TSTP Solution File: GRP702+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP702+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% 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  : 300s
% DateTime : Thu Aug 31 00:23:14 EDT 2023

% Result   : Theorem 0.20s 0.58s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   31 (  17 unt;  10 typ;   0 def)
%            Number of atoms       :   29 (  28 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   15 (   7   ~;   4   |;   4   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :   31 (   0 sgn;  22   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    ld: ( $i * $i ) > $i ).

tff(decl_23,type,
    mult: ( $i * $i ) > $i ).

tff(decl_24,type,
    rd: ( $i * $i ) > $i ).

tff(decl_25,type,
    unit: $i ).

tff(decl_26,type,
    op_c: $i ).

tff(decl_27,type,
    op_d: $i ).

tff(decl_28,type,
    op_e: $i ).

tff(decl_29,type,
    op_f: $i ).

tff(decl_30,type,
    esk1_0: $i ).

tff(decl_31,type,
    esk2_0: $i ).

fof(goals,conjecture,
    ! [X4,X5] :
      ( mult(op_d,mult(X4,X5)) = mult(mult(op_d,X4),X5)
      & mult(X4,mult(X5,op_d)) = mult(mult(X4,X5),op_d)
      & mult(X4,mult(op_d,X5)) = mult(mult(X4,op_d),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(f02,axiom,
    ! [X1,X2] : ld(X2,mult(X2,X1)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).

fof(f11,axiom,
    ! [X2] : op_d = ld(X2,mult(op_c,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f11) ).

fof(f08,axiom,
    ! [X1,X2] : mult(op_c,mult(X2,X1)) = mult(mult(op_c,X2),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).

fof(f10,axiom,
    ! [X1,X2] : mult(X2,mult(op_c,X1)) = mult(mult(X2,op_c),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f10) ).

fof(f09,axiom,
    ! [X1,X2] : mult(X2,mult(X1,op_c)) = mult(mult(X2,X1),op_c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f09) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X4,X5] :
        ( mult(op_d,mult(X4,X5)) = mult(mult(op_d,X4),X5)
        & mult(X4,mult(X5,op_d)) = mult(mult(X4,X5),op_d)
        & mult(X4,mult(op_d,X5)) = mult(mult(X4,op_d),X5) ),
    inference(assume_negation,[status(cth)],[goals]) ).

fof(c_0_7,plain,
    ! [X8,X9] : ld(X9,mult(X9,X8)) = X8,
    inference(variable_rename,[status(thm)],[f02]) ).

fof(c_0_8,plain,
    ! [X25] : op_d = ld(X25,mult(op_c,X25)),
    inference(variable_rename,[status(thm)],[f11]) ).

fof(c_0_9,negated_conjecture,
    ( mult(op_d,mult(esk1_0,esk2_0)) != mult(mult(op_d,esk1_0),esk2_0)
    | mult(esk1_0,mult(esk2_0,op_d)) != mult(mult(esk1_0,esk2_0),op_d)
    | mult(esk1_0,mult(op_d,esk2_0)) != mult(mult(esk1_0,op_d),esk2_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

cnf(c_0_10,plain,
    ld(X1,mult(X1,X2)) = X2,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,plain,
    op_d = ld(X1,mult(op_c,X1)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_12,plain,
    ! [X19,X20] : mult(op_c,mult(X20,X19)) = mult(mult(op_c,X20),X19),
    inference(variable_rename,[status(thm)],[f08]) ).

fof(c_0_13,plain,
    ! [X23,X24] : mult(X24,mult(op_c,X23)) = mult(mult(X24,op_c),X23),
    inference(variable_rename,[status(thm)],[f10]) ).

fof(c_0_14,plain,
    ! [X21,X22] : mult(X22,mult(X21,op_c)) = mult(mult(X22,X21),op_c),
    inference(variable_rename,[status(thm)],[f09]) ).

cnf(c_0_15,negated_conjecture,
    ( mult(op_d,mult(esk1_0,esk2_0)) != mult(mult(op_d,esk1_0),esk2_0)
    | mult(esk1_0,mult(esk2_0,op_d)) != mult(mult(esk1_0,esk2_0),op_d)
    | mult(esk1_0,mult(op_d,esk2_0)) != mult(mult(esk1_0,op_d),esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_16,plain,
    op_d = op_c,
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

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

cnf(c_0_18,plain,
    mult(X1,mult(op_c,X2)) = mult(mult(X1,op_c),X2),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19,plain,
    mult(X1,mult(X2,op_c)) = mult(mult(X1,X2),op_c),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_20,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_16]),c_0_16]),c_0_18]),c_0_16]),c_0_16]),c_0_19]),c_0_16])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : GRP702+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n026.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    : 300
% 0.13/0.35  % DateTime   : Mon Aug 28 21:35:35 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.58  % Version  : CSE_E---1.5
% 0.20/0.58  % Problem  : theBenchmark.p
% 0.20/0.58  % Proof found
% 0.20/0.58  % SZS status Theorem for theBenchmark.p
% 0.20/0.58  % SZS output start Proof
% See solution above
% 0.20/0.59  % Total time : 0.007000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.010000 s
%------------------------------------------------------------------------------