TSTP Solution File: BOO014-10 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : BOO014-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n008.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 : Wed Aug 30 18:05:49 EDT 2023
% Result : Unsatisfiable 39.18s 39.30s
% Output : CNFRefutation 39.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 40
% Syntax : Number of formulae : 288 ( 274 unt; 14 typ; 0 def)
% Number of atoms : 274 ( 273 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 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 : 19 ( 7 >; 12 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 455 ( 8 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ifeq2: ( $i * $i * $i * $i ) > $i ).
tff(decl_23,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(decl_24,type,
add: ( $i * $i ) > $i ).
tff(decl_25,type,
sum: ( $i * $i * $i ) > $i ).
tff(decl_26,type,
true: $i ).
tff(decl_27,type,
multiply: ( $i * $i ) > $i ).
tff(decl_28,type,
product: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
additive_identity: $i ).
tff(decl_30,type,
multiplicative_identity: $i ).
tff(decl_31,type,
inverse: $i > $i ).
tff(decl_32,type,
x: $i ).
tff(decl_33,type,
y: $i ).
tff(decl_34,type,
x_plus_y: $i ).
tff(decl_35,type,
x_inverse_times_y_inverse: $i ).
cnf(distributivity5,axiom,
ifeq(product(X1,X2,X3),true,ifeq(sum(X4,X3,X5),true,ifeq(sum(X4,X2,X6),true,ifeq(sum(X4,X1,X7),true,product(X7,X6,X5),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity5) ).
cnf(additive_inverse2,axiom,
sum(X1,inverse(X1),multiplicative_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse2) ).
cnf(ifeq_axiom_001,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
cnf(addition_is_well_defined,axiom,
ifeq2(sum(X1,X2,X3),true,ifeq2(sum(X1,X2,X4),true,X4,X3),X3) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
cnf(ifeq_axiom,axiom,
ifeq2(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(commutativity_of_addition,axiom,
ifeq(sum(X1,X2,X3),true,sum(X2,X1,X3),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
cnf(additive_inverse1,axiom,
sum(inverse(X1),X1,multiplicative_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X1),X1,additive_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse1) ).
cnf(multiplication_is_well_defined,axiom,
ifeq2(product(X1,X2,X3),true,ifeq2(product(X1,X2,X4),true,X4,X3),X3) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X1,X1) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity1) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
cnf(commutativity_of_multiplication,axiom,
ifeq(product(X1,X2,X3),true,product(X2,X1,X3),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_multiplication) ).
cnf(multiplicative_inverse2,axiom,
product(X1,inverse(X1),additive_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse2) ).
cnf(distributivity1,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X4,X5),true,ifeq(product(X1,X6,X7),true,ifeq(sum(X6,X4,X2),true,sum(X7,X5,X3),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
cnf(x_inverse_times_y_inverse,negated_conjecture,
product(inverse(x),inverse(y),x_inverse_times_y_inverse) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_inverse_times_y_inverse) ).
cnf(distributivity6,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X5,X6),true,ifeq(sum(X7,X5,X2),true,ifeq(sum(X7,X4,X1),true,sum(X7,X6,X3),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity6) ).
cnf(x_plus_y,negated_conjecture,
sum(x,y,x_plus_y) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_plus_y) ).
cnf(distributivity7,axiom,
ifeq(product(X1,X2,X3),true,ifeq(sum(X3,X4,X5),true,ifeq(sum(X2,X4,X6),true,ifeq(sum(X1,X4,X7),true,product(X7,X6,X5),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity7) ).
cnf(multiplicative_identity2,axiom,
product(X1,multiplicative_identity,X1) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity2) ).
cnf(distributivity3,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X2,X5),true,ifeq(product(X6,X2,X7),true,ifeq(sum(X6,X4,X1),true,sum(X7,X5,X3),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity3) ).
cnf(distributivity4,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X2,X5),true,ifeq(sum(X5,X3,X6),true,ifeq(sum(X4,X1,X7),true,product(X7,X2,X6),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity4) ).
cnf(distributivity8,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X5,X6),true,ifeq(sum(X5,X7,X2),true,ifeq(sum(X4,X7,X1),true,sum(X6,X7,X3),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity8) ).
cnf(prove_equation,negated_conjecture,
inverse(x_plus_y) != x_inverse_times_y_inverse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
cnf(c_0_26,axiom,
ifeq(product(X1,X2,X3),true,ifeq(sum(X4,X3,X5),true,ifeq(sum(X4,X2,X6),true,ifeq(sum(X4,X1,X7),true,product(X7,X6,X5),true),true),true),true) = true,
distributivity5 ).
cnf(c_0_27,axiom,
sum(X1,inverse(X1),multiplicative_identity) = true,
additive_inverse2 ).
cnf(c_0_28,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom_001 ).
cnf(c_0_29,plain,
ifeq(product(inverse(X1),X2,X3),true,ifeq(sum(X1,X3,X4),true,ifeq(sum(X1,X2,X5),true,product(multiplicative_identity,X5,X4),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_30,axiom,
sum(X1,X2,add(X1,X2)) = true,
closure_of_addition ).
cnf(c_0_31,axiom,
ifeq2(sum(X1,X2,X3),true,ifeq2(sum(X1,X2,X4),true,X4,X3),X3) = X3,
addition_is_well_defined ).
cnf(c_0_32,axiom,
sum(additive_identity,X1,X1) = true,
additive_identity1 ).
cnf(c_0_33,axiom,
ifeq2(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_34,axiom,
ifeq(sum(X1,X2,X3),true,sum(X2,X1,X3),true) = true,
commutativity_of_addition ).
cnf(c_0_35,axiom,
sum(inverse(X1),X1,multiplicative_identity) = true,
additive_inverse1 ).
cnf(c_0_36,axiom,
sum(X1,additive_identity,X1) = true,
additive_identity2 ).
cnf(c_0_37,plain,
ifeq(product(inverse(X1),X2,X3),true,ifeq(sum(X1,X3,X4),true,product(multiplicative_identity,add(X1,X2),X4),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_28]) ).
cnf(c_0_38,axiom,
product(inverse(X1),X1,additive_identity) = true,
multiplicative_inverse1 ).
cnf(c_0_39,plain,
ifeq2(sum(additive_identity,X1,X2),true,X1,X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_40,plain,
sum(X1,X2,add(X2,X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_30]),c_0_28]) ).
cnf(c_0_41,axiom,
ifeq2(product(X1,X2,X3),true,ifeq2(product(X1,X2,X4),true,X4,X3),X3) = X3,
multiplication_is_well_defined ).
cnf(c_0_42,axiom,
product(multiplicative_identity,X1,X1) = true,
multiplicative_identity1 ).
cnf(c_0_43,plain,
ifeq(product(X1,X2,X3),true,ifeq(sum(inverse(X1),X3,X4),true,ifeq(sum(inverse(X1),X2,X5),true,product(multiplicative_identity,X5,X4),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_35]),c_0_28]) ).
cnf(c_0_44,plain,
ifeq(product(additive_identity,X1,X2),true,ifeq(sum(X3,X2,X4),true,ifeq(sum(X3,X1,X5),true,product(X3,X5,X4),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_36]),c_0_28]) ).
cnf(c_0_45,axiom,
product(X1,X2,multiply(X1,X2)) = true,
closure_of_multiplication ).
cnf(c_0_46,plain,
ifeq(sum(X1,additive_identity,X2),true,product(multiplicative_identity,add(X1,X1),X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_28]) ).
cnf(c_0_47,plain,
add(X1,additive_identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_33]) ).
cnf(c_0_48,plain,
ifeq2(product(multiplicative_identity,X1,X2),true,X1,X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_33]) ).
cnf(c_0_49,plain,
ifeq(product(X1,X1,X2),true,ifeq(sum(inverse(X1),X2,X3),true,product(multiplicative_identity,multiplicative_identity,X3),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_35]),c_0_28]) ).
cnf(c_0_50,axiom,
ifeq(product(X1,X2,X3),true,product(X2,X1,X3),true) = true,
commutativity_of_multiplication ).
cnf(c_0_51,plain,
ifeq(product(additive_identity,additive_identity,X1),true,ifeq(sum(X2,X1,X3),true,product(X2,X2,X3),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_36]),c_0_28]) ).
cnf(c_0_52,plain,
ifeq2(product(X1,X2,X3),true,multiply(X1,X2),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_45]),c_0_33]) ).
cnf(c_0_53,plain,
product(multiplicative_identity,add(X1,X1),X1) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_30]),c_0_47]),c_0_28]) ).
cnf(c_0_54,plain,
multiply(multiplicative_identity,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_45]),c_0_33]) ).
cnf(c_0_55,plain,
ifeq(product(inverse(X1),X2,additive_identity),true,ifeq(sum(X1,X2,X3),true,product(multiplicative_identity,X3,X1),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_36]),c_0_28]) ).
cnf(c_0_56,axiom,
product(X1,inverse(X1),additive_identity) = true,
multiplicative_inverse2 ).
cnf(c_0_57,plain,
ifeq(product(X1,X1,X2),true,product(multiplicative_identity,multiplicative_identity,add(inverse(X1),X2)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_30]),c_0_28]) ).
cnf(c_0_58,plain,
product(X1,X2,multiply(X2,X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_45]),c_0_28]) ).
cnf(c_0_59,plain,
ifeq(product(additive_identity,additive_identity,X1),true,product(X2,X2,add(X2,X1)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_30]),c_0_28]) ).
cnf(c_0_60,plain,
add(X1,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_33]) ).
cnf(c_0_61,plain,
ifeq(sum(X1,inverse(inverse(X1)),X2),true,product(multiplicative_identity,X2,X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_28]) ).
cnf(c_0_62,plain,
product(multiplicative_identity,multiplicative_identity,add(inverse(X1),multiply(X1,X1))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_45]),c_0_28]) ).
cnf(c_0_63,plain,
multiply(X1,multiplicative_identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_58]),c_0_33]) ).
cnf(c_0_64,plain,
ifeq2(sum(X1,X2,X3),true,add(X1,X2),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_30]),c_0_33]) ).
cnf(c_0_65,plain,
product(X1,X1,add(X1,multiply(additive_identity,additive_identity))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_45]),c_0_28]) ).
cnf(c_0_66,plain,
ifeq(product(additive_identity,X1,X2),true,ifeq(sum(X3,X1,X4),true,product(X3,X4,add(X3,X2)),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_30]),c_0_28]) ).
cnf(c_0_67,plain,
sum(X1,X1,X1) = true,
inference(spm,[status(thm)],[c_0_30,c_0_60]) ).
cnf(c_0_68,plain,
product(multiplicative_identity,add(X1,inverse(inverse(X1))),X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_30]),c_0_28]) ).
cnf(c_0_69,plain,
add(inverse(X1),multiply(X1,X1)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_62]),c_0_63]),c_0_33]) ).
cnf(c_0_70,plain,
add(X1,X2) = add(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_40]),c_0_33]) ).
cnf(c_0_71,plain,
multiply(X1,X1) = add(X1,multiply(additive_identity,additive_identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_65]),c_0_33]) ).
cnf(c_0_72,plain,
ifeq(product(additive_identity,X1,X2),true,product(X1,X1,add(X1,X2)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_28]) ).
cnf(c_0_73,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_68]),c_0_54]),c_0_33]) ).
cnf(c_0_74,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X4,X5),true,ifeq(product(X1,X6,X7),true,ifeq(sum(X6,X4,X2),true,sum(X7,X5,X3),true),true),true),true) = true,
distributivity1 ).
cnf(c_0_75,negated_conjecture,
product(inverse(x),inverse(y),x_inverse_times_y_inverse) = true,
x_inverse_times_y_inverse ).
cnf(c_0_76,plain,
sum(inverse(X1),multiply(X1,X1),multiplicative_identity) = true,
inference(spm,[status(thm)],[c_0_30,c_0_69]) ).
cnf(c_0_77,plain,
multiply(X1,X1) = add(multiply(additive_identity,additive_identity),X1),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_78,plain,
product(X1,X1,add(X1,multiply(additive_identity,X1))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_45]),c_0_28]) ).
cnf(c_0_79,plain,
ifeq(product(X1,X2,additive_identity),true,ifeq(sum(inverse(X1),X2,X3),true,product(multiplicative_identity,X3,inverse(X1)),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_36]),c_0_28]) ).
cnf(c_0_80,plain,
sum(inverse(inverse(X1)),X1,X1) = true,
inference(spm,[status(thm)],[c_0_40,c_0_73]) ).
cnf(c_0_81,negated_conjecture,
ifeq(product(inverse(x),X1,X2),true,ifeq(product(inverse(x),X3,X4),true,ifeq(sum(inverse(y),X3,X1),true,sum(x_inverse_times_y_inverse,X4,X2),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_28]) ).
cnf(c_0_82,plain,
sum(inverse(X1),add(multiply(additive_identity,additive_identity),X1),multiplicative_identity) = true,
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_83,plain,
add(X1,multiply(additive_identity,X1)) = multiply(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_78]),c_0_33]) ).
cnf(c_0_84,plain,
product(multiplicative_identity,X1,inverse(inverse(X1))) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_38]),c_0_28]),c_0_28]) ).
cnf(c_0_85,negated_conjecture,
ifeq(product(inverse(x),X1,X2),true,ifeq(sum(inverse(y),X1,inverse(y)),true,sum(x_inverse_times_y_inverse,X2,x_inverse_times_y_inverse),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_75]),c_0_28]) ).
cnf(c_0_86,plain,
ifeq(product(X1,X2,X3),true,ifeq(sum(X4,X3,X5),true,ifeq(sum(X4,X2,X6),true,product(add(X4,X1),X6,X5),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_30]),c_0_28]) ).
cnf(c_0_87,plain,
ifeq(product(additive_identity,X1,inverse(X2)),true,ifeq(sum(X2,X1,X3),true,product(X2,X3,multiplicative_identity),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_27]),c_0_28]) ).
cnf(c_0_88,plain,
sum(inverse(multiply(additive_identity,multiply(additive_identity,additive_identity))),multiply(additive_identity,additive_identity),multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_71]),c_0_60]) ).
cnf(c_0_89,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_84]),c_0_54]),c_0_33]) ).
cnf(c_0_90,negated_conjecture,
ifeq(product(inverse(x),additive_identity,X1),true,sum(x_inverse_times_y_inverse,X1,x_inverse_times_y_inverse),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_36]),c_0_28]) ).
cnf(c_0_91,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_58]),c_0_33]) ).
cnf(c_0_92,plain,
ifeq(product(X1,X2,additive_identity),true,ifeq(sum(X3,X2,X4),true,product(add(X3,X1),X4,X3),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_36]),c_0_28]) ).
cnf(c_0_93,plain,
ifeq2(product(inverse(X1),X1,X2),true,additive_identity,X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_38]),c_0_33]) ).
cnf(c_0_94,plain,
product(inverse(multiply(additive_identity,multiply(additive_identity,additive_identity))),multiplicative_identity,multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]),c_0_45]),c_0_28]),c_0_28]) ).
cnf(c_0_95,plain,
ifeq(sum(X1,multiply(additive_identity,X2),X3),true,ifeq(sum(X1,X2,X4),true,product(X1,X4,X3),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_28]) ).
cnf(c_0_96,negated_conjecture,
sum(x_inverse_times_y_inverse,multiply(additive_identity,inverse(x)),x_inverse_times_y_inverse) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_45]),c_0_91]),c_0_28]) ).
cnf(c_0_97,plain,
ifeq(sum(X1,X2,X3),true,product(add(X1,inverse(X2)),X3,X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_38]),c_0_28]) ).
cnf(c_0_98,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_58]),c_0_33]) ).
cnf(c_0_99,plain,
inverse(multiply(additive_identity,multiply(additive_identity,additive_identity))) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_94]),c_0_63]),c_0_33]) ).
cnf(c_0_100,plain,
ifeq(product(X1,X2,X3),true,ifeq(sum(inverse(X1),X3,X4),true,product(multiplicative_identity,add(inverse(X1),X2),X4),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_30]),c_0_28]) ).
cnf(c_0_101,negated_conjecture,
ifeq(sum(x_inverse_times_y_inverse,inverse(x),X1),true,product(x_inverse_times_y_inverse,X1,x_inverse_times_y_inverse),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_28]) ).
cnf(c_0_102,plain,
product(add(X1,inverse(X2)),add(X1,X2),X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_30]),c_0_28]) ).
cnf(c_0_103,plain,
ifeq(product(additive_identity,X1,X2),true,ifeq(sum(X3,X2,X4),true,product(X3,add(X3,X1),X4),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_30]),c_0_28]) ).
cnf(c_0_104,plain,
multiply(additive_identity,multiply(additive_identity,additive_identity)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_63]) ).
cnf(c_0_105,plain,
ifeq(product(X1,X2,X1),true,product(multiplicative_identity,add(inverse(X1),X2),multiplicative_identity),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_35]),c_0_28]) ).
cnf(c_0_106,negated_conjecture,
product(x_inverse_times_y_inverse,add(x_inverse_times_y_inverse,inverse(x)),x_inverse_times_y_inverse) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_30]),c_0_28]) ).
cnf(c_0_107,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X5,X6),true,ifeq(sum(X7,X5,X2),true,ifeq(sum(X7,X4,X1),true,sum(X7,X6,X3),true),true),true),true) = true,
distributivity6 ).
cnf(c_0_108,plain,
multiply(add(X1,X2),add(X1,inverse(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_102]),c_0_33]),c_0_91]) ).
cnf(c_0_109,plain,
ifeq(product(additive_identity,X1,additive_identity),true,product(X2,add(X2,X1),X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_36]),c_0_28]) ).
cnf(c_0_110,plain,
product(additive_identity,multiply(additive_identity,additive_identity),additive_identity) = true,
inference(spm,[status(thm)],[c_0_45,c_0_104]) ).
cnf(c_0_111,negated_conjecture,
sum(x,y,x_plus_y) = true,
x_plus_y ).
cnf(c_0_112,negated_conjecture,
product(multiplicative_identity,add(inverse(x_inverse_times_y_inverse),add(x_inverse_times_y_inverse,inverse(x))),multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_28]) ).
cnf(c_0_113,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(additive_identity,X4,X5),true,ifeq(sum(X1,X4,X2),true,sum(X1,X5,X3),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_36]),c_0_28]) ).
cnf(c_0_114,plain,
multiply(add(X1,X2),add(inverse(X2),X1)) = X1,
inference(spm,[status(thm)],[c_0_108,c_0_70]) ).
cnf(c_0_115,plain,
add(X1,multiply(inverse(X1),inverse(X1))) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_69,c_0_89]) ).
cnf(c_0_116,plain,
product(X1,add(X1,multiply(additive_identity,additive_identity)),X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_28]) ).
cnf(c_0_117,negated_conjecture,
ifeq(product(y,X1,X2),true,ifeq(sum(x,X2,X3),true,ifeq(sum(x,X1,X4),true,product(x_plus_y,X4,X3),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_111]),c_0_28]) ).
cnf(c_0_118,axiom,
ifeq(product(X1,X2,X3),true,ifeq(sum(X3,X4,X5),true,ifeq(sum(X2,X4,X6),true,ifeq(sum(X1,X4,X7),true,product(X7,X6,X5),true),true),true),true) = true,
distributivity7 ).
cnf(c_0_119,negated_conjecture,
add(inverse(x_inverse_times_y_inverse),add(x_inverse_times_y_inverse,inverse(x))) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_112]),c_0_54]),c_0_33]) ).
cnf(c_0_120,plain,
ifeq(product(X1,X2,X3),true,ifeq(sum(X1,X4,X2),true,sum(X1,multiply(additive_identity,X4),X3),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_45]),c_0_28]) ).
cnf(c_0_121,axiom,
product(X1,multiplicative_identity,X1) = true,
multiplicative_identity2 ).
cnf(c_0_122,plain,
add(X1,multiply(X1,X1)) = multiply(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(spm,[status(thm)],[c_0_114,c_0_115]),c_0_89]),c_0_89]),c_0_63]),c_0_89]),c_0_89]),c_0_70]) ).
cnf(c_0_123,plain,
product(X1,multiply(X1,X1),X1) = true,
inference(spm,[status(thm)],[c_0_116,c_0_71]) ).
cnf(c_0_124,negated_conjecture,
ifeq(product(y,y,X1),true,ifeq(sum(x,X1,X2),true,product(x_plus_y,x_plus_y,X2),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_111]),c_0_28]) ).
cnf(c_0_125,negated_conjecture,
ifeq(product(x,X1,X2),true,ifeq(sum(X2,y,X3),true,ifeq(sum(X1,y,X4),true,product(x_plus_y,X4,X3),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_111]),c_0_28]) ).
cnf(c_0_126,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X2,X5),true,ifeq(product(X6,X2,X7),true,ifeq(sum(X6,X4,X1),true,sum(X7,X5,X3),true),true),true),true) = true,
distributivity3 ).
cnf(c_0_127,negated_conjecture,
add(x_inverse_times_y_inverse,add(x_inverse_times_y_inverse,inverse(x))) = add(x_inverse_times_y_inverse,inverse(x)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_119]),c_0_63]),c_0_70]) ).
cnf(c_0_128,plain,
ifeq(sum(X1,X2,multiplicative_identity),true,sum(X1,multiply(additive_identity,X2),X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_28]) ).
cnf(c_0_129,plain,
ifeq(product(additive_identity,X1,X2),true,ifeq(sum(X3,X1,X4),true,sum(X3,X2,multiply(X3,X4)),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_45]),c_0_28]) ).
cnf(c_0_130,plain,
sum(X1,multiply(X1,X1),multiply(X1,X1)) = true,
inference(spm,[status(thm)],[c_0_30,c_0_122]) ).
cnf(c_0_131,plain,
multiply(X1,multiply(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_123]),c_0_33]) ).
cnf(c_0_132,plain,
ifeq(product(inverse(X1),additive_identity,X2),true,ifeq(sum(X1,X2,X3),true,product(multiplicative_identity,X1,X3),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_36]),c_0_28]) ).
cnf(c_0_133,negated_conjecture,
ifeq(product(y,y,X1),true,product(x_plus_y,x_plus_y,add(x,X1)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_30]),c_0_28]) ).
cnf(c_0_134,negated_conjecture,
ifeq(product(x,x,X1),true,ifeq(sum(X1,y,X2),true,product(x_plus_y,x_plus_y,X2),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_111]),c_0_28]) ).
cnf(c_0_135,negated_conjecture,
ifeq(product(X1,inverse(y),X2),true,ifeq(product(X3,inverse(y),X4),true,ifeq(sum(inverse(x),X3,X1),true,sum(x_inverse_times_y_inverse,X4,X2),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_75]),c_0_28]) ).
cnf(c_0_136,negated_conjecture,
sum(x_inverse_times_y_inverse,add(x_inverse_times_y_inverse,inverse(x)),add(x_inverse_times_y_inverse,inverse(x))) = true,
inference(spm,[status(thm)],[c_0_30,c_0_127]) ).
cnf(c_0_137,negated_conjecture,
multiply(x_inverse_times_y_inverse,add(x_inverse_times_y_inverse,inverse(x))) = x_inverse_times_y_inverse,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_106]),c_0_33]) ).
cnf(c_0_138,plain,
sum(inverse(X1),multiply(additive_identity,multiply(X1,X1)),inverse(X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_76]),c_0_28]) ).
cnf(c_0_139,plain,
ifeq(product(additive_identity,multiply(X1,X1),X2),true,sum(X1,X2,X1),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_131]),c_0_28]) ).
cnf(c_0_140,plain,
ifeq(product(inverse(X1),additive_identity,X2),true,product(multiplicative_identity,X1,add(X1,X2)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_30]),c_0_28]) ).
cnf(c_0_141,negated_conjecture,
product(x_plus_y,x_plus_y,add(x,multiply(y,y))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_45]),c_0_28]) ).
cnf(c_0_142,negated_conjecture,
ifeq(product(x,x,X1),true,product(x_plus_y,x_plus_y,add(X1,y)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_30]),c_0_28]) ).
cnf(c_0_143,negated_conjecture,
ifeq(product(X1,inverse(y),X2),true,ifeq(sum(inverse(x),X1,inverse(x)),true,sum(x_inverse_times_y_inverse,X2,x_inverse_times_y_inverse),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_75]),c_0_28]) ).
cnf(c_0_144,plain,
ifeq(product(X1,X2,X3),true,ifeq(sum(X3,X4,X5),true,ifeq(sum(X2,X4,X6),true,product(add(X1,X4),X6,X5),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_30]),c_0_28]) ).
cnf(c_0_145,negated_conjecture,
ifeq(product(additive_identity,add(x_inverse_times_y_inverse,inverse(x)),X1),true,sum(x_inverse_times_y_inverse,X1,x_inverse_times_y_inverse),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_136]),c_0_137]),c_0_28]) ).
cnf(c_0_146,plain,
multiply(add(X1,X2),add(X2,inverse(X1))) = X2,
inference(spm,[status(thm)],[c_0_108,c_0_70]) ).
cnf(c_0_147,plain,
add(inverse(X1),multiply(additive_identity,multiply(X1,X1))) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_138]),c_0_33]) ).
cnf(c_0_148,plain,
sum(X1,multiply(additive_identity,multiply(X1,X1)),X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_45]),c_0_28]) ).
cnf(c_0_149,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X2,X5),true,ifeq(sum(X5,X3,X6),true,ifeq(sum(X4,X1,X7),true,product(X7,X2,X6),true),true),true),true) = true,
distributivity4 ).
cnf(c_0_150,plain,
product(multiplicative_identity,X1,add(X1,multiply(additive_identity,inverse(X1)))) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_45]),c_0_91]),c_0_28]) ).
cnf(c_0_151,plain,
ifeq(product(additive_identity,X1,X2),true,product(X2,add(X2,X1),X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_67]),c_0_28]) ).
cnf(c_0_152,negated_conjecture,
add(x,multiply(y,y)) = multiply(x_plus_y,x_plus_y),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_141]),c_0_33]) ).
cnf(c_0_153,negated_conjecture,
product(x_plus_y,x_plus_y,add(y,multiply(x,x))) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_45]),c_0_28]),c_0_70]) ).
cnf(c_0_154,negated_conjecture,
ifeq(product(additive_identity,inverse(y),X1),true,sum(x_inverse_times_y_inverse,X1,x_inverse_times_y_inverse),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_36]),c_0_28]) ).
cnf(c_0_155,plain,
ifeq(product(X1,X2,additive_identity),true,ifeq(sum(X2,X3,X4),true,product(add(X1,X3),X4,X3),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_32]),c_0_28]) ).
cnf(c_0_156,negated_conjecture,
sum(inverse(x_inverse_times_y_inverse),add(x_inverse_times_y_inverse,inverse(x)),multiplicative_identity) = true,
inference(spm,[status(thm)],[c_0_30,c_0_119]) ).
cnf(c_0_157,negated_conjecture,
sum(x_inverse_times_y_inverse,multiply(additive_identity,add(x_inverse_times_y_inverse,inverse(x))),x_inverse_times_y_inverse) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_45]),c_0_28]) ).
cnf(c_0_158,plain,
multiply(inverse(X1),add(X1,multiply(additive_identity,multiply(X1,X1)))) = multiply(additive_identity,multiply(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_89]),c_0_70]) ).
cnf(c_0_159,plain,
add(X1,multiply(additive_identity,multiply(X1,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_148]),c_0_33]) ).
cnf(c_0_160,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(inverse(X1),X2,X4),true,ifeq(sum(X4,X3,X5),true,product(multiplicative_identity,X2,X5),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_35]),c_0_28]) ).
cnf(c_0_161,plain,
ifeq(product(additive_identity,additive_identity,X1),true,product(inverse(X1),inverse(X1),multiplicative_identity),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_35]),c_0_28]) ).
cnf(c_0_162,plain,
add(X1,multiply(additive_identity,inverse(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_150]),c_0_54]),c_0_33]) ).
cnf(c_0_163,plain,
product(multiply(additive_identity,X1),add(X1,multiply(additive_identity,X1)),multiply(additive_identity,X1)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_45]),c_0_28]),c_0_70]) ).
cnf(c_0_164,negated_conjecture,
sum(x,multiply(y,y),multiply(x_plus_y,x_plus_y)) = true,
inference(spm,[status(thm)],[c_0_30,c_0_152]) ).
cnf(c_0_165,negated_conjecture,
add(y,multiply(x,x)) = multiply(x_plus_y,x_plus_y),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_153]),c_0_33]) ).
cnf(c_0_166,negated_conjecture,
sum(x_inverse_times_y_inverse,multiply(additive_identity,inverse(y)),x_inverse_times_y_inverse) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_45]),c_0_28]) ).
cnf(c_0_167,plain,
ifeq(sum(X1,X2,X3),true,product(add(inverse(X1),X2),X3,X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_38]),c_0_28]) ).
cnf(c_0_168,negated_conjecture,
sum(inverse(x_inverse_times_y_inverse),multiply(additive_identity,add(x_inverse_times_y_inverse,inverse(x))),inverse(x_inverse_times_y_inverse)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_156]),c_0_28]) ).
cnf(c_0_169,negated_conjecture,
add(x_inverse_times_y_inverse,multiply(additive_identity,add(x_inverse_times_y_inverse,inverse(x)))) = x_inverse_times_y_inverse,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_157]),c_0_33]) ).
cnf(c_0_170,plain,
multiply(additive_identity,multiply(X1,X1)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_158,c_0_159]),c_0_91]),c_0_98]) ).
cnf(c_0_171,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(inverse(X1),X2,inverse(X3)),true,product(multiplicative_identity,X2,multiplicative_identity),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_35]),c_0_28]) ).
cnf(c_0_172,plain,
product(inverse(multiply(additive_identity,additive_identity)),inverse(multiply(additive_identity,additive_identity)),multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_45]),c_0_28]) ).
cnf(c_0_173,plain,
inverse(multiplicative_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_56]),c_0_33]) ).
cnf(c_0_174,plain,
add(inverse(X1),multiply(additive_identity,X1)) = inverse(X1),
inference(spm,[status(thm)],[c_0_162,c_0_89]) ).
cnf(c_0_175,plain,
product(multiply(additive_identity,X1),multiply(X1,X1),multiply(additive_identity,X1)) = true,
inference(rw,[status(thm)],[c_0_163,c_0_83]) ).
cnf(c_0_176,negated_conjecture,
ifeq(product(additive_identity,multiply(y,y),X1),true,ifeq(sum(x,X1,X2),true,product(x,multiply(x_plus_y,x_plus_y),X2),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_164]),c_0_28]) ).
cnf(c_0_177,plain,
ifeq(product(additive_identity,X1,additive_identity),true,ifeq(sum(X2,X1,X3),true,product(X2,X3,X2),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_36]),c_0_28]) ).
cnf(c_0_178,negated_conjecture,
sum(y,multiply(x,x),multiply(x_plus_y,x_plus_y)) = true,
inference(spm,[status(thm)],[c_0_30,c_0_165]) ).
cnf(c_0_179,negated_conjecture,
ifeq(sum(x_inverse_times_y_inverse,inverse(y),X1),true,product(x_inverse_times_y_inverse,X1,x_inverse_times_y_inverse),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_166]),c_0_28]) ).
cnf(c_0_180,negated_conjecture,
product(x_inverse_times_y_inverse,inverse(x_inverse_times_y_inverse),multiply(additive_identity,add(x_inverse_times_y_inverse,inverse(x)))) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_89]),c_0_169]),c_0_28]) ).
cnf(c_0_181,negated_conjecture,
product(inverse(y),inverse(x),x_inverse_times_y_inverse) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_75]),c_0_28]) ).
cnf(c_0_182,plain,
product(additive_identity,multiply(X1,X1),additive_identity) = true,
inference(spm,[status(thm)],[c_0_45,c_0_170]) ).
cnf(c_0_183,plain,
product(multiplicative_identity,inverse(multiply(additive_identity,additive_identity)),multiplicative_identity) = true,
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_171,c_0_172]),c_0_89]),c_0_173]),c_0_56]),c_0_28]),c_0_28]) ).
cnf(c_0_184,plain,
sum(multiply(additive_identity,X1),inverse(X1),inverse(X1)) = true,
inference(spm,[status(thm)],[c_0_40,c_0_174]) ).
cnf(c_0_185,plain,
sum(X1,multiply(additive_identity,X1),multiply(X1,X1)) = true,
inference(spm,[status(thm)],[c_0_30,c_0_83]) ).
cnf(c_0_186,plain,
product(multiplicative_identity,add(inverse(multiply(additive_identity,X1)),multiply(X1,X1)),multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_175]),c_0_28]) ).
cnf(c_0_187,negated_conjecture,
ifeq(product(additive_identity,multiply(y,y),additive_identity),true,product(x,multiply(x_plus_y,x_plus_y),x),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_36]),c_0_28]) ).
cnf(c_0_188,negated_conjecture,
ifeq(product(additive_identity,multiply(x,x),additive_identity),true,product(y,multiply(x_plus_y,x_plus_y),y),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_28]) ).
cnf(c_0_189,negated_conjecture,
product(x_inverse_times_y_inverse,add(x_inverse_times_y_inverse,inverse(y)),x_inverse_times_y_inverse) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_30]),c_0_28]) ).
cnf(c_0_190,negated_conjecture,
multiply(additive_identity,add(x_inverse_times_y_inverse,inverse(x))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_180]),c_0_98]),c_0_33]) ).
cnf(c_0_191,negated_conjecture,
ifeq(sum(X1,x_inverse_times_y_inverse,X2),true,ifeq(sum(X1,inverse(x),X3),true,product(add(X1,inverse(y)),X3,X2),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_181]),c_0_28]) ).
cnf(c_0_192,plain,
product(X1,add(X1,multiply(X2,X2)),X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_182]),c_0_28]) ).
cnf(c_0_193,plain,
multiply(add(X1,inverse(X2)),add(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_114,c_0_89]) ).
cnf(c_0_194,plain,
inverse(multiply(additive_identity,additive_identity)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_183]),c_0_54]),c_0_33]) ).
cnf(c_0_195,plain,
product(multiply(X1,X1),inverse(X1),multiply(additive_identity,X1)) = true,
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_184]),c_0_89]),c_0_70]),c_0_83]),c_0_28]) ).
cnf(c_0_196,plain,
ifeq(product(additive_identity,multiply(additive_identity,X1),X2),true,sum(X1,X2,X1),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_185]),c_0_131]),c_0_28]) ).
cnf(c_0_197,plain,
add(inverse(multiply(additive_identity,X1)),multiply(X1,X1)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_186]),c_0_54]),c_0_33]) ).
cnf(c_0_198,negated_conjecture,
product(x,multiply(x_plus_y,x_plus_y),x) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_187,c_0_182]),c_0_28]) ).
cnf(c_0_199,negated_conjecture,
product(y,multiply(x_plus_y,x_plus_y),y) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_188,c_0_182]),c_0_28]) ).
cnf(c_0_200,negated_conjecture,
product(multiplicative_identity,add(inverse(x_inverse_times_y_inverse),add(x_inverse_times_y_inverse,inverse(y))),multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_189]),c_0_28]) ).
cnf(c_0_201,negated_conjecture,
ifeq(product(X1,X2,X3),true,ifeq(sum(X4,inverse(y),X2),true,ifeq(sum(X4,inverse(x),X1),true,sum(X4,x_inverse_times_y_inverse,X3),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_75]),c_0_28]) ).
cnf(c_0_202,negated_conjecture,
product(additive_identity,add(x_inverse_times_y_inverse,inverse(x)),additive_identity) = true,
inference(spm,[status(thm)],[c_0_45,c_0_190]) ).
cnf(c_0_203,negated_conjecture,
ifeq(sum(inverse(x),x_inverse_times_y_inverse,X1),true,product(add(inverse(x),inverse(y)),inverse(x),X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_67]),c_0_28]) ).
cnf(c_0_204,plain,
multiply(X1,add(X1,multiply(X2,X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_192]),c_0_33]) ).
cnf(c_0_205,plain,
multiply(add(multiply(additive_identity,additive_identity),inverse(X1)),multiply(X1,X1)) = multiply(additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_193,c_0_71]) ).
cnf(c_0_206,plain,
multiply(additive_identity,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_194]),c_0_63]) ).
cnf(c_0_207,plain,
add(additive_identity,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_30]),c_0_33]) ).
cnf(c_0_208,plain,
multiply(inverse(X1),multiply(X1,X1)) = multiply(additive_identity,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_195]),c_0_33]),c_0_91]) ).
cnf(c_0_209,negated_conjecture,
ifeq(product(y,additive_identity,X1),true,ifeq(sum(x,X1,X2),true,product(x_plus_y,x,X2),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_36]),c_0_28]) ).
cnf(c_0_210,plain,
sum(X1,multiply(additive_identity,multiply(additive_identity,X1)),X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_45]),c_0_28]) ).
cnf(c_0_211,plain,
add(multiply(X1,X1),inverse(multiply(additive_identity,X1))) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_70,c_0_197]) ).
cnf(c_0_212,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X5,X6),true,ifeq(sum(X5,X7,X2),true,ifeq(sum(X4,X7,X1),true,sum(X6,X7,X3),true),true),true),true) = true,
distributivity8 ).
cnf(c_0_213,negated_conjecture,
product(multiplicative_identity,add(inverse(x),multiply(x_plus_y,x_plus_y)),multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_198]),c_0_28]) ).
cnf(c_0_214,negated_conjecture,
product(multiplicative_identity,add(inverse(y),multiply(x_plus_y,x_plus_y)),multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_199]),c_0_28]) ).
cnf(c_0_215,negated_conjecture,
add(inverse(x_inverse_times_y_inverse),add(x_inverse_times_y_inverse,inverse(y))) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_200]),c_0_54]),c_0_33]) ).
cnf(c_0_216,negated_conjecture,
ifeq(sum(X1,inverse(y),X2),true,ifeq(sum(X1,inverse(x),X3),true,sum(X1,x_inverse_times_y_inverse,multiply(X2,X3)),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_58]),c_0_28]) ).
cnf(c_0_217,negated_conjecture,
product(X1,add(X1,add(x_inverse_times_y_inverse,inverse(x))),X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_202]),c_0_28]) ).
cnf(c_0_218,negated_conjecture,
product(add(inverse(x),inverse(y)),inverse(x),add(x_inverse_times_y_inverse,inverse(x))) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_30]),c_0_70]),c_0_28]) ).
cnf(c_0_219,plain,
multiply(X1,add(X1,add(multiply(additive_identity,additive_identity),X2))) = X1,
inference(spm,[status(thm)],[c_0_204,c_0_77]) ).
cnf(c_0_220,plain,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_205,c_0_206]),c_0_207]),c_0_208]),c_0_206]) ).
cnf(c_0_221,negated_conjecture,
ifeq(product(y,additive_identity,X1),true,product(x_plus_y,x,add(x,X1)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_30]),c_0_28]) ).
cnf(c_0_222,plain,
add(X1,multiply(additive_identity,multiply(additive_identity,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_210]),c_0_33]) ).
cnf(c_0_223,plain,
multiply(X1,multiply(inverse(X1),inverse(X1))) = multiply(additive_identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_208,c_0_89]) ).
cnf(c_0_224,plain,
add(multiply(X1,X1),inverse(multiply(X1,additive_identity))) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_211,c_0_91]) ).
cnf(c_0_225,negated_conjecture,
ifeq(product(X1,X2,X3),true,ifeq(sum(inverse(y),X4,X2),true,ifeq(sum(inverse(x),X4,X1),true,sum(x_inverse_times_y_inverse,X4,X3),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_75]),c_0_28]) ).
cnf(c_0_226,negated_conjecture,
add(inverse(x),multiply(x_plus_y,x_plus_y)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_213]),c_0_54]),c_0_33]) ).
cnf(c_0_227,negated_conjecture,
add(inverse(y),multiply(x_plus_y,x_plus_y)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_214]),c_0_54]),c_0_33]) ).
cnf(c_0_228,negated_conjecture,
sum(inverse(x_inverse_times_y_inverse),add(x_inverse_times_y_inverse,inverse(y)),multiplicative_identity) = true,
inference(spm,[status(thm)],[c_0_30,c_0_215]) ).
cnf(c_0_229,negated_conjecture,
ifeq(sum(inverse(y),inverse(x),X1),true,sum(inverse(y),x_inverse_times_y_inverse,multiply(inverse(y),X1)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_67]),c_0_28]) ).
cnf(c_0_230,negated_conjecture,
multiply(X1,add(X1,add(x_inverse_times_y_inverse,inverse(x)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_217]),c_0_33]) ).
cnf(c_0_231,negated_conjecture,
multiply(inverse(x),add(inverse(x),inverse(y))) = add(x_inverse_times_y_inverse,inverse(x)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_218]),c_0_91]),c_0_33]) ).
cnf(c_0_232,plain,
multiply(X1,add(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_220]),c_0_207]) ).
cnf(c_0_233,negated_conjecture,
product(x_plus_y,x,add(x,multiply(additive_identity,y))) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_45]),c_0_28]),c_0_91]) ).
cnf(c_0_234,negated_conjecture,
product(add(inverse(x_inverse_times_y_inverse),inverse(add(x_inverse_times_y_inverse,inverse(x)))),multiplicative_identity,inverse(x_inverse_times_y_inverse)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_156]),c_0_28]) ).
cnf(c_0_235,plain,
multiply(X1,add(inverse(X1),multiply(additive_identity,multiply(additive_identity,X1)))) = multiply(additive_identity,multiply(additive_identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_222]),c_0_70]) ).
cnf(c_0_236,plain,
multiply(X1,add(multiply(additive_identity,additive_identity),inverse(X1))) = multiply(additive_identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_223,c_0_77]) ).
cnf(c_0_237,plain,
add(multiply(X1,X1),multiply(X1,additive_identity)) = multiply(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_224]),c_0_63]) ).
cnf(c_0_238,negated_conjecture,
ifeq(sum(inverse(y),X1,multiplicative_identity),true,ifeq(sum(inverse(x),X1,X2),true,sum(x_inverse_times_y_inverse,X1,X2),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_121]),c_0_28]) ).
cnf(c_0_239,negated_conjecture,
sum(inverse(x),multiply(x_plus_y,x_plus_y),multiplicative_identity) = true,
inference(spm,[status(thm)],[c_0_30,c_0_226]) ).
cnf(c_0_240,negated_conjecture,
sum(inverse(y),multiply(x_plus_y,x_plus_y),multiplicative_identity) = true,
inference(spm,[status(thm)],[c_0_30,c_0_227]) ).
cnf(c_0_241,negated_conjecture,
product(add(inverse(x_inverse_times_y_inverse),inverse(add(x_inverse_times_y_inverse,inverse(y)))),multiplicative_identity,inverse(x_inverse_times_y_inverse)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_228]),c_0_28]) ).
cnf(c_0_242,negated_conjecture,
ifeq(sum(inverse(y),inverse(x),add(inverse(y),add(x_inverse_times_y_inverse,inverse(x)))),true,sum(inverse(y),x_inverse_times_y_inverse,inverse(y)),true) = true,
inference(spm,[status(thm)],[c_0_229,c_0_230]) ).
cnf(c_0_243,negated_conjecture,
add(x_inverse_times_y_inverse,inverse(x)) = inverse(x),
inference(rw,[status(thm)],[c_0_231,c_0_232]) ).
cnf(c_0_244,negated_conjecture,
add(x,multiply(additive_identity,y)) = multiply(x,x_plus_y),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_233]),c_0_33]),c_0_91]) ).
cnf(c_0_245,negated_conjecture,
add(inverse(x_inverse_times_y_inverse),inverse(add(x_inverse_times_y_inverse,inverse(x)))) = inverse(x_inverse_times_y_inverse),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_234]),c_0_63]),c_0_33]) ).
cnf(c_0_246,plain,
multiply(additive_identity,inverse(multiply(X1,X1))) = multiply(additive_identity,additive_identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_170]),c_0_70]),c_0_236]) ).
cnf(c_0_247,plain,
add(multiply(X1,additive_identity),add(multiply(additive_identity,additive_identity),X1)) = add(multiply(additive_identity,additive_identity),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_237,c_0_77]),c_0_70]) ).
cnf(c_0_248,plain,
add(X1,multiply(X1,additive_identity)) = multiply(X1,X1),
inference(spm,[status(thm)],[c_0_83,c_0_91]) ).
cnf(c_0_249,negated_conjecture,
sum(x_inverse_times_y_inverse,multiply(x_plus_y,x_plus_y),multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_238,c_0_239]),c_0_240]),c_0_28]),c_0_28]) ).
cnf(c_0_250,negated_conjecture,
add(inverse(x_inverse_times_y_inverse),inverse(add(x_inverse_times_y_inverse,inverse(y)))) = inverse(x_inverse_times_y_inverse),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_241]),c_0_63]),c_0_33]) ).
cnf(c_0_251,negated_conjecture,
sum(inverse(y),x_inverse_times_y_inverse,inverse(y)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_242,c_0_243]),c_0_70]),c_0_40]),c_0_28]) ).
cnf(c_0_252,plain,
ifeq(product(additive_identity,X1,X2),true,ifeq(sum(X2,X3,X4),true,ifeq(sum(X1,X3,X5),true,product(X3,X5,X4),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_32]),c_0_28]) ).
cnf(c_0_253,negated_conjecture,
sum(multiply(additive_identity,y),x,multiply(x,x_plus_y)) = true,
inference(spm,[status(thm)],[c_0_40,c_0_244]) ).
cnf(c_0_254,negated_conjecture,
sum(inverse(x_inverse_times_y_inverse),inverse(add(x_inverse_times_y_inverse,inverse(x))),inverse(x_inverse_times_y_inverse)) = true,
inference(spm,[status(thm)],[c_0_30,c_0_245]) ).
cnf(c_0_255,plain,
product(additive_identity,inverse(multiply(X1,X1)),multiply(additive_identity,additive_identity)) = true,
inference(spm,[status(thm)],[c_0_45,c_0_246]) ).
cnf(c_0_256,plain,
multiply(X1,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)],[c_0_247,c_0_206]),c_0_207]),c_0_70]),c_0_248]),c_0_206]),c_0_207]) ).
cnf(c_0_257,negated_conjecture,
add(x_inverse_times_y_inverse,multiply(x_plus_y,x_plus_y)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_249]),c_0_33]) ).
cnf(c_0_258,negated_conjecture,
sum(inverse(x_inverse_times_y_inverse),inverse(add(x_inverse_times_y_inverse,inverse(y))),inverse(x_inverse_times_y_inverse)) = true,
inference(spm,[status(thm)],[c_0_30,c_0_250]) ).
cnf(c_0_259,negated_conjecture,
add(x_inverse_times_y_inverse,inverse(y)) = inverse(y),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_251]),c_0_70]),c_0_33]) ).
cnf(c_0_260,negated_conjecture,
ifeq(product(additive_identity,X1,multiply(additive_identity,y)),true,ifeq(sum(X1,x,X2),true,product(x,X2,multiply(x,x_plus_y)),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_252,c_0_253]),c_0_28]) ).
cnf(c_0_261,negated_conjecture,
sum(inverse(x_inverse_times_y_inverse),x,inverse(x_inverse_times_y_inverse)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_254,c_0_243]),c_0_89]) ).
cnf(c_0_262,plain,
product(additive_identity,inverse(X1),additive_identity) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_255,c_0_206]),c_0_256]) ).
cnf(c_0_263,negated_conjecture,
multiply(x,x_plus_y) = x,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_244,c_0_220]),c_0_47]) ).
cnf(c_0_264,negated_conjecture,
add(inverse(x_inverse_times_y_inverse),multiply(x_plus_y,x_plus_y)) = multiply(x_plus_y,x_plus_y),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_257]),c_0_54]),c_0_70]) ).
cnf(c_0_265,negated_conjecture,
ifeq(product(x,X1,x),true,ifeq(sum(X1,y,X2),true,product(x_plus_y,X2,x_plus_y),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_111]),c_0_28]) ).
cnf(c_0_266,negated_conjecture,
sum(inverse(x_inverse_times_y_inverse),y,inverse(x_inverse_times_y_inverse)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_258,c_0_259]),c_0_89]) ).
cnf(c_0_267,negated_conjecture,
product(x,inverse(x_inverse_times_y_inverse),x) = true,
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_260,c_0_261]),c_0_220]),c_0_262]),c_0_263]),c_0_28]),c_0_28]) ).
cnf(c_0_268,negated_conjecture,
multiply(inverse(x_inverse_times_y_inverse),multiply(x_plus_y,x_plus_y)) = inverse(x_inverse_times_y_inverse),
inference(spm,[status(thm)],[c_0_204,c_0_264]) ).
cnf(c_0_269,negated_conjecture,
product(x_plus_y,inverse(x_inverse_times_y_inverse),x_plus_y) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_265,c_0_266]),c_0_267]),c_0_28]),c_0_28]) ).
cnf(c_0_270,negated_conjecture,
multiply(x_plus_y,inverse(x_inverse_times_y_inverse)) = inverse(x_inverse_times_y_inverse),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_268,c_0_256]),c_0_91]) ).
cnf(c_0_271,negated_conjecture,
inverse(x_inverse_times_y_inverse) = x_plus_y,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_269]),c_0_270]),c_0_33]) ).
cnf(c_0_272,negated_conjecture,
inverse(x_plus_y) != x_inverse_times_y_inverse,
prove_equation ).
cnf(c_0_273,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_271]),c_0_272]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : BOO014-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.15 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36 % Computer : n008.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 08:24:02 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.57 start to proof: theBenchmark
% 39.18/39.30 % Version : CSE_E---1.5
% 39.18/39.30 % Problem : theBenchmark.p
% 39.18/39.30 % Proof found
% 39.18/39.30 % SZS status Theorem for theBenchmark.p
% 39.18/39.30 % SZS output start Proof
% See solution above
% 39.18/39.31 % Total time : 38.724000 s
% 39.18/39.31 % SZS output end Proof
% 39.18/39.31 % Total time : 38.729000 s
%------------------------------------------------------------------------------