TSTP Solution File: BOO015-10 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : BOO015-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n029.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 18:05:50 EDT 2023
% Result : Unsatisfiable 19.85s 19.89s
% Output : CNFRefutation 19.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 69
% Number of leaves : 39
% Syntax : Number of formulae : 281 ( 267 unt; 14 typ; 0 def)
% Number of atoms : 267 ( 266 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 : 403 ( 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_times_y: $i ).
tff(decl_35,type,
x_inverse_plus_y_inverse: $i ).
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(additive_identity1,axiom,
sum(additive_identity,X1,X1) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
cnf(ifeq_axiom_001,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
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(x_times_y,negated_conjecture,
product(x,y,x_times_y) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_times_y) ).
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(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
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(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(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
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(multiplicative_inverse1,axiom,
product(inverse(X1),X1,additive_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse1) ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X1,X1) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity1) ).
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(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(additive_identity2,axiom,
sum(X1,additive_identity,X1) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
cnf(multiplicative_identity2,axiom,
product(X1,multiplicative_identity,X1) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity2) ).
cnf(additive_inverse1,axiom,
sum(inverse(X1),X1,multiplicative_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).
cnf(multiplicative_inverse2,axiom,
product(X1,inverse(X1),additive_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse2) ).
cnf(x_inverse_plus_y_inverse,negated_conjecture,
sum(inverse(x),inverse(y),x_inverse_plus_y_inverse) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_inverse_plus_y_inverse) ).
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(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(prove_equation,negated_conjecture,
inverse(x_times_y) != x_inverse_plus_y_inverse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
cnf(c_0_25,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_26,axiom,
sum(additive_identity,X1,X1) = true,
additive_identity1 ).
cnf(c_0_27,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom_001 ).
cnf(c_0_28,axiom,
ifeq(product(X1,X2,X3),true,product(X2,X1,X3),true) = true,
commutativity_of_multiplication ).
cnf(c_0_29,negated_conjecture,
product(x,y,x_times_y) = true,
x_times_y ).
cnf(c_0_30,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(additive_identity,X2,X4),true,ifeq(sum(X4,X3,X5),true,product(X1,X2,X5),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_31,negated_conjecture,
product(y,x,x_times_y) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_27]) ).
cnf(c_0_32,axiom,
ifeq2(sum(X1,X2,X3),true,ifeq2(sum(X1,X2,X4),true,X4,X3),X3) = X3,
addition_is_well_defined ).
cnf(c_0_33,axiom,
sum(X1,X2,add(X1,X2)) = true,
closure_of_addition ).
cnf(c_0_34,axiom,
ifeq2(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_35,axiom,
ifeq(sum(X1,X2,X3),true,sum(X2,X1,X3),true) = true,
commutativity_of_addition ).
cnf(c_0_36,negated_conjecture,
ifeq(product(additive_identity,x,X1),true,ifeq(sum(X1,x_times_y,X2),true,product(y,x,X2),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_27]) ).
cnf(c_0_37,plain,
ifeq2(sum(X1,X2,X3),true,add(X1,X2),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_38,plain,
sum(X1,X2,add(X2,X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_33]),c_0_27]) ).
cnf(c_0_39,axiom,
ifeq2(product(X1,X2,X3),true,ifeq2(product(X1,X2,X4),true,X4,X3),X3) = X3,
multiplication_is_well_defined ).
cnf(c_0_40,axiom,
product(X1,X2,multiply(X1,X2)) = true,
closure_of_multiplication ).
cnf(c_0_41,negated_conjecture,
ifeq(product(additive_identity,x,X1),true,product(y,x,add(X1,x_times_y)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_33]),c_0_27]) ).
cnf(c_0_42,plain,
add(X1,X2) = add(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_34]) ).
cnf(c_0_43,plain,
ifeq2(product(X1,X2,X3),true,multiply(X1,X2),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_34]) ).
cnf(c_0_44,plain,
product(X1,X2,multiply(X2,X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_40]),c_0_27]) ).
cnf(c_0_45,negated_conjecture,
ifeq2(product(x,y,X1),true,X1,x_times_y) = x_times_y,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_29]),c_0_34]) ).
cnf(c_0_46,negated_conjecture,
product(y,x,add(x_times_y,multiply(additive_identity,x))) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_40]),c_0_27]),c_0_42]) ).
cnf(c_0_47,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_34]) ).
cnf(c_0_48,negated_conjecture,
multiply(x,y) = x_times_y,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_40]),c_0_34]) ).
cnf(c_0_49,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_50,negated_conjecture,
add(x_times_y,multiply(additive_identity,x)) = x_times_y,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_46]),c_0_47]),c_0_48]),c_0_34]) ).
cnf(c_0_51,axiom,
sum(X1,inverse(X1),multiplicative_identity) = true,
additive_inverse2 ).
cnf(c_0_52,plain,
ifeq(sum(X1,multiply(X2,X3),X4),true,ifeq(sum(X1,X3,X5),true,ifeq(sum(X1,X2,X6),true,product(X6,X5,X4),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_40]),c_0_27]) ).
cnf(c_0_53,negated_conjecture,
sum(x_times_y,multiply(additive_identity,x),x_times_y) = true,
inference(spm,[status(thm)],[c_0_33,c_0_50]) ).
cnf(c_0_54,plain,
ifeq2(sum(additive_identity,X1,X2),true,X1,X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_26]),c_0_34]) ).
cnf(c_0_55,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_49,c_0_51]),c_0_27]) ).
cnf(c_0_56,negated_conjecture,
ifeq(sum(x_times_y,x,X1),true,ifeq(sum(x_times_y,additive_identity,X2),true,product(X2,X1,x_times_y),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_27]) ).
cnf(c_0_57,plain,
add(X1,additive_identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_38]),c_0_34]) ).
cnf(c_0_58,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_55,c_0_33]),c_0_27]) ).
cnf(c_0_59,axiom,
product(inverse(X1),X1,additive_identity) = true,
multiplicative_inverse1 ).
cnf(c_0_60,axiom,
product(multiplicative_identity,X1,X1) = true,
multiplicative_identity1 ).
cnf(c_0_61,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_62,negated_conjecture,
ifeq(sum(x_times_y,x,X1),true,product(x_times_y,X1,x_times_y),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_33]),c_0_57]),c_0_27]) ).
cnf(c_0_63,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_58,c_0_59]),c_0_27]) ).
cnf(c_0_64,plain,
ifeq2(product(multiplicative_identity,X1,X2),true,X1,X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_60]),c_0_34]) ).
cnf(c_0_65,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_66,plain,
ifeq(product(X1,add(X2,X3),X4),true,ifeq(product(X5,X2,X6),true,ifeq(sum(X3,X5,X1),true,sum(X3,X6,X4),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_38]),c_0_27]) ).
cnf(c_0_67,negated_conjecture,
product(x_times_y,add(x,x_times_y),x_times_y) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_33]),c_0_27]),c_0_42]) ).
cnf(c_0_68,plain,
product(multiplicative_identity,add(X1,X1),X1) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_33]),c_0_57]),c_0_27]) ).
cnf(c_0_69,plain,
multiply(multiplicative_identity,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_40]),c_0_34]) ).
cnf(c_0_70,axiom,
sum(X1,additive_identity,X1) = true,
additive_identity2 ).
cnf(c_0_71,plain,
ifeq(product(X1,add(X2,X3),X4),true,ifeq(product(X1,X3,X5),true,ifeq(product(X1,X2,X6),true,sum(X6,X5,X4),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_33]),c_0_27]) ).
cnf(c_0_72,negated_conjecture,
ifeq(product(X1,x,X2),true,ifeq(sum(x_times_y,X1,x_times_y),true,sum(x_times_y,X2,x_times_y),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_27]) ).
cnf(c_0_73,plain,
add(X1,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_68]),c_0_69]),c_0_34]) ).
cnf(c_0_74,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_49,c_0_70]),c_0_27]) ).
cnf(c_0_75,negated_conjecture,
ifeq(product(x_times_y,x_times_y,X1),true,ifeq(product(x_times_y,x,X2),true,sum(X2,X1,x_times_y),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_67]),c_0_27]) ).
cnf(c_0_76,negated_conjecture,
ifeq(sum(x_times_y,X1,x_times_y),true,sum(x_times_y,multiply(X1,x),x_times_y),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_40]),c_0_27]) ).
cnf(c_0_77,plain,
sum(X1,X1,X1) = true,
inference(spm,[status(thm)],[c_0_33,c_0_73]) ).
cnf(c_0_78,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_74,c_0_33]),c_0_27]) ).
cnf(c_0_79,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_74,c_0_33]),c_0_27]) ).
cnf(c_0_80,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_49,c_0_33]),c_0_27]) ).
cnf(c_0_81,negated_conjecture,
ifeq(product(x_times_y,x_times_y,X1),true,sum(multiply(x,x_times_y),X1,x_times_y),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_40]),c_0_47]),c_0_27]) ).
cnf(c_0_82,negated_conjecture,
sum(x_times_y,multiply(x,x_times_y),x_times_y) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_47]),c_0_27]) ).
cnf(c_0_83,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_78,c_0_77]),c_0_27]) ).
cnf(c_0_84,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_79,c_0_77]),c_0_27]) ).
cnf(c_0_85,plain,
ifeq(sum(X1,multiply(X2,X3),X4),true,ifeq(sum(X1,X3,X5),true,product(add(X1,X2),X5,X4),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_40]),c_0_27]) ).
cnf(c_0_86,negated_conjecture,
sum(multiply(x,x_times_y),multiply(x_times_y,x_times_y),x_times_y) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_40]),c_0_27]) ).
cnf(c_0_87,negated_conjecture,
add(x_times_y,multiply(x,x_times_y)) = x_times_y,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_82]),c_0_34]) ).
cnf(c_0_88,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_83,c_0_40]),c_0_27]),c_0_42]) ).
cnf(c_0_89,plain,
product(X1,X1,add(X1,multiply(additive_identity,X1))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_40]),c_0_27]) ).
cnf(c_0_90,negated_conjecture,
ifeq(sum(multiply(x,x_times_y),x_times_y,X1),true,product(x_times_y,X1,x_times_y),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_42]),c_0_87]),c_0_27]) ).
cnf(c_0_91,negated_conjecture,
ifeq(product(X1,y,X2),true,ifeq(sum(x_times_y,X2,X3),true,ifeq(sum(x,X1,X4),true,product(X4,y,X3),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_29]),c_0_27]) ).
cnf(c_0_92,plain,
ifeq(product(inverse(X1),X2,inverse(X1)),true,ifeq(sum(X1,X2,X3),true,product(multiplicative_identity,X3,multiplicative_identity),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_51]),c_0_27]) ).
cnf(c_0_93,axiom,
product(X1,multiplicative_identity,X1) = true,
multiplicative_identity2 ).
cnf(c_0_94,axiom,
sum(inverse(X1),X1,multiplicative_identity) = true,
additive_inverse1 ).
cnf(c_0_95,plain,
multiply(multiply(additive_identity,X1),add(X1,multiply(additive_identity,X1))) = multiply(additive_identity,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_88]),c_0_34]) ).
cnf(c_0_96,plain,
add(X1,multiply(additive_identity,X1)) = multiply(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_89]),c_0_34]) ).
cnf(c_0_97,negated_conjecture,
product(x_times_y,x_times_y,x_times_y) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_33]),c_0_42]),c_0_87]),c_0_27]) ).
cnf(c_0_98,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_55,c_0_70]),c_0_27]) ).
cnf(c_0_99,axiom,
product(X1,inverse(X1),additive_identity) = true,
multiplicative_inverse2 ).
cnf(c_0_100,negated_conjecture,
ifeq(sum(x_times_y,y,X1),true,ifeq(sum(x,multiplicative_identity,X2),true,product(X2,y,X1),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_60]),c_0_27]) ).
cnf(c_0_101,plain,
ifeq(sum(X1,multiplicative_identity,X2),true,product(multiplicative_identity,X2,multiplicative_identity),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_27]) ).
cnf(c_0_102,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_49,c_0_94]),c_0_27]) ).
cnf(c_0_103,plain,
multiply(multiply(additive_identity,X1),multiply(X1,X1)) = multiply(additive_identity,X1),
inference(rw,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_104,negated_conjecture,
multiply(x_times_y,x_times_y) = x_times_y,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_97]),c_0_34]) ).
cnf(c_0_105,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_98,c_0_99]),c_0_27]) ).
cnf(c_0_106,negated_conjecture,
ifeq(sum(x_times_y,y,X1),true,product(add(multiplicative_identity,x),y,X1),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_33]),c_0_27]),c_0_42]) ).
cnf(c_0_107,plain,
product(multiplicative_identity,add(X1,multiplicative_identity),multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_33]),c_0_27]) ).
cnf(c_0_108,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_102,c_0_33]),c_0_27]) ).
cnf(c_0_109,negated_conjecture,
multiply(x_times_y,multiply(additive_identity,x_times_y)) = multiply(additive_identity,x_times_y),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_47]) ).
cnf(c_0_110,plain,
product(multiplicative_identity,add(X1,inverse(inverse(X1))),X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_33]),c_0_27]) ).
cnf(c_0_111,negated_conjecture,
product(add(multiplicative_identity,x),y,add(y,x_times_y)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_33]),c_0_27]),c_0_42]) ).
cnf(c_0_112,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_107]),c_0_69]),c_0_34]) ).
cnf(c_0_113,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_108,c_0_94]),c_0_27]) ).
cnf(c_0_114,negated_conjecture,
product(multiply(additive_identity,x_times_y),x_times_y,multiply(additive_identity,x_times_y)) = true,
inference(spm,[status(thm)],[c_0_44,c_0_109]) ).
cnf(c_0_115,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_110]),c_0_69]),c_0_34]) ).
cnf(c_0_116,negated_conjecture,
multiply(y,add(multiplicative_identity,x)) = add(y,x_times_y),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_111]),c_0_34]),c_0_47]) ).
cnf(c_0_117,plain,
add(multiplicative_identity,X1) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_42,c_0_112]) ).
cnf(c_0_118,plain,
multiply(X1,multiplicative_identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_44]),c_0_34]) ).
cnf(c_0_119,negated_conjecture,
product(multiplicative_identity,add(x_times_y,inverse(multiply(additive_identity,x_times_y))),multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_27]),c_0_42]) ).
cnf(c_0_120,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_102,c_0_70]),c_0_27]) ).
cnf(c_0_121,plain,
sum(inverse(inverse(X1)),X1,X1) = true,
inference(spm,[status(thm)],[c_0_38,c_0_115]) ).
cnf(c_0_122,negated_conjecture,
add(y,x_times_y) = y,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_117]),c_0_118]) ).
cnf(c_0_123,negated_conjecture,
add(x_times_y,inverse(multiply(additive_identity,x_times_y))) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_119]),c_0_69]),c_0_34]) ).
cnf(c_0_124,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_120,c_0_121]),c_0_59]),c_0_27]),c_0_27]) ).
cnf(c_0_125,negated_conjecture,
sum(y,x_times_y,y) = true,
inference(spm,[status(thm)],[c_0_33,c_0_122]) ).
cnf(c_0_126,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_74,c_0_51]),c_0_27]) ).
cnf(c_0_127,negated_conjecture,
sum(inverse(multiply(additive_identity,x_times_y)),x_times_y,multiplicative_identity) = true,
inference(spm,[status(thm)],[c_0_38,c_0_123]) ).
cnf(c_0_128,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_124]),c_0_69]),c_0_34]) ).
cnf(c_0_129,negated_conjecture,
ifeq(product(additive_identity,x_times_y,X1),true,product(y,y,add(y,X1)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_125]),c_0_27]) ).
cnf(c_0_130,plain,
ifeq2(product(inverse(X1),X1,X2),true,additive_identity,X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_59]),c_0_34]) ).
cnf(c_0_131,negated_conjecture,
product(inverse(multiply(additive_identity,x_times_y)),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_126,c_0_127]),c_0_128]),c_0_40]),c_0_27]),c_0_27]) ).
cnf(c_0_132,negated_conjecture,
product(y,y,add(y,multiply(additive_identity,x_times_y))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_40]),c_0_27]) ).
cnf(c_0_133,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_44]),c_0_34]) ).
cnf(c_0_134,negated_conjecture,
inverse(multiply(additive_identity,x_times_y)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_131]),c_0_118]),c_0_34]) ).
cnf(c_0_135,negated_conjecture,
add(y,multiply(additive_identity,x_times_y)) = multiply(y,y),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_132]),c_0_34]) ).
cnf(c_0_136,negated_conjecture,
multiply(additive_identity,x_times_y) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_118]) ).
cnf(c_0_137,plain,
product(multiply(additive_identity,X1),multiply(X1,X1),multiply(additive_identity,X1)) = true,
inference(rw,[status(thm)],[c_0_88,c_0_96]) ).
cnf(c_0_138,negated_conjecture,
multiply(y,y) = y,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_135,c_0_136]),c_0_57]) ).
cnf(c_0_139,negated_conjecture,
product(multiply(additive_identity,y),y,multiply(additive_identity,y)) = true,
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_140,negated_conjecture,
product(multiplicative_identity,add(y,inverse(multiply(additive_identity,y))),multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_139]),c_0_27]),c_0_42]) ).
cnf(c_0_141,negated_conjecture,
add(y,inverse(multiply(additive_identity,y))) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_140]),c_0_69]),c_0_34]) ).
cnf(c_0_142,negated_conjecture,
sum(inverse(multiply(additive_identity,y)),y,multiplicative_identity) = true,
inference(spm,[status(thm)],[c_0_38,c_0_141]) ).
cnf(c_0_143,negated_conjecture,
ifeq(sum(X1,x_times_y,X2),true,ifeq(sum(X1,x,X3),true,product(add(X1,y),X3,X2),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_31]),c_0_27]) ).
cnf(c_0_144,negated_conjecture,
product(inverse(multiply(additive_identity,y)),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_126,c_0_142]),c_0_128]),c_0_40]),c_0_27]),c_0_27]) ).
cnf(c_0_145,negated_conjecture,
ifeq(sum(x,x_times_y,X1),true,product(add(x,y),x,X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_77]),c_0_27]) ).
cnf(c_0_146,negated_conjecture,
inverse(multiply(additive_identity,y)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_144]),c_0_118]),c_0_34]) ).
cnf(c_0_147,negated_conjecture,
product(add(x,y),x,add(x,x_times_y)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_33]),c_0_27]) ).
cnf(c_0_148,negated_conjecture,
multiply(additive_identity,y) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_146]),c_0_118]) ).
cnf(c_0_149,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_78,c_0_70]),c_0_27]) ).
cnf(c_0_150,negated_conjecture,
product(additive_identity,x_times_y,additive_identity) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_136]),c_0_136]) ).
cnf(c_0_151,negated_conjecture,
multiply(x,add(x,y)) = add(x,x_times_y),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_147]),c_0_47]),c_0_34]) ).
cnf(c_0_152,negated_conjecture,
product(additive_identity,y,additive_identity) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_148]),c_0_148]) ).
cnf(c_0_153,negated_conjecture,
product(X1,add(X1,x_times_y),X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_27]) ).
cnf(c_0_154,negated_conjecture,
ifeq2(product(x,add(x,y),X1),true,add(x,x_times_y),X1) = X1,
inference(spm,[status(thm)],[c_0_43,c_0_151]) ).
cnf(c_0_155,negated_conjecture,
product(X1,add(X1,y),X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_152]),c_0_27]) ).
cnf(c_0_156,negated_conjecture,
multiply(X1,add(X1,x_times_y)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_153]),c_0_34]) ).
cnf(c_0_157,negated_conjecture,
add(x,x_times_y) = x,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_34]) ).
cnf(c_0_158,negated_conjecture,
multiply(x,x) = x,
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_159,negated_conjecture,
product(multiply(additive_identity,x),x,multiply(additive_identity,x)) = true,
inference(spm,[status(thm)],[c_0_137,c_0_158]) ).
cnf(c_0_160,negated_conjecture,
product(multiplicative_identity,add(x,inverse(multiply(additive_identity,x))),multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_159]),c_0_27]),c_0_42]) ).
cnf(c_0_161,negated_conjecture,
add(x,inverse(multiply(additive_identity,x))) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_160]),c_0_69]),c_0_34]) ).
cnf(c_0_162,negated_conjecture,
sum(inverse(multiply(additive_identity,x)),x,multiplicative_identity) = true,
inference(spm,[status(thm)],[c_0_38,c_0_161]) ).
cnf(c_0_163,negated_conjecture,
product(inverse(multiply(additive_identity,x)),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_126,c_0_162]),c_0_128]),c_0_40]),c_0_27]),c_0_27]) ).
cnf(c_0_164,negated_conjecture,
inverse(multiply(additive_identity,x)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_163]),c_0_118]),c_0_34]) ).
cnf(c_0_165,negated_conjecture,
multiply(additive_identity,x) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_164]),c_0_118]) ).
cnf(c_0_166,negated_conjecture,
sum(inverse(x),inverse(y),x_inverse_plus_y_inverse) = true,
x_inverse_plus_y_inverse ).
cnf(c_0_167,negated_conjecture,
product(additive_identity,x,additive_identity) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_165]),c_0_165]) ).
cnf(c_0_168,negated_conjecture,
ifeq(product(additive_identity,y,X1),true,ifeq(sum(X1,x_times_y,X2),true,product(x,y,X2),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_29]),c_0_27]) ).
cnf(c_0_169,plain,
ifeq(product(X1,X2,additive_identity),true,ifeq(sum(X3,X2,X4),true,ifeq(sum(X3,X1,X5),true,product(X5,X4,X3),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_70]),c_0_27]) ).
cnf(c_0_170,negated_conjecture,
sum(inverse(y),inverse(x),x_inverse_plus_y_inverse) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_166]),c_0_27]) ).
cnf(c_0_171,negated_conjecture,
product(X1,add(X1,x),X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_167]),c_0_27]) ).
cnf(c_0_172,negated_conjecture,
ifeq(product(inverse(y),X1,X2),true,ifeq(sum(inverse(x),X2,X3),true,ifeq(sum(inverse(x),X1,X4),true,product(x_inverse_plus_y_inverse,X4,X3),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_166]),c_0_27]) ).
cnf(c_0_173,negated_conjecture,
ifeq(product(additive_identity,y,X1),true,product(x,y,add(X1,x_times_y)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_33]),c_0_27]) ).
cnf(c_0_174,negated_conjecture,
ifeq(product(inverse(x),X1,additive_identity),true,ifeq(sum(inverse(y),X1,X2),true,product(x_inverse_plus_y_inverse,X2,inverse(y)),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_27]) ).
cnf(c_0_175,negated_conjecture,
product(multiplicative_identity,add(inverse(X1),add(X1,x)),multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_171]),c_0_27]) ).
cnf(c_0_176,negated_conjecture,
ifeq(product(inverse(y),X1,additive_identity),true,ifeq(sum(inverse(x),X1,X2),true,product(x_inverse_plus_y_inverse,X2,inverse(x)),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_70]),c_0_27]) ).
cnf(c_0_177,negated_conjecture,
product(x,y,add(x_times_y,multiply(additive_identity,y))) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_40]),c_0_27]),c_0_42]) ).
cnf(c_0_178,plain,
ifeq(product(X1,X2,X3),true,ifeq(sum(X4,X3,X5),true,ifeq(sum(X4,X1,X6),true,product(X6,add(X4,X2),X5),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_33]),c_0_27]) ).
cnf(c_0_179,negated_conjecture,
ifeq(sum(inverse(y),x,X1),true,product(x_inverse_plus_y_inverse,X1,inverse(y)),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_99]),c_0_128]),c_0_27]) ).
cnf(c_0_180,negated_conjecture,
add(inverse(X1),add(X1,x)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_175]),c_0_69]),c_0_34]) ).
cnf(c_0_181,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_182,negated_conjecture,
ifeq(sum(inverse(x),y,X1),true,product(x_inverse_plus_y_inverse,X1,inverse(x)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_59]),c_0_27]) ).
cnf(c_0_183,negated_conjecture,
product(multiplicative_identity,add(inverse(X1),add(X1,y)),multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_155]),c_0_27]) ).
cnf(c_0_184,negated_conjecture,
add(x_times_y,multiply(additive_identity,y)) = x_times_y,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_177]),c_0_48]),c_0_34]) ).
cnf(c_0_185,plain,
ifeq(product(X1,X2,X3),true,ifeq(sum(inverse(X3),X1,X4),true,product(X4,add(inverse(X3),X2),multiplicative_identity),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_94]),c_0_27]) ).
cnf(c_0_186,negated_conjecture,
product(x_inverse_plus_y_inverse,add(x,inverse(y)),inverse(y)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_33]),c_0_42]),c_0_27]) ).
cnf(c_0_187,negated_conjecture,
add(X1,add(x,inverse(X1))) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_128]),c_0_42]) ).
cnf(c_0_188,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_181,c_0_33]),c_0_27]) ).
cnf(c_0_189,negated_conjecture,
product(x_inverse_plus_y_inverse,add(y,inverse(x)),inverse(x)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_33]),c_0_42]),c_0_27]) ).
cnf(c_0_190,negated_conjecture,
add(inverse(X1),add(X1,y)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_183]),c_0_69]),c_0_34]) ).
cnf(c_0_191,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_74,c_0_40]),c_0_27]) ).
cnf(c_0_192,negated_conjecture,
sum(x_times_y,multiply(additive_identity,y),x_times_y) = true,
inference(spm,[status(thm)],[c_0_33,c_0_184]) ).
cnf(c_0_193,negated_conjecture,
ifeq(sum(y,x_inverse_plus_y_inverse,X1),true,product(X1,multiplicative_identity,multiplicative_identity),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_128]),c_0_128]),c_0_187]),c_0_27]) ).
cnf(c_0_194,plain,
ifeq(product(X1,X2,inverse(X3)),true,ifeq(sum(X2,X3,X4),true,product(add(X1,X3),X4,multiplicative_identity),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_94]),c_0_27]) ).
cnf(c_0_195,negated_conjecture,
product(add(y,inverse(x)),x_inverse_plus_y_inverse,inverse(x)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_189]),c_0_27]) ).
cnf(c_0_196,negated_conjecture,
add(X1,add(y,inverse(X1))) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_128]),c_0_42]) ).
cnf(c_0_197,negated_conjecture,
ifeq(sum(x_times_y,y,X1),true,product(x_times_y,X1,x_times_y),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_192]),c_0_27]) ).
cnf(c_0_198,negated_conjecture,
product(add(y,x_inverse_plus_y_inverse),multiplicative_identity,multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_33]),c_0_27]) ).
cnf(c_0_199,negated_conjecture,
ifeq(sum(x_inverse_plus_y_inverse,x,X1),true,product(multiplicative_identity,X1,multiplicative_identity),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_195]),c_0_42]),c_0_196]),c_0_27]) ).
cnf(c_0_200,negated_conjecture,
product(x_times_y,y,x_times_y) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_33]),c_0_42]),c_0_122]),c_0_27]) ).
cnf(c_0_201,negated_conjecture,
add(y,x_inverse_plus_y_inverse) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_198]),c_0_118]),c_0_34]) ).
cnf(c_0_202,negated_conjecture,
product(multiplicative_identity,add(x,x_inverse_plus_y_inverse),multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_33]),c_0_42]),c_0_27]) ).
cnf(c_0_203,negated_conjecture,
product(multiplicative_identity,add(y,inverse(x_times_y)),multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_200]),c_0_27]),c_0_42]) ).
cnf(c_0_204,plain,
ifeq(sum(X1,X2,X3),true,ifeq(sum(X1,inverse(X2),X4),true,product(X4,X3,X1),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_59]),c_0_27]) ).
cnf(c_0_205,negated_conjecture,
sum(y,x_inverse_plus_y_inverse,multiplicative_identity) = true,
inference(spm,[status(thm)],[c_0_33,c_0_201]) ).
cnf(c_0_206,negated_conjecture,
add(x,x_inverse_plus_y_inverse) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_202]),c_0_69]),c_0_34]) ).
cnf(c_0_207,plain,
ifeq(product(X1,X2,X3),true,ifeq(sum(inverse(X3),X2,X4),true,product(add(inverse(X3),X1),X4,multiplicative_identity),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_94]),c_0_27]) ).
cnf(c_0_208,negated_conjecture,
add(y,inverse(x_times_y)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_203]),c_0_69]),c_0_34]) ).
cnf(c_0_209,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_210,negated_conjecture,
ifeq(sum(y,inverse(x_inverse_plus_y_inverse),X1),true,product(X1,multiplicative_identity,y),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_205]),c_0_27]) ).
cnf(c_0_211,negated_conjecture,
sum(x,x_inverse_plus_y_inverse,multiplicative_identity) = true,
inference(spm,[status(thm)],[c_0_33,c_0_206]) ).
cnf(c_0_212,negated_conjecture,
ifeq(sum(inverse(x_times_y),x,X1),true,product(multiplicative_identity,X1,multiplicative_identity),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_31]),c_0_42]),c_0_208]),c_0_27]) ).
cnf(c_0_213,negated_conjecture,
ifeq(product(X1,y,X2),true,ifeq(product(X3,y,X4),true,ifeq(sum(x,X3,X1),true,sum(x_times_y,X4,X2),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_29]),c_0_27]) ).
cnf(c_0_214,negated_conjecture,
multiply(X1,add(X1,y)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_155]),c_0_34]) ).
cnf(c_0_215,negated_conjecture,
product(add(y,inverse(x_inverse_plus_y_inverse)),multiplicative_identity,y) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_33]),c_0_27]) ).
cnf(c_0_216,negated_conjecture,
ifeq(sum(x,inverse(x_inverse_plus_y_inverse),X1),true,product(X1,multiplicative_identity,x),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_211]),c_0_27]) ).
cnf(c_0_217,negated_conjecture,
product(multiplicative_identity,add(x,inverse(x_times_y)),multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_33]),c_0_27]),c_0_42]) ).
cnf(c_0_218,negated_conjecture,
ifeq(product(X1,y,X2),true,ifeq(sum(x,X1,x),true,sum(x_times_y,X2,x_times_y),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_29]),c_0_27]) ).
cnf(c_0_219,negated_conjecture,
multiply(X1,add(y,X1)) = X1,
inference(spm,[status(thm)],[c_0_214,c_0_42]) ).
cnf(c_0_220,negated_conjecture,
add(y,inverse(x_inverse_plus_y_inverse)) = y,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_215]),c_0_118]),c_0_34]) ).
cnf(c_0_221,negated_conjecture,
product(add(x,inverse(x_inverse_plus_y_inverse)),multiplicative_identity,x) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_33]),c_0_27]) ).
cnf(c_0_222,negated_conjecture,
add(x,inverse(x_times_y)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_217]),c_0_69]),c_0_34]) ).
cnf(c_0_223,negated_conjecture,
product(multiplicative_identity,add(inverse(X1),add(X1,x_times_y)),multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_153]),c_0_27]) ).
cnf(c_0_224,negated_conjecture,
ifeq(sum(x,X1,x),true,sum(x_times_y,multiply(y,X1),x_times_y),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_44]),c_0_27]) ).
cnf(c_0_225,negated_conjecture,
multiply(y,inverse(x_inverse_plus_y_inverse)) = inverse(x_inverse_plus_y_inverse),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_220]),c_0_47]) ).
cnf(c_0_226,negated_conjecture,
add(x,inverse(x_inverse_plus_y_inverse)) = x,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_221]),c_0_118]),c_0_34]) ).
cnf(c_0_227,negated_conjecture,
sum(inverse(x_times_y),x,multiplicative_identity) = true,
inference(spm,[status(thm)],[c_0_38,c_0_222]) ).
cnf(c_0_228,negated_conjecture,
add(inverse(X1),add(X1,x_times_y)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_223]),c_0_69]),c_0_34]) ).
cnf(c_0_229,negated_conjecture,
ifeq(sum(x,inverse(x_inverse_plus_y_inverse),x),true,sum(x_times_y,inverse(x_inverse_plus_y_inverse),x_times_y),true) = true,
inference(spm,[status(thm)],[c_0_224,c_0_225]) ).
cnf(c_0_230,negated_conjecture,
sum(x,inverse(x_inverse_plus_y_inverse),x) = true,
inference(spm,[status(thm)],[c_0_33,c_0_226]) ).
cnf(c_0_231,negated_conjecture,
ifeq(sum(inverse(x_times_y),inverse(x),X1),true,product(X1,multiplicative_identity,inverse(x_times_y)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_227]),c_0_27]) ).
cnf(c_0_232,negated_conjecture,
add(inverse(X1),add(x_times_y,X1)) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_228,c_0_42]) ).
cnf(c_0_233,negated_conjecture,
sum(x_times_y,inverse(x_inverse_plus_y_inverse),x_times_y) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_229,c_0_230]),c_0_27]) ).
cnf(c_0_234,negated_conjecture,
product(add(inverse(x),inverse(x_times_y)),multiplicative_identity,inverse(x_times_y)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_33]),c_0_27]),c_0_42]) ).
cnf(c_0_235,negated_conjecture,
sum(inverse(X1),add(x_times_y,X1),multiplicative_identity) = true,
inference(spm,[status(thm)],[c_0_33,c_0_232]) ).
cnf(c_0_236,negated_conjecture,
add(x_times_y,inverse(x_inverse_plus_y_inverse)) = x_times_y,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_233]),c_0_34]) ).
cnf(c_0_237,negated_conjecture,
add(inverse(x),inverse(x_times_y)) = inverse(x_times_y),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_234]),c_0_118]),c_0_34]) ).
cnf(c_0_238,negated_conjecture,
sum(inverse(x_times_y),y,multiplicative_identity) = true,
inference(spm,[status(thm)],[c_0_38,c_0_208]) ).
cnf(c_0_239,negated_conjecture,
ifeq(product(inverse(x),X1,X2),true,ifeq(sum(X2,inverse(y),X3),true,ifeq(sum(X1,inverse(y),X4),true,product(x_inverse_plus_y_inverse,X4,X3),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_166]),c_0_27]) ).
cnf(c_0_240,negated_conjecture,
sum(x_inverse_plus_y_inverse,x_times_y,multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_236]),c_0_128]) ).
cnf(c_0_241,negated_conjecture,
sum(inverse(x),inverse(x_times_y),inverse(x_times_y)) = true,
inference(spm,[status(thm)],[c_0_33,c_0_237]) ).
cnf(c_0_242,negated_conjecture,
ifeq(sum(inverse(x_times_y),inverse(y),X1),true,product(X1,multiplicative_identity,inverse(x_times_y)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_238]),c_0_27]) ).
cnf(c_0_243,negated_conjecture,
ifeq(product(inverse(x),X1,inverse(x)),true,ifeq(sum(X1,inverse(y),X2),true,product(x_inverse_plus_y_inverse,X2,x_inverse_plus_y_inverse),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_166]),c_0_27]) ).
cnf(c_0_244,negated_conjecture,
ifeq(sum(x_inverse_plus_y_inverse,inverse(x_times_y),X1),true,product(X1,multiplicative_identity,x_inverse_plus_y_inverse),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_240]),c_0_27]) ).
cnf(c_0_245,negated_conjecture,
ifeq(sum(inverse(x),x_times_y,X1),true,product(X1,inverse(x_times_y),inverse(x)),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_241]),c_0_128]),c_0_27]) ).
cnf(c_0_246,negated_conjecture,
product(add(inverse(y),inverse(x_times_y)),multiplicative_identity,inverse(x_times_y)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_242,c_0_33]),c_0_27]),c_0_42]) ).
cnf(c_0_247,negated_conjecture,
ifeq(product(inverse(x),X1,inverse(x)),true,product(x_inverse_plus_y_inverse,add(X1,inverse(y)),x_inverse_plus_y_inverse),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_243,c_0_33]),c_0_27]) ).
cnf(c_0_248,negated_conjecture,
product(add(x_inverse_plus_y_inverse,inverse(x_times_y)),multiplicative_identity,x_inverse_plus_y_inverse) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_33]),c_0_27]) ).
cnf(c_0_249,negated_conjecture,
ifeq(product(X1,X2,inverse(x)),true,ifeq(sum(inverse(y),X1,X3),true,product(X3,add(inverse(y),X2),x_inverse_plus_y_inverse),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_170]),c_0_27]) ).
cnf(c_0_250,negated_conjecture,
product(add(x_times_y,inverse(x)),inverse(x_times_y),inverse(x)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_245,c_0_33]),c_0_42]),c_0_27]) ).
cnf(c_0_251,negated_conjecture,
add(inverse(y),inverse(x_times_y)) = inverse(x_times_y),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_246]),c_0_118]),c_0_34]) ).
cnf(c_0_252,negated_conjecture,
product(x_inverse_plus_y_inverse,add(inverse(y),add(x_times_y,inverse(x))),x_inverse_plus_y_inverse) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_153]),c_0_42]),c_0_27]),c_0_42]) ).
cnf(c_0_253,negated_conjecture,
add(x_inverse_plus_y_inverse,inverse(x_times_y)) = x_inverse_plus_y_inverse,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_248]),c_0_118]),c_0_34]) ).
cnf(c_0_254,negated_conjecture,
ifeq(sum(inverse(y),add(x_times_y,inverse(x)),X1),true,product(X1,inverse(x_times_y),x_inverse_plus_y_inverse),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_249,c_0_250]),c_0_251]),c_0_27]) ).
cnf(c_0_255,negated_conjecture,
product(multiplicative_identity,add(inverse(x_inverse_plus_y_inverse),add(inverse(y),add(x_times_y,inverse(x)))),multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_252]),c_0_27]) ).
cnf(c_0_256,negated_conjecture,
sum(inverse(x_times_y),x_inverse_plus_y_inverse,x_inverse_plus_y_inverse) = true,
inference(spm,[status(thm)],[c_0_38,c_0_253]) ).
cnf(c_0_257,negated_conjecture,
product(add(inverse(y),add(x_times_y,inverse(x))),inverse(x_times_y),x_inverse_plus_y_inverse) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_254,c_0_33]),c_0_27]) ).
cnf(c_0_258,negated_conjecture,
add(inverse(x_inverse_plus_y_inverse),add(inverse(y),add(x_times_y,inverse(x)))) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_255]),c_0_69]),c_0_34]) ).
cnf(c_0_259,negated_conjecture,
ifeq(sum(inverse(x_times_y),inverse(x_inverse_plus_y_inverse),X1),true,product(X1,x_inverse_plus_y_inverse,inverse(x_times_y)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_256]),c_0_27]) ).
cnf(c_0_260,negated_conjecture,
ifeq(sum(inverse(x_inverse_plus_y_inverse),inverse(x_times_y),X1),true,product(multiplicative_identity,X1,multiplicative_identity),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_257]),c_0_258]),c_0_27]) ).
cnf(c_0_261,negated_conjecture,
product(add(inverse(x_times_y),inverse(x_inverse_plus_y_inverse)),x_inverse_plus_y_inverse,inverse(x_times_y)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_259,c_0_33]),c_0_27]) ).
cnf(c_0_262,negated_conjecture,
product(multiplicative_identity,add(inverse(x_times_y),inverse(x_inverse_plus_y_inverse)),multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_33]),c_0_42]),c_0_27]) ).
cnf(c_0_263,negated_conjecture,
multiply(x_inverse_plus_y_inverse,add(inverse(x_times_y),inverse(x_inverse_plus_y_inverse))) = inverse(x_times_y),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_261]),c_0_34]),c_0_47]) ).
cnf(c_0_264,negated_conjecture,
add(inverse(x_times_y),inverse(x_inverse_plus_y_inverse)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_262]),c_0_69]),c_0_34]) ).
cnf(c_0_265,negated_conjecture,
inverse(x_times_y) != x_inverse_plus_y_inverse,
prove_equation ).
cnf(c_0_266,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_263,c_0_264]),c_0_118]),c_0_265]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO015-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 08:07:10 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.54 start to proof: theBenchmark
% 19.85/19.89 % Version : CSE_E---1.5
% 19.85/19.89 % Problem : theBenchmark.p
% 19.85/19.89 % Proof found
% 19.85/19.89 % SZS status Theorem for theBenchmark.p
% 19.85/19.89 % SZS output start Proof
% See solution above
% 19.85/19.90 % Total time : 19.338000 s
% 19.85/19.90 % SZS output end Proof
% 19.85/19.90 % Total time : 19.343000 s
%------------------------------------------------------------------------------