%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP699-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n006.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 0.22s 0.64s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   24 (  17 unt;   7 typ;   0 def)
%            Number of atoms       :   17 (  16 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   :   30 (   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(c08,axiom,
    mult(mult(X1,X2),mult(X2,mult(X3,X2))) = mult(mult(X1,mult(X2,mult(X2,X3))),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).

cnf(c06,axiom,
    mult(unit,X1) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).

cnf(c01,axiom,
    mult(X1,ld(X1,X2)) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).

cnf(c02,axiom,
    ld(X1,mult(X1,X2)) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).

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

cnf(c_0_5,axiom,
    mult(mult(X1,X2),mult(X2,mult(X3,X2))) = mult(mult(X1,mult(X2,mult(X2,X3))),X2),
    c08 ).

cnf(c_0_6,axiom,
    mult(unit,X1) = X1,
    c06 ).

cnf(c_0_7,plain,
    mult(mult(X1,mult(X1,X2)),X1) = mult(X1,mult(X1,mult(X2,X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_6]) ).

cnf(c_0_8,axiom,
    mult(X1,ld(X1,X2)) = X2,
    c01 ).

cnf(c_0_9,axiom,
    ld(X1,mult(X1,X2)) = X2,
    c02 ).

cnf(c_0_10,plain,
    mult(X1,mult(X1,mult(ld(X1,X2),X1))) = mult(mult(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

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

cnf(c_0_12,plain,
    mult(mult(X1,X2),mult(X2,mult(ld(X2,X3),X2))) = mult(mult(X1,mult(X2,X3)),X2),
    inference(spm,[status(thm)],[c_0_5,c_0_8]) ).

cnf(c_0_13,plain,
    mult(X1,mult(ld(X1,ld(X1,X2)),X1)) = ld(X1,mult(X2,X1)),
    inference(spm,[status(thm)],[c_0_11,c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    mult(mult(a,b),c) != mult(mult(a,c),ld(c,mult(b,c))),
    goals ).

cnf(c_0_15,plain,
    mult(mult(X1,X2),ld(X2,mult(X3,X2))) = mult(mult(X1,X3),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_8]) ).

cnf(c_0_16,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : GRP699-1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n006.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 29 01:41:51 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.22/0.60  start to proof: theBenchmark
% 0.22/0.64  % Version  : CSE_E---1.5
% 0.22/0.64  % Problem  : theBenchmark.p
% 0.22/0.64  % Proof found
% 0.22/0.64  % SZS status Theorem for theBenchmark.p
% 0.22/0.64  % SZS output start Proof
% See solution above
% 0.22/0.64  % Total time : 0.029000 s
% 0.22/0.64  % SZS output end Proof
% 0.22/0.64  % Total time : 0.032000 s
%------------------------------------------------------------------------------