%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP698-1 : 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 : n016.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 00:23:12 EDT 2023

% Result   : Unsatisfiable 0.45s 0.59s
% Output   : CNFRefutation 0.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   23 (  16 unt;   7 typ;   0 def)
%            Number of atoms       :   16 (  15 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    5 (   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    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   27 (   0 sgn;   0   !;   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,
    a: $i ).

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

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

cnf(c07,axiom,
    mult(mult(mult(X1,X2),X1),mult(X1,X3)) = mult(X1,mult(mult(mult(X2,X1),X1),X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).

cnf(c05,axiom,
    mult(X1,unit) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).

cnf(c04,axiom,
    rd(mult(X1,X2),X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).

cnf(c03,axiom,
    mult(rd(X1,X2),X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).

cnf(goals,negated_conjecture,
    mult(a,mult(b,c)) != mult(rd(mult(a,b),a),mult(a,c)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

cnf(c_0_5,axiom,
    mult(mult(mult(X1,X2),X1),mult(X1,X3)) = mult(X1,mult(mult(mult(X2,X1),X1),X3)),
    c07 ).

cnf(c_0_6,axiom,
    mult(X1,unit) = X1,
    c05 ).

cnf(c_0_7,axiom,
    rd(mult(X1,X2),X2) = X1,
    c04 ).

cnf(c_0_8,plain,
    mult(mult(mult(X1,X2),X1),X1) = mult(X1,mult(mult(X2,X1),X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_6]) ).

cnf(c_0_9,plain,
    rd(mult(X1,mult(mult(X2,X1),X1)),X1) = mult(mult(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_10,axiom,
    mult(rd(X1,X2),X2) = X1,
    c03 ).

cnf(c_0_11,plain,
    rd(mult(X1,mult(X2,X1)),X1) = mult(mult(X1,rd(X2,X1)),X1),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_12,plain,
    mult(mult(X1,rd(rd(X2,X1),X1)),X1) = rd(mult(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_11,c_0_10]) ).

cnf(c_0_13,negated_conjecture,
    mult(a,mult(b,c)) != mult(rd(mult(a,b),a),mult(a,c)),
    goals ).

cnf(c_0_14,plain,
    mult(rd(mult(X1,X2),X1),mult(X1,X3)) = mult(X1,mult(X2,X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_12]),c_0_10]),c_0_10]) ).

cnf(c_0_15,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : GRP698-1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n016.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 29 02:14:45 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.45/0.57  start to proof: theBenchmark
% 0.45/0.59  % Version  : CSE_E---1.5
% 0.45/0.59  % Problem  : theBenchmark.p
% 0.45/0.59  % Proof found
% 0.45/0.59  % SZS status Theorem for theBenchmark.p
% 0.45/0.59  % SZS output start Proof
% See solution above
% 0.45/0.59  % Total time : 0.014000 s
% 0.45/0.59  % SZS output end Proof
% 0.45/0.59  % Total time : 0.017000 s
%------------------------------------------------------------------------------