TSTP Solution File: BOO014-3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : BOO014-3 : TPTP v8.1.2. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n019.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 1.19s 1.31s
% Output : CNFRefutation 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 35
% Syntax : Number of formulae : 162 ( 89 unt; 11 typ; 0 def)
% Number of atoms : 281 ( 46 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 264 ( 134 ~; 130 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 5 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 285 ( 14 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
add: ( $i * $i ) > $i ).
tff(decl_23,type,
sum: ( $i * $i * $i ) > $o ).
tff(decl_24,type,
multiply: ( $i * $i ) > $i ).
tff(decl_25,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_26,type,
additive_identity: $i ).
tff(decl_27,type,
multiplicative_identity: $i ).
tff(decl_28,type,
inverse: $i > $i ).
tff(decl_29,type,
x: $i ).
tff(decl_30,type,
y: $i ).
tff(decl_31,type,
x_plus_y: $i ).
tff(decl_32,type,
x_inverse_times_y_inverse: $i ).
cnf(distributivity8,axiom,
( sum(X6,X2,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X5)
| ~ product(X1,X4,X6)
| ~ product(X3,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity8) ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_identity1) ).
cnf(multiplicative_identity2,axiom,
product(X1,multiplicative_identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_identity2) ).
cnf(addition_is_well_defined,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',addition_is_well_defined) ).
cnf(additive_inverse1,axiom,
sum(inverse(X1),X1,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_inverse1) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',commutativity_of_addition) ).
cnf(inverse_is_self_cancelling,axiom,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_is_self_cancelling) ).
cnf(distributivity1,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity1) ).
cnf(multiplication_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplication_is_well_defined) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',closure_of_multiplication) ).
cnf(commutativity_of_multiplication,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',commutativity_of_multiplication) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity2) ).
cnf(x_inverse_times_y_inverse,hypothesis,
product(inverse(x),inverse(y),x_inverse_times_y_inverse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_inverse_times_y_inverse) ).
cnf(distributivity7,axiom,
( product(X3,X5,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X5)
| ~ product(X1,X4,X6)
| ~ sum(X6,X2,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity7) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
cnf(additive_inverse2,axiom,
sum(X1,inverse(X1),multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_inverse2) ).
cnf(x_plus_y,hypothesis,
sum(x,y,x_plus_y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_plus_y) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse1) ).
cnf(distributivity6,axiom,
( sum(X1,X6,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ product(X2,X4,X6)
| ~ product(X3,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity6) ).
cnf(distributivity4,axiom,
( product(X6,X2,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ sum(X3,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity4) ).
cnf(multiplicative_inverse2,axiom,
product(X1,inverse(X1),additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse2) ).
cnf(inverse_is_unique,axiom,
( X2 = X3
| ~ sum(X1,X2,multiplicative_identity)
| ~ sum(X1,X3,multiplicative_identity)
| ~ product(X1,X2,additive_identity)
| ~ product(X1,X3,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_is_unique) ).
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_24,axiom,
( sum(X6,X2,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X5)
| ~ product(X1,X4,X6)
| ~ product(X3,X5,X7) ),
distributivity8 ).
cnf(c_0_25,axiom,
product(multiplicative_identity,X1,X1),
multiplicative_identity1 ).
cnf(c_0_26,plain,
( sum(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ sum(X4,X2,multiplicative_identity)
| ~ sum(X5,X2,X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,axiom,
product(X1,multiplicative_identity,X1),
multiplicative_identity2 ).
cnf(c_0_28,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_29,axiom,
sum(inverse(X1),X1,multiplicative_identity),
additive_inverse1 ).
cnf(c_0_30,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X2,multiplicative_identity)
| ~ sum(multiplicative_identity,X2,X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_32,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_33,plain,
( X1 = multiplicative_identity
| ~ sum(inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( sum(inverse(X1),X1,X2)
| ~ sum(multiplicative_identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_35,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_31]) ).
cnf(c_0_36,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
cnf(c_0_37,plain,
add(inverse(X1),X1) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_33,c_0_31]) ).
cnf(c_0_38,axiom,
inverse(inverse(X1)) = X1,
inverse_is_self_cancelling ).
cnf(c_0_39,plain,
sum(inverse(X1),X1,add(multiplicative_identity,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
cnf(c_0_40,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
distributivity1 ).
cnf(c_0_43,plain,
add(multiplicative_identity,X1) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_39]),c_0_40]),c_0_41]) ).
cnf(c_0_44,plain,
( sum(X1,X2,X3)
| ~ product(X3,X4,X2)
| ~ product(X3,X5,X1)
| ~ sum(X5,X4,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_42,c_0_27]) ).
cnf(c_0_45,plain,
sum(X1,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_36,c_0_43]) ).
cnf(c_0_46,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined ).
cnf(c_0_47,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_48,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
commutativity_of_multiplication ).
cnf(c_0_49,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_50,plain,
( sum(X1,X2,X2)
| ~ product(X2,X3,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_27]),c_0_45])]) ).
cnf(c_0_51,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,plain,
product(X1,X2,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_48,c_0_47]) ).
cnf(c_0_53,plain,
( X1 = X2
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_49]) ).
cnf(c_0_54,plain,
sum(multiply(X1,X2),X1,X1),
inference(spm,[status(thm)],[c_0_50,c_0_47]) ).
cnf(c_0_55,hypothesis,
product(inverse(x),inverse(y),x_inverse_times_y_inverse),
x_inverse_times_y_inverse ).
cnf(c_0_56,axiom,
( product(X3,X5,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X5)
| ~ product(X1,X4,X6)
| ~ sum(X6,X2,X7) ),
distributivity7 ).
cnf(c_0_57,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_58,plain,
multiply(additive_identity,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,hypothesis,
product(inverse(y),inverse(x),x_inverse_times_y_inverse),
inference(spm,[status(thm)],[c_0_48,c_0_55]) ).
cnf(c_0_60,plain,
( product(X1,X2,X3)
| ~ sum(multiply(X4,X5),X6,X3)
| ~ sum(X5,X6,X2)
| ~ sum(X4,X6,X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_47]) ).
cnf(c_0_61,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_62,plain,
multiply(X1,additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,hypothesis,
sum(x_inverse_times_y_inverse,inverse(y),inverse(y)),
inference(spm,[status(thm)],[c_0_50,c_0_59]) ).
cnf(c_0_64,plain,
( product(X1,X2,X3)
| ~ sum(additive_identity,X2,X3)
| ~ sum(X4,X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).
cnf(c_0_65,hypothesis,
sum(inverse(y),x_inverse_times_y_inverse,inverse(y)),
inference(spm,[status(thm)],[c_0_32,c_0_63]) ).
cnf(c_0_66,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_61]) ).
cnf(c_0_67,hypothesis,
( product(inverse(y),x_inverse_times_y_inverse,X1)
| ~ sum(additive_identity,x_inverse_times_y_inverse,X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_68,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_66,c_0_31]) ).
cnf(c_0_69,plain,
( sum(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ sum(X5,X2,multiplicative_identity)
| ~ sum(X4,X2,X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_27]) ).
cnf(c_0_70,hypothesis,
product(inverse(y),x_inverse_times_y_inverse,x_inverse_times_y_inverse),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_31]),c_0_68]) ).
cnf(c_0_71,hypothesis,
( sum(x_inverse_times_y_inverse,X1,X2)
| ~ sum(inverse(y),X1,X2)
| ~ sum(x_inverse_times_y_inverse,X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_72,axiom,
sum(X1,inverse(X1),multiplicative_identity),
additive_inverse2 ).
cnf(c_0_73,hypothesis,
( sum(x_inverse_times_y_inverse,inverse(x_inverse_times_y_inverse),X1)
| ~ sum(inverse(y),inverse(x_inverse_times_y_inverse),X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_74,hypothesis,
sum(x_inverse_times_y_inverse,inverse(x_inverse_times_y_inverse),add(inverse(y),inverse(x_inverse_times_y_inverse))),
inference(spm,[status(thm)],[c_0_73,c_0_31]) ).
cnf(c_0_75,plain,
( sum(X1,X2,multiply(X3,X4))
| ~ product(X5,X6,X1)
| ~ sum(X6,X2,X4)
| ~ sum(X5,X2,X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_47]) ).
cnf(c_0_76,hypothesis,
add(inverse(y),inverse(x_inverse_times_y_inverse)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_74]),c_0_41]) ).
cnf(c_0_77,plain,
( X1 = X2
| ~ product(X2,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_27]) ).
cnf(c_0_78,hypothesis,
( sum(x_inverse_times_y_inverse,X1,multiply(X2,X3))
| ~ sum(inverse(y),X1,X3)
| ~ sum(inverse(x),X1,X2) ),
inference(spm,[status(thm)],[c_0_75,c_0_55]) ).
cnf(c_0_79,hypothesis,
sum(inverse(y),inverse(x_inverse_times_y_inverse),multiplicative_identity),
inference(spm,[status(thm)],[c_0_31,c_0_76]) ).
cnf(c_0_80,plain,
multiply(X1,multiplicative_identity) = X1,
inference(spm,[status(thm)],[c_0_77,c_0_47]) ).
cnf(c_0_81,hypothesis,
( sum(x_inverse_times_y_inverse,inverse(x_inverse_times_y_inverse),X1)
| ~ sum(inverse(x),inverse(x_inverse_times_y_inverse),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]) ).
cnf(c_0_82,hypothesis,
sum(x,y,x_plus_y),
x_plus_y ).
cnf(c_0_83,plain,
( product(add(X1,X2),X2,X3)
| ~ sum(additive_identity,X2,X3) ),
inference(spm,[status(thm)],[c_0_64,c_0_31]) ).
cnf(c_0_84,axiom,
product(inverse(X1),X1,additive_identity),
multiplicative_inverse1 ).
cnf(c_0_85,hypothesis,
sum(x_inverse_times_y_inverse,inverse(x_inverse_times_y_inverse),add(inverse(x),inverse(x_inverse_times_y_inverse))),
inference(spm,[status(thm)],[c_0_81,c_0_31]) ).
cnf(c_0_86,hypothesis,
sum(y,x,x_plus_y),
inference(spm,[status(thm)],[c_0_32,c_0_82]) ).
cnf(c_0_87,plain,
add(X1,multiply(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_54]),c_0_40]) ).
cnf(c_0_88,plain,
product(add(X1,X2),X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_31]),c_0_68]) ).
cnf(c_0_89,plain,
( sum(additive_identity,X1,X2)
| ~ sum(inverse(X3),X1,multiplicative_identity)
| ~ sum(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_84]) ).
cnf(c_0_90,hypothesis,
add(inverse(x),inverse(x_inverse_times_y_inverse)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_85]),c_0_41]) ).
cnf(c_0_91,hypothesis,
( product(x_plus_y,x,X1)
| ~ sum(additive_identity,x,X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_86]) ).
cnf(c_0_92,plain,
add(X1,multiply(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_87,c_0_57]) ).
cnf(c_0_93,plain,
multiply(X1,add(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_88]),c_0_57]) ).
cnf(c_0_94,plain,
( sum(additive_identity,X1,add(X2,X1))
| ~ sum(inverse(X2),X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_89,c_0_31]) ).
cnf(c_0_95,hypothesis,
sum(inverse(x),inverse(x_inverse_times_y_inverse),multiplicative_identity),
inference(spm,[status(thm)],[c_0_31,c_0_90]) ).
cnf(c_0_96,hypothesis,
product(x_plus_y,x,x),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_31]),c_0_68]) ).
cnf(c_0_97,plain,
sum(X1,multiply(X2,X1),X1),
inference(spm,[status(thm)],[c_0_31,c_0_92]) ).
cnf(c_0_98,plain,
multiply(X1,add(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_93,c_0_40]) ).
cnf(c_0_99,hypothesis,
sum(additive_identity,inverse(x_inverse_times_y_inverse),add(x,inverse(x_inverse_times_y_inverse))),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_100,hypothesis,
sum(additive_identity,inverse(x_inverse_times_y_inverse),add(y,inverse(x_inverse_times_y_inverse))),
inference(spm,[status(thm)],[c_0_94,c_0_79]) ).
cnf(c_0_101,hypothesis,
( sum(x,X1,multiply(X2,X3))
| ~ sum(x,X1,X3)
| ~ sum(x_plus_y,X1,X2) ),
inference(spm,[status(thm)],[c_0_75,c_0_96]) ).
cnf(c_0_102,plain,
sum(add(X1,X2),X1,add(X1,X2)),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_103,hypothesis,
add(x,inverse(x_inverse_times_y_inverse)) = inverse(x_inverse_times_y_inverse),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_99]),c_0_68]) ).
cnf(c_0_104,hypothesis,
add(y,inverse(x_inverse_times_y_inverse)) = inverse(x_inverse_times_y_inverse),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_100]),c_0_68]) ).
cnf(c_0_105,hypothesis,
( sum(x,inverse(x),X1)
| ~ sum(x_plus_y,inverse(x),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_72]),c_0_80]) ).
cnf(c_0_106,hypothesis,
( product(X1,x_plus_y,X2)
| ~ sum(multiply(X3,y),x,X2)
| ~ sum(X3,x,X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_86]) ).
cnf(c_0_107,hypothesis,
sum(inverse(x_inverse_times_y_inverse),x,inverse(x_inverse_times_y_inverse)),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_108,hypothesis,
multiply(y,inverse(x_inverse_times_y_inverse)) = y,
inference(spm,[status(thm)],[c_0_98,c_0_104]) ).
cnf(c_0_109,hypothesis,
( X1 = x_plus_y
| ~ sum(x,y,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_82]) ).
cnf(c_0_110,axiom,
( sum(X1,X6,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ product(X2,X4,X6)
| ~ product(X3,X5,X7) ),
distributivity6 ).
cnf(c_0_111,hypothesis,
sum(x,inverse(x),add(x_plus_y,inverse(x))),
inference(spm,[status(thm)],[c_0_105,c_0_31]) ).
cnf(c_0_112,axiom,
( product(X6,X2,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ sum(X3,X5,X7) ),
distributivity4 ).
cnf(c_0_113,axiom,
product(X1,inverse(X1),additive_identity),
multiplicative_inverse2 ).
cnf(c_0_114,hypothesis,
( product(inverse(x_inverse_times_y_inverse),x_plus_y,X1)
| ~ sum(y,x,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_57]),c_0_108]) ).
cnf(c_0_115,hypothesis,
add(x,y) = x_plus_y,
inference(spm,[status(thm)],[c_0_109,c_0_31]) ).
cnf(c_0_116,plain,
( sum(X1,X2,multiply(X3,X4))
| ~ product(X5,X6,X2)
| ~ sum(X1,X6,X4)
| ~ sum(X1,X5,X3) ),
inference(spm,[status(thm)],[c_0_110,c_0_47]) ).
cnf(c_0_117,hypothesis,
add(x_plus_y,inverse(x)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_111]),c_0_41]) ).
cnf(c_0_118,plain,
( product(X1,inverse(X2),X3)
| ~ product(X4,inverse(X2),X5)
| ~ sum(X5,additive_identity,X3)
| ~ sum(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_119,hypothesis,
product(inverse(x_inverse_times_y_inverse),x_plus_y,x_plus_y),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_31]),c_0_40]),c_0_115]) ).
cnf(c_0_120,hypothesis,
( sum(X1,x_inverse_times_y_inverse,multiply(X2,X3))
| ~ sum(X1,inverse(x),X3)
| ~ sum(X1,inverse(y),X2) ),
inference(spm,[status(thm)],[c_0_116,c_0_59]) ).
cnf(c_0_121,hypothesis,
sum(x_plus_y,inverse(x),multiplicative_identity),
inference(spm,[status(thm)],[c_0_31,c_0_117]) ).
cnf(c_0_122,plain,
( product(X1,inverse(X2),X3)
| ~ sum(multiply(X4,inverse(X2)),additive_identity,X3)
| ~ sum(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_118,c_0_47]) ).
cnf(c_0_123,hypothesis,
sum(x_plus_y,inverse(x_inverse_times_y_inverse),inverse(x_inverse_times_y_inverse)),
inference(spm,[status(thm)],[c_0_50,c_0_119]) ).
cnf(c_0_124,plain,
( X1 = additive_identity
| ~ product(inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_84]) ).
cnf(c_0_125,hypothesis,
( sum(x_plus_y,x_inverse_times_y_inverse,X1)
| ~ sum(x_plus_y,inverse(y),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_80]) ).
cnf(c_0_126,hypothesis,
( product(inverse(x_inverse_times_y_inverse),x_inverse_times_y_inverse,X1)
| ~ sum(multiply(x_plus_y,x_inverse_times_y_inverse),additive_identity,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_38]),c_0_38]) ).
cnf(c_0_127,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_53,c_0_31]) ).
cnf(c_0_128,plain,
multiply(inverse(X1),X1) = additive_identity,
inference(spm,[status(thm)],[c_0_124,c_0_47]) ).
cnf(c_0_129,hypothesis,
sum(x_plus_y,x_inverse_times_y_inverse,add(x_plus_y,inverse(y))),
inference(spm,[status(thm)],[c_0_125,c_0_31]) ).
cnf(c_0_130,hypothesis,
( product(x_plus_y,y,X1)
| ~ sum(additive_identity,y,X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_82]) ).
cnf(c_0_131,hypothesis,
product(inverse(x_inverse_times_y_inverse),x_inverse_times_y_inverse,multiply(x_plus_y,x_inverse_times_y_inverse)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_31]),c_0_127]) ).
cnf(c_0_132,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_128,c_0_38]) ).
cnf(c_0_133,plain,
( sum(multiply(X1,X2),X3,multiply(X4,X5))
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_75,c_0_47]) ).
cnf(c_0_134,hypothesis,
add(x_plus_y,inverse(y)) = add(x_plus_y,x_inverse_times_y_inverse),
inference(spm,[status(thm)],[c_0_35,c_0_129]) ).
cnf(c_0_135,hypothesis,
product(x_plus_y,y,y),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_31]),c_0_68]) ).
cnf(c_0_136,axiom,
( X2 = X3
| ~ sum(X1,X2,multiplicative_identity)
| ~ sum(X1,X3,multiplicative_identity)
| ~ product(X1,X2,additive_identity)
| ~ product(X1,X3,additive_identity) ),
inverse_is_unique ).
cnf(c_0_137,hypothesis,
multiply(x_plus_y,x_inverse_times_y_inverse) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_131]),c_0_57]),c_0_132]) ).
cnf(c_0_138,plain,
( sum(multiply(X1,inverse(X2)),X2,X3)
| ~ sum(X1,X2,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_29]),c_0_80]) ).
cnf(c_0_139,hypothesis,
sum(x_plus_y,inverse(y),add(x_plus_y,x_inverse_times_y_inverse)),
inference(spm,[status(thm)],[c_0_31,c_0_134]) ).
cnf(c_0_140,hypothesis,
multiply(y,x_plus_y) = y,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_135]),c_0_57]) ).
cnf(c_0_141,plain,
( sum(X1,X2,X3)
| ~ product(X4,X5,X2)
| ~ sum(X1,X4,multiplicative_identity)
| ~ sum(X1,X5,X3) ),
inference(spm,[status(thm)],[c_0_110,c_0_25]) ).
cnf(c_0_142,plain,
( X1 = inverse(X2)
| ~ product(X2,X1,additive_identity)
| ~ sum(X2,X1,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_113]),c_0_72])]) ).
cnf(c_0_143,hypothesis,
product(x_plus_y,x_inverse_times_y_inverse,additive_identity),
inference(spm,[status(thm)],[c_0_47,c_0_137]) ).
cnf(c_0_144,negated_conjecture,
inverse(x_plus_y) != x_inverse_times_y_inverse,
prove_equation ).
cnf(c_0_145,hypothesis,
sum(y,inverse(y),add(x_plus_y,x_inverse_times_y_inverse)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_38]),c_0_57]),c_0_140]) ).
cnf(c_0_146,hypothesis,
( sum(X1,x_inverse_times_y_inverse,X2)
| ~ sum(X1,inverse(y),multiplicative_identity)
| ~ sum(X1,inverse(x),X2) ),
inference(spm,[status(thm)],[c_0_141,c_0_59]) ).
cnf(c_0_147,hypothesis,
~ sum(x_plus_y,x_inverse_times_y_inverse,multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_144]) ).
cnf(c_0_148,hypothesis,
add(x_plus_y,x_inverse_times_y_inverse) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_145]),c_0_41]) ).
cnf(c_0_149,hypothesis,
~ sum(x_plus_y,inverse(y),multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_121]),c_0_147]) ).
cnf(c_0_150,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_148]),c_0_149]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : BOO014-3 : TPTP v8.1.2. Bugfixed v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 08:35:13 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.56 start to proof: theBenchmark
% 1.19/1.31 % Version : CSE_E---1.5
% 1.19/1.31 % Problem : theBenchmark.p
% 1.19/1.31 % Proof found
% 1.19/1.31 % SZS status Theorem for theBenchmark.p
% 1.19/1.31 % SZS output start Proof
% See solution above
% 1.19/1.32 % Total time : 0.741000 s
% 1.19/1.32 % SZS output end Proof
% 1.19/1.32 % Total time : 0.745000 s
%------------------------------------------------------------------------------