%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP028-3 : TPTP v8.1.2. Released v1.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n021.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 00:13:42 EDT 2023

% Result   : Unsatisfiable 0.19s 0.58s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   17 (   8 unt;   5 typ;   0 def)
%            Number of atoms       :   21 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   20 (  11   ~;   9   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   5   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   0 con; 1-2 aty)
%            Number of variables   :   33 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    right_solution: ( $i * $i ) > $i ).

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

cnf(associativity2,axiom,
    ( product(X3,X4,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X1,X5,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).

cnf(right_soln,hypothesis,
    product(X1,right_solution(X1,X2),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_soln) ).

cnf(left_soln,hypothesis,
    product(left_solution(X1,X2),X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_soln) ).

cnf(prove_there_is_a_right_identity,negated_conjecture,
    ~ product(not_identity(X1),X1,not_identity(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_a_right_identity) ).

cnf(c_0_4,axiom,
    ( product(X3,X4,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X1,X5,X6) ),
    associativity2 ).

cnf(c_0_5,hypothesis,
    product(X1,right_solution(X1,X2),X2),
    right_soln ).

cnf(c_0_6,hypothesis,
    ( product(X1,right_solution(X2,X3),X4)
    | ~ product(X5,X3,X4)
    | ~ product(X5,X2,X1) ),
    inference(spm,[status(thm)],[c_0_4,c_0_5]) ).

cnf(c_0_7,hypothesis,
    product(left_solution(X1,X2),X1,X2),
    left_soln ).

cnf(c_0_8,hypothesis,
    ( product(X1,right_solution(X2,X3),X4)
    | ~ product(left_solution(X3,X4),X2,X1) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_9,negated_conjecture,
    ~ product(not_identity(X1),X1,not_identity(X1)),
    prove_there_is_a_right_identity ).

cnf(c_0_10,hypothesis,
    product(X1,right_solution(X2,X2),X1),
    inference(spm,[status(thm)],[c_0_8,c_0_7]) ).

cnf(c_0_11,negated_conjecture,
    $false,
    inference(spm,[status(thm)],[c_0_9,c_0_10]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GRP028-3 : TPTP v8.1.2. Released v1.1.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n021.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon Aug 28 19:47:28 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.58  % Version  : CSE_E---1.5
% 0.19/0.58  % Problem  : theBenchmark.p
% 0.19/0.58  % Proof found
% 0.19/0.58  % SZS status Theorem for theBenchmark.p
% 0.19/0.58  % SZS output start Proof
% See solution above
% 0.19/0.58  % Total time : 0.004000 s
% 0.19/0.58  % SZS output end Proof
% 0.19/0.58  % Total time : 0.007000 s
%------------------------------------------------------------------------------