TSTP Solution File: GRP129-1.003 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP129-1.003 : 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 : n018.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 00:16:57 EDT 2023

% Result   : Unsatisfiable 0.20s 0.65s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   39
%            Number of leaves      :   20
% Syntax   : Number of formulae    :  126 (  29 unt;   6 typ;   0 def)
%            Number of atoms       :  300 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  324 ( 144   ~; 180   |;   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  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   68 (   1 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,
    e_3: $i ).

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

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

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

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

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

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(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_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(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(c_0_14,axiom,
    ( product(X1,X2,e_1)
    | product(X1,X2,e_2)
    | product(X1,X2,e_3)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    product_total_function1 ).

cnf(c_0_15,axiom,
    group_element(e_3),
    element_3 ).

cnf(c_0_16,plain,
    ( 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_14,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,plain,
    ( product(e_3,e_3,e_1)
    | product(e_3,e_3,e_2)
    | product(e_3,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_16,c_0_15]) ).

cnf(c_0_19,axiom,
    ~ equalish(e_2,e_3),
    e_2_is_not_e_3 ).

cnf(c_0_20,plain,
    ( product(e_3,e_3,e_3)
    | product(e_3,e_3,e_2)
    | equalish(X1,e_3)
    | ~ product(e_3,X1,e_1) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_21,axiom,
    ( equalish(X1,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X3) ),
    product_left_cancellation ).

cnf(c_0_22,plain,
    ( product(e_3,e_3,e_2)
    | product(e_3,e_3,e_3)
    | ~ product(e_3,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_23,plain,
    ( product(e_3,e_3,e_2)
    | equalish(X1,e_3)
    | ~ product(e_3,e_2,e_1)
    | ~ product(X1,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_24,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    product_total_function2 ).

cnf(c_0_25,plain,
    ( product(e_3,e_3,e_2)
    | ~ product(e_3,e_2,e_1)
    | ~ product(e_2,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_19,c_0_23]) ).

cnf(c_0_26,axiom,
    ~ equalish(e_1,e_2),
    e_1_is_not_e_2 ).

cnf(c_0_27,plain,
    ( equalish(X1,e_2)
    | ~ product(e_3,e_2,e_1)
    | ~ product(e_2,e_3,e_3)
    | ~ product(e_3,e_3,X1) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_28,negated_conjecture,
    ( product(X3,X1,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X3,X4) ),
    qg3 ).

cnf(c_0_29,axiom,
    group_element(e_2),
    element_2 ).

cnf(c_0_30,plain,
    ( ~ product(e_2,e_3,e_3)
    | ~ product(e_3,e_3,e_1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).

cnf(c_0_31,plain,
    ( product(X1,e_2,e_3)
    | product(X1,e_2,e_2)
    | product(X1,e_2,e_1)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_29]) ).

cnf(c_0_32,plain,
    ( product(e_3,e_3,e_3)
    | product(e_3,e_3,e_2)
    | ~ product(e_2,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_30,c_0_18]) ).

cnf(c_0_33,plain,
    ( product(e_3,e_2,e_1)
    | product(e_3,e_2,e_2)
    | product(e_3,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_31,c_0_15]) ).

cnf(c_0_34,plain,
    ( product(e_3,e_3,e_2)
    | equalish(X1,e_3)
    | ~ product(e_2,e_3,e_3)
    | ~ product(X1,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_21,c_0_32]) ).

cnf(c_0_35,plain,
    ( product(e_3,e_2,e_3)
    | product(e_3,e_2,e_2)
    | equalish(X1,e_3)
    | ~ product(X1,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_21,c_0_33]) ).

cnf(c_0_36,plain,
    ( product(e_3,e_3,e_2)
    | ~ product(e_2,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_19,c_0_34]) ).

cnf(c_0_37,plain,
    ( product(e_3,e_2,e_2)
    | product(e_3,e_2,e_3)
    | ~ product(e_2,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_35]) ).

cnf(c_0_38,plain,
    ( equalish(X1,e_3)
    | ~ product(e_2,e_3,e_3)
    | ~ product(e_3,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_17,c_0_36]) ).

cnf(c_0_39,plain,
    ( product(e_2,e_3,e_1)
    | product(e_2,e_3,e_2)
    | product(e_2,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_16,c_0_29]) ).

cnf(c_0_40,negated_conjecture,
    ( product(e_3,e_2,e_2)
    | ~ product(e_2,e_2,e_1)
    | ~ product(X1,e_3,e_2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_37]),c_0_28]) ).

cnf(c_0_41,plain,
    ( ~ product(e_2,e_3,e_3)
    | ~ product(e_3,e_2,e_2) ),
    inference(spm,[status(thm)],[c_0_19,c_0_38]) ).

cnf(c_0_42,plain,
    ( product(e_2,e_3,e_3)
    | product(e_2,e_3,e_2)
    | equalish(X1,e_3)
    | ~ product(e_2,X1,e_1) ),
    inference(spm,[status(thm)],[c_0_17,c_0_39]) ).

cnf(c_0_43,negated_conjecture,
    ( ~ product(e_2,e_2,e_1)
    | ~ product(e_2,e_3,e_3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_36]),c_0_41]) ).

cnf(c_0_44,plain,
    ( product(e_2,e_3,e_2)
    | product(e_2,e_3,e_3)
    | ~ product(e_2,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_42]) ).

cnf(c_0_45,axiom,
    group_element(e_1),
    element_1 ).

cnf(c_0_46,negated_conjecture,
    ( product(e_2,e_3,e_2)
    | ~ product(e_2,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_47,plain,
    ( product(e_1,e_2,e_1)
    | product(e_1,e_2,e_2)
    | product(e_1,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_31,c_0_45]) ).

cnf(c_0_48,negated_conjecture,
    ( product(e_3,e_2,e_2)
    | ~ product(e_2,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_40,c_0_46]) ).

cnf(c_0_49,axiom,
    ~ equalish(e_2,e_1),
    e_2_is_not_e_1 ).

cnf(c_0_50,plain,
    ( product(e_1,e_2,e_3)
    | product(e_1,e_2,e_2)
    | equalish(X1,e_1)
    | ~ product(X1,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_21,c_0_47]) ).

cnf(c_0_51,axiom,
    ~ equalish(e_1,e_3),
    e_1_is_not_e_3 ).

cnf(c_0_52,negated_conjecture,
    ( equalish(X1,e_3)
    | ~ product(e_2,e_2,e_1)
    | ~ product(X1,e_2,e_2) ),
    inference(spm,[status(thm)],[c_0_21,c_0_48]) ).

cnf(c_0_53,negated_conjecture,
    ( equalish(X1,e_2)
    | ~ product(e_2,e_2,e_1)
    | ~ product(e_3,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_17,c_0_48]) ).

cnf(c_0_54,negated_conjecture,
    ( product(e_3,X1,e_2)
    | ~ product(e_2,e_2,e_1)
    | ~ product(X1,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_28,c_0_46]) ).

cnf(c_0_55,plain,
    ( product(e_1,e_2,e_2)
    | product(e_1,e_2,e_3)
    | ~ product(e_2,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_56,negated_conjecture,
    ( ~ product(e_2,e_2,e_1)
    | ~ product(e_1,e_2,e_2) ),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_57,negated_conjecture,
    ( ~ product(e_2,e_2,e_1)
    | ~ product(e_3,e_1,e_2) ),
    inference(spm,[status(thm)],[c_0_26,c_0_53]) ).

cnf(c_0_58,plain,
    ( product(e_2,e_2,e_1)
    | product(e_2,e_2,e_2)
    | product(e_2,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_31,c_0_29]) ).

cnf(c_0_59,negated_conjecture,
    ~ product(e_2,e_2,e_1),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_57]) ).

cnf(c_0_60,plain,
    ( product(e_2,e_2,e_3)
    | product(e_2,e_2,e_2) ),
    inference(sr,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_61,plain,
    ( product(e_2,e_2,e_2)
    | equalish(X1,e_2)
    | ~ product(X1,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_21,c_0_60]) ).

cnf(c_0_62,axiom,
    ~ equalish(e_3,e_1),
    e_3_is_not_e_1 ).

cnf(c_0_63,plain,
    ( product(e_2,e_2,e_2)
    | ~ product(e_1,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_26,c_0_61]) ).

cnf(c_0_64,plain,
    ( product(e_1,e_2,e_2)
    | product(e_1,e_2,e_3)
    | ~ product(e_3,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_62,c_0_50]) ).

cnf(c_0_65,plain,
    ( product(e_2,e_2,e_2)
    | equalish(X1,e_2)
    | ~ product(e_2,X1,e_3) ),
    inference(spm,[status(thm)],[c_0_17,c_0_60]) ).

cnf(c_0_66,negated_conjecture,
    ( product(e_2,e_2,e_2)
    | product(e_2,X1,e_3)
    | ~ product(X1,e_2,e_2) ),
    inference(spm,[status(thm)],[c_0_28,c_0_60]) ).

cnf(c_0_67,plain,
    ( product(e_1,e_2,e_2)
    | product(e_2,e_2,e_2)
    | ~ product(e_3,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_63,c_0_64]) ).

cnf(c_0_68,plain,
    ( product(e_2,e_2,e_2)
    | ~ product(e_2,e_1,e_3) ),
    inference(spm,[status(thm)],[c_0_26,c_0_65]) ).

cnf(c_0_69,axiom,
    ~ equalish(e_3,e_2),
    e_3_is_not_e_2 ).

cnf(c_0_70,plain,
    ( product(e_1,e_3,e_1)
    | product(e_1,e_3,e_2)
    | product(e_1,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_16,c_0_45]) ).

cnf(c_0_71,negated_conjecture,
    ( product(e_2,e_2,e_2)
    | ~ product(e_3,e_2,e_1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).

cnf(c_0_72,plain,
    ( product(e_2,e_2,e_2)
    | ~ product(e_3,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_69,c_0_61]) ).

cnf(c_0_73,plain,
    ( product(e_1,e_3,e_3)
    | product(e_1,e_3,e_2)
    | equalish(X1,e_1)
    | ~ product(X1,e_3,e_1) ),
    inference(spm,[status(thm)],[c_0_21,c_0_70]) ).

cnf(c_0_74,negated_conjecture,
    ( product(e_3,e_2,e_2)
    | product(e_2,e_2,e_2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_33]),c_0_72]) ).

cnf(c_0_75,plain,
    ( product(e_2,e_2,e_2)
    | ~ product(e_2,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_69,c_0_65]) ).

cnf(c_0_76,plain,
    ( product(e_1,e_3,e_2)
    | product(e_1,e_3,e_3)
    | ~ product(e_2,e_3,e_1) ),
    inference(spm,[status(thm)],[c_0_49,c_0_73]) ).

cnf(c_0_77,negated_conjecture,
    product(e_2,e_2,e_2),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_74]),c_0_75]) ).

cnf(c_0_78,plain,
    ( product(e_1,e_3,e_3)
    | product(e_1,e_3,e_2)
    | equalish(X1,e_3)
    | ~ product(e_1,X1,e_1) ),
    inference(spm,[status(thm)],[c_0_17,c_0_70]) ).

cnf(c_0_79,plain,
    ( product(e_1,e_3,e_2)
    | equalish(X1,e_3)
    | ~ product(e_2,e_3,e_1)
    | ~ product(e_1,X1,e_3) ),
    inference(spm,[status(thm)],[c_0_17,c_0_76]) ).

cnf(c_0_80,negated_conjecture,
    ( equalish(X1,e_2)
    | ~ product(X1,e_2,e_2) ),
    inference(spm,[status(thm)],[c_0_21,c_0_77]) ).

cnf(c_0_81,plain,
    ( product(e_1,e_3,e_2)
    | product(e_1,e_3,e_3)
    | ~ product(e_1,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_78]) ).

cnf(c_0_82,plain,
    ( equalish(X1,e_3)
    | ~ product(e_2,e_3,e_3)
    | ~ product(X1,e_3,e_2) ),
    inference(spm,[status(thm)],[c_0_21,c_0_36]) ).

cnf(c_0_83,plain,
    ( product(e_1,e_3,e_2)
    | ~ product(e_2,e_3,e_1)
    | ~ product(e_1,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_19,c_0_79]) ).

cnf(c_0_84,plain,
    ( product(e_1,e_2,e_2)
    | equalish(X1,e_3)
    | ~ product(e_3,e_2,e_1)
    | ~ product(e_1,e_2,X1) ),
    inference(spm,[status(thm)],[c_0_24,c_0_64]) ).

cnf(c_0_85,negated_conjecture,
    ~ product(e_1,e_2,e_2),
    inference(spm,[status(thm)],[c_0_26,c_0_80]) ).

cnf(c_0_86,plain,
    ( product(e_1,e_3,e_2)
    | equalish(X1,e_1)
    | ~ product(e_1,e_2,e_1)
    | ~ product(X1,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_21,c_0_81]) ).

cnf(c_0_87,plain,
    ( ~ product(e_2,e_3,e_3)
    | ~ product(e_1,e_3,e_2) ),
    inference(spm,[status(thm)],[c_0_51,c_0_82]) ).

cnf(c_0_88,plain,
    ( product(e_3,e_3,e_3)
    | product(e_3,e_3,e_2)
    | equalish(X1,e_3)
    | ~ product(X1,e_3,e_1) ),
    inference(spm,[status(thm)],[c_0_21,c_0_18]) ).

cnf(c_0_89,plain,
    ( equalish(X1,e_1)
    | ~ product(e_2,e_3,e_1)
    | ~ product(e_1,e_2,e_3)
    | ~ product(X1,e_3,e_2) ),
    inference(spm,[status(thm)],[c_0_21,c_0_83]) ).

cnf(c_0_90,plain,
    ( product(e_1,e_2,e_2)
    | ~ product(e_3,e_2,e_1)
    | ~ product(e_1,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_51,c_0_84]) ).

cnf(c_0_91,plain,
    ( product(e_1,e_2,e_3)
    | product(e_1,e_2,e_1) ),
    inference(sr,[status(thm)],[c_0_47,c_0_85]) ).

cnf(c_0_92,plain,
    ( ~ product(e_1,e_2,e_1)
    | ~ product(e_2,e_3,e_3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_86]),c_0_87]) ).

cnf(c_0_93,plain,
    ( product(e_3,e_3,e_2)
    | product(e_3,e_3,e_3)
    | ~ product(e_2,e_3,e_1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_88]) ).

cnf(c_0_94,plain,
    ( ~ product(e_2,e_3,e_1)
    | ~ product(e_1,e_2,e_3)
    | ~ product(e_3,e_3,e_2) ),
    inference(spm,[status(thm)],[c_0_62,c_0_89]) ).

cnf(c_0_95,plain,
    ( product(e_1,e_2,e_3)
    | ~ product(e_3,e_2,e_1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_85]) ).

cnf(c_0_96,plain,
    ( product(e_1,e_2,e_3)
    | ~ product(e_2,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_92,c_0_91]) ).

cnf(c_0_97,plain,
    ( product(e_3,e_3,e_2)
    | equalish(X1,e_3)
    | ~ product(e_2,e_3,e_1)
    | ~ product(e_3,X1,e_3) ),
    inference(spm,[status(thm)],[c_0_17,c_0_93]) ).

cnf(c_0_98,negated_conjecture,
    ( equalish(X1,e_2)
    | ~ product(e_2,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_17,c_0_77]) ).

cnf(c_0_99,plain,
    ( ~ product(e_3,e_3,e_2)
    | ~ product(e_3,e_2,e_1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_28]) ).

cnf(c_0_100,negated_conjecture,
    ~ product(e_3,e_2,e_2),
    inference(spm,[status(thm)],[c_0_69,c_0_80]) ).

cnf(c_0_101,plain,
    ( equalish(X1,e_1)
    | ~ product(e_2,e_3,e_3)
    | ~ product(X1,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_21,c_0_96]) ).

cnf(c_0_102,plain,
    ( product(e_3,e_3,e_2)
    | ~ product(e_2,e_3,e_1)
    | ~ product(e_3,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_19,c_0_97]) ).

cnf(c_0_103,negated_conjecture,
    ~ product(e_2,e_3,e_2),
    inference(spm,[status(thm)],[c_0_69,c_0_98]) ).

cnf(c_0_104,plain,
    ( ~ product(e_3,e_2,e_1)
    | ~ product(e_2,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_99,c_0_36]) ).

cnf(c_0_105,plain,
    ( product(e_3,e_2,e_3)
    | product(e_3,e_2,e_1) ),
    inference(sr,[status(thm)],[c_0_33,c_0_100]) ).

cnf(c_0_106,plain,
    ( ~ product(e_2,e_3,e_3)
    | ~ product(e_3,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_62,c_0_101]) ).

cnf(c_0_107,plain,
    ( equalish(X1,e_2)
    | ~ product(e_2,e_3,e_1)
    | ~ product(e_3,e_2,e_3)
    | ~ product(e_3,e_3,X1) ),
    inference(spm,[status(thm)],[c_0_24,c_0_102]) ).

cnf(c_0_108,plain,
    ( product(e_2,e_3,e_3)
    | product(e_2,e_3,e_1) ),
    inference(sr,[status(thm)],[c_0_39,c_0_103]) ).

cnf(c_0_109,plain,
    ~ product(e_2,e_3,e_3),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106]) ).

cnf(c_0_110,plain,
    ( ~ product(e_2,e_3,e_1)
    | ~ product(e_3,e_2,e_3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_107]),c_0_28]) ).

cnf(c_0_111,plain,
    product(e_2,e_3,e_1),
    inference(sr,[status(thm)],[c_0_108,c_0_109]) ).

cnf(c_0_112,negated_conjecture,
    ( product(e_2,e_3,e_3)
    | product(e_2,e_3,e_2)
    | product(e_3,X1,e_1)
    | ~ product(X1,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_28,c_0_39]) ).

cnf(c_0_113,plain,
    ~ product(e_3,e_2,e_3),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_111])]) ).

cnf(c_0_114,plain,
    ( product(e_3,e_2,e_3)
    | product(e_3,e_2,e_2)
    | equalish(X1,e_2)
    | ~ product(e_3,X1,e_1) ),
    inference(spm,[status(thm)],[c_0_17,c_0_33]) ).

cnf(c_0_115,negated_conjecture,
    ( product(e_1,e_2,e_2)
    | product(e_3,e_1,e_1)
    | product(e_2,e_3,e_2)
    | product(e_2,e_3,e_3)
    | ~ product(e_3,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_112,c_0_64]) ).

cnf(c_0_116,plain,
    product(e_3,e_2,e_1),
    inference(sr,[status(thm)],[c_0_105,c_0_113]) ).

cnf(c_0_117,plain,
    ( product(e_3,e_2,e_2)
    | product(e_3,e_2,e_3)
    | ~ product(e_3,e_1,e_1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_114]) ).

cnf(c_0_118,negated_conjecture,
    product(e_3,e_1,e_1),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_115,c_0_116])]),c_0_85]),c_0_103]),c_0_109]) ).

cnf(c_0_119,plain,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_118])]),c_0_100]),c_0_113]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GRP129-1.003 : 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
% 0.13/0.35  % Computer : n018.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 29 01:27:47 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.20/0.65  % Version  : CSE_E---1.5
% 0.20/0.65  % Problem  : theBenchmark.p
% 0.20/0.65  % Proof found
% 0.20/0.65  % SZS status Theorem for theBenchmark.p
% 0.20/0.65  % SZS output start Proof
% See solution above
% 0.20/0.66  % Total time : 0.062000 s
% 0.20/0.66  % SZS output end Proof
% 0.20/0.66  % Total time : 0.065000 s
%------------------------------------------------------------------------------