%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP135-1.002 : TPTP v8.1.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n009.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 00:17:13 EDT 2023

% Result   : Unsatisfiable 0.59s 0.62s
% Output   : CNFRefutation 0.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   41 (  13 unt;   5 typ;   0 def)
%            Number of atoms       :   74 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   67 (  29   ~;  38   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   37 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    e_1: $i ).

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

tff(decl_24,type,
    e_2: $i ).

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

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

cnf(product_total_function1,axiom,
    ( product(X1,X2,e_1)
    | product(X1,X2,e_2)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).

cnf(element_2,axiom,
    group_element(e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).

cnf(element_1,axiom,
    group_element(e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).

cnf(qg3,negated_conjecture,
    ( product(X4,X1,X2)
    | ~ product(X1,X2,X3)
    | ~ product(X3,X1,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).

cnf(product_right_cancellation,axiom,
    ( equalish(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).

cnf(e_1_is_not_e_2,axiom,
    ~ equalish(e_1,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).

cnf(product_left_cancellation,axiom,
    ( equalish(X1,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).

cnf(c_0_7,axiom,
    ( product(X1,X2,e_1)
    | product(X1,X2,e_2)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    product_total_function1 ).

cnf(c_0_8,axiom,
    group_element(e_2),
    element_2 ).

cnf(c_0_9,plain,
    ( product(X1,e_2,e_2)
    | product(X1,e_2,e_1)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_10,axiom,
    group_element(e_1),
    element_1 ).

cnf(c_0_11,negated_conjecture,
    ( product(X4,X1,X2)
    | ~ product(X1,X2,X3)
    | ~ product(X3,X1,X4) ),
    qg3 ).

cnf(c_0_12,plain,
    ( product(e_1,e_2,e_1)
    | product(e_1,e_2,e_2) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_13,negated_conjecture,
    ( product(e_1,e_2,e_2)
    | product(e_1,e_2,X1)
    | ~ product(e_2,X1,e_1) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_14,plain,
    ( product(e_2,e_2,e_1)
    | product(e_2,e_2,e_2) ),
    inference(spm,[status(thm)],[c_0_9,c_0_8]) ).

cnf(c_0_15,negated_conjecture,
    ( product(e_2,e_2,e_2)
    | product(e_1,e_2,e_2) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_16,negated_conjecture,
    ( product(e_2,e_2,e_2)
    | product(e_2,e_2,X1)
    | ~ product(e_2,X1,e_1) ),
    inference(spm,[status(thm)],[c_0_11,c_0_15]) ).

cnf(c_0_17,axiom,
    ( equalish(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X3) ),
    product_right_cancellation ).

cnf(c_0_18,negated_conjecture,
    product(e_2,e_2,e_2),
    inference(spm,[status(thm)],[c_0_16,c_0_14]) ).

cnf(c_0_19,plain,
    ( product(X1,e_1,e_2)
    | product(X1,e_1,e_1)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_7,c_0_10]) ).

cnf(c_0_20,axiom,
    ~ equalish(e_1,e_2),
    e_1_is_not_e_2 ).

cnf(c_0_21,negated_conjecture,
    ( equalish(X1,e_2)
    | ~ product(e_2,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_22,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_2) ),
    inference(spm,[status(thm)],[c_0_19,c_0_10]) ).

cnf(c_0_23,axiom,
    ( equalish(X1,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X3) ),
    product_left_cancellation ).

cnf(c_0_24,plain,
    ( product(e_2,e_1,e_1)
    | product(e_2,e_1,e_2) ),
    inference(spm,[status(thm)],[c_0_19,c_0_8]) ).

cnf(c_0_25,negated_conjecture,
    ~ product(e_2,e_1,e_2),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_26,negated_conjecture,
    ( product(e_1,e_1,e_2)
    | product(e_1,e_1,X1)
    | ~ product(e_1,X1,e_1) ),
    inference(spm,[status(thm)],[c_0_11,c_0_22]) ).

cnf(c_0_27,negated_conjecture,
    ( equalish(X1,e_2)
    | ~ product(X1,e_2,e_2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_18]) ).

cnf(c_0_28,plain,
    product(e_2,e_1,e_1),
    inference(sr,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_29,negated_conjecture,
    ( product(e_1,e_2,e_2)
    | product(e_1,e_1,e_2) ),
    inference(spm,[status(thm)],[c_0_26,c_0_12]) ).

cnf(c_0_30,negated_conjecture,
    ~ product(e_1,e_2,e_2),
    inference(spm,[status(thm)],[c_0_20,c_0_27]) ).

cnf(c_0_31,negated_conjecture,
    ( product(e_1,e_1,X1)
    | ~ product(e_1,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_11,c_0_28]) ).

cnf(c_0_32,negated_conjecture,
    product(e_1,e_1,e_2),
    inference(sr,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_33,plain,
    ( equalish(X1,e_2)
    | ~ product(X1,e_1,e_1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_28]) ).

cnf(c_0_34,negated_conjecture,
    product(e_1,e_1,e_1),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_35,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_33]),c_0_34])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : GRP135-1.002 : TPTP v8.1.2. Released v1.2.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n009.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon Aug 28 22:53:20 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.59/0.61  start to proof: theBenchmark
% 0.59/0.62  % Version  : CSE_E---1.5
% 0.59/0.62  % Problem  : theBenchmark.p
% 0.59/0.62  % Proof found
% 0.59/0.62  % SZS status Theorem for theBenchmark.p
% 0.59/0.62  % SZS output start Proof
% See solution above
% 0.59/0.63  % Total time : 0.004000 s
% 0.59/0.63  % SZS output end Proof
% 0.59/0.63  % Total time : 0.007000 s
%------------------------------------------------------------------------------