),multiplication(X4,X5)),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).

fof(test_3,axiom,
    ! [X4,X5] :
      ( test(X4)
     => ( c(X4) = X5
      <=> complement(X4,X5) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).

fof(additive_commutativity,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).

fof(left_distributivity,axiom,
    ! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).

fof(multiplicative_left_identity,axiom,
    ! [X1] : multiplication(one,X1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).

fof(right_distributivity,axiom,
    ! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).

fof(multiplicative_right_identity,axiom,
    ! [X1] : multiplication(X1,one) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_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)],[additive_idempotence]) ).

fof(c_0_13,plain,
    ! [X6,X7,X6,X7] :
      ( ( multiplication(X6,X7) = zero
        | ~ complement(X7,X6) )
      & ( multiplication(X7,X6) = zero
        | ~ complement(X7,X6) )
      & ( addition(X6,X7) = one
        | ~ complement(X7,X6) )
      & ( multiplication(X6,X7) != zero
        | multiplication(X7,X6) != zero
        | addition(X6,X7) != one
        | complement(X7,X6) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])])])]) ).

fof(c_0_14,plain,
    ! [X6,X6,X8] :
      ( ( ~ test(X6)
        | complement(esk3_1(X6),X6) )
      & ( ~ complement(X8,X6)
        | test(X6) ) ),
    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)],[test_1])])])])])]) ).

fof(c_0_15,negated_conjecture,
    ~ ! [X4,X5] :
        ( ( test(X5)
          & test(X4) )
       => one = addition(addition(addition(addition(multiplication(X5,X4),multiplication(c(X5),X4)),multiplication(X4,X5)),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))) ),
    inference(assume_negation,[status(cth)],[goals]) ).

fof(c_0_16,plain,
    ! [X6,X7,X7] :
      ( ( c(X6) != X7
        | complement(X6,X7)
        | ~ test(X6) )
      & ( ~ complement(X6,X7)
        | c(X6) = X7
        | ~ test(X6) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])])])]) ).

cnf(c_0_17,plain,
    addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,plain,
    ( addition(X2,X1) = one
    | ~ complement(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20,plain,
    ( complement(esk3_1(X1),X1)
    | ~ test(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_21,negated_conjecture,
    ( test(esk2_0)
    & test(esk1_0)
    & one != addition(addition(addition(addition(multiplication(esk2_0,esk1_0),multiplication(c(esk2_0),esk1_0)),multiplication(esk1_0,esk2_0)),multiplication(c(esk1_0),esk2_0)),multiplication(c(esk1_0),c(esk2_0))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).

fof(c_0_22,plain,
    ! [X3,X4] : addition(X3,X4) = addition(X4,X3),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

fof(c_0_23,plain,
    ! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
    inference(variable_rename,[status(thm)],[left_distributivity]) ).

cnf(c_0_24,plain,
    ( complement(X1,X2)
    | ~ test(X1)
    | c(X1) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_25,plain,
    addition(X1,addition(X1,X2)) = addition(X1,X2),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_26,plain,
    ( addition(X1,esk3_1(X1)) = one
    | ~ test(X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

fof(c_0_27,plain,
    ! [X2] : multiplication(one,X2) = X2,
    inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).

cnf(c_0_28,negated_conjecture,
    one != addition(addition(addition(addition(multiplication(esk2_0,esk1_0),multiplication(c(esk2_0),esk1_0)),multiplication(esk1_0,esk2_0)),multiplication(c(esk1_0),esk2_0)),multiplication(c(esk1_0),c(esk2_0))),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_29,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_30,plain,
    multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_31,plain,
    ( addition(X1,X2) = one
    | c(X2) != X1
    | ~ test(X2) ),
    inference(spm,[status(thm)],[c_0_19,c_0_24]) ).

cnf(c_0_32,plain,
    ( addition(X1,one) = one
    | ~ test(X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_33,negated_conjecture,
    test(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_34,plain,
    multiplication(one,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_35,negated_conjecture,
    test(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_36,negated_conjecture,
    addition(multiplication(c(esk1_0),c(esk2_0)),addition(multiplication(c(esk1_0),esk2_0),addition(multiplication(esk1_0,esk2_0),multiplication(addition(esk2_0,c(esk2_0)),esk1_0)))) != one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_29]),c_0_29]),c_0_30]) ).

cnf(c_0_37,plain,
    addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_29]),c_0_17]) ).

cnf(c_0_38,plain,
    ( addition(X1,c(X1)) = one
    | ~ test(X1) ),
    inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_31]),c_0_29]) ).

fof(c_0_39,plain,
    ! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
    inference(variable_rename,[status(thm)],[right_distributivity]) ).

fof(c_0_40,plain,
    ! [X2] : multiplication(X2,one) = X2,
    inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).

cnf(c_0_41,negated_conjecture,
    addition(one,esk2_0) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_29]) ).

cnf(c_0_42,plain,
    addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
    inference(spm,[status(thm)],[c_0_30,c_0_34]) ).

cnf(c_0_43,negated_conjecture,
    addition(one,esk1_0) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_35]),c_0_29]) ).

cnf(c_0_44,negated_conjecture,
    addition(multiplication(esk1_0,esk2_0),addition(multiplication(c(esk1_0),esk2_0),addition(multiplication(c(esk1_0),c(esk2_0)),multiplication(addition(esk2_0,c(esk2_0)),esk1_0)))) != one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_37]),c_0_37]) ).

cnf(c_0_45,negated_conjecture,
    addition(esk2_0,c(esk2_0)) = one,
    inference(spm,[status(thm)],[c_0_38,c_0_33]) ).

cnf(c_0_46,plain,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_47,plain,
    multiplication(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_48,negated_conjecture,
    addition(esk1_0,c(esk1_0)) = one,
    inference(spm,[status(thm)],[c_0_38,c_0_35]) ).

cnf(c_0_49,negated_conjecture,
    addition(one,addition(esk2_0,X1)) = addition(one,X1),
    inference(spm,[status(thm)],[c_0_17,c_0_41]) ).

cnf(c_0_50,negated_conjecture,
    addition(X1,multiplication(esk1_0,X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_34]) ).

cnf(c_0_51,negated_conjecture,
    addition(esk1_0,addition(multiplication(esk1_0,esk2_0),c(esk1_0))) != one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45]),c_0_34]),c_0_29]),c_0_37]),c_0_46]),c_0_45]),c_0_47]),c_0_37]) ).

cnf(c_0_52,negated_conjecture,
    addition(esk1_0,addition(X1,c(esk1_0))) = addition(X1,one),
    inference(spm,[status(thm)],[c_0_37,c_0_48]) ).

cnf(c_0_53,negated_conjecture,
    addition(one,multiplication(esk1_0,esk2_0)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_41]) ).

cnf(c_0_54,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_29]),c_0_53])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE010+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : run_ET %s %d
% 0.13/0.34  % Computer : n004.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Thu Jun 16 15:58:54 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       : 0.016 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             : 55
% 0.24/1.43  # Proof object clause steps            : 32
% 0.24/1.43  # Proof object formula steps           : 23
% 0.24/1.43  # Proof object conjectures             : 18
% 0.24/1.43  # Proof object clause conjectures      : 15
% 0.24/1.43  # Proof object formula conjectures     : 3
% 0.24/1.43  # Proof object initial clauses used    : 13
% 0.24/1.43  # Proof object initial formulas used   : 11
% 0.24/1.43  # Proof object generating inferences   : 15
% 0.24/1.43  # Proof object simplifying inferences  : 25
% 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    : 1
% 0.24/1.43  # Initial clauses                      : 25
% 0.24/1.43  # Removed in clause preprocessing      : 0
% 0.24/1.43  # Initial clauses in saturation        : 25
% 0.24/1.43  # Processed clauses                    : 1055
% 0.24/1.43  # ...of these trivial                  : 140
% 0.24/1.43  # ...subsumed                          : 564
% 0.24/1.43  # ...remaining for further processing  : 351
% 0.24/1.43  # Other redundant clauses eliminated   : 4
% 0.24/1.43  # Clauses deleted for lack of memory   : 0
% 0.24/1.43  # Backward-subsumed                    : 47
% 0.24/1.43  # Backward-rewritten                   : 27
% 0.24/1.43  # Generated clauses                    : 10220
% 0.24/1.43  # ...of the previous two non-trivial   : 7514
% 0.24/1.43  # Contextual simplify-reflections      : 226
% 0.24/1.43  # Paramodulations                      : 10209
% 0.24/1.43  # Factorizations                       : 0
% 0.24/1.43  # Equation resolutions                 : 11
% 0.24/1.43  # Current number of processed clauses  : 277
% 0.24/1.43  #    Positive orientable unit clauses  : 86
% 0.24/1.43  #    Positive unorientable unit clauses: 17
% 0.24/1.43  #    Negative unit clauses             : 7
% 0.24/1.43  #    Non-unit-clauses                  : 167
% 0.24/1.43  # Current number of unprocessed clauses: 5289
% 0.24/1.43  # ...number of literals in the above   : 9689
% 0.24/1.43  # Current number of archived formulas  : 0
% 0.24/1.43  # Current number of archived clauses   : 74
% 0.24/1.43  # Clause-clause subsumption calls (NU) : 7750
% 0.24/1.43  # Rec. Clause-clause subsumption calls : 6431
% 0.24/1.43  # Non-unit clause-clause subsumptions  : 471
% 0.24/1.43  # Unit Clause-clause subsumption calls : 430
% 0.24/1.43  # Rewrite failures with RHS unbound    : 0
% 0.24/1.43  # BW rewrite match attempts            : 172
% 0.24/1.43  # BW rewrite match successes           : 105
% 0.24/1.43  # Condensation attempts                : 0
% 0.24/1.43  # Condensation successes               : 0
% 0.24/1.43  # Termbank termtop insertions          : 116331
% 0.24/1.43  
% 0.24/1.43  # -------------------------------------------------
% 0.24/1.43  # User time                : 0.161 s
% 0.24/1.43  # System time              : 0.007 s
% 0.24/1.43  # Total time               : 0.168 s
% 0.24/1.43  # Maximum resident set size: 8364 pages
% 0.24/23.44  eprover: CPU time limit exceeded, terminating
% 0.24/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.45  eprover: No such file or directory
% 0.24/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.46  eprover: No such file or directory
% 0.24/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.46  eprover: No such file or directory
% 0.24/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.47  eprover: No such file or directory
% 0.24/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.47  eprover: No such file or directory
% 0.24/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.48  eprover: No such file or directory
% 0.24/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.48  eprover: No such file or directory
% 0.24/23.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.49  eprover: No such file or directory
% 0.24/23.50  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.50  eprover: No such file or directory
% 0.24/23.50  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.50  eprover: No such file or directory
% 0.24/23.51  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.51  eprover: No such file or directory
%------------------------------------------------------------------------------