%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP682-10 : 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 : n010.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 00:23:02 EDT 2023

% Result   : Unsatisfiable 0.20s 0.64s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   26 (  20 unt;   6 typ;   0 def)
%            Number of atoms       :   20 (  19 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    :    4 (   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    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   36 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

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

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

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

tff(decl_27,type,
    x2: $i ).

cnf(f05,axiom,
    ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).

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

cnf(f07,axiom,
    ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).

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

cnf(f04,axiom,
    mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).

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

cnf(goal,negated_conjecture,
    ld(ld(x0,x1),mult(ld(x0,x1),x2)) != ld(x0,mult(x0,x2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).

cnf(c_0_7,axiom,
    ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
    f05 ).

cnf(c_0_8,axiom,
    ld(X1,mult(X1,X1)) = X1,
    f01 ).

cnf(c_0_9,axiom,
    ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
    f07 ).

cnf(c_0_10,axiom,
    mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
    f03 ).

cnf(c_0_11,axiom,
    mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
    f04 ).

cnf(c_0_12,axiom,
    rd(mult(X1,X1),X1) = X1,
    f02 ).

cnf(c_0_13,plain,
    mult(ld(X1,mult(X1,X2)),X3) = ld(X1,mult(X1,mult(X2,X3))),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_14,plain,
    ld(X1,X1) = rd(X1,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_8]),c_0_11]),c_0_12]) ).

cnf(c_0_15,plain,
    ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = ld(X1,mult(X1,mult(X3,X4))),
    inference(rw,[status(thm)],[c_0_7,c_0_13]) ).

cnf(c_0_16,plain,
    mult(X1,rd(X1,X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_14]),c_0_8]) ).

cnf(c_0_17,negated_conjecture,
    ld(ld(x0,x1),mult(ld(x0,x1),x2)) != ld(x0,mult(x0,x2)),
    goal ).

cnf(c_0_18,plain,
    ld(ld(X1,X2),mult(ld(X1,X2),X3)) = ld(X1,mult(X1,X3)),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_19,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : GRP682-10 : TPTP v8.1.2. Released v8.1.0.
% 0.12/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n010.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 21:30:34 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.62  start to proof: theBenchmark
% 0.20/0.64  % Version  : CSE_E---1.5
% 0.20/0.64  % Problem  : theBenchmark.p
% 0.20/0.64  % Proof found
% 0.20/0.64  % SZS status Theorem for theBenchmark.p
% 0.20/0.64  % SZS output start Proof
% See solution above
% 0.20/0.64  % Total time : 0.007000 s
% 0.20/0.64  % SZS output end Proof
% 0.20/0.64  % Total time : 0.010000 s
%------------------------------------------------------------------------------