TSTP Solution File: BOO017-10 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : BOO017-10 : 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 18:05:51 EDT 2023
% Result : Unsatisfiable 14.80s 14.84s
% Output : CNFRefutation 14.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 35
% Syntax : Number of formulae : 142 ( 129 unt; 13 typ; 0 def)
% Number of atoms : 129 ( 128 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 : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 266 ( 4 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,
z: $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(x_plus_y,hypothesis,
sum(x,y,z) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_plus_y) ).
cnf(ifeq_axiom_001,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
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(multiplicative_identity2,axiom,
product(X1,multiplicative_identity,X1) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity2) ).
cnf(additive_inverse2,axiom,
sum(X1,inverse(X1),multiplicative_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse2) ).
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(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(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(additive_identity1,axiom,
sum(additive_identity,X1,X1) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
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(multiplicative_inverse1,axiom,
product(inverse(X1),X1,additive_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse1) ).
cnf(multiplicative_inverse2,axiom,
product(X1,inverse(X1),additive_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse2) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
cnf(additive_inverse1,axiom,
sum(inverse(X1),X1,multiplicative_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).
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(prove_product,negated_conjecture,
product(x,z,x) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_product) ).
cnf(c_0_22,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_23,hypothesis,
sum(x,y,z) = true,
x_plus_y ).
cnf(c_0_24,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom_001 ).
cnf(c_0_25,hypothesis,
ifeq(product(y,X1,X2),true,ifeq(sum(x,X2,X3),true,ifeq(sum(x,X1,X4),true,product(z,X4,X3),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_26,axiom,
ifeq2(sum(X1,X2,X3),true,ifeq2(sum(X1,X2,X4),true,X4,X3),X3) = X3,
addition_is_well_defined ).
cnf(c_0_27,axiom,
sum(X1,X2,add(X1,X2)) = true,
closure_of_addition ).
cnf(c_0_28,axiom,
ifeq2(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_29,axiom,
ifeq(sum(X1,X2,X3),true,sum(X2,X1,X3),true) = true,
commutativity_of_addition ).
cnf(c_0_30,hypothesis,
ifeq(product(y,X1,y),true,ifeq(sum(x,X1,X2),true,product(z,X2,z),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_23]),c_0_24]) ).
cnf(c_0_31,axiom,
product(X1,multiplicative_identity,X1) = true,
multiplicative_identity2 ).
cnf(c_0_32,plain,
ifeq2(sum(X1,X2,X3),true,add(X1,X2),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_33,plain,
sum(X1,X2,add(X2,X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_27]),c_0_24]) ).
cnf(c_0_34,hypothesis,
ifeq(sum(x,multiplicative_identity,X1),true,product(z,X1,z),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_24]) ).
cnf(c_0_35,plain,
add(X1,X2) = add(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_28]) ).
cnf(c_0_36,axiom,
sum(X1,inverse(X1),multiplicative_identity) = true,
additive_inverse2 ).
cnf(c_0_37,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_38,axiom,
ifeq(product(X1,X2,X3),true,product(X2,X1,X3),true) = true,
commutativity_of_multiplication ).
cnf(c_0_39,hypothesis,
product(z,add(multiplicative_identity,x),z) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_27]),c_0_24]),c_0_35]) ).
cnf(c_0_40,axiom,
ifeq2(product(X1,X2,X3),true,ifeq2(product(X1,X2,X4),true,X4,X3),X3) = X3,
multiplication_is_well_defined ).
cnf(c_0_41,axiom,
product(multiplicative_identity,X1,X1) = true,
multiplicative_identity1 ).
cnf(c_0_42,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_22,c_0_36]),c_0_24]) ).
cnf(c_0_43,axiom,
sum(additive_identity,X1,X1) = true,
additive_identity1 ).
cnf(c_0_44,plain,
ifeq(product(add(X1,X2),X3,X4),true,ifeq(product(X2,X3,X5),true,ifeq(product(X1,X3,X6),true,sum(X6,X5,X4),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_27]),c_0_24]) ).
cnf(c_0_45,hypothesis,
product(add(multiplicative_identity,x),z,z) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_24]) ).
cnf(c_0_46,plain,
ifeq2(product(multiplicative_identity,X1,X2),true,X1,X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_28]) ).
cnf(c_0_47,axiom,
product(X1,X2,multiply(X1,X2)) = true,
closure_of_multiplication ).
cnf(c_0_48,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_49,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_42,c_0_27]),c_0_24]) ).
cnf(c_0_50,axiom,
product(inverse(X1),X1,additive_identity) = true,
multiplicative_inverse1 ).
cnf(c_0_51,plain,
ifeq2(sum(additive_identity,X1,X2),true,X1,X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_43]),c_0_28]) ).
cnf(c_0_52,hypothesis,
ifeq(product(x,z,X1),true,ifeq(product(multiplicative_identity,z,X2),true,sum(X2,X1,z),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_24]) ).
cnf(c_0_53,plain,
multiply(multiplicative_identity,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_28]) ).
cnf(c_0_54,hypothesis,
ifeq(product(y,X1,X2),true,ifeq(product(x,X1,X3),true,ifeq(sum(X3,X2,X4),true,product(z,X1,X4),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_23]),c_0_24]) ).
cnf(c_0_55,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_49,c_0_50]),c_0_24]) ).
cnf(c_0_56,plain,
add(X1,additive_identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_33]),c_0_28]) ).
cnf(c_0_57,hypothesis,
ifeq(product(x,z,X1),true,sum(z,X1,z),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_47]),c_0_53]),c_0_24]) ).
cnf(c_0_58,hypothesis,
ifeq(product(y,X1,X2),true,ifeq(product(x,X1,additive_identity),true,product(z,X1,X2),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_43]),c_0_24]) ).
cnf(c_0_59,axiom,
product(X1,inverse(X1),additive_identity) = true,
multiplicative_inverse2 ).
cnf(c_0_60,hypothesis,
ifeq(product(y,inverse(x),X1),true,ifeq(sum(x,X1,X2),true,product(z,multiplicative_identity,X2),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_36]),c_0_24]) ).
cnf(c_0_61,axiom,
sum(X1,additive_identity,X1) = true,
additive_identity2 ).
cnf(c_0_62,plain,
ifeq2(product(X1,X2,X3),true,multiply(X1,X2),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_47]),c_0_28]) ).
cnf(c_0_63,plain,
product(multiplicative_identity,add(X1,X1),X1) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_27]),c_0_56]),c_0_24]) ).
cnf(c_0_64,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_22,c_0_47]),c_0_24]) ).
cnf(c_0_65,hypothesis,
sum(z,multiply(x,z),z) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_47]),c_0_24]) ).
cnf(c_0_66,hypothesis,
ifeq(product(y,inverse(x),X1),true,product(z,inverse(x),X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_24]) ).
cnf(c_0_67,hypothesis,
ifeq(product(y,inverse(x),X1),true,product(z,multiplicative_identity,add(x,X1)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_27]),c_0_24]) ).
cnf(c_0_68,plain,
product(X1,X2,multiply(X2,X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_47]),c_0_24]) ).
cnf(c_0_69,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_22,c_0_61]),c_0_24]) ).
cnf(c_0_70,plain,
add(X1,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_53]),c_0_28]) ).
cnf(c_0_71,hypothesis,
ifeq(sum(z,z,X1),true,ifeq(sum(z,x,X2),true,product(X2,X1,z),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_24]) ).
cnf(c_0_72,hypothesis,
product(z,inverse(x),multiply(y,inverse(x))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_47]),c_0_24]) ).
cnf(c_0_73,hypothesis,
product(z,multiplicative_identity,add(x,multiply(y,inverse(x)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_47]),c_0_24]) ).
cnf(c_0_74,plain,
multiply(X1,multiplicative_identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_68]),c_0_28]) ).
cnf(c_0_75,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_69,c_0_27]),c_0_24]) ).
cnf(c_0_76,plain,
sum(X1,X1,X1) = true,
inference(spm,[status(thm)],[c_0_27,c_0_70]) ).
cnf(c_0_77,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_69,c_0_27]),c_0_24]) ).
cnf(c_0_78,hypothesis,
ifeq(sum(z,z,X1),true,product(add(x,z),X1,z),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_27]),c_0_24]),c_0_35]) ).
cnf(c_0_79,plain,
ifeq(product(inverse(X1),X2,X3),true,ifeq(sum(X1,X2,X4),true,product(multiplicative_identity,X4,add(X1,X3)),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_27]),c_0_24]) ).
cnf(c_0_80,hypothesis,
product(inverse(x),z,multiply(y,inverse(x))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_72]),c_0_24]) ).
cnf(c_0_81,hypothesis,
add(x,multiply(y,inverse(x))) = z,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_73]),c_0_74]),c_0_28]) ).
cnf(c_0_82,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_75,c_0_76]),c_0_24]) ).
cnf(c_0_83,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_77,c_0_76]),c_0_24]) ).
cnf(c_0_84,hypothesis,
product(add(x,z),add(z,z),z) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_27]),c_0_24]) ).
cnf(c_0_85,hypothesis,
ifeq(sum(x,z,X1),true,product(multiplicative_identity,X1,z),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]),c_0_24]) ).
cnf(c_0_86,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_82,c_0_47]),c_0_24]),c_0_35]) ).
cnf(c_0_87,plain,
product(X1,X1,add(X1,multiply(additive_identity,X1))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_47]),c_0_24]) ).
cnf(c_0_88,hypothesis,
multiply(add(x,z),add(z,z)) = z,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_84]),c_0_28]) ).
cnf(c_0_89,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_68]),c_0_28]) ).
cnf(c_0_90,hypothesis,
product(multiplicative_identity,add(x,z),z) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_27]),c_0_24]) ).
cnf(c_0_91,axiom,
sum(inverse(X1),X1,multiplicative_identity) = true,
additive_inverse1 ).
cnf(c_0_92,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_62,c_0_86]),c_0_28]) ).
cnf(c_0_93,plain,
add(X1,multiply(additive_identity,X1)) = multiply(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_87]),c_0_28]) ).
cnf(c_0_94,hypothesis,
multiply(z,add(x,z)) = z,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_70]),c_0_89]) ).
cnf(c_0_95,hypothesis,
add(x,z) = z,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_90]),c_0_53]),c_0_28]) ).
cnf(c_0_96,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_42,c_0_61]),c_0_24]) ).
cnf(c_0_97,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_22,c_0_91]),c_0_24]) ).
cnf(c_0_98,plain,
multiply(multiply(additive_identity,X1),multiply(X1,X1)) = multiply(additive_identity,X1),
inference(rw,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_99,hypothesis,
multiply(z,z) = z,
inference(rw,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_100,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_96,c_0_59]),c_0_24]) ).
cnf(c_0_101,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_97,c_0_27]),c_0_24]) ).
cnf(c_0_102,hypothesis,
multiply(z,multiply(additive_identity,z)) = multiply(additive_identity,z),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_89]) ).
cnf(c_0_103,plain,
product(multiplicative_identity,add(X1,inverse(inverse(X1))),X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_27]),c_0_24]) ).
cnf(c_0_104,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_101,c_0_91]),c_0_24]) ).
cnf(c_0_105,hypothesis,
product(multiply(additive_identity,z),z,multiply(additive_identity,z)) = true,
inference(spm,[status(thm)],[c_0_68,c_0_102]) ).
cnf(c_0_106,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_103]),c_0_53]),c_0_28]) ).
cnf(c_0_107,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_108,hypothesis,
product(multiplicative_identity,add(z,inverse(multiply(additive_identity,z))),multiplicative_identity) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_35]),c_0_24]) ).
cnf(c_0_109,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_97,c_0_61]),c_0_24]) ).
cnf(c_0_110,plain,
sum(inverse(inverse(X1)),X1,X1) = true,
inference(spm,[status(thm)],[c_0_33,c_0_106]) ).
cnf(c_0_111,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_107,c_0_43]),c_0_24]) ).
cnf(c_0_112,hypothesis,
add(z,inverse(multiply(additive_identity,z))) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_108]),c_0_53]),c_0_28]) ).
cnf(c_0_113,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_109,c_0_110]),c_0_50]),c_0_24]),c_0_24]) ).
cnf(c_0_114,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_22,c_0_27]),c_0_24]) ).
cnf(c_0_115,plain,
ifeq(product(additive_identity,X1,inverse(X2)),true,ifeq(sum(X1,X2,X3),true,product(X2,X3,multiplicative_identity),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_91]),c_0_24]) ).
cnf(c_0_116,hypothesis,
sum(z,inverse(multiply(additive_identity,z)),multiplicative_identity) = true,
inference(spm,[status(thm)],[c_0_27,c_0_112]) ).
cnf(c_0_117,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_113]),c_0_53]),c_0_28]) ).
cnf(c_0_118,plain,
ifeq(product(X1,X2,X3),true,ifeq(sum(X4,X2,X5),true,product(add(X4,X1),X5,add(X4,X3)),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_27]),c_0_24]) ).
cnf(c_0_119,hypothesis,
sum(x,z,z) = true,
inference(spm,[status(thm)],[c_0_27,c_0_95]) ).
cnf(c_0_120,plain,
ifeq2(product(inverse(X1),X1,X2),true,additive_identity,X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_50]),c_0_28]) ).
cnf(c_0_121,hypothesis,
product(inverse(multiply(additive_identity,z)),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_115,c_0_116]),c_0_117]),c_0_47]),c_0_24]),c_0_24]) ).
cnf(c_0_122,hypothesis,
ifeq(product(X1,z,X2),true,product(add(x,X1),z,add(x,X2)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_24]) ).
cnf(c_0_123,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_68]),c_0_28]) ).
cnf(c_0_124,hypothesis,
inverse(multiply(additive_identity,z)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_121]),c_0_74]),c_0_28]) ).
cnf(c_0_125,hypothesis,
product(add(x,X1),z,add(x,multiply(X1,z))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_47]),c_0_24]) ).
cnf(c_0_126,hypothesis,
multiply(additive_identity,z) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_74]) ).
cnf(c_0_127,negated_conjecture,
product(x,z,x) != true,
prove_product ).
cnf(c_0_128,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_56]),c_0_56]),c_0_127]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO017-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.34 % Computer : n029.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sun Aug 27 08:42:40 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 14.80/14.84 % Version : CSE_E---1.5
% 14.80/14.84 % Problem : theBenchmark.p
% 14.80/14.84 % Proof found
% 14.80/14.84 % SZS status Theorem for theBenchmark.p
% 14.80/14.84 % SZS output start Proof
% See solution above
% 14.80/14.85 % Total time : 14.267000 s
% 14.80/14.85 % SZS output end Proof
% 14.80/14.85 % Total time : 14.271000 s
%------------------------------------------------------------------------------