TSTP Solution File: GRP124-3.004 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP124-3.004 : 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 : n020.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 00:16:13 EDT 2023

% Result   : Unsatisfiable 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   31
% Syntax   : Number of formulae    :  112 (  34 unt;  11 typ;   0 def)
%            Number of atoms       :  264 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  235 (  72   ~; 163   |;   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  :   12 (   6   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   57 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    e_0: $i ).

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

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

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

tff(decl_30,type,
    equalish: ( $i * $i ) > $o ).

tff(decl_31,type,
    group_element: $i > $o ).

tff(decl_32,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)
    | 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_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_idempotence,axiom,
    product(X1,X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).

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_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(qg2_2,negated_conjecture,
    ( equalish(X2,X5)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X5,X3)
    | ~ product(X6,X1,X2)
    | ~ product(X6,X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg2_2) ).

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

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

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

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_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(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_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(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_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(c_0_20,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_21,axiom,
    group_element(e_4),
    element_4 ).

cnf(c_0_22,axiom,
    ( equalish(X1,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X3) ),
    product_left_cancellation ).

cnf(c_0_23,axiom,
    product(X1,X1,X1),
    product_idempotence ).

cnf(c_0_24,plain,
    ( product(X1,e_4,e_1)
    | product(X1,e_4,e_2)
    | product(X1,e_4,e_3)
    | product(X1,e_4,e_4)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_25,axiom,
    group_element(e_3),
    element_3 ).

cnf(c_0_26,axiom,
    ( equalish(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X3) ),
    product_right_cancellation ).

cnf(c_0_27,plain,
    ( equalish(X1,X2)
    | ~ product(X1,X2,X2) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_28,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_24,c_0_25]) ).

cnf(c_0_29,axiom,
    ~ equalish(e_3,e_4),
    e_3_is_not_e_4 ).

cnf(c_0_30,negated_conjecture,
    ( equalish(X2,X5)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X5,X3)
    | ~ product(X6,X1,X2)
    | ~ product(X6,X4,X5) ),
    qg2_2 ).

cnf(c_0_31,plain,
    ( equalish(X1,X2)
    | ~ product(X2,X1,X2) ),
    inference(spm,[status(thm)],[c_0_26,c_0_23]) ).

cnf(c_0_32,plain,
    ( product(e_3,e_4,e_1)
    | product(e_3,e_4,e_2)
    | product(e_3,e_4,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).

cnf(c_0_33,axiom,
    ~ equalish(e_4,e_3),
    e_4_is_not_e_3 ).

cnf(c_0_34,axiom,
    group_element(e_2),
    element_2 ).

cnf(c_0_35,negated_conjecture,
    ( equalish(X1,X2)
    | ~ product(X2,X3,X1)
    | ~ product(X2,X2,X4)
    | ~ product(X3,X1,X4) ),
    inference(spm,[status(thm)],[c_0_30,c_0_23]) ).

cnf(c_0_36,plain,
    ( product(e_3,e_4,e_1)
    | product(e_3,e_4,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).

cnf(c_0_37,axiom,
    ~ equalish(e_2,e_3),
    e_2_is_not_e_3 ).

cnf(c_0_38,plain,
    ( product(X1,e_2,e_1)
    | product(X1,e_2,e_2)
    | product(X1,e_2,e_3)
    | product(X1,e_2,e_4)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_34]) ).

cnf(c_0_39,plain,
    ( product(X1,e_3,e_1)
    | product(X1,e_3,e_2)
    | product(X1,e_3,e_3)
    | product(X1,e_3,e_4)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_25]) ).

cnf(c_0_40,plain,
    ( product(e_2,e_4,e_1)
    | product(e_2,e_4,e_2)
    | product(e_2,e_4,e_3)
    | product(e_2,e_4,e_4) ),
    inference(spm,[status(thm)],[c_0_24,c_0_34]) ).

cnf(c_0_41,axiom,
    ~ equalish(e_2,e_4),
    e_2_is_not_e_4 ).

cnf(c_0_42,axiom,
    group_element(e_1),
    element_1 ).

cnf(c_0_43,negated_conjecture,
    ( product(e_3,e_4,e_1)
    | ~ product(e_3,e_3,X1)
    | ~ product(e_4,e_2,X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).

cnf(c_0_44,plain,
    ( product(e_4,e_2,e_1)
    | product(e_4,e_2,e_2)
    | product(e_4,e_2,e_3)
    | product(e_4,e_2,e_4) ),
    inference(spm,[status(thm)],[c_0_38,c_0_21]) ).

cnf(c_0_45,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_39,c_0_21]) ).

cnf(c_0_46,plain,
    ( product(e_2,e_4,e_1)
    | product(e_2,e_4,e_2)
    | product(e_2,e_4,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_40]),c_0_41]) ).

cnf(c_0_47,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_24,c_0_42]) ).

cnf(c_0_48,axiom,
    ~ equalish(e_1,e_4),
    e_1_is_not_e_4 ).

cnf(c_0_49,negated_conjecture,
    ( product(e_3,e_4,e_1)
    | ~ product(e_4,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_43,c_0_23]) ).

cnf(c_0_50,plain,
    ( product(e_4,e_2,e_1)
    | product(e_4,e_2,e_2)
    | product(e_4,e_2,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_44]),c_0_41]) ).

cnf(c_0_51,plain,
    ( product(e_4,e_3,e_1)
    | product(e_4,e_3,e_2)
    | product(e_4,e_3,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_45]),c_0_29]) ).

cnf(c_0_52,plain,
    ( product(e_2,e_4,e_1)
    | product(e_2,e_4,e_2)
    | equalish(X1,e_2)
    | ~ product(X1,e_4,e_3) ),
    inference(spm,[status(thm)],[c_0_22,c_0_46]) ).

cnf(c_0_53,plain,
    ( product(e_1,e_4,e_1)
    | product(e_1,e_4,e_2)
    | product(e_1,e_4,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_47]),c_0_48]) ).

cnf(c_0_54,axiom,
    ~ equalish(e_1,e_2),
    e_1_is_not_e_2 ).

cnf(c_0_55,negated_conjecture,
    ( product(e_3,e_4,e_1)
    | product(e_4,e_2,e_1)
    | product(e_4,e_2,e_2) ),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_56,axiom,
    ~ equalish(e_4,e_2),
    e_4_is_not_e_2 ).

cnf(c_0_57,plain,
    ( product(e_4,e_3,e_1)
    | product(e_4,e_3,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_51]),c_0_33]) ).

cnf(c_0_58,plain,
    ( product(e_2,e_4,e_1)
    | product(e_2,e_4,e_2)
    | product(e_1,e_4,e_1)
    | product(e_1,e_4,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).

cnf(c_0_59,negated_conjecture,
    ( product(e_3,e_4,e_1)
    | product(e_4,e_2,e_1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_55]),c_0_56]) ).

cnf(c_0_60,negated_conjecture,
    ( product(e_4,e_3,e_1)
    | ~ product(e_4,e_4,X1)
    | ~ product(e_3,e_2,X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_57]),c_0_41]) ).

cnf(c_0_61,plain,
    ( product(e_2,e_4,e_1)
    | product(e_1,e_4,e_1)
    | product(e_1,e_4,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_58]),c_0_56]) ).

cnf(c_0_62,negated_conjecture,
    ( product(e_3,e_4,e_1)
    | equalish(X1,e_2)
    | ~ product(e_4,X1,e_1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_59]) ).

cnf(c_0_63,negated_conjecture,
    ( product(e_4,e_3,e_1)
    | ~ product(e_3,e_2,e_4) ),
    inference(spm,[status(thm)],[c_0_60,c_0_23]) ).

cnf(c_0_64,axiom,
    ~ equalish(e_3,e_2),
    e_3_is_not_e_2 ).

cnf(c_0_65,plain,
    ( product(e_1,e_4,e_1)
    | product(e_1,e_4,e_2)
    | equalish(X1,e_2)
    | ~ product(X1,e_4,e_1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_61]) ).

cnf(c_0_66,negated_conjecture,
    ( product(e_3,e_4,e_1)
    | ~ product(e_3,e_2,e_4) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).

cnf(c_0_67,negated_conjecture,
    ( product(e_1,e_4,e_1)
    | product(e_1,e_4,e_2)
    | ~ product(e_3,e_2,e_4) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_64]) ).

cnf(c_0_68,plain,
    ( product(e_3,e_2,e_1)
    | product(e_3,e_2,e_2)
    | product(e_3,e_2,e_3)
    | product(e_3,e_2,e_4) ),
    inference(spm,[status(thm)],[c_0_38,c_0_25]) ).

cnf(c_0_69,negated_conjecture,
    ( product(e_1,e_4,e_1)
    | product(e_1,e_4,e_2)
    | 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_67,c_0_68]) ).

cnf(c_0_70,negated_conjecture,
    ( product(e_1,e_4,e_1)
    | product(e_1,e_4,e_2)
    | product(e_3,e_2,e_1)
    | product(e_3,e_2,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_69]),c_0_37]) ).

cnf(c_0_71,negated_conjecture,
    ( product(e_3,e_4,e_1)
    | equalish(X1,e_4)
    | ~ product(X1,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_59]) ).

cnf(c_0_72,negated_conjecture,
    ( product(e_1,e_4,e_1)
    | product(e_1,e_4,e_2)
    | product(e_3,e_2,e_1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_70]),c_0_64]) ).

cnf(c_0_73,plain,
    ( product(X1,e_1,e_1)
    | product(X1,e_1,e_2)
    | product(X1,e_1,e_3)
    | product(X1,e_1,e_4)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_42]) ).

cnf(c_0_74,negated_conjecture,
    ( product(e_3,e_4,e_1)
    | product(e_1,e_4,e_1)
    | product(e_1,e_4,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_29]) ).

cnf(c_0_75,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_73,c_0_21]) ).

cnf(c_0_76,negated_conjecture,
    ( product(e_4,e_2,e_1)
    | product(e_4,e_2,e_2)
    | ~ product(e_4,e_4,X1)
    | ~ product(e_2,e_3,X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_50]),c_0_29]) ).

cnf(c_0_77,negated_conjecture,
    ( product(e_1,e_4,e_1)
    | product(e_1,e_4,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_74]),c_0_64]) ).

cnf(c_0_78,axiom,
    ~ equalish(e_2,e_1),
    e_2_is_not_e_1 ).

cnf(c_0_79,plain,
    ( product(e_4,e_2,e_1)
    | product(e_4,e_2,e_2)
    | equalish(X1,e_2)
    | ~ product(e_4,X1,e_3) ),
    inference(spm,[status(thm)],[c_0_26,c_0_50]) ).

cnf(c_0_80,plain,
    ( product(e_4,e_1,e_1)
    | product(e_4,e_1,e_2)
    | product(e_4,e_1,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_75]),c_0_48]) ).

cnf(c_0_81,negated_conjecture,
    ( product(e_4,e_2,e_1)
    | product(e_4,e_2,e_2)
    | ~ product(e_2,e_3,e_4) ),
    inference(spm,[status(thm)],[c_0_76,c_0_23]) ).

cnf(c_0_82,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_39,c_0_34]) ).

cnf(c_0_83,negated_conjecture,
    ( product(e_1,e_4,e_1)
    | ~ product(e_1,e_1,X1)
    | ~ product(e_4,e_2,X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_77]),c_0_78]) ).

cnf(c_0_84,plain,
    ( product(e_4,e_2,e_1)
    | product(e_4,e_2,e_2)
    | product(e_4,e_1,e_1)
    | product(e_4,e_1,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_54]) ).

cnf(c_0_85,negated_conjecture,
    ( product(e_4,e_2,e_1)
    | product(e_4,e_2,e_2)
    | 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_81,c_0_82]) ).

cnf(c_0_86,negated_conjecture,
    ( product(e_1,e_4,e_1)
    | ~ product(e_4,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_83,c_0_23]) ).

cnf(c_0_87,plain,
    ( product(e_4,e_2,e_1)
    | product(e_4,e_1,e_1)
    | product(e_4,e_1,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_84]),c_0_56]) ).

cnf(c_0_88,negated_conjecture,
    ( product(e_4,e_2,e_1)
    | product(e_2,e_3,e_1)
    | product(e_2,e_3,e_2)
    | product(e_2,e_3,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_85]),c_0_56]) ).

cnf(c_0_89,plain,
    ( product(e_4,e_3,e_1)
    | equalish(X1,e_3)
    | ~ product(e_4,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_26,c_0_57]) ).

cnf(c_0_90,negated_conjecture,
    ( product(e_1,e_4,e_1)
    | product(e_4,e_1,e_1)
    | product(e_4,e_1,e_2) ),
    inference(spm,[status(thm)],[c_0_86,c_0_87]) ).

cnf(c_0_91,axiom,
    ~ equalish(e_1,e_3),
    e_1_is_not_e_3 ).

cnf(c_0_92,negated_conjecture,
    ( product(e_1,e_4,e_1)
    | 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_86,c_0_88]) ).

cnf(c_0_93,negated_conjecture,
    ( product(e_4,e_3,e_1)
    | product(e_1,e_4,e_1)
    | product(e_4,e_1,e_1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]) ).

cnf(c_0_94,negated_conjecture,
    ( product(e_1,e_4,e_1)
    | product(e_2,e_3,e_1)
    | product(e_2,e_3,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_92]),c_0_37]) ).

cnf(c_0_95,negated_conjecture,
    ( product(e_1,e_4,e_1)
    | product(e_4,e_1,e_1)
    | equalish(X1,e_4)
    | ~ product(X1,e_3,e_1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_93]) ).

cnf(c_0_96,negated_conjecture,
    ( product(e_1,e_4,e_1)
    | product(e_2,e_3,e_1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_94]),c_0_64]) ).

cnf(c_0_97,negated_conjecture,
    ( product(e_1,e_4,e_1)
    | product(e_4,e_1,e_1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_41]) ).

cnf(c_0_98,axiom,
    ~ equalish(e_4,e_1),
    e_4_is_not_e_1 ).

cnf(c_0_99,negated_conjecture,
    product(e_1,e_4,e_1),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_97]),c_0_98]) ).

cnf(c_0_100,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_99]),c_0_98]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : GRP124-3.004 : TPTP v8.1.2. Released v1.2.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.33  % Computer : n020.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Mon Aug 28 20:45:28 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.59  % Total time : 0.024000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.027000 s
%------------------------------------------------------------------------------