%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP010-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n018.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 00:13:35 EDT 2023

% Result   : Unsatisfiable 0.20s 0.58s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   19 (  14 unt;   5 typ;   0 def)
%            Number of atoms       :   14 (  13 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    :    3 (   1 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   :   14 (   0 sgn;   0   !;   0   ?;   0   :)

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

tff(decl_23,type,
    identity: $i ).

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

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

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

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

cnf(left_inverse,axiom,
    multiply(inverse(X1),X1) = identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).

cnf(left_identity,axiom,
    multiply(identity,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).

cnf(c_times_b_is_e,hypothesis,
    multiply(c,b) = identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_times_b_is_e) ).

cnf(prove_b_times_c_is_e,negated_conjecture,
    multiply(b,c) != identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_times_c_is_e) ).

cnf(c_0_5,axiom,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    associativity ).

cnf(c_0_6,axiom,
    multiply(inverse(X1),X1) = identity,
    left_inverse ).

cnf(c_0_7,axiom,
    multiply(identity,X1) = X1,
    left_identity ).

cnf(c_0_8,hypothesis,
    multiply(c,b) = identity,
    c_times_b_is_e ).

cnf(c_0_9,plain,
    multiply(inverse(X1),multiply(X1,X2)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7]) ).

cnf(c_0_10,hypothesis,
    multiply(c,multiply(b,X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_8]),c_0_7]) ).

cnf(c_0_11,hypothesis,
    multiply(inverse(c),X1) = multiply(b,X1),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_12,negated_conjecture,
    multiply(b,c) != identity,
    prove_b_times_c_is_e ).

cnf(c_0_13,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_11]),c_0_12]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GRP010-4 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n018.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Mon Aug 28 20:17:32 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.58  % Version  : CSE_E---1.5
% 0.20/0.58  % Problem  : theBenchmark.p
% 0.20/0.58  % Proof found
% 0.20/0.58  % SZS status Theorem for theBenchmark.p
% 0.20/0.58  % SZS output start Proof
% See solution above
% 0.20/0.58  % Total time : 0.004000 s
% 0.20/0.58  % SZS output end Proof
% 0.20/0.58  % Total time : 0.006000 s
%------------------------------------------------------------------------------