TSTP Solution File: GRP766-1 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : GRP766-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n010.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 17:43:17 EDT 2023

% Result   : Unsatisfiable 8.97s 1.54s
% Output   : CNFRefutation 8.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   18
% Syntax   : Number of clauses     :  117 ( 117 unt;   0 nHn;   5 RR)
%            Number of literals    :  117 ( 116 equ;   4 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   4 con; 0-2 aty)
%            Number of variables   :  216 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(sos08,axiom,
    difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
    file('/export/starexec/sandbox2/tmp/tmp.DND07bL7GD/E---3.1_27348.p',sos08) ).

cnf(sos07,axiom,
    difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
    file('/export/starexec/sandbox2/tmp/tmp.DND07bL7GD/E---3.1_27348.p',sos07) ).

cnf(sos03,axiom,
    product(X1,difference(X1,X2)) = X2,
    file('/export/starexec/sandbox2/tmp/tmp.DND07bL7GD/E---3.1_27348.p',sos03) ).

cnf(sos04,axiom,
    difference(X1,product(X1,X2)) = X2,
    file('/export/starexec/sandbox2/tmp/tmp.DND07bL7GD/E---3.1_27348.p',sos04) ).

cnf(sos01,axiom,
    product(X1,one) = X1,
    file('/export/starexec/sandbox2/tmp/tmp.DND07bL7GD/E---3.1_27348.p',sos01) ).

cnf(sos05,axiom,
    quotient(product(X1,X2),X2) = X1,
    file('/export/starexec/sandbox2/tmp/tmp.DND07bL7GD/E---3.1_27348.p',sos05) ).

cnf(sos06,axiom,
    product(quotient(X1,X2),X2) = X1,
    file('/export/starexec/sandbox2/tmp/tmp.DND07bL7GD/E---3.1_27348.p',sos06) ).

cnf(sos02,axiom,
    product(one,X1) = X1,
    file('/export/starexec/sandbox2/tmp/tmp.DND07bL7GD/E---3.1_27348.p',sos02) ).

cnf(sos12,axiom,
    eta(X1) = product(i(X1),X1),
    file('/export/starexec/sandbox2/tmp/tmp.DND07bL7GD/E---3.1_27348.p',sos12) ).

cnf(sos09,axiom,
    i(X1) = difference(X1,one),
    file('/export/starexec/sandbox2/tmp/tmp.DND07bL7GD/E---3.1_27348.p',sos09) ).

cnf(sos15,axiom,
    product(i(i(X1)),X2) = product(eta(X1),product(X1,X2)),
    file('/export/starexec/sandbox2/tmp/tmp.DND07bL7GD/E---3.1_27348.p',sos15) ).

cnf(sos11,axiom,
    product(i(X1),X1) = product(X1,j(X1)),
    file('/export/starexec/sandbox2/tmp/tmp.DND07bL7GD/E---3.1_27348.p',sos11) ).

cnf(sos10,axiom,
    j(X1) = quotient(one,X1),
    file('/export/starexec/sandbox2/tmp/tmp.DND07bL7GD/E---3.1_27348.p',sos10) ).

cnf(sos16,axiom,
    product(X1,product(eta(X1),X2)) = product(j(j(X1)),X2),
    file('/export/starexec/sandbox2/tmp/tmp.DND07bL7GD/E---3.1_27348.p',sos16) ).

cnf(sos17,axiom,
    product(X1,product(X2,eta(X1))) = product(product(X1,X2),eta(X1)),
    file('/export/starexec/sandbox2/tmp/tmp.DND07bL7GD/E---3.1_27348.p',sos17) ).

cnf(sos19,axiom,
    t(eta(X1),product(X2,X3)) = product(t(eta(X1),X2),t(eta(X1),X3)),
    file('/export/starexec/sandbox2/tmp/tmp.DND07bL7GD/E---3.1_27348.p',sos19) ).

cnf(sos18,axiom,
    t(X1,X2) = quotient(product(X1,X2),X1),
    file('/export/starexec/sandbox2/tmp/tmp.DND07bL7GD/E---3.1_27348.p',sos18) ).

cnf(goals,negated_conjecture,
    product(eta(x0),product(x1,x2)) != product(product(eta(x0),x1),x2),
    file('/export/starexec/sandbox2/tmp/tmp.DND07bL7GD/E---3.1_27348.p',goals) ).

cnf(c_0_18,axiom,
    difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
    sos08 ).

cnf(c_0_19,axiom,
    difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
    sos07 ).

cnf(c_0_20,plain,
    quotient(difference(X1,product(product(X1,X2),X3)),X3) = difference(product(X3,X1),product(X3,product(X1,X2))),
    inference(rw,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_21,axiom,
    product(X1,difference(X1,X2)) = X2,
    sos03 ).

cnf(c_0_22,axiom,
    difference(X1,product(X1,X2)) = X2,
    sos04 ).

cnf(c_0_23,axiom,
    product(X1,one) = X1,
    sos01 ).

cnf(c_0_24,axiom,
    quotient(product(X1,X2),X2) = X1,
    sos05 ).

cnf(c_0_25,plain,
    quotient(difference(X1,product(X2,X3)),X3) = difference(product(X3,X1),product(X3,X2)),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_26,plain,
    difference(X1,X1) = one,
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_27,plain,
    quotient(X1,difference(X2,X1)) = X2,
    inference(spm,[status(thm)],[c_0_24,c_0_21]) ).

cnf(c_0_28,plain,
    difference(product(X1,product(X2,X1)),product(X1,X2)) = quotient(one,X1),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_29,plain,
    quotient(product(X1,X2),quotient(one,X1)) = product(X1,product(X2,X1)),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_30,axiom,
    product(quotient(X1,X2),X2) = X1,
    sos06 ).

cnf(c_0_31,axiom,
    product(one,X1) = X1,
    sos02 ).

cnf(c_0_32,axiom,
    eta(X1) = product(i(X1),X1),
    sos12 ).

cnf(c_0_33,axiom,
    i(X1) = difference(X1,one),
    sos09 ).

cnf(c_0_34,plain,
    product(X1,product(product(X2,quotient(one,X1)),X1)) = difference(quotient(one,X1),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_29]),c_0_30]),c_0_31]) ).

cnf(c_0_35,axiom,
    product(i(i(X1)),X2) = product(eta(X1),product(X1,X2)),
    sos15 ).

cnf(c_0_36,plain,
    eta(X1) = product(difference(X1,one),X1),
    inference(rw,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_37,axiom,
    product(i(X1),X1) = product(X1,j(X1)),
    sos11 ).

cnf(c_0_38,axiom,
    j(X1) = quotient(one,X1),
    sos10 ).

cnf(c_0_39,plain,
    product(product(X1,product(X2,X1)),quotient(one,X1)) = product(X1,X2),
    inference(spm,[status(thm)],[c_0_21,c_0_28]) ).

cnf(c_0_40,plain,
    difference(quotient(one,X1),quotient(X2,quotient(one,X1))) = product(X1,product(X2,X1)),
    inference(spm,[status(thm)],[c_0_34,c_0_30]) ).

cnf(c_0_41,plain,
    product(difference(X1,one),product(X2,difference(X1,one))) = quotient(product(difference(X1,one),X2),X1),
    inference(spm,[status(thm)],[c_0_29,c_0_27]) ).

cnf(c_0_42,plain,
    product(difference(difference(X1,one),one),X2) = product(product(difference(X1,one),X1),product(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_33]),c_0_33]),c_0_36]) ).

cnf(c_0_43,plain,
    product(difference(X1,one),X1) = product(X1,quotient(one,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_33]),c_0_38]) ).

cnf(c_0_44,plain,
    product(product(X1,X2),quotient(one,X1)) = product(X1,quotient(X2,X1)),
    inference(spm,[status(thm)],[c_0_39,c_0_30]) ).

cnf(c_0_45,axiom,
    product(X1,product(eta(X1),X2)) = product(j(j(X1)),X2),
    sos16 ).

cnf(c_0_46,plain,
    quotient(product(difference(X1,one),X2),X1) = difference(X1,quotient(X2,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_27]),c_0_41]) ).

cnf(c_0_47,plain,
    difference(quotient(X1,X2),X1) = X2,
    inference(spm,[status(thm)],[c_0_22,c_0_30]) ).

cnf(c_0_48,plain,
    product(product(X1,quotient(one,X1)),product(X1,X2)) = product(difference(difference(X1,one),one),X2),
    inference(rw,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_49,plain,
    product(X1,quotient(difference(X1,X2),X1)) = product(X2,quotient(one,X1)),
    inference(spm,[status(thm)],[c_0_44,c_0_21]) ).

cnf(c_0_50,plain,
    product(X1,product(product(difference(X1,one),X1),X2)) = product(quotient(one,quotient(one,X1)),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_38]),c_0_38]),c_0_36]) ).

cnf(c_0_51,plain,
    difference(X1,quotient(difference(difference(X1,one),X2),X1)) = quotient(X2,X1),
    inference(spm,[status(thm)],[c_0_46,c_0_21]) ).

cnf(c_0_52,plain,
    product(quotient(one,X1),quotient(one,quotient(one,X1))) = product(X1,quotient(one,X1)),
    inference(spm,[status(thm)],[c_0_43,c_0_47]) ).

cnf(c_0_53,plain,
    product(product(X1,quotient(one,X1)),X1) = difference(difference(X1,one),one),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_23]),c_0_23]) ).

cnf(c_0_54,plain,
    difference(X1,product(X2,quotient(one,X1))) = quotient(difference(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_22,c_0_49]) ).

cnf(c_0_55,plain,
    difference(one,X1) = X1,
    inference(spm,[status(thm)],[c_0_31,c_0_21]) ).

cnf(c_0_56,plain,
    product(X1,product(difference(X1,X2),X1)) = quotient(X2,quotient(one,X1)),
    inference(spm,[status(thm)],[c_0_29,c_0_21]) ).

cnf(c_0_57,plain,
    product(difference(X1,quotient(X2,X1)),X1) = product(difference(X1,one),X2),
    inference(spm,[status(thm)],[c_0_30,c_0_46]) ).

cnf(c_0_58,plain,
    quotient(difference(X1,product(X2,quotient(one,X2))),X2) = difference(product(X2,X1),one),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_43]),c_0_21]) ).

cnf(c_0_59,plain,
    product(X1,product(product(X1,quotient(one,X1)),X2)) = product(quotient(one,quotient(one,X1)),X2),
    inference(rw,[status(thm)],[c_0_50,c_0_43]) ).

cnf(c_0_60,plain,
    quotient(difference(difference(X1,one),X2),X1) = product(X1,quotient(X2,X1)),
    inference(spm,[status(thm)],[c_0_21,c_0_51]) ).

cnf(c_0_61,axiom,
    product(X1,product(X2,eta(X1))) = product(product(X1,X2),eta(X1)),
    sos17 ).

cnf(c_0_62,plain,
    product(product(X1,quotient(one,X1)),product(quotient(one,X1),X2)) = product(difference(X1,one),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_52]),c_0_47]) ).

cnf(c_0_63,plain,
    product(product(X1,quotient(one,X1)),quotient(one,X1)) = difference(X1,one),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_52]),c_0_47]) ).

cnf(c_0_64,plain,
    quotient(quotient(difference(X1,X2),X1),quotient(one,X1)) = product(quotient(one,X1),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_54]),c_0_30]),c_0_55]) ).

cnf(c_0_65,plain,
    quotient(quotient(X1,X2),quotient(one,X2)) = product(X2,product(difference(X2,one),X1)),
    inference(spm,[status(thm)],[c_0_56,c_0_57]) ).

cnf(c_0_66,axiom,
    t(eta(X1),product(X2,X3)) = product(t(eta(X1),X2),t(eta(X1),X3)),
    sos19 ).

cnf(c_0_67,axiom,
    t(X1,X2) = quotient(product(X1,X2),X1),
    sos18 ).

cnf(c_0_68,plain,
    difference(X1,product(X2,quotient(one,X2))) = product(difference(product(X2,X1),one),X2),
    inference(spm,[status(thm)],[c_0_30,c_0_58]) ).

cnf(c_0_69,plain,
    product(X1,product(X1,quotient(one,X1))) = quotient(one,quotient(one,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_23]),c_0_23]) ).

cnf(c_0_70,plain,
    difference(X1,product(product(X1,X2),quotient(X3,X1))) = quotient(product(X2,X3),X1),
    inference(spm,[status(thm)],[c_0_19,c_0_30]) ).

cnf(c_0_71,plain,
    product(product(X1,quotient(X2,X1)),X1) = difference(difference(X1,one),X2),
    inference(spm,[status(thm)],[c_0_30,c_0_60]) ).

cnf(c_0_72,plain,
    product(X1,product(X2,product(difference(X1,one),X1))) = product(product(X1,X2),product(difference(X1,one),X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_36]),c_0_36]) ).

cnf(c_0_73,plain,
    product(difference(X1,one),difference(quotient(one,X1),X2)) = product(product(X1,quotient(one,X1)),X2),
    inference(spm,[status(thm)],[c_0_62,c_0_21]) ).

cnf(c_0_74,plain,
    product(quotient(one,X1),quotient(X2,quotient(one,X1))) = quotient(difference(X1,X2),quotient(one,X1)),
    inference(spm,[status(thm)],[c_0_60,c_0_47]) ).

cnf(c_0_75,plain,
    quotient(difference(X1,one),quotient(one,X1)) = product(X1,quotient(one,X1)),
    inference(spm,[status(thm)],[c_0_24,c_0_63]) ).

cnf(c_0_76,plain,
    product(X1,product(difference(X1,one),difference(X1,X2))) = product(quotient(one,X1),X2),
    inference(rw,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_77,plain,
    quotient(product(product(difference(X1,one),X1),product(X2,X3)),product(difference(X1,one),X1)) = product(quotient(product(product(difference(X1,one),X1),X2),product(difference(X1,one),X1)),quotient(product(product(difference(X1,one),X1),X3),product(difference(X1,one),X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_36]),c_0_36]),c_0_36]),c_0_67]),c_0_67]),c_0_67]) ).

cnf(c_0_78,plain,
    product(X1,product(difference(product(X2,X1),one),X2)) = product(X2,quotient(one,X2)),
    inference(spm,[status(thm)],[c_0_21,c_0_68]) ).

cnf(c_0_79,plain,
    product(product(X1,quotient(one,X1)),quotient(one,quotient(one,X1))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_52]),c_0_47]) ).

cnf(c_0_80,plain,
    product(difference(X1,one),product(X1,quotient(one,X1))) = quotient(one,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_27]),c_0_43]) ).

cnf(c_0_81,plain,
    product(product(X1,X2),quotient(X3,X1)) = product(X1,quotient(product(X2,X3),X1)),
    inference(spm,[status(thm)],[c_0_21,c_0_70]) ).

cnf(c_0_82,plain,
    difference(X1,difference(quotient(one,X1),X2)) = product(product(X2,quotient(one,X1)),X1),
    inference(spm,[status(thm)],[c_0_22,c_0_34]) ).

cnf(c_0_83,plain,
    difference(difference(X1,one),difference(X1,X2)) = product(product(X2,quotient(one,X1)),X1),
    inference(spm,[status(thm)],[c_0_71,c_0_49]) ).

cnf(c_0_84,plain,
    product(product(X1,X2),product(X1,quotient(one,X1))) = product(X1,product(X2,product(X1,quotient(one,X1)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_43]),c_0_43]) ).

cnf(c_0_85,plain,
    product(quotient(X1,X2),product(X2,quotient(X1,X2))) = quotient(X1,quotient(one,quotient(X1,X2))),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_86,plain,
    product(difference(difference(X1,one),one),quotient(one,X1)) = product(difference(X1,one),quotient(one,quotient(one,X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_52]),c_0_52]),c_0_48]),c_0_47]) ).

cnf(c_0_87,plain,
    quotient(product(product(X1,quotient(one,X1)),X2),difference(quotient(one,X1),X2)) = difference(X1,one),
    inference(spm,[status(thm)],[c_0_24,c_0_73]) ).

cnf(c_0_88,plain,
    product(product(X1,quotient(one,X1)),product(quotient(one,quotient(one,X1)),X2)) = product(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_74]),c_0_75]),c_0_47]) ).

cnf(c_0_89,plain,
    difference(X1,product(quotient(one,X1),X2)) = product(difference(X1,one),difference(X1,X2)),
    inference(spm,[status(thm)],[c_0_22,c_0_76]) ).

cnf(c_0_90,plain,
    product(quotient(product(product(X1,quotient(one,X1)),X2),product(X1,quotient(one,X1))),quotient(product(product(X1,quotient(one,X1)),X3),product(X1,quotient(one,X1)))) = quotient(product(product(X1,quotient(one,X1)),product(X2,X3)),product(X1,quotient(one,X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_43]),c_0_43]),c_0_43]),c_0_43]),c_0_43]),c_0_43]) ).

cnf(c_0_91,plain,
    product(product(X1,quotient(one,X1)),quotient(one,product(X1,quotient(one,X1)))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]),c_0_30]) ).

cnf(c_0_92,plain,
    product(X1,quotient(product(difference(X1,X2),X3),X1)) = product(X2,quotient(X3,X1)),
    inference(spm,[status(thm)],[c_0_81,c_0_21]) ).

cnf(c_0_93,plain,
    product(product(X1,quotient(one,X2)),X2) = product(product(X1,X2),difference(X2,one)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_27]),c_0_83]) ).

cnf(c_0_94,plain,
    difference(product(X1,quotient(one,X1)),product(difference(difference(X1,one),one),X2)) = product(X1,X2),
    inference(spm,[status(thm)],[c_0_22,c_0_48]) ).

cnf(c_0_95,plain,
    product(difference(X1,one),quotient(one,quotient(one,X1))) = product(X1,quotient(one,quotient(one,quotient(one,X1)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_84]),c_0_85]),c_0_86]) ).

cnf(c_0_96,plain,
    quotient(product(X1,X2),product(X1,difference(quotient(one,X1),X2))) = difference(X1,one),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]),c_0_47]) ).

cnf(c_0_97,plain,
    difference(quotient(product(product(X1,quotient(one,X1)),X2),product(X1,quotient(one,X1))),quotient(product(product(X1,quotient(one,X1)),product(X2,X3)),product(X1,quotient(one,X1)))) = quotient(product(product(X1,quotient(one,X1)),X3),product(X1,quotient(one,X1))),
    inference(spm,[status(thm)],[c_0_22,c_0_90]) ).

cnf(c_0_98,plain,
    quotient(one,product(X1,quotient(one,X1))) = difference(product(X1,quotient(one,X1)),one),
    inference(spm,[status(thm)],[c_0_22,c_0_91]) ).

cnf(c_0_99,plain,
    quotient(product(difference(X1,X2),X3),X1) = difference(X1,product(X2,quotient(X3,X1))),
    inference(spm,[status(thm)],[c_0_22,c_0_92]) ).

cnf(c_0_100,plain,
    difference(difference(X1,one),difference(X1,X2)) = product(product(X2,X1),difference(X1,one)),
    inference(rw,[status(thm)],[c_0_83,c_0_93]) ).

cnf(c_0_101,plain,
    difference(product(X1,quotient(one,X1)),product(product(X1,quotient(one,quotient(one,quotient(one,X1)))),X2)) = product(product(X1,quotient(one,X1)),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_84]),c_0_19]),c_0_53]),c_0_19]),c_0_48]),c_0_94]),c_0_30]),c_0_86]),c_0_95]) ).

cnf(c_0_102,plain,
    quotient(product(X1,product(quotient(one,X1),X2)),product(X1,X2)) = difference(X1,one),
    inference(spm,[status(thm)],[c_0_96,c_0_22]) ).

cnf(c_0_103,plain,
    product(X1,difference(product(X2,quotient(one,X2)),one)) = quotient(X1,product(X2,quotient(one,X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_76]),c_0_21]),c_0_98]),c_0_98]),c_0_99]),c_0_31]),c_0_100]),c_0_30]),c_0_21]) ).

cnf(c_0_104,plain,
    product(difference(X1,one),quotient(X2,difference(X1,one))) = product(product(difference(X1,one),X2),X1),
    inference(spm,[status(thm)],[c_0_44,c_0_27]) ).

cnf(c_0_105,plain,
    difference(difference(product(X1,quotient(one,X1)),one),one) = product(X1,quotient(one,X1)),
    inference(spm,[status(thm)],[c_0_47,c_0_98]) ).

cnf(c_0_106,plain,
    quotient(product(product(X1,quotient(one,X1)),product(product(X2,product(X1,quotient(one,X1))),X3)),product(X1,quotient(one,X1))) = product(product(X1,quotient(one,X1)),quotient(product(X2,product(product(X1,quotient(one,X1)),X3)),product(X1,quotient(one,X1)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_19]),c_0_48]),c_0_86]),c_0_95]),c_0_101]),c_0_81]) ).

cnf(c_0_107,plain,
    product(difference(X1,one),product(X1,X2)) = product(X1,product(quotient(one,X1),X2)),
    inference(spm,[status(thm)],[c_0_30,c_0_102]) ).

cnf(c_0_108,plain,
    product(difference(product(X1,quotient(one,X1)),one),X2) = difference(product(X1,quotient(one,X1)),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_103]),c_0_104]),c_0_24]),c_0_105]) ).

cnf(c_0_109,negated_conjecture,
    product(eta(x0),product(x1,x2)) != product(product(eta(x0),x1),x2),
    goals ).

cnf(c_0_110,plain,
    difference(difference(X1,product(product(X1,X2),X3)),product(X2,product(X3,X1))) = X1,
    inference(spm,[status(thm)],[c_0_47,c_0_19]) ).

cnf(c_0_111,plain,
    product(product(X1,product(X2,quotient(one,X2))),X3) = product(X1,product(product(X2,quotient(one,X2)),X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_106]),c_0_22]),c_0_30]),c_0_107]),c_0_98]),c_0_108]),c_0_21]) ).

cnf(c_0_112,negated_conjecture,
    product(product(difference(x0,one),x0),product(x1,x2)) != product(product(product(difference(x0,one),x0),x1),x2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_36]),c_0_36]) ).

cnf(c_0_113,plain,
    difference(product(product(X1,quotient(one,X1)),X2),product(product(X1,quotient(one,X1)),product(X2,X3))) = X3,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_22]) ).

cnf(c_0_114,negated_conjecture,
    product(product(product(x0,quotient(one,x0)),x1),x2) != product(product(x0,quotient(one,x0)),product(x1,x2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_43]),c_0_43]) ).

cnf(c_0_115,plain,
    product(product(product(X1,quotient(one,X1)),X2),X3) = product(product(X1,quotient(one,X1)),product(X2,X3)),
    inference(spm,[status(thm)],[c_0_21,c_0_113]) ).

cnf(c_0_116,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_115])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem    : GRP766-1 : TPTP v8.1.2. Released v4.1.0.
% 0.02/0.10  % Command    : run_E %s %d THM
% 0.10/0.30  % Computer : n010.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit   : 2400
% 0.10/0.30  % WCLimit    : 300
% 0.10/0.30  % DateTime   : Tue Oct  3 02:27:05 EDT 2023
% 0.10/0.31  % CPUTime    : 
% 0.16/0.41  Running first-order theorem proving
% 0.16/0.41  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.DND07bL7GD/E---3.1_27348.p
% 8.97/1.54  # Version: 3.1pre001
% 8.97/1.54  # Preprocessing class: FSMSSMSSSSSNFFN.
% 8.97/1.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.97/1.54  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.97/1.54  # Starting new_bool_3 with 300s (1) cores
% 8.97/1.54  # Starting new_bool_1 with 300s (1) cores
% 8.97/1.54  # Starting sh5l with 300s (1) cores
% 8.97/1.54  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 27426 completed with status 0
% 8.97/1.54  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 8.97/1.54  # Preprocessing class: FSMSSMSSSSSNFFN.
% 8.97/1.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.97/1.54  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.97/1.54  # No SInE strategy applied
% 8.97/1.54  # Search class: FUUPM-FFMF22-MFFFFFNN
% 8.97/1.54  # partial match(1): FUUPM-FFSF22-MFFFFFNN
% 8.97/1.54  # Scheduled 9 strats onto 5 cores with 1500 seconds (1500 total)
% 8.97/1.54  # Starting G-E--_107_C37_F1_PI_AE_Q4_CS_SP_PS_S0Y with 406s (1) cores
% 8.97/1.54  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 8.97/1.54  # Starting U----_206d_05_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 8.97/1.54  # Starting U----_102_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 8.97/1.54  # Starting G-E--_300_C01_F1_SE_CS_SP_S0Y with 136s (1) cores
% 8.97/1.54  # U----_206d_05_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 27435 completed with status 0
% 8.97/1.54  # Result found by U----_206d_05_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 8.97/1.54  # Preprocessing class: FSMSSMSSSSSNFFN.
% 8.97/1.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.97/1.54  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.97/1.54  # No SInE strategy applied
% 8.97/1.54  # Search class: FUUPM-FFMF22-MFFFFFNN
% 8.97/1.54  # partial match(1): FUUPM-FFSF22-MFFFFFNN
% 8.97/1.54  # Scheduled 9 strats onto 5 cores with 1500 seconds (1500 total)
% 8.97/1.54  # Starting G-E--_107_C37_F1_PI_AE_Q4_CS_SP_PS_S0Y with 406s (1) cores
% 8.97/1.54  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 8.97/1.54  # Starting U----_206d_05_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 8.97/1.54  # Preprocessing time       : 0.001 s
% 8.97/1.54  # Presaturation interreduction done
% 8.97/1.54  
% 8.97/1.54  # Proof found!
% 8.97/1.54  # SZS status Unsatisfiable
% 8.97/1.54  # SZS output start CNFRefutation
% See solution above
% 8.99/1.54  # Parsed axioms                        : 20
% 8.99/1.54  # Removed by relevancy pruning/SinE    : 0
% 8.99/1.54  # Initial clauses                      : 20
% 8.99/1.54  # Removed in clause preprocessing      : 5
% 8.99/1.54  # Initial clauses in saturation        : 15
% 8.99/1.54  # Processed clauses                    : 1215
% 8.99/1.54  # ...of these trivial                  : 641
% 8.99/1.54  # ...subsumed                          : 0
% 8.99/1.54  # ...remaining for further processing  : 574
% 8.99/1.54  # Other redundant clauses eliminated   : 0
% 8.99/1.54  # Clauses deleted for lack of memory   : 0
% 8.99/1.54  # Backward-subsumed                    : 0
% 8.99/1.54  # Backward-rewritten                   : 204
% 8.99/1.54  # Generated clauses                    : 67235
% 8.99/1.54  # ...of the previous two non-redundant : 47366
% 8.99/1.54  # ...aggressively subsumed             : 0
% 8.99/1.54  # Contextual simplify-reflections      : 0
% 8.99/1.54  # Paramodulations                      : 67235
% 8.99/1.54  # Factorizations                       : 0
% 8.99/1.54  # NegExts                              : 0
% 8.99/1.54  # Equation resolutions                 : 0
% 8.99/1.54  # Total rewrite steps                  : 263095
% 8.99/1.54  # Propositional unsat checks           : 0
% 8.99/1.54  #    Propositional check models        : 0
% 8.99/1.54  #    Propositional check unsatisfiable : 0
% 8.99/1.54  #    Propositional clauses             : 0
% 8.99/1.54  #    Propositional clauses after purity: 0
% 8.99/1.54  #    Propositional unsat core size     : 0
% 8.99/1.54  #    Propositional preprocessing time  : 0.000
% 8.99/1.54  #    Propositional encoding time       : 0.000
% 8.99/1.54  #    Propositional solver time         : 0.000
% 8.99/1.54  #    Success case prop preproc time    : 0.000
% 8.99/1.54  #    Success case prop encoding time   : 0.000
% 8.99/1.54  #    Success case prop solver time     : 0.000
% 8.99/1.54  # Current number of processed clauses  : 355
% 8.99/1.54  #    Positive orientable unit clauses  : 355
% 8.99/1.54  #    Positive unorientable unit clauses: 0
% 8.99/1.54  #    Negative unit clauses             : 0
% 8.99/1.54  #    Non-unit-clauses                  : 0
% 8.99/1.54  # Current number of unprocessed clauses: 45449
% 8.99/1.54  # ...number of literals in the above   : 45449
% 8.99/1.54  # Current number of archived formulas  : 0
% 8.99/1.54  # Current number of archived clauses   : 224
% 8.99/1.54  # Clause-clause subsumption calls (NU) : 0
% 8.99/1.54  # Rec. Clause-clause subsumption calls : 0
% 8.99/1.54  # Non-unit clause-clause subsumptions  : 0
% 8.99/1.54  # Unit Clause-clause subsumption calls : 3
% 8.99/1.54  # Rewrite failures with RHS unbound    : 0
% 8.99/1.54  # BW rewrite match attempts            : 972
% 8.99/1.54  # BW rewrite match successes           : 163
% 8.99/1.54  # Condensation attempts                : 0
% 8.99/1.54  # Condensation successes               : 0
% 8.99/1.54  # Termbank termtop insertions          : 2031148
% 8.99/1.54  
% 8.99/1.54  # -------------------------------------------------
% 8.99/1.54  # User time                : 1.040 s
% 8.99/1.54  # System time              : 0.039 s
% 8.99/1.54  # Total time               : 1.079 s
% 8.99/1.54  # Maximum resident set size: 1664 pages
% 8.99/1.54  
% 8.99/1.54  # -------------------------------------------------
% 8.99/1.54  # User time                : 5.189 s
% 8.99/1.54  # System time              : 0.207 s
% 8.99/1.54  # Total time               : 5.396 s
% 8.99/1.54  # Maximum resident set size: 1692 pages
% 8.99/1.54  % E---3.1 exiting
% 8.99/1.54  % E---3.1 exiting
%------------------------------------------------------------------------------