%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP710-10 : TPTP v8.1.2. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n011.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 00:23:17 EDT 2023

% Result   : Unsatisfiable 0.20s 0.55s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   27 (  22 unt;   5 typ;   0 def)
%            Number of atoms       :   22 (  21 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   34 (   3 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    unit: $i ).

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

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

tff(decl_25,type,
    x0: $i ).

tff(decl_26,type,
    x1: $i ).

cnf(f01,axiom,
    mult(X1,unit) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).

cnf(f03,axiom,
    mult(X1,mult(X2,mult(X2,X3))) = mult(mult(mult(X1,X2),X2),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).

cnf(f05,axiom,
    mult(i(X1),X1) = unit,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).

cnf(f02,axiom,
    mult(unit,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).

cnf(goal,negated_conjecture,
    mult(x0,X1) != x1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).

cnf(c_0_5,axiom,
    mult(X1,unit) = X1,
    f01 ).

cnf(c_0_6,axiom,
    mult(X1,mult(X2,mult(X2,X3))) = mult(mult(mult(X1,X2),X2),X3),
    f03 ).

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

cnf(c_0_8,axiom,
    mult(i(X1),X1) = unit,
    f05 ).

cnf(c_0_9,axiom,
    mult(unit,X1) = X1,
    f02 ).

cnf(c_0_10,plain,
    mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))),
    inference(rw,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_11,plain,
    mult(i(X1),mult(X1,X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).

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

cnf(c_0_13,plain,
    mult(i(mult(X1,X1)),mult(X1,mult(X1,X2))) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_8]),c_0_9]) ).

cnf(c_0_14,plain,
    i(i(X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_11]),c_0_8]),c_0_5]) ).

cnf(c_0_15,plain,
    mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_9]),c_0_9]) ).

cnf(c_0_16,plain,
    mult(X1,mult(X1,mult(i(mult(X1,X1)),X2))) = X2,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]) ).

cnf(c_0_17,plain,
    mult(i(X1),mult(X1,X2)) = X2,
    inference(spm,[status(thm)],[c_0_12,c_0_16]) ).

cnf(c_0_18,negated_conjecture,
    mult(x0,X1) != x1,
    goal ).

cnf(c_0_19,plain,
    mult(X1,mult(i(X1),X2)) = X2,
    inference(spm,[status(thm)],[c_0_17,c_0_14]) ).

cnf(c_0_20,negated_conjecture,
    X1 != x1,
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_21,negated_conjecture,
    $false,
    inference(er,[status(thm)],[c_0_20]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : GRP710-10 : TPTP v8.1.2. Released v8.1.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n011.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 02:29:56 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.20/0.53  start to proof: theBenchmark
% 0.20/0.55  % Version  : CSE_E---1.5
% 0.20/0.55  % Problem  : theBenchmark.p
% 0.20/0.55  % Proof found
% 0.20/0.55  % SZS status Theorem for theBenchmark.p
% 0.20/0.55  % SZS output start Proof
% See solution above
% 0.20/0.55  % Total time : 0.008000 s
% 0.20/0.55  % SZS output end Proof
% 0.20/0.55  % Total time : 0.011000 s
%------------------------------------------------------------------------------