TSTP Solution File: KLE099+1 by Enigma---0.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Enigma---0.5.1
% Problem  : KLE099+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : enigmatic-eprover.py %s %d 1

% 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 01:50:07 EDT 2022

% Result   : Theorem 8.05s 2.32s
% Output   : CNFRefutation 8.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   64 (  61 unt;   0 def)
%            Number of atoms       :   67 (  66 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    7 (   4   ~;   0   |;   1   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :  100 (   5 sgn  54   !;   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/KLE001+0.ax',additive_associativity) ).

fof(additive_idempotence,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).

fof(left_distributivity,axiom,
    ! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).

fof(domain1,axiom,
    ! [X4] : multiplication(antidomain(X4),X4) = zero,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain1) ).

fof(additive_identity,axiom,
    ! [X1] : addition(X1,zero) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).

fof(right_distributivity,axiom,
    ! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).

fof(additive_commutativity,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).

fof(goals,conjecture,
    ! [X4,X5,X6] :
      ( addition(forward_diamond(X4,domain(X5)),domain(X6)) = domain(X6)
     => multiplication(antidomain(X6),multiplication(X4,domain(X5))) = zero ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(forward_diamond,axiom,
    ! [X4,X5] : forward_diamond(X4,X5) = domain(multiplication(X4,domain(X5))),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).

fof(domain4,axiom,
    ! [X4] : domain(X4) = antidomain(antidomain(X4)),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).

fof(domain3,axiom,
    ! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain3) ).

fof(multiplicative_left_identity,axiom,
    ! [X1] : multiplication(one,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).

fof(multiplicative_associativity,axiom,
    ! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).

fof(left_annihilation,axiom,
    ! [X1] : multiplication(zero,X1) = zero,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).

fof(multiplicative_right_identity,axiom,
    ! [X1] : multiplication(X1,one) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).

fof(c_0_15,plain,
    ! [X9,X10,X11] : addition(X11,addition(X10,X9)) = addition(addition(X11,X10),X9),
    inference(variable_rename,[status(thm)],[additive_associativity]) ).

fof(c_0_16,plain,
    ! [X13] : addition(X13,X13) = X13,
    inference(variable_rename,[status(thm)],[additive_idempotence]) ).

fof(c_0_17,plain,
    ! [X22,X23,X24] : multiplication(addition(X22,X23),X24) = addition(multiplication(X22,X24),multiplication(X23,X24)),
    inference(variable_rename,[status(thm)],[left_distributivity]) ).

fof(c_0_18,plain,
    ! [X29] : multiplication(antidomain(X29),X29) = zero,
    inference(variable_rename,[status(thm)],[domain1]) ).

fof(c_0_19,plain,
    ! [X12] : addition(X12,zero) = X12,
    inference(variable_rename,[status(thm)],[additive_identity]) ).

fof(c_0_20,plain,
    ! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
    inference(variable_rename,[status(thm)],[right_distributivity]) ).

cnf(c_0_21,plain,
    addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

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

fof(c_0_23,plain,
    ! [X7,X8] : addition(X7,X8) = addition(X8,X7),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

fof(c_0_24,negated_conjecture,
    ~ ! [X4,X5,X6] :
        ( addition(forward_diamond(X4,domain(X5)),domain(X6)) = domain(X6)
       => multiplication(antidomain(X6),multiplication(X4,domain(X5))) = zero ),
    inference(assume_negation,[status(cth)],[goals]) ).

fof(c_0_25,plain,
    ! [X42,X43] : forward_diamond(X42,X43) = domain(multiplication(X42,domain(X43))),
    inference(variable_rename,[status(thm)],[forward_diamond]) ).

fof(c_0_26,plain,
    ! [X33] : domain(X33) = antidomain(antidomain(X33)),
    inference(variable_rename,[status(thm)],[domain4]) ).

cnf(c_0_27,plain,
    multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_28,plain,
    multiplication(antidomain(X1),X1) = zero,
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_29,plain,
    addition(X1,zero) = X1,
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

fof(c_0_30,plain,
    ! [X32] : addition(antidomain(antidomain(X32)),antidomain(X32)) = one,
    inference(variable_rename,[status(thm)],[domain3]) ).

cnf(c_0_31,plain,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_32,plain,
    addition(X1,addition(X1,X2)) = addition(X1,X2),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_33,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

fof(c_0_34,negated_conjecture,
    ( addition(forward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0)) = domain(esk3_0)
    & multiplication(antidomain(esk3_0),multiplication(esk1_0,domain(esk2_0))) != zero ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).

cnf(c_0_35,plain,
    forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_36,plain,
    domain(X1) = antidomain(antidomain(X1)),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_37,plain,
    multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).

cnf(c_0_38,plain,
    addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

fof(c_0_39,plain,
    ! [X18] : multiplication(one,X18) = X18,
    inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).

fof(c_0_40,plain,
    ! [X14,X15,X16] : multiplication(X14,multiplication(X15,X16)) = multiplication(multiplication(X14,X15),X16),
    inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).

cnf(c_0_41,plain,
    multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_28]),c_0_29]) ).

cnf(c_0_42,plain,
    addition(X1,addition(X2,X1)) = addition(X2,X1),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

fof(c_0_43,plain,
    ! [X26] : multiplication(zero,X26) = zero,
    inference(variable_rename,[status(thm)],[left_annihilation]) ).

cnf(c_0_44,negated_conjecture,
    addition(forward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0)) = domain(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_45,plain,
    forward_diamond(X1,X2) = antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_36]) ).

fof(c_0_46,plain,
    ! [X17] : multiplication(X17,one) = X17,
    inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).

cnf(c_0_47,plain,
    multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
    inference(spm,[status(thm)],[c_0_37,c_0_33]) ).

cnf(c_0_48,plain,
    addition(antidomain(X1),antidomain(antidomain(X1))) = one,
    inference(rw,[status(thm)],[c_0_38,c_0_33]) ).

cnf(c_0_49,plain,
    multiplication(one,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_50,plain,
    multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_51,plain,
    multiplication(antidomain(addition(X1,X2)),X2) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_28]) ).

cnf(c_0_52,plain,
    multiplication(zero,X1) = zero,
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_53,negated_conjecture,
    addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(esk2_0))))))),antidomain(antidomain(esk3_0))) = antidomain(antidomain(esk3_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_36]),c_0_36]),c_0_36]),c_0_45]) ).

cnf(c_0_54,plain,
    multiplication(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_55,plain,
    multiplication(antidomain(antidomain(X1)),X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).

cnf(c_0_56,plain,
    multiplication(antidomain(addition(X1,X2)),multiplication(X2,X3)) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).

cnf(c_0_57,negated_conjecture,
    addition(antidomain(antidomain(esk3_0)),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(esk2_0)))))))) = antidomain(antidomain(esk3_0)),
    inference(rw,[status(thm)],[c_0_53,c_0_33]) ).

cnf(c_0_58,plain,
    antidomain(antidomain(antidomain(X1))) = antidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_48]),c_0_54]),c_0_55]) ).

cnf(c_0_59,negated_conjecture,
    multiplication(antidomain(esk3_0),multiplication(esk1_0,domain(esk2_0))) != zero,
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_60,plain,
    multiplication(antidomain(addition(X1,antidomain(antidomain(X2)))),X2) = zero,
    inference(spm,[status(thm)],[c_0_56,c_0_55]) ).

cnf(c_0_61,negated_conjecture,
    addition(antidomain(antidomain(esk3_0)),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0)))))) = antidomain(antidomain(esk3_0)),
    inference(rw,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_62,negated_conjecture,
    multiplication(antidomain(esk3_0),multiplication(esk1_0,antidomain(antidomain(esk2_0)))) != zero,
    inference(rw,[status(thm)],[c_0_59,c_0_36]) ).

cnf(c_0_63,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_58]),c_0_62]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : KLE099+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.10  % Command  : enigmatic-eprover.py %s %d 1
% 0.10/0.28  % Computer : n032.cluster.edu
% 0.10/0.28  % Model    : x86_64 x86_64
% 0.10/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28  % Memory   : 8042.1875MB
% 0.10/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.28  % CPULimit : 300
% 0.12/0.28  % WCLimit  : 600
% 0.12/0.28  % DateTime : Thu Jun 16 15:18:31 EDT 2022
% 0.12/0.28  % CPUTime  : 
% 0.13/0.35  # ENIGMATIC: Selected SinE mode:
% 0.13/0.35  # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35  # Filter: axfilter_auto   0 goes into file theBenchmark_axfilter_auto   0.p
% 0.13/0.35  # Filter: axfilter_auto   1 goes into file theBenchmark_axfilter_auto   1.p
% 0.13/0.35  # Filter: axfilter_auto   2 goes into file theBenchmark_axfilter_auto   2.p
% 8.05/2.32  # ENIGMATIC: Solved by autoschedule:
% 8.05/2.32  # No SInE strategy applied
% 8.05/2.32  # Trying AutoSched0 for 150 seconds
% 8.05/2.32  # AutoSched0-Mode selected heuristic G_E___100_C18_F1_PI_AE_Q4_CS_SP_PS_S0Y
% 8.05/2.32  # and selection function SelectMaxLComplexAvoidPosPred.
% 8.05/2.32  #
% 8.05/2.32  # Preprocessing time       : 0.019 s
% 8.05/2.32  # Presaturation interreduction done
% 8.05/2.32  
% 8.05/2.32  # Proof found!
% 8.05/2.32  # SZS status Theorem
% 8.05/2.32  # SZS output start CNFRefutation
% See solution above
% 8.05/2.32  # Training examples: 0 positive, 0 negative
% 8.05/2.32  
% 8.05/2.32  # -------------------------------------------------
% 8.05/2.32  # User time                : 0.025 s
% 8.05/2.32  # System time              : 0.007 s
% 8.05/2.32  # Total time               : 0.032 s
% 8.05/2.32  # Maximum resident set size: 7120 pages
% 8.05/2.32  
%------------------------------------------------------------------------------