TSTP Solution File: GRP127-4.004 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : GRP127-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% 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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 17:38:25 EDT 2023

% Result   : Unsatisfiable 0.78s 0.61s
% Output   : CNFRefutation 0.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   35
%            Number of leaves      :   23
% Syntax   : Number of clauses     :  147 (  43 unt;  48 nHn; 145 RR)
%            Number of literals    :  355 (   0 equ; 154 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            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)

% Comments : 
%------------------------------------------------------------------------------
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/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.p',product_total_function1) ).

cnf(element_4,axiom,
    group_element(e_4),
    file('/export/starexec/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.p',element_4) ).

cnf(product_right_cancellation,axiom,
    ( equalish(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X3) ),
    file('/export/starexec/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.p',product_right_cancellation) ).

cnf(product_idempotence,axiom,
    product(X1,X1,X1),
    file('/export/starexec/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.p',product_idempotence) ).

cnf(element_1,axiom,
    group_element(e_1),
    file('/export/starexec/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.p',element_1) ).

cnf(product_left_cancellation,axiom,
    ( equalish(X1,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X3) ),
    file('/export/starexec/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.p',product_left_cancellation) ).

cnf(e_4_is_not_e_1,axiom,
    ~ equalish(e_4,e_1),
    file('/export/starexec/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.p',e_4_is_not_e_1) ).

cnf(element_3,axiom,
    group_element(e_3),
    file('/export/starexec/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.p',element_3) ).

cnf(e_1_is_not_e_4,axiom,
    ~ equalish(e_1,e_4),
    file('/export/starexec/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.p',e_1_is_not_e_4) ).

cnf(e_3_is_not_e_1,axiom,
    ~ equalish(e_3,e_1),
    file('/export/starexec/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.p',e_3_is_not_e_1) ).

cnf(e_2_is_not_e_1,axiom,
    ~ equalish(e_2,e_1),
    file('/export/starexec/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.p',e_2_is_not_e_1) ).

cnf(e_3_is_not_e_4,axiom,
    ~ equalish(e_3,e_4),
    file('/export/starexec/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.p',e_3_is_not_e_4) ).

cnf(e_1_is_not_e_3,axiom,
    ~ equalish(e_1,e_3),
    file('/export/starexec/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.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/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.p',qg3) ).

cnf(e_4_is_not_e_3,axiom,
    ~ equalish(e_4,e_3),
    file('/export/starexec/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.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/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.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/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.p',column_surjectivity) ).

cnf(product_total_function2,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.p',product_total_function2) ).

cnf(e_2_is_not_e_4,axiom,
    ~ equalish(e_2,e_4),
    file('/export/starexec/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.p',e_2_is_not_e_4) ).

cnf(e_4_is_not_e_2,axiom,
    ~ equalish(e_4,e_2),
    file('/export/starexec/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.p',e_4_is_not_e_2) ).

cnf(e_2_is_not_e_3,axiom,
    ~ equalish(e_2,e_3),
    file('/export/starexec/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.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/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.p',qg3_1) ).

cnf(qg3_2,negated_conjecture,
    ( product(X1,X2,X3)
    | ~ product(X3,X2,X4)
    | ~ product(X2,X4,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.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
% 0.04/0.13  % Problem    : GRP127-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.13/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n007.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   : 2400
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Oct  3 02:48:40 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.22/0.53  Running first-order theorem proving
% 0.22/0.53  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.kykvIK2WeV/E---3.1_15134.p
% 0.78/0.61  # Version: 3.1pre001
% 0.78/0.61  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.78/0.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.78/0.61  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.78/0.61  # Starting new_bool_3 with 300s (1) cores
% 0.78/0.61  # Starting new_bool_1 with 300s (1) cores
% 0.78/0.61  # Starting sh5l with 300s (1) cores
% 0.78/0.61  # new_bool_1 with pid 15251 completed with status 0
% 0.78/0.61  # Result found by new_bool_1
% 0.78/0.61  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.78/0.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.78/0.61  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.78/0.61  # Starting new_bool_3 with 300s (1) cores
% 0.78/0.61  # Starting new_bool_1 with 300s (1) cores
% 0.78/0.61  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.78/0.61  # Search class: FGUNF-FFSS00-SFFFFFNN
% 0.78/0.61  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.78/0.61  # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.78/0.61  # SAT001_MinMin_p005000_rr_RG with pid 15257 completed with status 0
% 0.78/0.61  # Result found by SAT001_MinMin_p005000_rr_RG
% 0.78/0.61  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.78/0.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.78/0.61  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.78/0.61  # Starting new_bool_3 with 300s (1) cores
% 0.78/0.61  # Starting new_bool_1 with 300s (1) cores
% 0.78/0.61  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.78/0.61  # Search class: FGUNF-FFSS00-SFFFFFNN
% 0.78/0.61  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.78/0.61  # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.78/0.61  # Preprocessing time       : 0.002 s
% 0.78/0.61  # Presaturation interreduction done
% 0.78/0.61  
% 0.78/0.61  # Proof found!
% 0.78/0.61  # SZS status Unsatisfiable
% 0.78/0.61  # SZS output start CNFRefutation
% See solution above
% 0.78/0.61  # Parsed axioms                        : 26
% 0.78/0.61  # Removed by relevancy pruning/SinE    : 0
% 0.78/0.61  # Initial clauses                      : 26
% 0.78/0.61  # Removed in clause preprocessing      : 0
% 0.78/0.61  # Initial clauses in saturation        : 26
% 0.78/0.61  # Processed clauses                    : 699
% 0.78/0.61  # ...of these trivial                  : 1
% 0.78/0.61  # ...subsumed                          : 135
% 0.78/0.61  # ...remaining for further processing  : 563
% 0.78/0.61  # Other redundant clauses eliminated   : 0
% 0.78/0.61  # Clauses deleted for lack of memory   : 0
% 0.78/0.61  # Backward-subsumed                    : 289
% 0.78/0.61  # Backward-rewritten                   : 42
% 0.78/0.61  # Generated clauses                    : 1876
% 0.78/0.61  # ...of the previous two non-redundant : 1796
% 0.78/0.61  # ...aggressively subsumed             : 0
% 0.78/0.61  # Contextual simplify-reflections      : 17
% 0.78/0.61  # Paramodulations                      : 1846
% 0.78/0.61  # Factorizations                       : 0
% 0.78/0.61  # NegExts                              : 0
% 0.78/0.61  # Equation resolutions                 : 0
% 0.78/0.61  # Total rewrite steps                  : 66
% 0.78/0.61  # Propositional unsat checks           : 0
% 0.78/0.61  #    Propositional check models        : 0
% 0.78/0.61  #    Propositional check unsatisfiable : 0
% 0.78/0.61  #    Propositional clauses             : 0
% 0.78/0.61  #    Propositional clauses after purity: 0
% 0.78/0.61  #    Propositional unsat core size     : 0
% 0.78/0.61  #    Propositional preprocessing time  : 0.000
% 0.78/0.61  #    Propositional encoding time       : 0.000
% 0.78/0.61  #    Propositional solver time         : 0.000
% 0.78/0.61  #    Success case prop preproc time    : 0.000
% 0.78/0.61  #    Success case prop encoding time   : 0.000
% 0.78/0.61  #    Success case prop solver time     : 0.000
% 0.78/0.61  # Current number of processed clauses  : 176
% 0.78/0.61  #    Positive orientable unit clauses  : 12
% 0.78/0.61  #    Positive unorientable unit clauses: 0
% 0.78/0.61  #    Negative unit clauses             : 38
% 0.78/0.61  #    Non-unit-clauses                  : 126
% 0.78/0.61  # Current number of unprocessed clauses: 988
% 0.78/0.61  # ...number of literals in the above   : 3994
% 0.78/0.61  # Current number of archived formulas  : 0
% 0.78/0.61  # Current number of archived clauses   : 387
% 0.78/0.61  # Clause-clause subsumption calls (NU) : 14874
% 0.78/0.61  # Rec. Clause-clause subsumption calls : 10642
% 0.78/0.61  # Non-unit clause-clause subsumptions  : 190
% 0.78/0.61  # Unit Clause-clause subsumption calls : 2037
% 0.78/0.61  # Rewrite failures with RHS unbound    : 0
% 0.78/0.61  # BW rewrite match attempts            : 42
% 0.78/0.61  # BW rewrite match successes           : 5
% 0.78/0.61  # Condensation attempts                : 0
% 0.78/0.61  # Condensation successes               : 0
% 0.78/0.61  # Termbank termtop insertions          : 20235
% 0.78/0.61  
% 0.78/0.61  # -------------------------------------------------
% 0.78/0.61  # User time                : 0.065 s
% 0.78/0.61  # System time              : 0.003 s
% 0.78/0.61  # Total time               : 0.068 s
% 0.78/0.61  # Maximum resident set size: 1624 pages
% 0.78/0.61  
% 0.78/0.61  # -------------------------------------------------
% 0.78/0.61  # User time                : 0.066 s
% 0.78/0.61  # System time              : 0.007 s
% 0.78/0.61  # Total time               : 0.072 s
% 0.78/0.61  # Maximum resident set size: 1688 pages
% 0.78/0.61  % E---3.1 exiting
% 0.78/0.61  % E---3.1 exiting
%------------------------------------------------------------------------------