%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP123-9.003 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n017.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 00:16:12 EDT 2023

% Result   : Unsatisfiable 0.19s 0.60s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   54 (  24 unt;   8 typ;   0 def)
%            Number of atoms       :   93 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   92 (  45   ~;  47   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   5   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   62 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    group_element: $i > $o ).

tff(decl_23,type,
    e_1: $i ).

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

tff(decl_25,type,
    e_2: $i ).

tff(decl_26,type,
    e_3: $i ).

tff(decl_27,type,
    equalish: ( $i * $i ) > $o ).

tff(decl_28,type,
    product1: ( $i * $i * $i ) > $o ).

tff(decl_29,type,
    product2: ( $i * $i * $i ) > $o ).

cnf(product1_right_cancellation,axiom,
    ( equalish(X2,X4)
    | ~ product1(X1,X2,X3)
    | ~ product1(X1,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_right_cancellation) ).

cnf(product1_idempotence,axiom,
    product1(X1,X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_idempotence) ).

cnf(product1_left_cancellation,axiom,
    ( equalish(X1,X4)
    | ~ product1(X1,X2,X3)
    | ~ product1(X4,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_left_cancellation) ).

cnf(product1_total_function1,axiom,
    ( product1(X1,X2,e_1)
    | product1(X1,X2,e_2)
    | product1(X1,X2,e_3)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_total_function1) ).

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

cnf(element_3,axiom,
    group_element(e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).

cnf(e_1_is_not_e_3,axiom,
    ~ equalish(e_1,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).

cnf(e_3_is_not_e_1,axiom,
    ~ equalish(e_3,e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).

cnf(product1_total_function2,axiom,
    ( equalish(X3,X4)
    | ~ product1(X1,X2,X3)
    | ~ product1(X1,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_total_function2) ).

cnf(product2_total_function2,axiom,
    ( equalish(X3,X4)
    | ~ product2(X1,X2,X3)
    | ~ product2(X1,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_total_function2) ).

cnf(product2_idempotence,axiom,
    product2(X1,X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_idempotence) ).

cnf(qg1a,negated_conjecture,
    ( product2(X4,X1,X2)
    | ~ product1(X1,X2,X3)
    | ~ product1(X3,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1a) ).

cnf(e_3_is_not_e_2,axiom,
    ~ equalish(e_3,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).

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

cnf(e_2_is_not_e_3,axiom,
    ~ equalish(e_2,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).

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(c_0_16,axiom,
    ( equalish(X2,X4)
    | ~ product1(X1,X2,X3)
    | ~ product1(X1,X4,X3) ),
    product1_right_cancellation ).

cnf(c_0_17,axiom,
    product1(X1,X1,X1),
    product1_idempotence ).

cnf(c_0_18,axiom,
    ( equalish(X1,X4)
    | ~ product1(X1,X2,X3)
    | ~ product1(X4,X2,X3) ),
    product1_left_cancellation ).

cnf(c_0_19,plain,
    ( equalish(X1,X2)
    | ~ product1(X2,X1,X2) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,axiom,
    ( product1(X1,X2,e_1)
    | product1(X1,X2,e_2)
    | product1(X1,X2,e_3)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    product1_total_function1 ).

cnf(c_0_21,axiom,
    group_element(e_1),
    element_1 ).

cnf(c_0_22,plain,
    ( equalish(X1,X2)
    | ~ product1(X1,X2,X2) ),
    inference(spm,[status(thm)],[c_0_18,c_0_17]) ).

cnf(c_0_23,plain,
    ( product1(e_1,X1,e_3)
    | product1(e_1,X1,e_2)
    | equalish(X1,e_1)
    | ~ group_element(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).

cnf(c_0_24,axiom,
    group_element(e_3),
    element_3 ).

cnf(c_0_25,axiom,
    ~ equalish(e_1,e_3),
    e_1_is_not_e_3 ).

cnf(c_0_26,axiom,
    ~ equalish(e_3,e_1),
    e_3_is_not_e_1 ).

cnf(c_0_27,axiom,
    ( equalish(X3,X4)
    | ~ product1(X1,X2,X3)
    | ~ product1(X1,X2,X4) ),
    product1_total_function2 ).

cnf(c_0_28,axiom,
    ( equalish(X3,X4)
    | ~ product2(X1,X2,X3)
    | ~ product2(X1,X2,X4) ),
    product2_total_function2 ).

cnf(c_0_29,axiom,
    product2(X1,X1,X1),
    product2_idempotence ).

cnf(c_0_30,negated_conjecture,
    ( product2(X4,X1,X2)
    | ~ product1(X1,X2,X3)
    | ~ product1(X3,X2,X4) ),
    qg1a ).

cnf(c_0_31,plain,
    product1(e_1,e_3,e_2),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]),c_0_25]),c_0_26]) ).

cnf(c_0_32,plain,
    ( equalish(X1,X2)
    | ~ product1(X2,X2,X1) ),
    inference(spm,[status(thm)],[c_0_27,c_0_17]) ).

cnf(c_0_33,plain,
    ( equalish(X1,X2)
    | ~ product2(X2,X2,X1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_34,negated_conjecture,
    ( product2(e_2,X1,e_3)
    | ~ product1(X1,e_3,e_1) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_35,axiom,
    ~ equalish(e_3,e_2),
    e_3_is_not_e_2 ).

cnf(c_0_36,plain,
    ( product1(X1,X1,e_3)
    | product1(X1,X1,e_2)
    | equalish(e_1,X1)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_20]) ).

cnf(c_0_37,negated_conjecture,
    ~ product1(e_2,e_3,e_1),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).

cnf(c_0_38,axiom,
    group_element(e_2),
    element_2 ).

cnf(c_0_39,plain,
    ( product1(X1,X1,e_2)
    | equalish(e_1,X1)
    | equalish(e_3,X1)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_36]) ).

cnf(c_0_40,negated_conjecture,
    ( product1(e_2,e_3,e_3)
    | product1(e_2,e_3,e_2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_20]),c_0_24]),c_0_38])]) ).

cnf(c_0_41,axiom,
    ~ equalish(e_2,e_3),
    e_2_is_not_e_3 ).

cnf(c_0_42,plain,
    ( equalish(e_3,X1)
    | equalish(e_1,X1)
    | equalish(X2,X1)
    | ~ product1(X1,X2,e_2)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_39]) ).

cnf(c_0_43,negated_conjecture,
    product1(e_2,e_3,e_2),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_40]),c_0_41]) ).

cnf(c_0_44,axiom,
    ~ equalish(e_1,e_2),
    e_1_is_not_e_2 ).

cnf(c_0_45,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_38])]),c_0_35]),c_0_44]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GRP123-9.003 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n017.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Aug 28 19:28:12 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.59  start to proof: theBenchmark
% 0.19/0.60  % Version  : CSE_E---1.5
% 0.19/0.60  % Problem  : theBenchmark.p
% 0.19/0.60  % Proof found
% 0.19/0.60  % SZS status Theorem for theBenchmark.p
% 0.19/0.60  % SZS output start Proof
% See solution above
% 0.19/0.61  % Total time : 0.008000 s
% 0.19/0.61  % SZS output end Proof
% 0.19/0.61  % Total time : 0.011000 s
%------------------------------------------------------------------------------