TSTP Solution File: GRP770-1 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : GRP770-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n021.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 17:50:36 EDT 2023

% Result   : Unsatisfiable 35.50s 4.99s
% Output   : CNFRefutation 35.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   20
% Syntax   : Number of clauses     :  115 ( 115 unt;   0 nHn;   3 RR)
%            Number of literals    :  115 ( 114 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-2 aty)
%            Number of variables   :  218 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(sos12,axiom,
    eta(X1) = product(i(X1),X1),
    file('/export/starexec/sandbox/tmp/tmp.ROxt5kasOC/E---3.1_3689.p',sos12) ).

cnf(sos09,axiom,
    i(X1) = difference(X1,one),
    file('/export/starexec/sandbox/tmp/tmp.ROxt5kasOC/E---3.1_3689.p',sos09) ).

cnf(sos14,axiom,
    product(X1,product(eta(X1),X2)) = product(j(j(X1)),X2),
    file('/export/starexec/sandbox/tmp/tmp.ROxt5kasOC/E---3.1_3689.p',sos14) ).

cnf(sos10,axiom,
    j(X1) = quotient(one,X1),
    file('/export/starexec/sandbox/tmp/tmp.ROxt5kasOC/E---3.1_3689.p',sos10) ).

cnf(sos11,axiom,
    product(i(X1),X1) = product(X1,j(X1)),
    file('/export/starexec/sandbox/tmp/tmp.ROxt5kasOC/E---3.1_3689.p',sos11) ).

cnf(sos24,axiom,
    product(j(product(X1,X2)),X1) = j(X2),
    file('/export/starexec/sandbox/tmp/tmp.ROxt5kasOC/E---3.1_3689.p',sos24) ).

cnf(sos01,axiom,
    product(X1,one) = X1,
    file('/export/starexec/sandbox/tmp/tmp.ROxt5kasOC/E---3.1_3689.p',sos01) ).

cnf(sos05,axiom,
    quotient(product(X1,X2),X2) = X1,
    file('/export/starexec/sandbox/tmp/tmp.ROxt5kasOC/E---3.1_3689.p',sos05) ).

cnf(sos07,axiom,
    difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
    file('/export/starexec/sandbox/tmp/tmp.ROxt5kasOC/E---3.1_3689.p',sos07) ).

cnf(sos06,axiom,
    product(quotient(X1,X2),X2) = X1,
    file('/export/starexec/sandbox/tmp/tmp.ROxt5kasOC/E---3.1_3689.p',sos06) ).

cnf(sos03,axiom,
    product(X1,difference(X1,X2)) = X2,
    file('/export/starexec/sandbox/tmp/tmp.ROxt5kasOC/E---3.1_3689.p',sos03) ).

cnf(sos08,axiom,
    difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
    file('/export/starexec/sandbox/tmp/tmp.ROxt5kasOC/E---3.1_3689.p',sos08) ).

cnf(sos04,axiom,
    difference(X1,product(X1,X2)) = X2,
    file('/export/starexec/sandbox/tmp/tmp.ROxt5kasOC/E---3.1_3689.p',sos04) ).

cnf(sos02,axiom,
    product(one,X1) = X1,
    file('/export/starexec/sandbox/tmp/tmp.ROxt5kasOC/E---3.1_3689.p',sos02) ).

cnf(sos17,axiom,
    quotient(j(X1),X1) = product(j(X1),i(X1)),
    file('/export/starexec/sandbox/tmp/tmp.ROxt5kasOC/E---3.1_3689.p',sos17) ).

cnf(sos23,axiom,
    product(X1,i(product(X2,X1))) = i(X2),
    file('/export/starexec/sandbox/tmp/tmp.ROxt5kasOC/E---3.1_3689.p',sos23) ).

cnf(sos22,axiom,
    product(j(j(X1)),j(product(X2,X1))) = j(X2),
    file('/export/starexec/sandbox/tmp/tmp.ROxt5kasOC/E---3.1_3689.p',sos22) ).

cnf(sos16,axiom,
    product(eta(X1),product(X2,X3)) = product(product(eta(X1),X2),X3),
    file('/export/starexec/sandbox/tmp/tmp.ROxt5kasOC/E---3.1_3689.p',sos16) ).

cnf(sos13,axiom,
    product(i(i(X1)),X2) = product(eta(X1),product(X1,X2)),
    file('/export/starexec/sandbox/tmp/tmp.ROxt5kasOC/E---3.1_3689.p',sos13) ).

cnf(goals,negated_conjecture,
    product(x0,product(x1,x2)) != product(quotient(product(x0,x1),x0),product(x0,x2)),
    file('/export/starexec/sandbox/tmp/tmp.ROxt5kasOC/E---3.1_3689.p',goals) ).

cnf(c_0_20,axiom,
    eta(X1) = product(i(X1),X1),
    sos12 ).

cnf(c_0_21,axiom,
    i(X1) = difference(X1,one),
    sos09 ).

cnf(c_0_22,axiom,
    product(X1,product(eta(X1),X2)) = product(j(j(X1)),X2),
    sos14 ).

cnf(c_0_23,axiom,
    j(X1) = quotient(one,X1),
    sos10 ).

cnf(c_0_24,plain,
    eta(X1) = product(difference(X1,one),X1),
    inference(rw,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_25,axiom,
    product(i(X1),X1) = product(X1,j(X1)),
    sos11 ).

cnf(c_0_26,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_22,c_0_23]),c_0_23]),c_0_24]) ).

cnf(c_0_27,plain,
    product(difference(X1,one),X1) = product(X1,quotient(one,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_21]),c_0_23]) ).

cnf(c_0_28,axiom,
    product(j(product(X1,X2)),X1) = j(X2),
    sos24 ).

cnf(c_0_29,plain,
    product(X1,product(product(X1,quotient(one,X1)),X2)) = product(quotient(one,quotient(one,X1)),X2),
    inference(rw,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_30,axiom,
    product(X1,one) = X1,
    sos01 ).

cnf(c_0_31,axiom,
    quotient(product(X1,X2),X2) = X1,
    sos05 ).

cnf(c_0_32,plain,
    product(quotient(one,product(X1,X2)),X1) = quotient(one,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_23]),c_0_23]) ).

cnf(c_0_33,axiom,
    difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
    sos07 ).

cnf(c_0_34,axiom,
    product(quotient(X1,X2),X2) = X1,
    sos06 ).

cnf(c_0_35,plain,
    product(X1,product(X1,quotient(one,X1))) = quotient(one,quotient(one,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_30]) ).

cnf(c_0_36,plain,
    quotient(quotient(one,X1),X2) = quotient(one,product(X2,X1)),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_37,axiom,
    product(X1,difference(X1,X2)) = X2,
    sos03 ).

cnf(c_0_38,plain,
    difference(X1,product(product(X1,X2),quotient(X3,X1))) = quotient(product(X2,X3),X1),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_39,axiom,
    difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
    sos08 ).

cnf(c_0_40,plain,
    quotient(one,product(product(X1,quotient(one,X1)),quotient(one,X1))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_35]),c_0_36]) ).

cnf(c_0_41,plain,
    product(product(X1,X2),quotient(X3,X1)) = product(X1,quotient(product(X2,X3),X1)),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_42,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_39,c_0_33]) ).

cnf(c_0_43,axiom,
    difference(X1,product(X1,X2)) = X2,
    sos04 ).

cnf(c_0_44,plain,
    quotient(one,product(X1,quotient(one,product(X1,X1)))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_30]),c_0_36]) ).

cnf(c_0_45,plain,
    quotient(difference(X1,product(X2,X3)),X3) = difference(product(X3,X1),product(X3,X2)),
    inference(spm,[status(thm)],[c_0_42,c_0_37]) ).

cnf(c_0_46,plain,
    difference(X1,X1) = one,
    inference(spm,[status(thm)],[c_0_43,c_0_30]) ).

cnf(c_0_47,plain,
    product(X1,product(X1,quotient(one,product(X1,X1)))) = one,
    inference(spm,[status(thm)],[c_0_34,c_0_44]) ).

cnf(c_0_48,axiom,
    product(one,X1) = X1,
    sos02 ).

cnf(c_0_49,axiom,
    quotient(j(X1),X1) = product(j(X1),i(X1)),
    sos17 ).

cnf(c_0_50,axiom,
    product(X1,i(product(X2,X1))) = i(X2),
    sos23 ).

cnf(c_0_51,plain,
    difference(product(X1,product(X2,X1)),product(X1,X2)) = quotient(one,X1),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_52,plain,
    quotient(difference(X1,X2),X2) = difference(product(X2,X1),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_47]),c_0_48]),c_0_30]) ).

cnf(c_0_53,plain,
    difference(quotient(X1,X2),X1) = X2,
    inference(spm,[status(thm)],[c_0_43,c_0_34]) ).

cnf(c_0_54,plain,
    quotient(quotient(one,X1),X1) = product(quotient(one,X1),difference(X1,one)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_21]),c_0_23]),c_0_23]) ).

cnf(c_0_55,plain,
    product(X1,difference(product(X2,X1),one)) = difference(X2,one),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_21]),c_0_21]) ).

cnf(c_0_56,plain,
    difference(product(X1,X2),product(X1,quotient(X2,X1))) = quotient(one,X1),
    inference(spm,[status(thm)],[c_0_51,c_0_34]) ).

cnf(c_0_57,plain,
    quotient(X1,difference(X2,X1)) = X2,
    inference(spm,[status(thm)],[c_0_31,c_0_37]) ).

cnf(c_0_58,plain,
    difference(product(X1,quotient(X1,X2)),X1) = quotient(X2,X1),
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_59,plain,
    product(quotient(one,X1),difference(X1,one)) = quotient(one,product(X1,X1)),
    inference(rw,[status(thm)],[c_0_54,c_0_36]) ).

cnf(c_0_60,plain,
    product(X1,difference(X2,one)) = difference(quotient(X2,X1),one),
    inference(spm,[status(thm)],[c_0_55,c_0_34]) ).

cnf(c_0_61,plain,
    product(quotient(one,X1),quotient(X1,X2)) = quotient(one,X2),
    inference(spm,[status(thm)],[c_0_32,c_0_34]) ).

cnf(c_0_62,plain,
    difference(product(quotient(X1,X2),product(X2,X1)),X1) = quotient(one,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_56]),c_0_36]),c_0_34]),c_0_34]) ).

cnf(c_0_63,plain,
    quotient(X1,quotient(X2,X1)) = product(X1,quotient(X1,X2)),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_64,plain,
    quotient(X1,one) = X1,
    inference(spm,[status(thm)],[c_0_30,c_0_34]) ).

cnf(c_0_65,plain,
    quotient(one,difference(X1,X2)) = product(quotient(one,X2),X1),
    inference(spm,[status(thm)],[c_0_32,c_0_37]) ).

cnf(c_0_66,plain,
    difference(quotient(X1,quotient(one,X1)),one) = quotient(one,product(X1,X1)),
    inference(rw,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_67,plain,
    difference(quotient(one,X1),quotient(one,X2)) = quotient(X1,X2),
    inference(spm,[status(thm)],[c_0_43,c_0_61]) ).

cnf(c_0_68,plain,
    product(quotient(X1,X2),product(X2,X1)) = product(X1,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_62]),c_0_63]),c_0_64]) ).

cnf(c_0_69,plain,
    product(difference(product(X1,X2),X1),X1) = difference(X2,X1),
    inference(spm,[status(thm)],[c_0_34,c_0_52]) ).

cnf(c_0_70,axiom,
    product(j(j(X1)),j(product(X2,X1))) = j(X2),
    sos22 ).

cnf(c_0_71,plain,
    quotient(one,quotient(one,product(X1,X1))) = quotient(X1,quotient(one,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_64]),c_0_48]) ).

cnf(c_0_72,plain,
    difference(product(quotient(one,X1),X2),one) = difference(X2,X1),
    inference(spm,[status(thm)],[c_0_53,c_0_65]) ).

cnf(c_0_73,plain,
    quotient(X1,difference(X2,one)) = difference(quotient(one,X1),X2),
    inference(spm,[status(thm)],[c_0_67,c_0_57]) ).

cnf(c_0_74,plain,
    difference(one,X1) = X1,
    inference(spm,[status(thm)],[c_0_48,c_0_37]) ).

cnf(c_0_75,plain,
    difference(quotient(X1,X2),product(X1,X1)) = product(X2,X1),
    inference(spm,[status(thm)],[c_0_43,c_0_68]) ).

cnf(c_0_76,plain,
    product(difference(X1,X2),X2) = difference(difference(X2,X1),X2),
    inference(spm,[status(thm)],[c_0_69,c_0_37]) ).

cnf(c_0_77,plain,
    quotient(product(X1,quotient(product(X2,X3),X1)),quotient(X3,X1)) = product(X1,X2),
    inference(spm,[status(thm)],[c_0_31,c_0_41]) ).

cnf(c_0_78,plain,
    product(quotient(one,quotient(one,X1)),quotient(one,product(X2,X1))) = quotient(one,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_23]),c_0_23]),c_0_23]),c_0_23]) ).

cnf(c_0_79,plain,
    quotient(X1,quotient(one,X1)) = product(X1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_44]),c_0_71]) ).

cnf(c_0_80,plain,
    difference(product(X1,X2),one) = difference(X2,difference(X1,one)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_64]),c_0_74]) ).

cnf(c_0_81,plain,
    difference(difference(X1,X2),X1) = difference(X2,product(X1,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_57]),c_0_76]) ).

cnf(c_0_82,plain,
    product(X1,quotient(product(difference(X1,X2),X3),X1)) = product(X2,quotient(X3,X1)),
    inference(spm,[status(thm)],[c_0_41,c_0_37]) ).

cnf(c_0_83,plain,
    quotient(product(X1,quotient(X2,X1)),quotient(X3,X1)) = product(X1,quotient(X2,X3)),
    inference(spm,[status(thm)],[c_0_77,c_0_34]) ).

cnf(c_0_84,plain,
    product(quotient(one,quotient(one,X1)),quotient(one,X2)) = quotient(one,quotient(X2,X1)),
    inference(spm,[status(thm)],[c_0_78,c_0_34]) ).

cnf(c_0_85,plain,
    quotient(one,product(X1,X1)) = difference(X1,difference(X1,one)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_79]),c_0_80]) ).

cnf(c_0_86,plain,
    product(difference(X1,X2),X2) = difference(X1,product(X2,X2)),
    inference(rw,[status(thm)],[c_0_76,c_0_81]) ).

cnf(c_0_87,plain,
    product(X1,quotient(difference(X1,X2),X1)) = product(X2,quotient(one,X1)),
    inference(spm,[status(thm)],[c_0_82,c_0_30]) ).

cnf(c_0_88,plain,
    quotient(product(X1,quotient(X2,X1)),X3) = product(X1,quotient(X2,product(X3,X1))),
    inference(spm,[status(thm)],[c_0_83,c_0_31]) ).

cnf(c_0_89,axiom,
    product(eta(X1),product(X2,X3)) = product(product(eta(X1),X2),X3),
    sos16 ).

cnf(c_0_90,axiom,
    product(i(i(X1)),X2) = product(eta(X1),product(X1,X2)),
    sos13 ).

cnf(c_0_91,plain,
    quotient(one,quotient(X1,product(X2,X2))) = product(product(X2,X2),quotient(one,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_65]),c_0_57]) ).

cnf(c_0_92,plain,
    product(product(X1,X1),quotient(one,X2)) = product(X1,quotient(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_86]),c_0_87]) ).

cnf(c_0_93,plain,
    product(X1,quotient(product(X2,X1),product(X3,X1))) = quotient(product(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_88,c_0_31]) ).

cnf(c_0_94,plain,
    product(X1,quotient(X1,product(X2,X1))) = quotient(X1,X2),
    inference(spm,[status(thm)],[c_0_63,c_0_31]) ).

cnf(c_0_95,plain,
    product(product(difference(X1,one),X1),product(X2,X3)) = product(product(product(difference(X1,one),X1),X2),X3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_24]),c_0_24]) ).

cnf(c_0_96,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_90,c_0_21]),c_0_21]),c_0_24]) ).

cnf(c_0_97,plain,
    quotient(one,quotient(X1,product(X2,X2))) = product(X2,quotient(X2,X1)),
    inference(rw,[status(thm)],[c_0_91,c_0_92]) ).

cnf(c_0_98,plain,
    quotient(product(X1,X2),product(X3,X2)) = difference(X2,quotient(product(X2,X1),X3)),
    inference(spm,[status(thm)],[c_0_43,c_0_93]) ).

cnf(c_0_99,plain,
    quotient(X1,product(X2,X1)) = difference(X1,quotient(X1,X2)),
    inference(spm,[status(thm)],[c_0_43,c_0_94]) ).

cnf(c_0_100,plain,
    product(product(product(X1,quotient(one,X1)),X2),X3) = product(product(X1,quotient(one,X1)),product(X2,X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_27]),c_0_27]) ).

cnf(c_0_101,plain,
    product(product(X1,quotient(one,X1)),product(X1,X2)) = product(difference(difference(X1,one),one),X2),
    inference(rw,[status(thm)],[c_0_96,c_0_27]) ).

cnf(c_0_102,plain,
    product(quotient(one,X1),quotient(one,quotient(one,X1))) = product(X1,quotient(one,X1)),
    inference(spm,[status(thm)],[c_0_27,c_0_53]) ).

cnf(c_0_103,plain,
    product(quotient(one,quotient(product(X1,X2),X1)),X1) = quotient(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_65]),c_0_99]),c_0_37]) ).

cnf(c_0_104,plain,
    product(X1,quotient(product(product(X1,quotient(one,X1)),product(X2,X3)),X1)) = product(product(quotient(one,quotient(one,X1)),X2),quotient(X3,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_29]),c_0_100]) ).

cnf(c_0_105,plain,
    product(product(X1,quotient(one,X1)),quotient(one,X2)) = product(difference(X1,one),quotient(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_61]),c_0_53]),c_0_102]) ).

cnf(c_0_106,plain,
    quotient(product(difference(X1,X2),X3),X1) = difference(X1,product(X2,quotient(X3,X1))),
    inference(spm,[status(thm)],[c_0_43,c_0_82]) ).

cnf(c_0_107,plain,
    quotient(one,quotient(product(X1,X2),X1)) = quotient(quotient(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_31,c_0_103]) ).

cnf(c_0_108,plain,
    quotient(one,quotient(product(X1,X2),product(X1,X3))) = quotient(quotient(X1,quotient(X2,X3)),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_84]),c_0_105]),c_0_106]),c_0_48]),c_0_37]),c_0_84]),c_0_36]),c_0_36]),c_0_84]) ).

cnf(c_0_109,plain,
    difference(quotient(quotient(X1,X2),X1),one) = quotient(product(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_53,c_0_107]) ).

cnf(c_0_110,plain,
    quotient(product(X1,quotient(X2,X3)),X1) = quotient(product(X1,X2),product(X1,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_108]),c_0_109]) ).

cnf(c_0_111,plain,
    quotient(product(X1,product(X2,X3)),product(X1,X3)) = quotient(product(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_110,c_0_31]) ).

cnf(c_0_112,negated_conjecture,
    product(x0,product(x1,x2)) != product(quotient(product(x0,x1),x0),product(x0,x2)),
    goals ).

cnf(c_0_113,plain,
    product(quotient(product(X1,X2),X1),product(X1,X3)) = product(X1,product(X2,X3)),
    inference(spm,[status(thm)],[c_0_34,c_0_111]) ).

cnf(c_0_114,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_113])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GRP770-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13  % Command    : run_E %s %d THM
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 2400
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Oct  3 02:36:44 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.20/0.48  Running first-order model finding
% 0.20/0.48  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.ROxt5kasOC/E---3.1_3689.p
% 35.50/4.99  # Version: 3.1pre001
% 35.50/4.99  # Preprocessing class: FSMSSMSSSSSNFFN.
% 35.50/4.99  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 35.50/4.99  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 35.50/4.99  # Starting new_bool_3 with 300s (1) cores
% 35.50/4.99  # Starting new_bool_1 with 300s (1) cores
% 35.50/4.99  # Starting sh5l with 300s (1) cores
% 35.50/4.99  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3766 completed with status 0
% 35.50/4.99  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 35.50/4.99  # Preprocessing class: FSMSSMSSSSSNFFN.
% 35.50/4.99  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 35.50/4.99  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 35.50/4.99  # No SInE strategy applied
% 35.50/4.99  # Search class: FUUPM-FFMF22-MFFFFFNN
% 35.50/4.99  # partial match(1): FUUPM-FFSF22-MFFFFFNN
% 35.50/4.99  # Scheduled 9 strats onto 5 cores with 1500 seconds (1500 total)
% 35.50/4.99  # Starting G-E--_107_C37_F1_PI_AE_Q4_CS_SP_PS_S0Y with 406s (1) cores
% 35.50/4.99  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 35.50/4.99  # Starting U----_206d_05_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 35.50/4.99  # Starting U----_102_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 35.50/4.99  # Starting G-E--_300_C01_F1_SE_CS_SP_S0Y with 136s (1) cores
% 35.50/4.99  # G-E--_107_C37_F1_PI_AE_Q4_CS_SP_PS_S0Y with pid 3772 completed with status 0
% 35.50/4.99  # Result found by G-E--_107_C37_F1_PI_AE_Q4_CS_SP_PS_S0Y
% 35.50/4.99  # Preprocessing class: FSMSSMSSSSSNFFN.
% 35.50/4.99  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 35.50/4.99  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 35.50/4.99  # No SInE strategy applied
% 35.50/4.99  # Search class: FUUPM-FFMF22-MFFFFFNN
% 35.50/4.99  # partial match(1): FUUPM-FFSF22-MFFFFFNN
% 35.50/4.99  # Scheduled 9 strats onto 5 cores with 1500 seconds (1500 total)
% 35.50/4.99  # Starting G-E--_107_C37_F1_PI_AE_Q4_CS_SP_PS_S0Y with 406s (1) cores
% 35.50/4.99  # Preprocessing time       : 0.001 s
% 35.50/4.99  # Presaturation interreduction done
% 35.50/4.99  
% 35.50/4.99  # Proof found!
% 35.50/4.99  # SZS status Unsatisfiable
% 35.50/4.99  # SZS output start CNFRefutation
% See solution above
% 35.50/4.99  # Parsed axioms                        : 25
% 35.50/4.99  # Removed by relevancy pruning/SinE    : 0
% 35.50/4.99  # Initial clauses                      : 25
% 35.50/4.99  # Removed in clause preprocessing      : 4
% 35.50/4.99  # Initial clauses in saturation        : 21
% 35.50/4.99  # Processed clauses                    : 2037
% 35.50/4.99  # ...of these trivial                  : 1099
% 35.50/4.99  # ...subsumed                          : 0
% 35.50/4.99  # ...remaining for further processing  : 938
% 35.50/4.99  # Other redundant clauses eliminated   : 0
% 35.50/4.99  # Clauses deleted for lack of memory   : 0
% 35.50/4.99  # Backward-subsumed                    : 0
% 35.50/4.99  # Backward-rewritten                   : 249
% 35.50/4.99  # Generated clauses                    : 292319
% 35.50/4.99  # ...of the previous two non-redundant : 239140
% 35.50/4.99  # ...aggressively subsumed             : 0
% 35.50/4.99  # Contextual simplify-reflections      : 0
% 35.50/4.99  # Paramodulations                      : 292319
% 35.50/4.99  # Factorizations                       : 0
% 35.50/4.99  # NegExts                              : 0
% 35.50/4.99  # Equation resolutions                 : 0
% 35.50/4.99  # Total rewrite steps                  : 1143449
% 35.50/4.99  # Propositional unsat checks           : 0
% 35.50/4.99  #    Propositional check models        : 0
% 35.50/4.99  #    Propositional check unsatisfiable : 0
% 35.50/4.99  #    Propositional clauses             : 0
% 35.50/4.99  #    Propositional clauses after purity: 0
% 35.50/4.99  #    Propositional unsat core size     : 0
% 35.50/4.99  #    Propositional preprocessing time  : 0.000
% 35.50/4.99  #    Propositional encoding time       : 0.000
% 35.50/4.99  #    Propositional solver time         : 0.000
% 35.50/4.99  #    Success case prop preproc time    : 0.000
% 35.50/4.99  #    Success case prop encoding time   : 0.000
% 35.50/4.99  #    Success case prop solver time     : 0.000
% 35.50/4.99  # Current number of processed clauses  : 668
% 35.50/4.99  #    Positive orientable unit clauses  : 668
% 35.50/4.99  #    Positive unorientable unit clauses: 0
% 35.50/4.99  #    Negative unit clauses             : 0
% 35.50/4.99  #    Non-unit-clauses                  : 0
% 35.50/4.99  # Current number of unprocessed clauses: 235772
% 35.50/4.99  # ...number of literals in the above   : 235772
% 35.50/4.99  # Current number of archived formulas  : 0
% 35.50/4.99  # Current number of archived clauses   : 274
% 35.50/4.99  # Clause-clause subsumption calls (NU) : 0
% 35.50/4.99  # Rec. Clause-clause subsumption calls : 0
% 35.50/4.99  # Non-unit clause-clause subsumptions  : 0
% 35.50/4.99  # Unit Clause-clause subsumption calls : 0
% 35.50/4.99  # Rewrite failures with RHS unbound    : 0
% 35.50/4.99  # BW rewrite match attempts            : 4285
% 35.50/4.99  # BW rewrite match successes           : 220
% 35.50/4.99  # Condensation attempts                : 0
% 35.50/4.99  # Condensation successes               : 0
% 35.50/4.99  # Termbank termtop insertions          : 7529159
% 35.50/4.99  
% 35.50/4.99  # -------------------------------------------------
% 35.50/4.99  # User time                : 4.066 s
% 35.50/4.99  # System time              : 0.180 s
% 35.50/4.99  # Total time               : 4.246 s
% 35.50/4.99  # Maximum resident set size: 1652 pages
% 35.50/4.99  
% 35.50/4.99  # -------------------------------------------------
% 35.50/4.99  # User time                : 20.839 s
% 35.50/4.99  # System time              : 0.946 s
% 35.50/4.99  # Total time               : 21.785 s
% 35.50/4.99  # Maximum resident set size: 1680 pages
% 35.50/4.99  % E---3.1 exiting
%------------------------------------------------------------------------------