%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP042-2 : 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 : n027.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 00:13:49 EDT 2023

% Result   : Unsatisfiable 0.21s 0.65s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   21 (   7 unt;   7 typ;   0 def)
%            Number of atoms       :   25 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   24 (  13   ~;  11   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   4   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   24 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

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

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

tff(decl_26,type,
    equalish: ( $i * $i ) > $o ).

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

tff(decl_28,type,
    b: $i ).

cnf(total_function2,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',total_function2) ).

cnf(left_identity,axiom,
    product(identity,X1,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',left_identity) ).

cnf(product_substitution3,axiom,
    ( product(X3,X4,X2)
    | ~ equalish(X1,X2)
    | ~ product(X3,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',product_substitution3) ).

cnf(a_equals_b,hypothesis,
    equalish(a,b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_b) ).

cnf(prove_symmetry,negated_conjecture,
    ~ equalish(b,a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_symmetry) ).

cnf(c_0_5,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    total_function2 ).

cnf(c_0_6,axiom,
    product(identity,X1,X1),
    left_identity ).

cnf(c_0_7,axiom,
    ( product(X3,X4,X2)
    | ~ equalish(X1,X2)
    | ~ product(X3,X4,X1) ),
    product_substitution3 ).

cnf(c_0_8,plain,
    ( equalish(X1,X2)
    | ~ product(identity,X2,X1) ),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_9,plain,
    ( product(identity,X1,X2)
    | ~ equalish(X1,X2) ),
    inference(spm,[status(thm)],[c_0_7,c_0_6]) ).

cnf(c_0_10,plain,
    ( equalish(X1,X2)
    | ~ equalish(X2,X1) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_11,hypothesis,
    equalish(a,b),
    a_equals_b ).

cnf(c_0_12,negated_conjecture,
    ~ equalish(b,a),
    prove_symmetry ).

cnf(c_0_13,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : GRP042-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n027.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 21:41:08 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.63  start to proof: theBenchmark
% 0.21/0.65  % Version  : CSE_E---1.5
% 0.21/0.65  % Problem  : theBenchmark.p
% 0.21/0.65  % Proof found
% 0.21/0.65  % SZS status Theorem for theBenchmark.p
% 0.21/0.65  % SZS output start Proof
% See solution above
% 0.21/0.65  % Total time : 0.004000 s
% 0.21/0.65  % SZS output end Proof
% 0.21/0.65  % Total time : 0.007000 s
%------------------------------------------------------------------------------