%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP657-10 : TPTP v8.1.2. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/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 00:22:48 EDT 2023

% Result   : Unsatisfiable 0.20s 0.56s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   25 (  19 unt;   6 typ;   0 def)
%            Number of atoms       :   19 (  18 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    4 (   4   ~;   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  :   10 (   6   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   0 con; 1-2 aty)
%            Number of variables   :   37 (   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,
    x1: $i > $i ).

tff(decl_26,type,
    x1_2: $i > $i ).

tff(decl_27,type,
    tuple: ( $i * $i ) > $i ).

cnf(f05,axiom,
    mult(mult(X1,X2),mult(X3,X1)) = mult(X1,mult(mult(X2,X3),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).

cnf(f01,axiom,
    mult(X1,ld(X1,X2)) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).

cnf(f02,axiom,
    ld(X1,mult(X1,X2)) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).

cnf(f04,axiom,
    rd(mult(X1,X2),X2) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).

cnf(goal,negated_conjecture,
    tuple(mult(X1,x1(X1)),mult(x1_2(X1),X1)) != tuple(x1(X1),x1_2(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).

cnf(c_0_5,axiom,
    mult(mult(X1,X2),mult(X3,X1)) = mult(X1,mult(mult(X2,X3),X1)),
    f05 ).

cnf(c_0_6,axiom,
    mult(X1,ld(X1,X2)) = X2,
    f01 ).

cnf(c_0_7,axiom,
    ld(X1,mult(X1,X2)) = X2,
    f02 ).

cnf(c_0_8,plain,
    mult(X1,mult(mult(ld(X1,X2),X3),X1)) = mult(X2,mult(X3,X1)),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_9,axiom,
    rd(mult(X1,X2),X2) = X1,
    f04 ).

cnf(c_0_10,plain,
    mult(mult(ld(X1,X2),X3),X1) = ld(X1,mult(X2,mult(X3,X1))),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,plain,
    rd(ld(X1,mult(X2,mult(X3,X1))),X1) = mult(ld(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_12,negated_conjecture,
    tuple(mult(X1,x1(X1)),mult(x1_2(X1),X1)) != tuple(x1(X1),x1_2(X1)),
    goal ).

cnf(c_0_13,plain,
    mult(ld(X1,X1),X2) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_7]),c_0_9]) ).

cnf(c_0_14,negated_conjecture,
    tuple(x1(ld(X1,X1)),mult(x1_2(ld(X1,X1)),ld(X1,X1))) != tuple(x1(ld(X1,X1)),x1_2(ld(X1,X1))),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_15,plain,
    rd(X1,X1) = ld(X2,X2),
    inference(spm,[status(thm)],[c_0_9,c_0_13]) ).

cnf(c_0_16,negated_conjecture,
    tuple(x1(rd(X1,X1)),mult(x1_2(rd(X1,X1)),rd(X1,X1))) != tuple(x1(rd(X1,X1)),x1_2(rd(X1,X1))),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_17,plain,
    mult(X1,rd(X2,X2)) = X1,
    inference(spm,[status(thm)],[c_0_6,c_0_15]) ).

cnf(c_0_18,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GRP657-10 : TPTP v8.1.2. Released v8.1.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n011.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 29 02:20:11 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.55  start to proof: theBenchmark
% 0.20/0.56  % Version  : CSE_E---1.5
% 0.20/0.56  % Problem  : theBenchmark.p
% 0.20/0.56  % Proof found
% 0.20/0.56  % SZS status Theorem for theBenchmark.p
% 0.20/0.56  % SZS output start Proof
% See solution above
% 0.20/0.56  % Total time : 0.004000 s
% 0.20/0.56  % SZS output end Proof
% 0.20/0.56  % Total time : 0.007000 s
%------------------------------------------------------------------------------