TSTP Solution File: GRP129-4.004 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : GRP129-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n026.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 17:38:54 EDT 2023

% Result   : Unsatisfiable 1.03s 0.61s
% Output   : CNFRefutation 1.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   41
%            Number of leaves      :   22
% Syntax   : Number of clauses     :  142 (  47 unt;  76 nHn; 142 RR)
%            Number of literals    :  369 (   0 equ; 103 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   :   92 (   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/sandbox/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',product_total_function1) ).

cnf(element_2,axiom,
    group_element(e_2),
    file('/export/starexec/sandbox/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',element_2) ).

cnf(qg3_1,negated_conjecture,
    ( product(X1,X2,X3)
    | ~ product(X3,X1,X4)
    | ~ product(X2,X3,X4) ),
    file('/export/starexec/sandbox/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',qg3_1) ).

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/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',column_surjectivity) ).

cnf(product_left_cancellation,axiom,
    ( equalish(X1,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X3) ),
    file('/export/starexec/sandbox/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',product_left_cancellation) ).

cnf(element_1,axiom,
    group_element(e_1),
    file('/export/starexec/sandbox/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',element_1) ).

cnf(e_1_is_not_e_2,axiom,
    ~ equalish(e_1,e_2),
    file('/export/starexec/sandbox/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',e_1_is_not_e_2) ).

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/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',row_surjectivity) ).

cnf(product_right_cancellation,axiom,
    ( equalish(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X3) ),
    file('/export/starexec/sandbox/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',product_right_cancellation) ).

cnf(product_total_function2,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',product_total_function2) ).

cnf(e_4_is_not_e_1,axiom,
    ~ equalish(e_4,e_1),
    file('/export/starexec/sandbox/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',e_4_is_not_e_1) ).

cnf(e_3_is_not_e_1,axiom,
    ~ equalish(e_3,e_1),
    file('/export/starexec/sandbox/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',e_3_is_not_e_1) ).

cnf(qg3,negated_conjecture,
    ( product(X3,X1,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X3,X4) ),
    file('/export/starexec/sandbox/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',qg3) ).

cnf(element_4,axiom,
    group_element(e_4),
    file('/export/starexec/sandbox/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',element_4) ).

cnf(e_4_is_not_e_2,axiom,
    ~ equalish(e_4,e_2),
    file('/export/starexec/sandbox/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',e_4_is_not_e_2) ).

cnf(e_1_is_not_e_4,axiom,
    ~ equalish(e_1,e_4),
    file('/export/starexec/sandbox/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',e_1_is_not_e_4) ).

cnf(e_3_is_not_e_4,axiom,
    ~ equalish(e_3,e_4),
    file('/export/starexec/sandbox/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',e_3_is_not_e_4) ).

cnf(element_3,axiom,
    group_element(e_3),
    file('/export/starexec/sandbox/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',element_3) ).

cnf(e_2_is_not_e_1,axiom,
    ~ equalish(e_2,e_1),
    file('/export/starexec/sandbox/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',e_2_is_not_e_1) ).

cnf(e_3_is_not_e_2,axiom,
    ~ equalish(e_3,e_2),
    file('/export/starexec/sandbox/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',e_3_is_not_e_2) ).

cnf(e_2_is_not_e_3,axiom,
    ~ equalish(e_2,e_3),
    file('/export/starexec/sandbox/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',e_2_is_not_e_3) ).

cnf(e_1_is_not_e_3,axiom,
    ~ equalish(e_1,e_3),
    file('/export/starexec/sandbox/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p',e_1_is_not_e_3) ).

cnf(c_0_22,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_23,axiom,
    group_element(e_2),
    element_2 ).

cnf(c_0_24,plain,
    ( product(X1,e_2,e_4)
    | 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_22,c_0_23]) ).

cnf(c_0_25,negated_conjecture,
    ( product(X1,X2,X3)
    | ~ product(X3,X1,X4)
    | ~ product(X2,X3,X4) ),
    qg3_1 ).

cnf(c_0_26,plain,
    ( product(e_2,e_2,e_1)
    | product(e_2,e_2,e_2)
    | product(e_2,e_2,e_3)
    | product(e_2,e_2,e_4) ),
    inference(spm,[status(thm)],[c_0_24,c_0_23]) ).

cnf(c_0_27,negated_conjecture,
    ( product(e_2,e_2,e_4)
    | product(e_2,e_2,e_3)
    | product(e_2,e_2,e_2)
    | product(e_2,X1,e_2)
    | ~ product(X1,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_28,negated_conjecture,
    ( product(e_2,e_2,e_2)
    | product(e_2,e_2,e_3)
    | product(e_2,e_2,e_4) ),
    inference(spm,[status(thm)],[c_0_27,c_0_26]) ).

cnf(c_0_29,negated_conjecture,
    ( product(e_2,e_2,e_3)
    | product(e_2,e_2,e_2)
    | product(e_2,X1,e_2)
    | ~ product(X1,e_2,e_4) ),
    inference(spm,[status(thm)],[c_0_25,c_0_28]) ).

cnf(c_0_30,negated_conjecture,
    ( product(e_2,e_2,e_2)
    | product(e_2,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_29,c_0_28]) ).

cnf(c_0_31,negated_conjecture,
    ( product(e_2,e_2,e_2)
    | product(e_2,X1,e_2)
    | ~ product(X1,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_25,c_0_30]) ).

cnf(c_0_32,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_33,axiom,
    ( equalish(X1,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X3) ),
    product_left_cancellation ).

cnf(c_0_34,negated_conjecture,
    product(e_2,e_2,e_2),
    inference(spm,[status(thm)],[c_0_31,c_0_30]) ).

cnf(c_0_35,plain,
    ( product(X1,e_4,e_2)
    | product(X1,e_3,e_2)
    | product(X1,e_2,e_2)
    | product(X1,e_1,e_2)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_23]) ).

cnf(c_0_36,axiom,
    group_element(e_1),
    element_1 ).

cnf(c_0_37,axiom,
    ~ equalish(e_1,e_2),
    e_1_is_not_e_2 ).

cnf(c_0_38,negated_conjecture,
    ( equalish(X1,e_2)
    | ~ product(X1,e_2,e_2) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_39,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_40,axiom,
    ( equalish(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X3) ),
    product_right_cancellation ).

cnf(c_0_41,plain,
    ( product(e_1,e_1,e_2)
    | product(e_1,e_2,e_2)
    | product(e_1,e_3,e_2)
    | product(e_1,e_4,e_2) ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_42,negated_conjecture,
    ~ product(e_1,e_2,e_2),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_43,plain,
    ( product(e_4,X1,e_2)
    | product(e_3,X1,e_2)
    | product(e_2,X1,e_2)
    | product(e_1,X1,e_2)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_39,c_0_23]) ).

cnf(c_0_44,negated_conjecture,
    ( equalish(X1,e_2)
    | ~ product(e_2,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_40,c_0_34]) ).

cnf(c_0_45,plain,
    ( product(e_1,e_4,e_2)
    | product(e_1,e_3,e_2)
    | product(e_1,e_1,e_2) ),
    inference(sr,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_46,plain,
    ( product(e_1,e_1,e_2)
    | product(e_2,e_1,e_2)
    | product(e_3,e_1,e_2)
    | product(e_4,e_1,e_2) ),
    inference(spm,[status(thm)],[c_0_43,c_0_36]) ).

cnf(c_0_47,negated_conjecture,
    ~ product(e_2,e_1,e_2),
    inference(spm,[status(thm)],[c_0_37,c_0_44]) ).

cnf(c_0_48,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    product_total_function2 ).

cnf(c_0_49,negated_conjecture,
    ( product(e_1,e_3,e_2)
    | product(e_1,e_4,e_2)
    | product(e_1,X1,e_1)
    | ~ product(X1,e_1,e_2) ),
    inference(spm,[status(thm)],[c_0_25,c_0_45]) ).

cnf(c_0_50,plain,
    ( product(e_4,e_1,e_2)
    | product(e_3,e_1,e_2)
    | product(e_1,e_1,e_2) ),
    inference(sr,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_51,plain,
    ( equalish(X1,e_2)
    | product(e_1,e_3,e_2)
    | product(e_1,e_4,e_2)
    | ~ product(e_1,e_1,X1) ),
    inference(spm,[status(thm)],[c_0_48,c_0_45]) ).

cnf(c_0_52,negated_conjecture,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_4,e_2)
    | product(e_1,e_3,e_2) ),
    inference(spm,[status(thm)],[c_0_49,c_0_45]) ).

cnf(c_0_53,plain,
    ( equalish(X1,e_1)
    | product(e_3,e_1,e_2)
    | product(e_4,e_1,e_2)
    | ~ product(e_1,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_40,c_0_50]) ).

cnf(c_0_54,negated_conjecture,
    ( product(e_1,e_4,e_2)
    | product(e_1,e_3,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_37]) ).

cnf(c_0_55,axiom,
    ~ equalish(e_4,e_1),
    e_4_is_not_e_1 ).

cnf(c_0_56,negated_conjecture,
    ( product(e_1,e_3,e_2)
    | product(e_4,e_1,e_2)
    | product(e_3,e_1,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).

cnf(c_0_57,axiom,
    ~ equalish(e_3,e_1),
    e_3_is_not_e_1 ).

cnf(c_0_58,negated_conjecture,
    ( product(e_1,e_3,e_2)
    | product(e_4,X1,e_1)
    | ~ product(X1,e_1,e_2) ),
    inference(spm,[status(thm)],[c_0_25,c_0_54]) ).

cnf(c_0_59,negated_conjecture,
    ( product(e_4,e_1,e_2)
    | product(e_3,e_1,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_56]),c_0_57]) ).

cnf(c_0_60,negated_conjecture,
    ( product(e_3,e_1,e_2)
    | product(e_4,e_4,e_1)
    | product(e_1,e_3,e_2) ),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_61,negated_conjecture,
    ( product(e_3,e_1,e_2)
    | product(e_1,X1,e_4)
    | ~ product(X1,e_4,e_2) ),
    inference(spm,[status(thm)],[c_0_25,c_0_59]) ).

cnf(c_0_62,negated_conjecture,
    ( product(X3,X1,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X3,X4) ),
    qg3 ).

cnf(c_0_63,negated_conjecture,
    ( product(e_4,e_4,e_1)
    | product(e_3,e_1,e_2)
    | product(e_3,X1,e_1)
    | ~ product(X1,e_1,e_2) ),
    inference(spm,[status(thm)],[c_0_25,c_0_60]) ).

cnf(c_0_64,negated_conjecture,
    ( product(e_1,e_3,e_2)
    | product(e_1,e_1,e_4)
    | product(e_3,e_1,e_2) ),
    inference(spm,[status(thm)],[c_0_61,c_0_54]) ).

cnf(c_0_65,axiom,
    group_element(e_4),
    element_4 ).

cnf(c_0_66,axiom,
    ~ equalish(e_4,e_2),
    e_4_is_not_e_2 ).

cnf(c_0_67,negated_conjecture,
    ( product(e_3,e_1,e_2)
    | product(e_1,X1,e_2)
    | ~ product(X1,e_4,e_1) ),
    inference(spm,[status(thm)],[c_0_62,c_0_59]) ).

cnf(c_0_68,negated_conjecture,
    ( product(e_3,e_4,e_1)
    | product(e_3,e_1,e_2)
    | product(e_4,e_4,e_1) ),
    inference(spm,[status(thm)],[c_0_63,c_0_59]) ).

cnf(c_0_69,negated_conjecture,
    ( product(e_3,e_1,e_2)
    | product(e_1,e_3,e_2)
    | product(e_1,X1,e_1)
    | ~ product(X1,e_1,e_4) ),
    inference(spm,[status(thm)],[c_0_25,c_0_64]) ).

cnf(c_0_70,plain,
    ( product(e_4,e_1,e_2)
    | product(e_4,e_2,e_2)
    | product(e_4,e_3,e_2)
    | product(e_4,e_4,e_2) ),
    inference(spm,[status(thm)],[c_0_35,c_0_65]) ).

cnf(c_0_71,negated_conjecture,
    ~ product(e_4,e_2,e_2),
    inference(spm,[status(thm)],[c_0_66,c_0_38]) ).

cnf(c_0_72,negated_conjecture,
    ( product(e_3,e_4,e_1)
    | product(e_1,e_4,e_2)
    | product(e_3,e_1,e_2) ),
    inference(spm,[status(thm)],[c_0_67,c_0_68]) ).

cnf(c_0_73,negated_conjecture,
    ( equalish(X1,e_4)
    | product(e_3,e_1,e_2)
    | product(e_1,e_3,e_2)
    | ~ product(e_1,e_1,X1) ),
    inference(spm,[status(thm)],[c_0_48,c_0_64]) ).

cnf(c_0_74,negated_conjecture,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_3,e_2)
    | product(e_3,e_1,e_2) ),
    inference(spm,[status(thm)],[c_0_69,c_0_64]) ).

cnf(c_0_75,axiom,
    ~ equalish(e_1,e_4),
    e_1_is_not_e_4 ).

cnf(c_0_76,plain,
    ( product(e_4,e_4,e_2)
    | product(e_4,e_3,e_2)
    | product(e_4,e_1,e_2) ),
    inference(sr,[status(thm)],[c_0_70,c_0_71]) ).

cnf(c_0_77,negated_conjecture,
    ( equalish(X1,e_4)
    | product(e_3,e_1,e_2)
    | product(e_3,e_4,e_1)
    | ~ product(e_1,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_40,c_0_72]) ).

cnf(c_0_78,negated_conjecture,
    ( product(e_1,e_3,e_2)
    | product(e_3,e_1,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]) ).

cnf(c_0_79,axiom,
    ~ equalish(e_3,e_4),
    e_3_is_not_e_4 ).

cnf(c_0_80,plain,
    ( equalish(X1,e_4)
    | product(e_4,e_3,e_2)
    | product(e_4,e_4,e_2)
    | ~ product(X1,e_1,e_2) ),
    inference(spm,[status(thm)],[c_0_33,c_0_76]) ).

cnf(c_0_81,negated_conjecture,
    ( product(e_3,e_4,e_1)
    | product(e_3,e_1,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).

cnf(c_0_82,negated_conjecture,
    ( product(e_3,e_4,e_1)
    | product(e_4,e_4,e_2)
    | product(e_4,e_3,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_79]) ).

cnf(c_0_83,negated_conjecture,
    ( product(e_4,e_3,e_2)
    | product(e_3,e_4,e_1)
    | product(e_4,X1,e_4)
    | ~ product(X1,e_4,e_2) ),
    inference(spm,[status(thm)],[c_0_25,c_0_82]) ).

cnf(c_0_84,negated_conjecture,
    ( equalish(X1,e_2)
    | product(e_4,e_3,e_2)
    | product(e_3,e_4,e_1)
    | ~ product(e_4,e_4,X1) ),
    inference(spm,[status(thm)],[c_0_48,c_0_82]) ).

cnf(c_0_85,negated_conjecture,
    ( product(e_4,e_4,e_4)
    | product(e_3,e_4,e_1)
    | product(e_4,e_3,e_2) ),
    inference(spm,[status(thm)],[c_0_83,c_0_82]) ).

cnf(c_0_86,negated_conjecture,
    ( product(e_3,e_4,e_1)
    | product(e_4,e_3,e_1)
    | product(e_1,e_3,e_2) ),
    inference(spm,[status(thm)],[c_0_58,c_0_81]) ).

cnf(c_0_87,plain,
    ( product(e_1,e_4,e_2)
    | product(e_2,e_4,e_2)
    | product(e_3,e_4,e_2)
    | product(e_4,e_4,e_2) ),
    inference(spm,[status(thm)],[c_0_43,c_0_65]) ).

cnf(c_0_88,negated_conjecture,
    ~ product(e_2,e_4,e_2),
    inference(spm,[status(thm)],[c_0_66,c_0_44]) ).

cnf(c_0_89,negated_conjecture,
    ( product(e_3,e_4,e_1)
    | product(e_4,e_3,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_66]) ).

cnf(c_0_90,negated_conjecture,
    ( equalish(X1,e_1)
    | product(e_4,e_3,e_1)
    | product(e_3,e_4,e_1)
    | ~ product(X1,e_3,e_2) ),
    inference(spm,[status(thm)],[c_0_33,c_0_86]) ).

cnf(c_0_91,axiom,
    group_element(e_3),
    element_3 ).

cnf(c_0_92,plain,
    ( product(e_4,e_4,e_2)
    | product(e_3,e_4,e_2)
    | product(e_1,e_4,e_2) ),
    inference(sr,[status(thm)],[c_0_87,c_0_88]) ).

cnf(c_0_93,negated_conjecture,
    ( equalish(X1,e_2)
    | product(e_3,e_4,e_1)
    | ~ product(e_4,e_3,X1) ),
    inference(spm,[status(thm)],[c_0_48,c_0_89]) ).

cnf(c_0_94,negated_conjecture,
    ( product(e_3,e_4,e_1)
    | product(e_4,e_3,e_1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_89]),c_0_55]) ).

cnf(c_0_95,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_22,c_0_91]) ).

cnf(c_0_96,plain,
    ( equalish(X1,e_4)
    | product(e_3,e_4,e_2)
    | product(e_4,e_4,e_2)
    | ~ product(e_1,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_40,c_0_92]) ).

cnf(c_0_97,negated_conjecture,
    product(e_3,e_4,e_1),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_37]) ).

cnf(c_0_98,plain,
    ( product(e_3,e_3,e_1)
    | product(e_3,e_3,e_2)
    | product(e_3,e_3,e_3)
    | product(e_3,e_3,e_4) ),
    inference(spm,[status(thm)],[c_0_95,c_0_91]) ).

cnf(c_0_99,negated_conjecture,
    ( equalish(X1,e_1)
    | product(e_3,e_1,e_2)
    | ~ product(e_4,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_40,c_0_59]) ).

cnf(c_0_100,negated_conjecture,
    ( product(e_3,e_1,e_2)
    | product(e_4,e_4,e_2)
    | product(e_3,e_4,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_78]),c_0_79]) ).

cnf(c_0_101,axiom,
    ~ equalish(e_2,e_1),
    e_2_is_not_e_1 ).

cnf(c_0_102,negated_conjecture,
    ( equalish(X1,e_1)
    | ~ product(e_3,e_4,X1) ),
    inference(spm,[status(thm)],[c_0_48,c_0_97]) ).

cnf(c_0_103,negated_conjecture,
    ( product(e_3,e_3,e_4)
    | product(e_3,e_3,e_3)
    | product(e_3,e_3,e_2)
    | product(e_3,X1,e_3)
    | ~ product(X1,e_3,e_1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_98]) ).

cnf(c_0_104,negated_conjecture,
    ( product(e_3,e_4,e_2)
    | product(e_3,e_1,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_55]) ).

cnf(c_0_105,negated_conjecture,
    ~ product(e_3,e_4,e_2),
    inference(spm,[status(thm)],[c_0_101,c_0_102]) ).

cnf(c_0_106,axiom,
    ~ equalish(e_3,e_2),
    e_3_is_not_e_2 ).

cnf(c_0_107,negated_conjecture,
    ( product(e_3,e_3,e_2)
    | product(e_3,e_3,e_3)
    | product(e_3,e_3,e_4) ),
    inference(spm,[status(thm)],[c_0_103,c_0_98]) ).

cnf(c_0_108,negated_conjecture,
    product(e_3,e_1,e_2),
    inference(sr,[status(thm)],[c_0_104,c_0_105]) ).

cnf(c_0_109,plain,
    ( product(e_2,e_3,e_1)
    | product(e_2,e_3,e_2)
    | product(e_2,e_3,e_3)
    | product(e_2,e_3,e_4) ),
    inference(spm,[status(thm)],[c_0_95,c_0_23]) ).

cnf(c_0_110,negated_conjecture,
    ~ product(e_2,e_3,e_2),
    inference(spm,[status(thm)],[c_0_106,c_0_44]) ).

cnf(c_0_111,negated_conjecture,
    ( product(e_3,e_3,e_3)
    | product(e_3,e_3,e_2)
    | product(e_3,X1,e_3)
    | ~ product(X1,e_3,e_4) ),
    inference(spm,[status(thm)],[c_0_25,c_0_107]) ).

cnf(c_0_112,negated_conjecture,
    ( equalish(X1,e_1)
    | ~ product(e_3,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_40,c_0_108]) ).

cnf(c_0_113,negated_conjecture,
    ( product(e_3,e_4,e_1)
    | product(e_1,X1,e_2)
    | ~ product(X1,e_3,e_1) ),
    inference(spm,[status(thm)],[c_0_62,c_0_81]) ).

cnf(c_0_114,plain,
    ( product(e_2,e_3,e_4)
    | product(e_2,e_3,e_3)
    | product(e_2,e_3,e_1) ),
    inference(sr,[status(thm)],[c_0_109,c_0_110]) ).

cnf(c_0_115,negated_conjecture,
    ( product(e_3,e_3,e_2)
    | product(e_3,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_111,c_0_107]) ).

cnf(c_0_116,negated_conjecture,
    ~ product(e_3,e_3,e_2),
    inference(spm,[status(thm)],[c_0_57,c_0_112]) ).

cnf(c_0_117,negated_conjecture,
    ( product(e_2,e_3,e_3)
    | product(e_2,e_3,e_4)
    | product(e_3,e_4,e_1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_42]) ).

cnf(c_0_118,negated_conjecture,
    ( product(e_3,e_4,e_2)
    | product(e_1,X1,e_2)
    | ~ product(X1,e_3,e_1) ),
    inference(spm,[status(thm)],[c_0_62,c_0_104]) ).

cnf(c_0_119,negated_conjecture,
    product(e_3,e_3,e_3),
    inference(sr,[status(thm)],[c_0_115,c_0_116]) ).

cnf(c_0_120,plain,
    ( product(X1,e_4,e_1)
    | product(X1,e_3,e_1)
    | product(X1,e_2,e_1)
    | product(X1,e_1,e_1)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_36]) ).

cnf(c_0_121,negated_conjecture,
    ( equalish(X1,e_2)
    | ~ product(e_2,e_2,X1) ),
    inference(spm,[status(thm)],[c_0_48,c_0_34]) ).

cnf(c_0_122,negated_conjecture,
    ( equalish(X1,e_1)
    | product(e_2,e_3,e_4)
    | product(e_2,e_3,e_3)
    | ~ product(e_3,e_4,X1) ),
    inference(spm,[status(thm)],[c_0_48,c_0_117]) ).

cnf(c_0_123,negated_conjecture,
    ( product(e_2,e_3,e_3)
    | product(e_2,e_3,e_4)
    | product(e_3,e_4,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_114]),c_0_42]) ).

cnf(c_0_124,axiom,
    ~ equalish(e_2,e_3),
    e_2_is_not_e_3 ).

cnf(c_0_125,negated_conjecture,
    ( equalish(X1,e_3)
    | ~ product(X1,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_33,c_0_119]) ).

cnf(c_0_126,plain,
    ( product(e_2,e_1,e_1)
    | product(e_2,e_2,e_1)
    | product(e_2,e_3,e_1)
    | product(e_2,e_4,e_1) ),
    inference(spm,[status(thm)],[c_0_120,c_0_23]) ).

cnf(c_0_127,negated_conjecture,
    ~ product(e_2,e_2,e_1),
    inference(spm,[status(thm)],[c_0_37,c_0_121]) ).

cnf(c_0_128,negated_conjecture,
    ( product(e_2,e_3,e_3)
    | product(e_2,e_3,e_4) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_101]) ).

cnf(c_0_129,negated_conjecture,
    ~ product(e_2,e_3,e_3),
    inference(spm,[status(thm)],[c_0_124,c_0_125]) ).

cnf(c_0_130,plain,
    ( product(e_2,e_4,e_1)
    | product(e_2,e_3,e_1)
    | product(e_2,e_1,e_1) ),
    inference(sr,[status(thm)],[c_0_126,c_0_127]) ).

cnf(c_0_131,negated_conjecture,
    ( product(e_4,X1,e_1)
    | ~ product(X1,e_3,e_4) ),
    inference(spm,[status(thm)],[c_0_62,c_0_97]) ).

cnf(c_0_132,negated_conjecture,
    product(e_2,e_3,e_4),
    inference(sr,[status(thm)],[c_0_128,c_0_129]) ).

cnf(c_0_133,negated_conjecture,
    ( equalish(X1,e_3)
    | ~ product(X1,e_4,e_1) ),
    inference(spm,[status(thm)],[c_0_33,c_0_97]) ).

cnf(c_0_134,axiom,
    ~ equalish(e_1,e_3),
    e_1_is_not_e_3 ).

cnf(c_0_135,negated_conjecture,
    ( product(e_2,e_3,e_1)
    | product(e_2,e_4,e_1)
    | product(e_1,X1,e_1)
    | ~ product(X1,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_62,c_0_130]) ).

cnf(c_0_136,negated_conjecture,
    product(e_4,e_2,e_1),
    inference(spm,[status(thm)],[c_0_131,c_0_132]) ).

cnf(c_0_137,negated_conjecture,
    ~ product(e_2,e_4,e_1),
    inference(spm,[status(thm)],[c_0_124,c_0_133]) ).

cnf(c_0_138,negated_conjecture,
    ~ product(e_1,e_4,e_1),
    inference(spm,[status(thm)],[c_0_134,c_0_133]) ).

cnf(c_0_139,negated_conjecture,
    ( product(e_1,X1,e_2)
    | ~ product(X1,e_3,e_1) ),
    inference(spm,[status(thm)],[c_0_62,c_0_108]) ).

cnf(c_0_140,negated_conjecture,
    product(e_2,e_3,e_1),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_137]),c_0_138]) ).

cnf(c_0_141,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_42]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : GRP129-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.14  % Command    : run_E %s %d THM
% 0.15/0.35  % Computer : n026.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 2400
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Tue Oct  3 02:33:29 EDT 2023
% 0.15/0.35  % CPUTime    : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.kZ0BJMXsim/E---3.1_14126.p
% 1.03/0.61  # Version: 3.1pre001
% 1.03/0.61  # Preprocessing class: FSMSSMSSSSSNFFN.
% 1.03/0.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.03/0.61  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.03/0.61  # Starting new_bool_3 with 300s (1) cores
% 1.03/0.61  # Starting new_bool_1 with 300s (1) cores
% 1.03/0.61  # Starting sh5l with 300s (1) cores
% 1.03/0.61  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 14204 completed with status 0
% 1.03/0.61  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.03/0.61  # Preprocessing class: FSMSSMSSSSSNFFN.
% 1.03/0.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.03/0.61  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.03/0.61  # No SInE strategy applied
% 1.03/0.61  # Search class: FGUNF-FFSS00-SFFFFFNN
% 1.03/0.61  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.03/0.61  # Starting SAT001_MinMin_p005000_rr_RG with 811s (1) cores
% 1.03/0.61  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.03/0.61  # Starting new_bool_3 with 136s (1) cores
% 1.03/0.61  # Starting new_bool_1 with 136s (1) cores
% 1.03/0.61  # Starting sh5l with 136s (1) cores
% 1.03/0.61  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 14210 completed with status 0
% 1.03/0.61  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.03/0.61  # Preprocessing class: FSMSSMSSSSSNFFN.
% 1.03/0.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.03/0.61  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.03/0.61  # No SInE strategy applied
% 1.03/0.61  # Search class: FGUNF-FFSS00-SFFFFFNN
% 1.03/0.61  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.03/0.61  # Starting SAT001_MinMin_p005000_rr_RG with 811s (1) cores
% 1.03/0.61  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.03/0.61  # Preprocessing time       : 0.001 s
% 1.03/0.61  # Presaturation interreduction done
% 1.03/0.61  
% 1.03/0.61  # Proof found!
% 1.03/0.61  # SZS status Unsatisfiable
% 1.03/0.61  # SZS output start CNFRefutation
% See solution above
% 1.03/0.61  # Parsed axioms                        : 25
% 1.03/0.61  # Removed by relevancy pruning/SinE    : 0
% 1.03/0.61  # Initial clauses                      : 25
% 1.03/0.61  # Removed in clause preprocessing      : 0
% 1.03/0.61  # Initial clauses in saturation        : 25
% 1.03/0.61  # Processed clauses                    : 1182
% 1.03/0.61  # ...of these trivial                  : 3
% 1.03/0.61  # ...subsumed                          : 328
% 1.03/0.61  # ...remaining for further processing  : 851
% 1.03/0.61  # Other redundant clauses eliminated   : 0
% 1.03/0.61  # Clauses deleted for lack of memory   : 0
% 1.03/0.61  # Backward-subsumed                    : 290
% 1.03/0.61  # Backward-rewritten                   : 135
% 1.03/0.61  # Generated clauses                    : 4417
% 1.03/0.61  # ...of the previous two non-redundant : 4360
% 1.03/0.61  # ...aggressively subsumed             : 0
% 1.03/0.61  # Contextual simplify-reflections      : 7
% 1.03/0.61  # Paramodulations                      : 4300
% 1.03/0.61  # Factorizations                       : 0
% 1.03/0.61  # NegExts                              : 0
% 1.03/0.61  # Equation resolutions                 : 0
% 1.03/0.61  # Total rewrite steps                  : 178
% 1.03/0.61  # Propositional unsat checks           : 0
% 1.03/0.61  #    Propositional check models        : 0
% 1.03/0.61  #    Propositional check unsatisfiable : 0
% 1.03/0.61  #    Propositional clauses             : 0
% 1.03/0.61  #    Propositional clauses after purity: 0
% 1.03/0.61  #    Propositional unsat core size     : 0
% 1.03/0.61  #    Propositional preprocessing time  : 0.000
% 1.03/0.61  #    Propositional encoding time       : 0.000
% 1.03/0.61  #    Propositional solver time         : 0.000
% 1.03/0.61  #    Success case prop preproc time    : 0.000
% 1.03/0.61  #    Success case prop encoding time   : 0.000
% 1.03/0.61  #    Success case prop solver time     : 0.000
% 1.03/0.61  # Current number of processed clauses  : 284
% 1.03/0.61  #    Positive orientable unit clauses  : 16
% 1.03/0.61  #    Positive unorientable unit clauses: 0
% 1.03/0.61  #    Negative unit clauses             : 38
% 1.03/0.61  #    Non-unit-clauses                  : 230
% 1.03/0.61  # Current number of unprocessed clauses: 3063
% 1.03/0.61  # ...number of literals in the above   : 15723
% 1.03/0.61  # Current number of archived formulas  : 0
% 1.03/0.61  # Current number of archived clauses   : 567
% 1.03/0.61  # Clause-clause subsumption calls (NU) : 27038
% 1.03/0.61  # Rec. Clause-clause subsumption calls : 8916
% 1.03/0.61  # Non-unit clause-clause subsumptions  : 549
% 1.03/0.61  # Unit Clause-clause subsumption calls : 2136
% 1.03/0.61  # Rewrite failures with RHS unbound    : 0
% 1.03/0.61  # BW rewrite match attempts            : 44
% 1.03/0.61  # BW rewrite match successes           : 12
% 1.03/0.61  # Condensation attempts                : 0
% 1.03/0.61  # Condensation successes               : 0
% 1.03/0.61  # Termbank termtop insertions          : 80365
% 1.03/0.61  
% 1.03/0.61  # -------------------------------------------------
% 1.03/0.61  # User time                : 0.112 s
% 1.03/0.61  # System time              : 0.005 s
% 1.03/0.61  # Total time               : 0.117 s
% 1.03/0.61  # Maximum resident set size: 1644 pages
% 1.03/0.61  
% 1.03/0.61  # -------------------------------------------------
% 1.03/0.61  # User time                : 0.569 s
% 1.03/0.61  # System time              : 0.016 s
% 1.03/0.61  # Total time               : 0.585 s
% 1.03/0.61  # Maximum resident set size: 1688 pages
% 1.03/0.61  % E---3.1 exiting
% 1.03/0.61  % E---3.1 exiting
%------------------------------------------------------------------------------