TSTP Solution File: GRP127-4.004 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP127-4.004 : 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 : n007.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 00:16:34 EDT 2023

% Result   : Unsatisfiable 0.53s 0.64s
% Output   : CNFRefutation 0.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   35
%            Number of leaves      :   30
% Syntax   : Number of formulae    :  154 (  43 unt;   7 typ;   0 def)
%            Number of atoms       :  355 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  362 ( 154   ~; 208   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   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    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :  102 (   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,
    e_4: $i ).

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

cnf(product_total_function1,axiom,
    ( product(X1,X2,e_1)
    | product(X1,X2,e_2)
    | product(X1,X2,e_3)
    | product(X1,X2,e_4)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).

cnf(element_4,axiom,
    group_element(e_4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).

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(product_idempotence,axiom,
    product(X1,X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).

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

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(e_4_is_not_e_1,axiom,
    ~ equalish(e_4,e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_1) ).

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

cnf(e_1_is_not_e_4,axiom,
    ~ equalish(e_1,e_4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_4) ).

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(e_2_is_not_e_1,axiom,
    ~ equalish(e_2,e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).

cnf(e_3_is_not_e_4,axiom,
    ~ equalish(e_3,e_4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).

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

cnf(e_4_is_not_e_3,axiom,
    ~ equalish(e_4,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).

cnf(row_surjectivity,axiom,
    ( product(e_1,X1,X2)
    | product(e_2,X1,X2)
    | product(e_3,X1,X2)
    | product(e_4,X1,X2)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',row_surjectivity) ).

cnf(column_surjectivity,axiom,
    ( product(X1,e_1,X2)
    | product(X1,e_2,X2)
    | product(X1,e_3,X2)
    | product(X1,e_4,X2)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',column_surjectivity) ).

cnf(product_total_function2,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).

cnf(e_2_is_not_e_4,axiom,
    ~ equalish(e_2,e_4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_4) ).

cnf(e_4_is_not_e_2,axiom,
    ~ equalish(e_4,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_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(qg3_1,negated_conjecture,
    ( product(X1,X2,X3)
    | ~ product(X4,X1,X2)
    | ~ product(X3,X1,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_1) ).

cnf(qg3_2,negated_conjecture,
    ( product(X1,X2,X3)
    | ~ product(X3,X2,X4)
    | ~ product(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_2) ).

cnf(c_0_23,axiom,
    ( product(X1,X2,e_1)
    | product(X1,X2,e_2)
    | product(X1,X2,e_3)
    | product(X1,X2,e_4)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    product_total_function1 ).

cnf(c_0_24,axiom,
    group_element(e_4),
    element_4 ).

cnf(c_0_25,axiom,
    ( equalish(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X3) ),
    product_right_cancellation ).

cnf(c_0_26,axiom,
    product(X1,X1,X1),
    product_idempotence ).

cnf(c_0_27,plain,
    ( product(X1,e_4,e_4)
    | product(X1,e_4,e_3)
    | product(X1,e_4,e_2)
    | product(X1,e_4,e_1)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_28,axiom,
    group_element(e_1),
    element_1 ).

cnf(c_0_29,axiom,
    ( equalish(X1,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X3) ),
    product_left_cancellation ).

cnf(c_0_30,plain,
    ( equalish(X1,X2)
    | ~ product(X2,X1,X2) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_31,plain,
    ( product(e_1,e_4,e_1)
    | product(e_1,e_4,e_2)
    | product(e_1,e_4,e_3)
    | product(e_1,e_4,e_4) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_32,axiom,
    ~ equalish(e_4,e_1),
    e_4_is_not_e_1 ).

cnf(c_0_33,axiom,
    group_element(e_3),
    element_3 ).

cnf(c_0_34,plain,
    ( equalish(X1,X2)
    | ~ product(X1,X2,X2) ),
    inference(spm,[status(thm)],[c_0_29,c_0_26]) ).

cnf(c_0_35,plain,
    ( product(e_1,e_4,e_4)
    | product(e_1,e_4,e_3)
    | product(e_1,e_4,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).

cnf(c_0_36,axiom,
    ~ equalish(e_1,e_4),
    e_1_is_not_e_4 ).

cnf(c_0_37,plain,
    ( product(X1,e_3,e_4)
    | product(X1,e_3,e_3)
    | product(X1,e_3,e_2)
    | product(X1,e_3,e_1)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_33]) ).

cnf(c_0_38,plain,
    ( product(e_1,e_4,e_2)
    | product(e_1,e_4,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).

cnf(c_0_39,plain,
    ( product(e_1,e_3,e_1)
    | product(e_1,e_3,e_2)
    | product(e_1,e_3,e_3)
    | product(e_1,e_3,e_4) ),
    inference(spm,[status(thm)],[c_0_37,c_0_28]) ).

cnf(c_0_40,axiom,
    ~ equalish(e_3,e_1),
    e_3_is_not_e_1 ).

cnf(c_0_41,plain,
    ( equalish(X1,e_1)
    | product(e_1,e_4,e_2)
    | ~ product(X1,e_4,e_3) ),
    inference(spm,[status(thm)],[c_0_29,c_0_38]) ).

cnf(c_0_42,plain,
    ( product(e_1,e_3,e_4)
    | product(e_1,e_3,e_3)
    | product(e_1,e_3,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_39]),c_0_40]) ).

cnf(c_0_43,plain,
    ( product(e_1,e_4,e_2)
    | ~ product(e_4,e_4,e_3) ),
    inference(spm,[status(thm)],[c_0_32,c_0_41]) ).

cnf(c_0_44,plain,
    ( equalish(X1,e_1)
    | product(e_1,e_3,e_2)
    | product(e_1,e_3,e_3)
    | ~ product(X1,e_3,e_4) ),
    inference(spm,[status(thm)],[c_0_29,c_0_42]) ).

cnf(c_0_45,axiom,
    ~ equalish(e_2,e_1),
    e_2_is_not_e_1 ).

cnf(c_0_46,axiom,
    ~ equalish(e_3,e_4),
    e_3_is_not_e_4 ).

cnf(c_0_47,plain,
    ( equalish(X1,e_4)
    | ~ product(e_4,e_4,e_3)
    | ~ product(e_1,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_25,c_0_43]) ).

cnf(c_0_48,plain,
    ( product(e_1,e_3,e_3)
    | product(e_1,e_3,e_2)
    | ~ product(e_4,e_3,e_4) ),
    inference(spm,[status(thm)],[c_0_32,c_0_44]) ).

cnf(c_0_49,axiom,
    ~ equalish(e_1,e_3),
    e_1_is_not_e_3 ).

cnf(c_0_50,negated_conjecture,
    ( product(X4,X1,X2)
    | ~ product(X1,X2,X3)
    | ~ product(X3,X1,X4) ),
    qg3 ).

cnf(c_0_51,plain,
    ( product(e_1,e_4,e_2)
    | ~ product(e_3,e_4,e_3) ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_52,plain,
    ( product(e_1,e_3,e_3)
    | product(e_1,e_3,e_2)
    | ~ product(e_2,e_3,e_4) ),
    inference(spm,[status(thm)],[c_0_45,c_0_44]) ).

cnf(c_0_53,plain,
    ( ~ product(e_4,e_4,e_3)
    | ~ product(e_1,e_3,e_2) ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_54,plain,
    ( product(e_1,e_3,e_2)
    | ~ product(e_4,e_3,e_4) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_48]),c_0_49]) ).

cnf(c_0_55,negated_conjecture,
    ( product(X1,X1,X2)
    | ~ product(X1,X2,X1) ),
    inference(spm,[status(thm)],[c_0_50,c_0_26]) ).

cnf(c_0_56,plain,
    ( equalish(X1,e_4)
    | ~ product(e_3,e_4,e_3)
    | ~ product(e_1,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_25,c_0_51]) ).

cnf(c_0_57,plain,
    ( product(e_1,e_3,e_3)
    | product(e_1,e_3,e_2)
    | ~ product(e_3,e_3,e_4) ),
    inference(spm,[status(thm)],[c_0_40,c_0_44]) ).

cnf(c_0_58,plain,
    ( product(e_1,e_3,e_2)
    | ~ product(e_2,e_3,e_4) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_52]),c_0_49]) ).

cnf(c_0_59,plain,
    ( product(e_4,e_3,e_1)
    | product(e_4,e_3,e_2)
    | product(e_4,e_3,e_3)
    | product(e_4,e_3,e_4) ),
    inference(spm,[status(thm)],[c_0_37,c_0_24]) ).

cnf(c_0_60,plain,
    ~ product(e_4,e_3,e_4),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).

cnf(c_0_61,plain,
    ( ~ product(e_3,e_4,e_3)
    | ~ product(e_1,e_3,e_2) ),
    inference(spm,[status(thm)],[c_0_46,c_0_56]) ).

cnf(c_0_62,plain,
    ( product(e_1,e_3,e_2)
    | ~ product(e_3,e_3,e_4) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_57]),c_0_49]) ).

cnf(c_0_63,axiom,
    ~ equalish(e_4,e_3),
    e_4_is_not_e_3 ).

cnf(c_0_64,plain,
    ( equalish(X1,e_3)
    | ~ product(e_2,e_3,e_4)
    | ~ product(e_1,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_25,c_0_58]) ).

cnf(c_0_65,negated_conjecture,
    ( product(e_1,e_4,e_2)
    | product(e_3,e_4,X1)
    | ~ product(e_4,X1,e_1) ),
    inference(spm,[status(thm)],[c_0_50,c_0_38]) ).

cnf(c_0_66,plain,
    ( product(e_4,e_3,e_3)
    | product(e_4,e_3,e_2)
    | product(e_4,e_3,e_1) ),
    inference(sr,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_67,plain,
    ~ product(e_3,e_4,e_3),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_55]) ).

cnf(c_0_68,plain,
    ( equalish(X1,e_1)
    | ~ product(e_2,e_3,e_4)
    | ~ product(X1,e_3,e_2) ),
    inference(spm,[status(thm)],[c_0_29,c_0_58]) ).

cnf(c_0_69,plain,
    ( ~ product(e_2,e_3,e_4)
    | ~ product(e_1,e_4,e_2) ),
    inference(spm,[status(thm)],[c_0_63,c_0_64]) ).

cnf(c_0_70,negated_conjecture,
    ( product(e_4,e_3,e_2)
    | product(e_4,e_3,e_3)
    | product(e_1,e_4,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]) ).

cnf(c_0_71,plain,
    ( ~ product(e_2,e_3,e_4)
    | ~ product(e_4,e_3,e_2) ),
    inference(spm,[status(thm)],[c_0_32,c_0_68]) ).

cnf(c_0_72,axiom,
    ( product(e_1,X1,X2)
    | product(e_2,X1,X2)
    | product(e_3,X1,X2)
    | product(e_4,X1,X2)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    row_surjectivity ).

cnf(c_0_73,negated_conjecture,
    ( product(e_4,e_3,e_3)
    | ~ product(e_2,e_3,e_4) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).

cnf(c_0_74,plain,
    ( product(e_4,X1,e_4)
    | product(e_3,X1,e_4)
    | product(e_2,X1,e_4)
    | product(e_1,X1,e_4)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_72,c_0_24]) ).

cnf(c_0_75,negated_conjecture,
    ~ product(e_2,e_3,e_4),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_73]),c_0_63]) ).

cnf(c_0_76,plain,
    ( equalish(X1,e_3)
    | ~ product(e_3,e_3,e_4)
    | ~ product(e_1,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_25,c_0_62]) ).

cnf(c_0_77,plain,
    ( equalish(X1,e_4)
    | product(e_1,e_4,e_2)
    | ~ product(e_1,X1,e_3) ),
    inference(spm,[status(thm)],[c_0_25,c_0_38]) ).

cnf(c_0_78,axiom,
    ( product(X1,e_1,X2)
    | product(X1,e_2,X2)
    | product(X1,e_3,X2)
    | product(X1,e_4,X2)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    column_surjectivity ).

cnf(c_0_79,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    product_total_function2 ).

cnf(c_0_80,plain,
    ( product(e_1,e_3,e_4)
    | product(e_3,e_3,e_4) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_33]),c_0_60]),c_0_75]) ).

cnf(c_0_81,plain,
    ( ~ product(e_3,e_3,e_4)
    | ~ product(e_1,e_4,e_2) ),
    inference(spm,[status(thm)],[c_0_63,c_0_76]) ).

cnf(c_0_82,plain,
    ( product(e_1,e_4,e_2)
    | ~ product(e_1,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_46,c_0_77]) ).

cnf(c_0_83,plain,
    ( product(X1,e_4,e_3)
    | product(X1,e_3,e_3)
    | product(X1,e_2,e_3)
    | product(X1,e_1,e_3)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_78,c_0_33]) ).

cnf(c_0_84,plain,
    ( equalish(X1,e_4)
    | product(e_3,e_3,e_4)
    | ~ product(e_1,e_3,X1) ),
    inference(spm,[status(thm)],[c_0_79,c_0_80]) ).

cnf(c_0_85,plain,
    ( ~ product(e_3,e_3,e_4)
    | ~ product(e_1,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_81,c_0_82]) ).

cnf(c_0_86,plain,
    ( product(e_1,e_1,e_3)
    | product(e_1,e_2,e_3)
    | product(e_1,e_3,e_3)
    | product(e_1,e_4,e_3) ),
    inference(spm,[status(thm)],[c_0_83,c_0_28]) ).

cnf(c_0_87,plain,
    ~ product(e_1,e_3,e_3),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_84]),c_0_85]) ).

cnf(c_0_88,axiom,
    ~ equalish(e_2,e_4),
    e_2_is_not_e_4 ).

cnf(c_0_89,plain,
    ( product(X1,e_1,e_4)
    | product(X1,e_1,e_3)
    | product(X1,e_1,e_2)
    | product(X1,e_1,e_1)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_28]) ).

cnf(c_0_90,plain,
    ( equalish(X1,X2)
    | ~ product(X2,X2,X1) ),
    inference(spm,[status(thm)],[c_0_79,c_0_26]) ).

cnf(c_0_91,plain,
    ( product(e_1,e_4,e_3)
    | product(e_1,e_2,e_3)
    | product(e_1,e_1,e_3) ),
    inference(sr,[status(thm)],[c_0_86,c_0_87]) ).

cnf(c_0_92,plain,
    ( product(e_1,e_4,e_2)
    | ~ product(e_1,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_88,c_0_77]) ).

cnf(c_0_93,plain,
    ( product(e_4,e_1,e_1)
    | product(e_4,e_1,e_2)
    | product(e_4,e_1,e_3)
    | product(e_4,e_1,e_4) ),
    inference(spm,[status(thm)],[c_0_89,c_0_24]) ).

cnf(c_0_94,plain,
    ( product(e_1,e_2,e_3)
    | product(e_1,e_4,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_40]) ).

cnf(c_0_95,axiom,
    ~ equalish(e_4,e_2),
    e_4_is_not_e_2 ).

cnf(c_0_96,plain,
    ( equalish(X1,e_2)
    | ~ product(e_1,e_2,e_3)
    | ~ product(e_1,e_4,X1) ),
    inference(spm,[status(thm)],[c_0_79,c_0_92]) ).

cnf(c_0_97,plain,
    ( product(e_4,e_1,e_4)
    | product(e_4,e_1,e_3)
    | product(e_4,e_1,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_93]),c_0_32]) ).

cnf(c_0_98,plain,
    ( product(X1,e_4,e_4)
    | product(X1,e_3,e_4)
    | product(X1,e_2,e_4)
    | product(X1,e_1,e_4)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_78,c_0_24]) ).

cnf(c_0_99,plain,
    ( equalish(X1,e_3)
    | product(e_1,e_2,e_3)
    | ~ product(e_1,e_4,X1) ),
    inference(spm,[status(thm)],[c_0_79,c_0_94]) ).

cnf(c_0_100,plain,
    ( ~ product(e_1,e_2,e_3)
    | ~ product(e_1,e_4,e_4) ),
    inference(spm,[status(thm)],[c_0_95,c_0_96]) ).

cnf(c_0_101,plain,
    ( product(e_4,e_1,e_2)
    | product(e_4,e_1,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_97]),c_0_36]) ).

cnf(c_0_102,plain,
    ( product(e_1,e_1,e_4)
    | product(e_1,e_2,e_4)
    | product(e_1,e_3,e_4)
    | product(e_1,e_4,e_4) ),
    inference(spm,[status(thm)],[c_0_98,c_0_28]) ).

cnf(c_0_103,plain,
    ~ product(e_1,e_4,e_4),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_99]),c_0_100]) ).

cnf(c_0_104,plain,
    ( equalish(X1,e_1)
    | product(e_4,e_1,e_2)
    | ~ product(e_4,X1,e_3) ),
    inference(spm,[status(thm)],[c_0_25,c_0_101]) ).

cnf(c_0_105,axiom,
    ~ equalish(e_2,e_3),
    e_2_is_not_e_3 ).

cnf(c_0_106,plain,
    ( equalish(X1,e_3)
    | product(e_1,e_3,e_2)
    | product(e_1,e_3,e_3)
    | ~ product(e_1,X1,e_4) ),
    inference(spm,[status(thm)],[c_0_25,c_0_42]) ).

cnf(c_0_107,plain,
    ( equalish(X1,e_2)
    | ~ product(e_3,e_3,e_4)
    | ~ product(e_1,e_3,X1) ),
    inference(spm,[status(thm)],[c_0_79,c_0_62]) ).

cnf(c_0_108,plain,
    ( product(e_1,e_3,e_4)
    | product(e_1,e_2,e_4)
    | product(e_1,e_1,e_4) ),
    inference(sr,[status(thm)],[c_0_102,c_0_103]) ).

cnf(c_0_109,plain,
    ( product(e_4,e_1,e_2)
    | ~ product(e_4,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_40,c_0_104]) ).

cnf(c_0_110,plain,
    ( product(e_1,e_3,e_3)
    | product(e_1,e_3,e_2)
    | ~ product(e_1,e_2,e_4) ),
    inference(spm,[status(thm)],[c_0_105,c_0_106]) ).

cnf(c_0_111,plain,
    ( ~ product(e_3,e_3,e_4)
    | ~ product(e_1,e_3,e_4) ),
    inference(spm,[status(thm)],[c_0_95,c_0_107]) ).

cnf(c_0_112,plain,
    ( product(e_1,e_2,e_4)
    | product(e_1,e_3,e_4) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_108]),c_0_32]) ).

cnf(c_0_113,negated_conjecture,
    ( product(X1,X2,X3)
    | ~ product(X4,X1,X2)
    | ~ product(X3,X1,X4) ),
    qg3_1 ).

cnf(c_0_114,plain,
    ( equalish(X1,e_4)
    | ~ product(e_4,e_3,e_3)
    | ~ product(X1,e_1,e_2) ),
    inference(spm,[status(thm)],[c_0_29,c_0_109]) ).

cnf(c_0_115,plain,
    ( product(e_1,e_3,e_2)
    | ~ product(e_1,e_2,e_4) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_110]),c_0_49]) ).

cnf(c_0_116,negated_conjecture,
    ( product(e_2,e_1,X1)
    | ~ product(e_4,e_3,e_3)
    | ~ product(e_1,X1,e_4) ),
    inference(spm,[status(thm)],[c_0_50,c_0_109]) ).

cnf(c_0_117,plain,
    ( product(e_1,e_2,e_4)
    | ~ product(e_3,e_3,e_4) ),
    inference(spm,[status(thm)],[c_0_111,c_0_112]) ).

cnf(c_0_118,negated_conjecture,
    ( product(X1,X1,X2)
    | ~ product(X2,X1,X1) ),
    inference(spm,[status(thm)],[c_0_113,c_0_26]) ).

cnf(c_0_119,plain,
    ( ~ product(e_4,e_3,e_3)
    | ~ product(e_2,e_1,e_2) ),
    inference(spm,[status(thm)],[c_0_88,c_0_114]) ).

cnf(c_0_120,plain,
    ( equalish(X1,e_3)
    | ~ product(e_1,e_2,e_4)
    | ~ product(e_1,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_25,c_0_115]) ).

cnf(c_0_121,negated_conjecture,
    ~ product(e_4,e_3,e_3),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118]),c_0_119]) ).

cnf(c_0_122,plain,
    ( equalish(X1,e_1)
    | ~ product(e_1,e_2,e_4)
    | ~ product(X1,e_3,e_2) ),
    inference(spm,[status(thm)],[c_0_29,c_0_115]) ).

cnf(c_0_123,plain,
    ( ~ product(e_1,e_2,e_4)
    | ~ product(e_1,e_4,e_2) ),
    inference(spm,[status(thm)],[c_0_63,c_0_120]) ).

cnf(c_0_124,negated_conjecture,
    ( product(e_1,e_4,e_2)
    | product(e_4,e_3,e_2) ),
    inference(sr,[status(thm)],[c_0_70,c_0_121]) ).

cnf(c_0_125,plain,
    ( ~ product(e_1,e_2,e_4)
    | ~ product(e_4,e_3,e_2) ),
    inference(spm,[status(thm)],[c_0_32,c_0_122]) ).

cnf(c_0_126,negated_conjecture,
    ( product(X1,X2,X3)
    | ~ product(X3,X2,X4)
    | ~ product(X2,X4,X1) ),
    qg3_2 ).

cnf(c_0_127,negated_conjecture,
    ~ product(e_1,e_2,e_4),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_125]) ).

cnf(c_0_128,plain,
    ( equalish(X1,e_3)
    | product(e_4,e_1,e_2)
    | ~ product(e_4,e_1,X1) ),
    inference(spm,[status(thm)],[c_0_79,c_0_101]) ).

cnf(c_0_129,negated_conjecture,
    ( product(e_4,e_1,e_2)
    | product(X1,e_1,e_4)
    | ~ product(e_1,e_3,X1) ),
    inference(spm,[status(thm)],[c_0_126,c_0_101]) ).

cnf(c_0_130,plain,
    product(e_1,e_3,e_4),
    inference(sr,[status(thm)],[c_0_112,c_0_127]) ).

cnf(c_0_131,plain,
    ( product(e_4,e_1,e_2)
    | ~ product(e_4,e_1,e_4) ),
    inference(spm,[status(thm)],[c_0_63,c_0_128]) ).

cnf(c_0_132,negated_conjecture,
    product(e_4,e_1,e_2),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_131]) ).

cnf(c_0_133,plain,
    ( product(e_1,e_2,e_3)
    | ~ product(e_1,e_4,e_2) ),
    inference(spm,[status(thm)],[c_0_105,c_0_99]) ).

cnf(c_0_134,negated_conjecture,
    ( equalish(X1,e_1)
    | ~ product(e_4,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_25,c_0_132]) ).

cnf(c_0_135,plain,
    ( equalish(X1,e_1)
    | ~ product(e_1,e_2,e_3)
    | ~ product(X1,e_4,e_2) ),
    inference(spm,[status(thm)],[c_0_29,c_0_92]) ).

cnf(c_0_136,negated_conjecture,
    ( product(e_4,e_3,e_2)
    | product(e_1,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_133,c_0_124]) ).

cnf(c_0_137,negated_conjecture,
    ~ product(e_4,e_3,e_2),
    inference(spm,[status(thm)],[c_0_40,c_0_134]) ).

cnf(c_0_138,plain,
    ( product(e_3,e_4,e_1)
    | product(e_3,e_4,e_2)
    | product(e_3,e_4,e_3)
    | product(e_3,e_4,e_4) ),
    inference(spm,[status(thm)],[c_0_27,c_0_33]) ).

cnf(c_0_139,negated_conjecture,
    ( product(e_4,e_3,X1)
    | ~ product(e_3,X1,e_1) ),
    inference(spm,[status(thm)],[c_0_50,c_0_130]) ).

cnf(c_0_140,plain,
    ( ~ product(e_1,e_2,e_3)
    | ~ product(e_3,e_4,e_2) ),
    inference(spm,[status(thm)],[c_0_40,c_0_135]) ).

cnf(c_0_141,negated_conjecture,
    product(e_1,e_2,e_3),
    inference(sr,[status(thm)],[c_0_136,c_0_137]) ).

cnf(c_0_142,plain,
    ( product(e_3,e_4,e_4)
    | product(e_3,e_4,e_2)
    | product(e_3,e_4,e_1) ),
    inference(sr,[status(thm)],[c_0_138,c_0_67]) ).

cnf(c_0_143,negated_conjecture,
    ~ product(e_3,e_4,e_1),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_139]),c_0_46]) ).

cnf(c_0_144,plain,
    ~ product(e_3,e_4,e_2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_141])]) ).

cnf(c_0_145,plain,
    product(e_3,e_4,e_4),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_142,c_0_143]),c_0_144]) ).

cnf(c_0_146,plain,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_145]),c_0_46]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : GRP127-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.06/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n007.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   : Tue Aug 29 02:01:28 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.48/0.57  start to proof: theBenchmark
% 0.53/0.64  % Version  : CSE_E---1.5
% 0.53/0.64  % Problem  : theBenchmark.p
% 0.53/0.64  % Proof found
% 0.53/0.64  % SZS status Theorem for theBenchmark.p
% 0.53/0.64  % SZS output start Proof
% See solution above
% 0.53/0.64  % Total time : 0.063000 s
% 0.53/0.64  % SZS output end Proof
% 0.53/0.64  % Total time : 0.066000 s
%------------------------------------------------------------------------------