TSTP Solution File: GRP765-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP765-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n012.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 00:23:39 EDT 2023

% Result   : Unsatisfiable 4.67s 4.74s
% Output   : CNFRefutation 4.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   43
%            Number of leaves      :   22
% Syntax   : Number of formulae    :  202 ( 193 unt;   9 typ;   0 def)
%            Number of atoms       :  193 ( 192 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    4 (   4   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    9 (   6   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-2 aty)
%            Number of variables   :  364 (   0 sgn;   0   !;   0   ?;   0   :)

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

tff(decl_23,type,
    product: ( $i * $i ) > $i ).

tff(decl_24,type,
    difference: ( $i * $i ) > $i ).

tff(decl_25,type,
    quotient: ( $i * $i ) > $i ).

tff(decl_26,type,
    i: $i > $i ).

tff(decl_27,type,
    j: $i > $i ).

tff(decl_28,type,
    eta: $i > $i ).

tff(decl_29,type,
    x0: $i ).

tff(decl_30,type,
    x1: $i ).

cnf(sos07,axiom,
    difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).

cnf(sos03,axiom,
    product(X1,difference(X1,X2)) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).

cnf(sos06,axiom,
    product(quotient(X1,X2),X2) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).

cnf(sos02,axiom,
    product(one,X1) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).

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/benchmark/theBenchmark.p',sos08) ).

cnf(sos04,axiom,
    difference(X1,product(X1,X2)) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).

cnf(sos05,axiom,
    quotient(product(X1,X2),X2) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).

cnf(sos01,axiom,
    product(X1,one) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).

cnf(sos11,axiom,
    product(i(X1),X1) = product(X1,j(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).

cnf(sos09,axiom,
    i(X1) = difference(X1,one),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).

cnf(sos10,axiom,
    j(X1) = quotient(one,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).

cnf(sos12,axiom,
    eta(X1) = product(i(X1),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).

cnf(goals,negated_conjecture,
    product(i(i(x0)),x1) != product(eta(x0),product(x0,x1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

cnf(c_0_13,axiom,
    difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
    sos07 ).

cnf(c_0_14,axiom,
    product(X1,difference(X1,X2)) = X2,
    sos03 ).

cnf(c_0_15,axiom,
    product(quotient(X1,X2),X2) = X1,
    sos06 ).

cnf(c_0_16,plain,
    quotient(product(difference(X1,X2),product(X3,X1)),X1) = difference(X1,product(X2,X3)),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_17,plain,
    product(difference(X1,product(X2,X3)),X1) = product(difference(X1,X2),product(X3,X1)),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_18,axiom,
    product(one,X1) = X1,
    sos02 ).

cnf(c_0_19,axiom,
    difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
    sos08 ).

cnf(c_0_20,axiom,
    difference(X1,product(X1,X2)) = X2,
    sos04 ).

cnf(c_0_21,plain,
    product(difference(X1,one),product(X2,X1)) = product(difference(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_22,plain,
    product(product(X1,X2),quotient(quotient(product(X3,product(X1,X2)),X2),X1)) = product(X1,product(X2,X3)),
    inference(spm,[status(thm)],[c_0_14,c_0_19]) ).

cnf(c_0_23,axiom,
    quotient(product(X1,X2),X2) = X1,
    sos05 ).

cnf(c_0_24,axiom,
    product(X1,one) = X1,
    sos01 ).

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

cnf(c_0_26,plain,
    product(product(X1,X2),quotient(difference(X2,X1),X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_21]),c_0_23]),c_0_14]),c_0_24]) ).

cnf(c_0_27,plain,
    difference(X1,X1) = one,
    inference(spm,[status(thm)],[c_0_20,c_0_24]) ).

cnf(c_0_28,plain,
    difference(difference(X1,one),product(X2,X1)) = product(product(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_25,c_0_20]) ).

cnf(c_0_29,axiom,
    product(i(X1),X1) = product(X1,j(X1)),
    sos11 ).

cnf(c_0_30,axiom,
    i(X1) = difference(X1,one),
    sos09 ).

cnf(c_0_31,axiom,
    j(X1) = quotient(one,X1),
    sos10 ).

cnf(c_0_32,plain,
    difference(product(X1,X2),X1) = quotient(difference(X2,X1),X1),
    inference(spm,[status(thm)],[c_0_20,c_0_26]) ).

cnf(c_0_33,plain,
    quotient(product(difference(X1,X2),X1),product(X2,X1)) = difference(X1,one),
    inference(spm,[status(thm)],[c_0_23,c_0_21]) ).

cnf(c_0_34,plain,
    difference(difference(X1,one),X1) = product(X1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_27]),c_0_18]) ).

cnf(c_0_35,plain,
    quotient(X1,one) = X1,
    inference(spm,[status(thm)],[c_0_24,c_0_15]) ).

cnf(c_0_36,plain,
    product(product(product(X1,X2),X1),difference(X1,one)) = difference(difference(X1,one),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_28]),c_0_14]),c_0_24]) ).

cnf(c_0_37,plain,
    product(difference(X1,one),X1) = product(X1,quotient(one,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).

cnf(c_0_38,plain,
    quotient(difference(difference(X1,X2),X1),X1) = difference(X2,X1),
    inference(spm,[status(thm)],[c_0_32,c_0_14]) ).

cnf(c_0_39,plain,
    product(product(X1,X1),difference(X1,one)) = difference(difference(X1,one),one),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_14]),c_0_35]) ).

cnf(c_0_40,plain,
    difference(difference(X1,one),difference(X1,X2)) = product(product(X2,X1),difference(X1,one)),
    inference(spm,[status(thm)],[c_0_36,c_0_14]) ).

cnf(c_0_41,plain,
    difference(difference(X1,one),product(product(X1,quotient(one,X1)),X2)) = quotient(product(X1,product(X2,difference(X1,one))),difference(X1,one)),
    inference(spm,[status(thm)],[c_0_13,c_0_37]) ).

cnf(c_0_42,plain,
    product(product(X1,quotient(X2,X1)),X1) = difference(difference(X1,one),X2),
    inference(spm,[status(thm)],[c_0_28,c_0_15]) ).

cnf(c_0_43,plain,
    difference(difference(X1,X2),X1) = product(difference(X2,X1),X1),
    inference(spm,[status(thm)],[c_0_15,c_0_38]) ).

cnf(c_0_44,plain,
    difference(product(X1,X1),difference(difference(X1,one),one)) = difference(X1,one),
    inference(spm,[status(thm)],[c_0_20,c_0_39]) ).

cnf(c_0_45,plain,
    difference(difference(difference(X1,one),one),product(X1,X1)) = difference(difference(X1,one),one),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_34]),c_0_14]),c_0_18]) ).

cnf(c_0_46,plain,
    difference(difference(X1,one),difference(difference(X1,one),one)) = quotient(X1,difference(X1,one)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_14]),c_0_24]) ).

cnf(c_0_47,plain,
    difference(quotient(X1,X2),X1) = X2,
    inference(spm,[status(thm)],[c_0_20,c_0_15]) ).

cnf(c_0_48,plain,
    product(difference(difference(X1,one),one),product(X1,X1)) = product(product(X1,X1),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_28]),c_0_45]) ).

cnf(c_0_49,plain,
    difference(X1,difference(X1,one)) = quotient(quotient(one,X1),X1),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_50,plain,
    product(X1,quotient(product(X2,product(X3,X1)),X1)) = product(product(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_14,c_0_13]) ).

cnf(c_0_51,plain,
    product(difference(product(X1,X1),one),product(product(X1,X1),X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_48]),c_0_44]),c_0_21]),c_0_27]),c_0_18]) ).

cnf(c_0_52,plain,
    quotient(X1,X1) = one,
    inference(spm,[status(thm)],[c_0_23,c_0_18]) ).

cnf(c_0_53,plain,
    quotient(X1,difference(X2,X1)) = X2,
    inference(spm,[status(thm)],[c_0_23,c_0_14]) ).

cnf(c_0_54,plain,
    product(X1,quotient(quotient(one,X1),X1)) = difference(X1,one),
    inference(spm,[status(thm)],[c_0_14,c_0_49]) ).

cnf(c_0_55,plain,
    product(product(X1,difference(product(X1,X1),one)),product(X1,X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_24]) ).

cnf(c_0_56,plain,
    quotient(X1,product(X1,X1)) = difference(X1,one),
    inference(spm,[status(thm)],[c_0_53,c_0_34]) ).

cnf(c_0_57,plain,
    quotient(product(X1,product(difference(product(X2,X1),X3),X2)),X2) = difference(X2,X3),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_58,plain,
    product(difference(difference(X1,one),one),difference(difference(X1,one),X2)) = difference(difference(X1,one),product(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_36]),c_0_28]),c_0_36]) ).

cnf(c_0_59,plain,
    difference(difference(X1,one),quotient(one,X1)) = product(X1,quotient(one,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_54]),c_0_37]) ).

cnf(c_0_60,plain,
    quotient(X1,quotient(difference(X2,X1),X1)) = product(X1,X2),
    inference(spm,[status(thm)],[c_0_23,c_0_26]) ).

cnf(c_0_61,plain,
    product(X1,difference(product(X1,X1),one)) = difference(X1,one),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_55]),c_0_56]) ).

cnf(c_0_62,plain,
    product(X1,product(difference(product(X2,X1),X3),X2)) = product(difference(X2,X3),X2),
    inference(spm,[status(thm)],[c_0_15,c_0_57]) ).

cnf(c_0_63,plain,
    difference(difference(X1,one),product(X2,product(X3,X1))) = product(product(product(X1,X2),X3),X1),
    inference(spm,[status(thm)],[c_0_42,c_0_50]) ).

cnf(c_0_64,plain,
    difference(X1,product(quotient(one,X1),X2)) = product(difference(X1,one),difference(X1,X2)),
    inference(spm,[status(thm)],[c_0_58,c_0_47]) ).

cnf(c_0_65,plain,
    difference(difference(difference(X1,one),one),X1) = 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_59,c_0_60]),c_0_35]),c_0_18]),c_0_35]),c_0_18]),c_0_37]) ).

cnf(c_0_66,plain,
    quotient(product(X1,quotient(one,X1)),X1) = difference(X1,one),
    inference(spm,[status(thm)],[c_0_23,c_0_37]) ).

cnf(c_0_67,plain,
    difference(product(X1,X1),one) = quotient(quotient(one,X1),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_61]),c_0_49]) ).

cnf(c_0_68,plain,
    difference(difference(product(X1,X1),one),X1) = product(product(X1,X1),X1),
    inference(spm,[status(thm)],[c_0_20,c_0_51]) ).

cnf(c_0_69,plain,
    difference(X1,product(difference(X2,X3),X2)) = product(difference(product(X2,X1),X3),X2),
    inference(spm,[status(thm)],[c_0_20,c_0_62]) ).

cnf(c_0_70,plain,
    product(difference(difference(X1,one),one),product(product(X1,X2),X1)) = product(product(product(X1,X1),X2),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_28]),c_0_53]) ).

cnf(c_0_71,plain,
    product(X1,difference(difference(X1,one),one)) = quotient(X1,difference(X1,one)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_65]),c_0_66]) ).

cnf(c_0_72,plain,
    product(product(X1,X1),quotient(quotient(one,X1),X1)) = one,
    inference(spm,[status(thm)],[c_0_14,c_0_67]) ).

cnf(c_0_73,plain,
    difference(quotient(quotient(one,X1),X1),X1) = product(product(X1,X1),X1),
    inference(rw,[status(thm)],[c_0_68,c_0_67]) ).

cnf(c_0_74,plain,
    difference(one,X1) = X1,
    inference(spm,[status(thm)],[c_0_18,c_0_14]) ).

cnf(c_0_75,plain,
    product(difference(product(X1,product(difference(X1,X2),X1)),X2),X1) = one,
    inference(spm,[status(thm)],[c_0_27,c_0_69]) ).

cnf(c_0_76,plain,
    product(quotient(X1,difference(X1,one)),product(X1,X2)) = product(X1,product(product(X1,X1),X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_70]),c_0_23]),c_0_71]) ).

cnf(c_0_77,plain,
    difference(quotient(quotient(one,X1),X1),one) = product(X1,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(spm,[status(thm)],[c_0_21,c_0_72]),c_0_24]),c_0_17]),c_0_73]),c_0_54]),c_0_36]),c_0_43]),c_0_74]) ).

cnf(c_0_78,plain,
    difference(product(X1,product(difference(X1,X2),X1)),X2) = quotient(one,X1),
    inference(spm,[status(thm)],[c_0_23,c_0_75]) ).

cnf(c_0_79,plain,
    product(product(X1,product(difference(X1,one),X2)),X1) = quotient(X2,difference(X1,one)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_28]),c_0_14]),c_0_24]) ).

cnf(c_0_80,plain,
    product(difference(X1,one),product(product(X2,X1),difference(X1,one))) = difference(X1,X2),
    inference(spm,[status(thm)],[c_0_14,c_0_40]) ).

cnf(c_0_81,plain,
    product(product(product(quotient(one,X1),X2),X1),difference(X1,one)) = difference(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_64]),c_0_20]) ).

cnf(c_0_82,plain,
    product(product(X1,quotient(X2,difference(X2,one))),X2) = product(product(X1,X2),product(X2,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_76]),c_0_50]) ).

cnf(c_0_83,plain,
    quotient(quotient(one,X1),X1) = quotient(one,product(X1,X1)),
    inference(spm,[status(thm)],[c_0_53,c_0_77]) ).

cnf(c_0_84,plain,
    product(X1,product(difference(X1,X2),X1)) = quotient(X2,quotient(one,X1)),
    inference(spm,[status(thm)],[c_0_53,c_0_78]) ).

cnf(c_0_85,plain,
    product(difference(X1,quotient(X2,X1)),X1) = product(difference(X1,one),X2),
    inference(spm,[status(thm)],[c_0_21,c_0_15]) ).

cnf(c_0_86,plain,
    product(X1,product(difference(X1,one),X2)) = quotient(quotient(X2,difference(X1,one)),X1),
    inference(spm,[status(thm)],[c_0_23,c_0_79]) ).

cnf(c_0_87,plain,
    product(difference(X1,one),product(X2,difference(X1,one))) = difference(X1,quotient(X2,X1)),
    inference(spm,[status(thm)],[c_0_80,c_0_15]) ).

cnf(c_0_88,plain,
    product(product(quotient(one,X1),X2),X1) = quotient(difference(X1,X2),difference(X1,one)),
    inference(spm,[status(thm)],[c_0_23,c_0_81]) ).

cnf(c_0_89,plain,
    quotient(product(product(X1,X2),product(X2,X2)),X2) = product(X1,quotient(X2,difference(X2,one))),
    inference(spm,[status(thm)],[c_0_23,c_0_82]) ).

cnf(c_0_90,plain,
    product(quotient(product(X1,product(X2,X3)),X3),quotient(product(X4,product(product(X3,X1),X2)),quotient(product(X1,product(X2,X3)),X3))) = product(product(quotient(product(X1,product(X2,X3)),X3),X4),X3),
    inference(spm,[status(thm)],[c_0_50,c_0_50]) ).

cnf(c_0_91,plain,
    product(product(X1,X1),quotient(one,product(X1,X1))) = one,
    inference(rw,[status(thm)],[c_0_72,c_0_83]) ).

cnf(c_0_92,plain,
    product(quotient(one,product(X1,X1)),X1) = quotient(one,X1),
    inference(spm,[status(thm)],[c_0_15,c_0_83]) ).

cnf(c_0_93,plain,
    quotient(quotient(X1,difference(X2,one)),X2) = quotient(quotient(X1,X2),quotient(one,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]) ).

cnf(c_0_94,plain,
    quotient(difference(difference(X1,one),quotient(X2,difference(X1,one))),difference(difference(X1,one),one)) = difference(difference(difference(X1,one),one),product(product(X1,X1),X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_45]),c_0_87]) ).

cnf(c_0_95,plain,
    quotient(difference(difference(X1,one),X2),difference(difference(X1,one),one)) = product(product(X1,X2),difference(X1,one)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_60]),c_0_18]),c_0_35]),c_0_35]),c_0_35]) ).

cnf(c_0_96,plain,
    product(X1,product(X2,quotient(X1,difference(X1,one)))) = product(product(X1,product(X2,X1)),X1),
    inference(spm,[status(thm)],[c_0_50,c_0_89]) ).

cnf(c_0_97,plain,
    product(product(X1,X2),quotient(X3,X1)) = product(X1,quotient(product(X2,X3),X1)),
    inference(spm,[status(thm)],[c_0_50,c_0_15]) ).

cnf(c_0_98,plain,
    product(difference(X1,one),quotient(X2,difference(X1,one))) = product(product(difference(X1,one),X2),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(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]),c_0_66]),c_0_24]),c_0_92]),c_0_66]),c_0_92]),c_0_66]) ).

cnf(c_0_99,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_14,c_0_64]),c_0_86]),c_0_93]) ).

cnf(c_0_100,plain,
    difference(difference(difference(X1,one),one),product(product(X1,X1),X2)) = product(product(X1,quotient(X2,difference(X1,one))),difference(X1,one)),
    inference(rw,[status(thm)],[c_0_94,c_0_95]) ).

cnf(c_0_101,plain,
    difference(product(X1,X2),product(X1,X3)) = quotient(difference(X2,product(X3,X1)),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_14]),c_0_16]) ).

cnf(c_0_102,plain,
    difference(X1,product(X2,quotient(one,X2))) = product(difference(product(X2,X1),one),X2),
    inference(spm,[status(thm)],[c_0_69,c_0_37]) ).

cnf(c_0_103,plain,
    product(product(X1,product(product(difference(X1,one),X2),X1)),X1) = product(X1,product(product(difference(X1,X2),X1),X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_98]),c_0_21]) ).

cnf(c_0_104,plain,
    product(difference(X1,one),product(product(X1,X1),X2)) = quotient(product(X1,quotient(X2,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(spm,[status(thm)],[c_0_99,c_0_100]),c_0_53]),c_0_93]),c_0_23]),c_0_53]),c_0_53]) ).

cnf(c_0_105,plain,
    quotient(difference(difference(X1,X2),product(X3,X1)),X1) = difference(X2,product(X1,X3)),
    inference(spm,[status(thm)],[c_0_101,c_0_14]) ).

cnf(c_0_106,plain,
    product(difference(product(X1,product(X1,X2)),one),X1) = quotient(difference(X2,one),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_15]) ).

cnf(c_0_107,plain,
    product(quotient(product(X1,product(X2,X1)),X1),difference(X1,one)) = quotient(product(X1,X2),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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_70]),c_0_87]),c_0_23]),c_0_13]),c_0_28]),c_0_36]),c_0_17]),c_0_43]),c_0_74]),c_0_104]),c_0_23]) ).

cnf(c_0_108,plain,
    difference(difference(X1,X2),product(X3,X1)) = product(difference(X2,product(X1,X3)),X1),
    inference(spm,[status(thm)],[c_0_15,c_0_105]) ).

cnf(c_0_109,plain,
    product(difference(product(X1,X2),one),X1) = quotient(difference(difference(X1,X2),one),X1),
    inference(spm,[status(thm)],[c_0_106,c_0_14]) ).

cnf(c_0_110,plain,
    quotient(product(X1,difference(product(X1,X1),X2)),X1) = product(difference(X1,X2),difference(X1,one)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_62]),c_0_23]) ).

cnf(c_0_111,plain,
    product(X1,quotient(product(difference(X1,X2),X3),X1)) = product(X2,quotient(X3,X1)),
    inference(spm,[status(thm)],[c_0_97,c_0_14]) ).

cnf(c_0_112,plain,
    product(product(difference(product(X1,X2),X3),X1),difference(X1,X3)) = difference(difference(difference(X1,X3),X2),X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_14]),c_0_69]) ).

cnf(c_0_113,plain,
    quotient(difference(difference(X1,difference(X1,X2)),one),X1) = product(difference(X2,one),X1),
    inference(spm,[status(thm)],[c_0_109,c_0_14]) ).

cnf(c_0_114,plain,
    product(product(difference(X1,X2),difference(X1,one)),X1) = product(X1,difference(product(X1,X1),X2)),
    inference(spm,[status(thm)],[c_0_15,c_0_110]) ).

cnf(c_0_115,plain,
    product(X1,quotient(difference(X1,X2),X1)) = product(X2,quotient(one,X1)),
    inference(spm,[status(thm)],[c_0_111,c_0_24]) ).

cnf(c_0_116,plain,
    difference(difference(difference(X1,X2),difference(X1,X3)),X2) = product(product(difference(X3,X2),X1),difference(X1,X2)),
    inference(spm,[status(thm)],[c_0_112,c_0_14]) ).

cnf(c_0_117,plain,
    difference(difference(X1,difference(X1,X2)),one) = product(product(difference(X2,one),X1),X1),
    inference(spm,[status(thm)],[c_0_15,c_0_113]) ).

cnf(c_0_118,plain,
    product(product(X1,difference(X2,one)),X2) = product(product(X1,X2),quotient(one,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_20]),c_0_101]),c_0_115]) ).

cnf(c_0_119,plain,
    product(product(X1,difference(X2,one)),difference(difference(X2,one),one)) = product(product(X1,X2),difference(X2,one)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_36]),c_0_21]),c_0_20]),c_0_40]) ).

cnf(c_0_120,plain,
    difference(product(product(X1,X2),difference(X2,one)),one) = product(product(difference(X1,one),X2),difference(X2,one)),
    inference(spm,[status(thm)],[c_0_116,c_0_40]) ).

cnf(c_0_121,plain,
    quotient(product(X1,product(X2,quotient(X3,X1))),quotient(X3,X1)) = difference(quotient(X3,X1),product(X3,X2)),
    inference(spm,[status(thm)],[c_0_13,c_0_15]) ).

cnf(c_0_122,plain,
    quotient(one,product(product(difference(X1,one),X2),X2)) = difference(X2,difference(X2,X1)),
    inference(spm,[status(thm)],[c_0_53,c_0_117]) ).

cnf(c_0_123,plain,
    product(difference(difference(difference(X1,one),X2),one),X1) = product(difference(difference(X1,X2),one),quotient(one,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_112]),c_0_109]),c_0_15]) ).

cnf(c_0_124,plain,
    product(product(X1,quotient(one,X2)),X2) = product(product(X1,X2),difference(X2,one)),
    inference(spm,[status(thm)],[c_0_119,c_0_47]) ).

cnf(c_0_125,plain,
    quotient(one,product(product(difference(X1,one),X2),difference(X2,one))) = product(product(X1,X2),difference(X2,one)),
    inference(spm,[status(thm)],[c_0_53,c_0_120]) ).

cnf(c_0_126,plain,
    difference(difference(X1,product(X2,X3)),product(product(difference(X1,X2),product(X3,X1)),X4)) = quotient(product(X1,product(X4,difference(X1,product(X2,X3)))),difference(X1,product(X2,X3))),
    inference(spm,[status(thm)],[c_0_121,c_0_16]) ).

cnf(c_0_127,plain,
    product(difference(X1,difference(X1,X2)),product(product(difference(X2,one),X1),X1)) = one,
    inference(spm,[status(thm)],[c_0_14,c_0_117]) ).

cnf(c_0_128,plain,
    product(difference(X1,X2),product(difference(X2,X3),X1)) = product(difference(X1,X3),X1),
    inference(spm,[status(thm)],[c_0_17,c_0_14]) ).

cnf(c_0_129,plain,
    quotient(product(X1,X2),quotient(one,X1)) = product(X1,product(X2,X1)),
    inference(spm,[status(thm)],[c_0_84,c_0_20]) ).

cnf(c_0_130,plain,
    difference(X1,difference(X1,difference(difference(X1,one),X2))) = product(product(difference(X1,X2),X1),difference(X1,one)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_124]),c_0_125]) ).

cnf(c_0_131,plain,
    product(X1,product(product(X2,X1),difference(X1,one))) = difference(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128]),c_0_37]),c_0_20]),c_0_18]),c_0_128]),c_0_37]),c_0_20]),c_0_128]),c_0_37]),c_0_20]),c_0_129]),c_0_124]) ).

cnf(c_0_132,plain,
    difference(quotient(one,X1),difference(X1,X2)) = difference(X1,difference(difference(X1,one),X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_130]),c_0_131]) ).

cnf(c_0_133,plain,
    difference(X1,difference(difference(X1,one),product(X1,X2))) = difference(quotient(one,X1),X2),
    inference(spm,[status(thm)],[c_0_132,c_0_20]) ).

cnf(c_0_134,plain,
    product(product(product(difference(X1,one),X2),X1),product(X1,X1)) = product(product(product(difference(X1,X2),X1),X1),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_97]),c_0_98]),c_0_21]) ).

cnf(c_0_135,plain,
    quotient(difference(difference(X1,one),X2),difference(X1,one)) = product(product(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_23,c_0_36]) ).

cnf(c_0_136,plain,
    difference(difference(X1,one),product(X1,X2)) = product(X1,difference(quotient(one,X1),X2)),
    inference(spm,[status(thm)],[c_0_14,c_0_133]) ).

cnf(c_0_137,plain,
    product(product(product(X1,product(X2,X2)),X2),X2) = product(product(product(X1,X2),X2),product(X2,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_115]),c_0_53]),c_0_135]),c_0_13]),c_0_15]) ).

cnf(c_0_138,plain,
    product(difference(quotient(X1,difference(X1,one)),X2),X1) = product(difference(X1,one),difference(X1,product(X2,X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_21]),c_0_69]),c_0_71]),c_0_53]) ).

cnf(c_0_139,plain,
    quotient(product(difference(X1,one),X2),X1) = difference(X1,quotient(X2,X1)),
    inference(spm,[status(thm)],[c_0_23,c_0_85]) ).

cnf(c_0_140,plain,
    product(product(X1,X2),quotient(X2,difference(X2,one))) = product(product(X1,product(X2,X2)),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_137]),c_0_89]) ).

cnf(c_0_141,plain,
    difference(quotient(X1,difference(X1,one)),product(X1,product(product(X1,X1),X2))) = product(X1,X2),
    inference(spm,[status(thm)],[c_0_20,c_0_76]) ).

cnf(c_0_142,plain,
    difference(X1,quotient(difference(X1,product(X2,X1)),X1)) = difference(quotient(X1,difference(X1,one)),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_138]),c_0_139]) ).

cnf(c_0_143,plain,
    product(product(X1,product(product(X2,X1),X1)),X1) = product(X1,product(product(X2,product(X1,X1)),X1)),
    inference(spm,[status(thm)],[c_0_96,c_0_140]) ).

cnf(c_0_144,plain,
    difference(quotient(X1,difference(X1,one)),product(X1,X2)) = product(X1,difference(product(X1,X1),X2)),
    inference(spm,[status(thm)],[c_0_141,c_0_14]) ).

cnf(c_0_145,plain,
    product(quotient(one,X1),quotient(one,X1)) = difference(X1,quotient(one,X1)),
    inference(spm,[status(thm)],[c_0_34,c_0_47]) ).

cnf(c_0_146,plain,
    product(X1,difference(product(X1,X1),product(product(X2,X1),X1))) = difference(X1,product(X2,product(X1,X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_20]),c_0_23]),c_0_144]) ).

cnf(c_0_147,plain,
    difference(difference(X1,quotient(one,X1)),difference(X1,one)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_145]),c_0_47]),c_0_47]) ).

cnf(c_0_148,plain,
    quotient(product(X1,quotient(one,X1)),difference(X1,one)) = difference(difference(X1,one),one),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_53]),c_0_37]) ).

cnf(c_0_149,plain,
    difference(quotient(one,X1),quotient(X2,X1)) = product(X1,product(X2,difference(X1,one))),
    inference(spm,[status(thm)],[c_0_131,c_0_15]) ).

cnf(c_0_150,plain,
    difference(product(X1,X1),product(product(X2,X1),X1)) = difference(X1,difference(X1,product(X2,product(X1,X1)))),
    inference(spm,[status(thm)],[c_0_20,c_0_146]) ).

cnf(c_0_151,plain,
    product(difference(X1,quotient(X2,X3)),product(X3,X1)) = product(difference(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_17,c_0_15]) ).

cnf(c_0_152,plain,
    difference(X1,quotient(one,X1)) = quotient(difference(X1,one),X1),
    inference(spm,[status(thm)],[c_0_53,c_0_147]) ).

cnf(c_0_153,plain,
    difference(quotient(one,X1),product(X1,X2)) = product(X1,difference(difference(X1,one),X2)),
    inference(spm,[status(thm)],[c_0_131,c_0_36]) ).

cnf(c_0_154,plain,
    quotient(product(product(X1,X2),difference(X2,one)),X2) = product(X1,quotient(one,X2)),
    inference(spm,[status(thm)],[c_0_23,c_0_124]) ).

cnf(c_0_155,plain,
    quotient(product(difference(X1,one),product(X2,difference(difference(X1,one),one))),difference(difference(X1,one),one)) = difference(difference(difference(X1,one),one),product(product(X1,quotient(one,X1)),X2)),
    inference(spm,[status(thm)],[c_0_121,c_0_148]) ).

cnf(c_0_156,plain,
    product(difference(X1,one),product(X2,difference(difference(X1,one),one))) = difference(X1,quotient(X2,difference(X1,one))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_60]),c_0_18]),c_0_35]),c_0_35]),c_0_35]) ).

cnf(c_0_157,plain,
    product(difference(product(X1,X2),product(product(X1,X3),X4)),X1) = difference(X2,product(X3,product(X4,X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_13]),c_0_15]) ).

cnf(c_0_158,plain,
    quotient(product(difference(product(X1,X2),X3),product(difference(X2,X1),X2)),product(X1,X2)) = difference(product(X1,X2),product(X3,difference(X2,one))),
    inference(spm,[status(thm)],[c_0_16,c_0_21]) ).

cnf(c_0_159,plain,
    difference(product(X1,X1),product(product(difference(X1,one),X2),X1)) = difference(X1,product(difference(product(X1,X1),X2),X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_85]),c_0_151]),c_0_69]) ).

cnf(c_0_160,plain,
    product(product(product(difference(X1,one),X2),X1),difference(X1,one)) = difference(difference(difference(X1,one),one),X2),
    inference(spm,[status(thm)],[c_0_36,c_0_119]) ).

cnf(c_0_161,plain,
    difference(quotient(difference(X1,one),X1),product(X2,X1)) = product(product(X1,difference(difference(X1,one),X2)),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_152]),c_0_153]) ).

cnf(c_0_162,plain,
    product(difference(X1,one),difference(difference(difference(X1,one),one),X2)) = difference(X1,product(difference(X1,one),X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_60]),c_0_18]),c_0_35]),c_0_35]),c_0_35]) ).

cnf(c_0_163,plain,
    product(quotient(one,X1),difference(X1,difference(difference(X1,one),X2))) = difference(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_130]),c_0_154]),c_0_23]) ).

cnf(c_0_164,plain,
    difference(difference(difference(X1,one),one),product(product(X1,quotient(one,X1)),X2)) = quotient(difference(X1,quotient(X2,difference(X1,one))),difference(difference(X1,one),one)),
    inference(rw,[status(thm)],[c_0_155,c_0_156]) ).

cnf(c_0_165,plain,
    difference(difference(X1,X2),product(X3,product(X4,X1))) = product(difference(X2,product(product(X1,X3),X4)),X1),
    inference(spm,[status(thm)],[c_0_157,c_0_14]) ).

cnf(c_0_166,plain,
    product(difference(X1,one),product(X1,quotient(one,X1))) = quotient(one,X1),
    inference(spm,[status(thm)],[c_0_14,c_0_59]) ).

cnf(c_0_167,plain,
    difference(product(X1,X1),difference(difference(difference(X1,one),one),X2)) = difference(X1,difference(product(X1,X1),X2)),
    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_158,c_0_159]),c_0_27]),c_0_18]),c_0_17]),c_0_23]),c_0_160]) ).

cnf(c_0_168,plain,
    difference(difference(difference(X1,one),X2),difference(difference(X1,one),X3)) = product(difference(X2,product(X3,X1)),difference(X1,one)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_36]),c_0_21]),c_0_20]) ).

cnf(c_0_169,plain,
    product(difference(X1,product(difference(X1,one),X2)),difference(X1,one)) = difference(product(X1,X1),product(X2,difference(X1,one))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_135]),c_0_24]),c_0_162]) ).

cnf(c_0_170,plain,
    difference(X1,product(difference(X1,one),X2)) = product(quotient(one,X1),difference(X1,X2)),
    inference(spm,[status(thm)],[c_0_163,c_0_20]) ).

cnf(c_0_171,plain,
    product(product(quotient(one,X1),X2),difference(X1,one)) = quotient(difference(X1,X2),difference(difference(X1,one),one)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_166]),c_0_74]),c_0_23]) ).

cnf(c_0_172,plain,
    difference(X1,difference(product(X1,X1),product(difference(difference(X1,one),one),X2))) = difference(product(X1,X1),X2),
    inference(spm,[status(thm)],[c_0_167,c_0_20]) ).

cnf(c_0_173,plain,
    product(difference(difference(X1,one),X2),difference(X1,one)) = difference(difference(X1,one),quotient(X2,X1)),
    inference(spm,[status(thm)],[c_0_36,c_0_42]) ).

cnf(c_0_174,plain,
    difference(product(X1,X1),difference(difference(X1,one),X2)) = product(difference(X1,product(X2,X1)),difference(X1,one)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_152]),c_0_135]),c_0_24]),c_0_53]) ).

cnf(c_0_175,plain,
    quotient(difference(X1,difference(X1,X2)),difference(difference(X1,one),one)) = difference(product(X1,X1),product(X2,difference(X1,one))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_169,c_0_170]),c_0_171]) ).

cnf(c_0_176,plain,
    difference(product(X1,X1),product(X2,difference(X1,one))) = difference(X1,product(difference(X1,X2),difference(X1,one))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_128]),c_0_173]),c_0_174]),c_0_15]),c_0_74]) ).

cnf(c_0_177,plain,
    quotient(difference(X1,difference(X1,X2)),difference(difference(X1,one),one)) = difference(X1,product(difference(X1,X2),difference(X1,one))),
    inference(rw,[status(thm)],[c_0_175,c_0_176]) ).

cnf(c_0_178,axiom,
    eta(X1) = product(i(X1),X1),
    sos12 ).

cnf(c_0_179,plain,
    product(difference(X1,product(X2,quotient(X3,X2))),X2) = difference(difference(X2,X1),X3),
    inference(spm,[status(thm)],[c_0_108,c_0_15]) ).

cnf(c_0_180,plain,
    quotient(difference(X1,X2),difference(difference(X1,one),one)) = difference(X1,product(X2,difference(X1,one))),
    inference(spm,[status(thm)],[c_0_177,c_0_20]) ).

cnf(c_0_181,negated_conjecture,
    product(i(i(x0)),x1) != product(eta(x0),product(x0,x1)),
    goals ).

cnf(c_0_182,plain,
    eta(X1) = product(difference(X1,one),X1),
    inference(rw,[status(thm)],[c_0_178,c_0_30]) ).

cnf(c_0_183,plain,
    difference(X1,product(X2,quotient(X3,X2))) = quotient(difference(difference(X2,X1),X3),X2),
    inference(spm,[status(thm)],[c_0_23,c_0_179]) ).

cnf(c_0_184,plain,
    difference(difference(X1,product(X2,difference(X1,one))),difference(X1,X2)) = difference(difference(X1,one),one),
    inference(spm,[status(thm)],[c_0_47,c_0_180]) ).

cnf(c_0_185,negated_conjecture,
    product(difference(difference(x0,one),one),x1) != product(product(difference(x0,one),x0),product(x0,x1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_181,c_0_30]),c_0_30]),c_0_182]) ).

cnf(c_0_186,plain,
    product(quotient(difference(difference(X1,X2),X3),X1),product(X1,X2)) = product(difference(X2,difference(difference(X1,one),X3)),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_42]),c_0_183]) ).

cnf(c_0_187,plain,
    difference(difference(X1,X2),difference(X1,quotient(X2,difference(X1,one)))) = difference(difference(X1,one),one),
    inference(spm,[status(thm)],[c_0_184,c_0_15]) ).

cnf(c_0_188,plain,
    quotient(difference(difference(X1,one),X2),X1) = product(X1,quotient(X2,X1)),
    inference(spm,[status(thm)],[c_0_23,c_0_42]) ).

cnf(c_0_189,plain,
    product(product(quotient(X1,difference(X2,one)),X2),difference(X2,one)) = product(X1,difference(difference(X2,one),one)),
    inference(spm,[status(thm)],[c_0_119,c_0_15]) ).

cnf(c_0_190,negated_conjecture,
    product(product(x0,quotient(one,x0)),product(x0,x1)) != product(difference(difference(x0,one),one),x1),
    inference(rw,[status(thm)],[c_0_185,c_0_37]) ).

cnf(c_0_191,plain,
    product(product(X1,quotient(one,X1)),product(X1,X2)) = product(difference(difference(X1,one),one),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_187]),c_0_188]),c_0_40]),c_0_189]),c_0_20]) ).

cnf(c_0_192,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_190,c_0_191])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : GRP765-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n012.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   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 29 01:14:54 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 0.21/0.59  start to proof: theBenchmark
% 4.67/4.74  % Version  : CSE_E---1.5
% 4.67/4.74  % Problem  : theBenchmark.p
% 4.67/4.74  % Proof found
% 4.67/4.74  % SZS status Theorem for theBenchmark.p
% 4.67/4.74  % SZS output start Proof
% See solution above
% 4.67/4.75  % Total time : 4.136000 s
% 4.67/4.75  % SZS output end Proof
% 4.67/4.75  % Total time : 4.139000 s
%------------------------------------------------------------------------------