TSTP Solution File: BOO014-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : BOO014-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n021.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 1.54s 1.69s
% Output : CNFRefutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 33
% Syntax : Number of formulae : 158 ( 83 unt; 11 typ; 0 def)
% Number of atoms : 275 ( 41 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 258 ( 130 ~; 128 |; 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 : 278 ( 13 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(additive_inverse1,axiom,
sum(inverse(X1),X1,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_inverse1) ).
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(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(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(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(x_plus_y,negated_conjecture,
sum(x,y,x_plus_y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_plus_y) ).
cnf(x_inverse_times_y_inverse,negated_conjecture,
product(inverse(x),inverse(y),x_inverse_times_y_inverse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_inverse_times_y_inverse) ).
cnf(additive_inverse2,axiom,
sum(X1,inverse(X1),multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_inverse2) ).
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(multiplicative_inverse2,axiom,
product(X1,inverse(X1),additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse2) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse1) ).
cnf(distributivity5,axiom,
( product(X3,X5,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ product(X2,X4,X6)
| ~ sum(X1,X6,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity5) ).
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_22,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_23,axiom,
product(multiplicative_identity,X1,X1),
multiplicative_identity1 ).
cnf(c_0_24,plain,
( sum(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ sum(X4,X2,multiplicative_identity)
| ~ sum(X5,X2,X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,axiom,
product(X1,multiplicative_identity,X1),
multiplicative_identity2 ).
cnf(c_0_26,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X2,multiplicative_identity)
| ~ sum(multiplicative_identity,X2,X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,axiom,
sum(inverse(X1),X1,multiplicative_identity),
additive_inverse1 ).
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(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_30,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_31,plain,
( sum(inverse(X1),X1,X2)
| ~ sum(multiplicative_identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_34,plain,
( X1 = multiplicative_identity
| ~ sum(inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_35,plain,
sum(inverse(X1),X1,add(multiplicative_identity,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_29]) ).
cnf(c_0_36,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_34,c_0_33]) ).
cnf(c_0_38,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_39,plain,
add(multiplicative_identity,X1) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_35]),c_0_36]),c_0_37]) ).
cnf(c_0_40,plain,
( sum(X1,X2,X3)
| ~ product(X3,X4,X2)
| ~ product(X3,X5,X1)
| ~ sum(X5,X4,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_38,c_0_25]) ).
cnf(c_0_41,plain,
sum(X1,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_33,c_0_39]) ).
cnf(c_0_42,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined ).
cnf(c_0_43,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_44,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
commutativity_of_multiplication ).
cnf(c_0_45,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_46,plain,
( sum(X1,X2,X2)
| ~ product(X2,X3,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_25]),c_0_41])]) ).
cnf(c_0_47,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,plain,
product(X1,X2,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_44,c_0_43]) ).
cnf(c_0_49,plain,
( X1 = X2
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_45]) ).
cnf(c_0_50,plain,
sum(multiply(X1,X2),X1,X1),
inference(spm,[status(thm)],[c_0_46,c_0_43]) ).
cnf(c_0_51,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_52,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,plain,
multiply(additive_identity,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,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_51,c_0_43]) ).
cnf(c_0_55,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_56,plain,
multiply(X1,additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,negated_conjecture,
sum(x,y,x_plus_y),
x_plus_y ).
cnf(c_0_58,plain,
( product(X1,X2,X3)
| ~ sum(additive_identity,X2,X3)
| ~ sum(X4,X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
cnf(c_0_59,negated_conjecture,
sum(y,x,x_plus_y),
inference(spm,[status(thm)],[c_0_30,c_0_57]) ).
cnf(c_0_60,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_55]) ).
cnf(c_0_61,negated_conjecture,
product(inverse(x),inverse(y),x_inverse_times_y_inverse),
x_inverse_times_y_inverse ).
cnf(c_0_62,negated_conjecture,
( product(x_plus_y,x,X1)
| ~ sum(additive_identity,x,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_63,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_60,c_0_29]) ).
cnf(c_0_64,negated_conjecture,
product(inverse(y),inverse(x),x_inverse_times_y_inverse),
inference(spm,[status(thm)],[c_0_44,c_0_61]) ).
cnf(c_0_65,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_22,c_0_43]) ).
cnf(c_0_66,negated_conjecture,
product(x_plus_y,x,x),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_29]),c_0_63]) ).
cnf(c_0_67,plain,
( X1 = X2
| ~ product(X2,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_25]) ).
cnf(c_0_68,negated_conjecture,
sum(x_inverse_times_y_inverse,inverse(y),inverse(y)),
inference(spm,[status(thm)],[c_0_46,c_0_64]) ).
cnf(c_0_69,negated_conjecture,
( sum(x,X1,multiply(X2,X3))
| ~ sum(x,X1,X3)
| ~ sum(x_plus_y,X1,X2) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_70,axiom,
sum(X1,inverse(X1),multiplicative_identity),
additive_inverse2 ).
cnf(c_0_71,plain,
multiply(X1,multiplicative_identity) = X1,
inference(spm,[status(thm)],[c_0_67,c_0_43]) ).
cnf(c_0_72,negated_conjecture,
sum(inverse(y),x_inverse_times_y_inverse,inverse(y)),
inference(spm,[status(thm)],[c_0_30,c_0_68]) ).
cnf(c_0_73,negated_conjecture,
( sum(x,inverse(x),X1)
| ~ sum(x_plus_y,inverse(x),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
cnf(c_0_74,negated_conjecture,
( product(inverse(y),x_inverse_times_y_inverse,X1)
| ~ sum(additive_identity,x_inverse_times_y_inverse,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_72]) ).
cnf(c_0_75,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_76,negated_conjecture,
sum(x,inverse(x),add(x_plus_y,inverse(x))),
inference(spm,[status(thm)],[c_0_73,c_0_29]) ).
cnf(c_0_77,plain,
( sum(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ sum(X5,X2,multiplicative_identity)
| ~ sum(X4,X2,X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_78,negated_conjecture,
product(inverse(y),x_inverse_times_y_inverse,x_inverse_times_y_inverse),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_29]),c_0_63]) ).
cnf(c_0_79,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_75,c_0_43]) ).
cnf(c_0_80,negated_conjecture,
add(x_plus_y,inverse(x)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_76]),c_0_37]) ).
cnf(c_0_81,negated_conjecture,
( 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_77,c_0_78]) ).
cnf(c_0_82,negated_conjecture,
( 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_79,c_0_64]) ).
cnf(c_0_83,negated_conjecture,
sum(x_plus_y,inverse(x),multiplicative_identity),
inference(spm,[status(thm)],[c_0_29,c_0_80]) ).
cnf(c_0_84,negated_conjecture,
( 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_81,c_0_70]) ).
cnf(c_0_85,negated_conjecture,
( 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_82,c_0_83]),c_0_71]) ).
cnf(c_0_86,negated_conjecture,
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_84,c_0_29]) ).
cnf(c_0_87,negated_conjecture,
( product(x_plus_y,y,X1)
| ~ sum(additive_identity,y,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_57]) ).
cnf(c_0_88,negated_conjecture,
sum(x_plus_y,x_inverse_times_y_inverse,add(x_plus_y,inverse(y))),
inference(spm,[status(thm)],[c_0_85,c_0_29]) ).
cnf(c_0_89,negated_conjecture,
( sum(x_inverse_times_y_inverse,X1,X2)
| ~ sum(inverse(y),X1,multiplicative_identity)
| ~ sum(inverse(x),X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_64]) ).
cnf(c_0_90,negated_conjecture,
add(inverse(y),inverse(x_inverse_times_y_inverse)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_86]),c_0_37]) ).
cnf(c_0_91,negated_conjecture,
product(x_plus_y,y,y),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_29]),c_0_63]) ).
cnf(c_0_92,negated_conjecture,
add(x_plus_y,inverse(y)) = add(x_plus_y,x_inverse_times_y_inverse),
inference(spm,[status(thm)],[c_0_32,c_0_88]) ).
cnf(c_0_93,axiom,
product(X1,inverse(X1),additive_identity),
multiplicative_inverse2 ).
cnf(c_0_94,negated_conjecture,
( sum(x_inverse_times_y_inverse,X1,add(inverse(x),X1))
| ~ sum(inverse(y),X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_89,c_0_29]) ).
cnf(c_0_95,negated_conjecture,
sum(inverse(y),inverse(x_inverse_times_y_inverse),multiplicative_identity),
inference(spm,[status(thm)],[c_0_29,c_0_90]) ).
cnf(c_0_96,negated_conjecture,
( sum(y,X1,X2)
| ~ sum(y,X1,multiplicative_identity)
| ~ sum(x_plus_y,X1,X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_91]) ).
cnf(c_0_97,negated_conjecture,
sum(x_plus_y,inverse(y),add(x_plus_y,x_inverse_times_y_inverse)),
inference(spm,[status(thm)],[c_0_29,c_0_92]) ).
cnf(c_0_98,plain,
( product(X1,X2,X3)
| ~ sum(inverse(X4),X5,X2)
| ~ sum(additive_identity,X5,X3)
| ~ sum(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_93]) ).
cnf(c_0_99,negated_conjecture,
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_94,c_0_95]) ).
cnf(c_0_100,plain,
( product(add(X1,X2),X2,X3)
| ~ sum(additive_identity,X2,X3) ),
inference(spm,[status(thm)],[c_0_58,c_0_29]) ).
cnf(c_0_101,negated_conjecture,
sum(y,inverse(y),add(x_plus_y,x_inverse_times_y_inverse)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_70])]) ).
cnf(c_0_102,plain,
( product(add(X1,X2),X3,X4)
| ~ sum(inverse(X2),X1,X3)
| ~ sum(additive_identity,X1,X4) ),
inference(spm,[status(thm)],[c_0_98,c_0_33]) ).
cnf(c_0_103,negated_conjecture,
add(inverse(x),inverse(x_inverse_times_y_inverse)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_99]),c_0_37]) ).
cnf(c_0_104,plain,
product(add(X1,X2),X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_29]),c_0_63]) ).
cnf(c_0_105,negated_conjecture,
add(x_plus_y,x_inverse_times_y_inverse) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_101]),c_0_37]) ).
cnf(c_0_106,plain,
( X1 = X2
| ~ product(multiplicative_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_23]) ).
cnf(c_0_107,plain,
( product(add(X1,X2),X3,X1)
| ~ sum(inverse(X2),X1,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_29]),c_0_63]) ).
cnf(c_0_108,negated_conjecture,
sum(inverse(x),inverse(x_inverse_times_y_inverse),multiplicative_identity),
inference(spm,[status(thm)],[c_0_29,c_0_103]) ).
cnf(c_0_109,plain,
( X1 = X2
| ~ product(add(X3,X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_104]) ).
cnf(c_0_110,axiom,
product(inverse(X1),X1,additive_identity),
multiplicative_inverse1 ).
cnf(c_0_111,plain,
( sum(additive_identity,X1,multiply(X2,X3))
| ~ sum(inverse(X4),X1,X3)
| ~ sum(X4,X1,X2) ),
inference(spm,[status(thm)],[c_0_65,c_0_93]) ).
cnf(c_0_112,negated_conjecture,
sum(x_plus_y,x_inverse_times_y_inverse,multiplicative_identity),
inference(spm,[status(thm)],[c_0_29,c_0_105]) ).
cnf(c_0_113,plain,
multiply(multiplicative_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_106,c_0_43]) ).
cnf(c_0_114,axiom,
( product(X3,X5,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ product(X2,X4,X6)
| ~ sum(X1,X6,X7) ),
distributivity5 ).
cnf(c_0_115,negated_conjecture,
product(add(x,inverse(x_inverse_times_y_inverse)),multiplicative_identity,inverse(x_inverse_times_y_inverse)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_36]) ).
cnf(c_0_116,plain,
( X1 = X2
| ~ product(add(X2,X3),X2,X1) ),
inference(spm,[status(thm)],[c_0_109,c_0_36]) ).
cnf(c_0_117,negated_conjecture,
product(add(y,inverse(x_inverse_times_y_inverse)),multiplicative_identity,inverse(x_inverse_times_y_inverse)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_95]),c_0_36]) ).
cnf(c_0_118,plain,
( sum(X1,additive_identity,multiply(X2,X3))
| ~ sum(X1,inverse(X4),X2)
| ~ sum(X1,X4,X3) ),
inference(spm,[status(thm)],[c_0_79,c_0_110]) ).
cnf(c_0_119,negated_conjecture,
( sum(additive_identity,x_inverse_times_y_inverse,X1)
| ~ sum(inverse(x_plus_y),x_inverse_times_y_inverse,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113]) ).
cnf(c_0_120,plain,
( product(X1,X2,X3)
| ~ sum(X4,multiply(X5,X6),X3)
| ~ sum(X4,X6,X2)
| ~ sum(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_43]) ).
cnf(c_0_121,negated_conjecture,
add(x,inverse(x_inverse_times_y_inverse)) = inverse(x_inverse_times_y_inverse),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_115]),c_0_71]) ).
cnf(c_0_122,plain,
multiply(X1,add(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_43]),c_0_52]) ).
cnf(c_0_123,negated_conjecture,
add(y,inverse(x_inverse_times_y_inverse)) = inverse(x_inverse_times_y_inverse),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_117]),c_0_71]) ).
cnf(c_0_124,negated_conjecture,
( sum(x_plus_y,additive_identity,X1)
| ~ sum(x_plus_y,inverse(x_inverse_times_y_inverse),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_112]),c_0_71]) ).
cnf(c_0_125,negated_conjecture,
sum(additive_identity,x_inverse_times_y_inverse,add(x_inverse_times_y_inverse,inverse(x_plus_y))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_29]),c_0_36]) ).
cnf(c_0_126,negated_conjecture,
( product(X1,x_plus_y,X2)
| ~ sum(x,multiply(X3,y),X2)
| ~ sum(x,X3,X1) ),
inference(spm,[status(thm)],[c_0_120,c_0_57]) ).
cnf(c_0_127,negated_conjecture,
sum(x,inverse(x_inverse_times_y_inverse),inverse(x_inverse_times_y_inverse)),
inference(spm,[status(thm)],[c_0_29,c_0_121]) ).
cnf(c_0_128,negated_conjecture,
multiply(y,inverse(x_inverse_times_y_inverse)) = y,
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_129,negated_conjecture,
( X1 = x_plus_y
| ~ sum(x,y,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_57]) ).
cnf(c_0_130,negated_conjecture,
sum(x_plus_y,additive_identity,add(x_plus_y,inverse(x_inverse_times_y_inverse))),
inference(spm,[status(thm)],[c_0_124,c_0_29]) ).
cnf(c_0_131,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_60,c_0_33]) ).
cnf(c_0_132,plain,
( sum(X1,X2,X3)
| ~ product(X4,X5,X2)
| ~ sum(X1,X4,multiplicative_identity)
| ~ sum(X1,X5,X3) ),
inference(spm,[status(thm)],[c_0_75,c_0_23]) ).
cnf(c_0_133,negated_conjecture,
add(x_inverse_times_y_inverse,inverse(x_plus_y)) = x_inverse_times_y_inverse,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_125]),c_0_63]) ).
cnf(c_0_134,negated_conjecture,
( product(inverse(x_inverse_times_y_inverse),x_plus_y,X1)
| ~ sum(x,y,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_52]),c_0_128]) ).
cnf(c_0_135,negated_conjecture,
add(x,y) = x_plus_y,
inference(spm,[status(thm)],[c_0_129,c_0_29]) ).
cnf(c_0_136,plain,
multiply(X1,add(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_104]),c_0_52]) ).
cnf(c_0_137,negated_conjecture,
add(x_plus_y,inverse(x_inverse_times_y_inverse)) = x_plus_y,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_130]),c_0_131]) ).
cnf(c_0_138,plain,
( sum(X1,additive_identity,X2)
| ~ sum(X1,inverse(X3),multiplicative_identity)
| ~ sum(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_132,c_0_110]) ).
cnf(c_0_139,negated_conjecture,
sum(inverse(x_plus_y),x_inverse_times_y_inverse,x_inverse_times_y_inverse),
inference(spm,[status(thm)],[c_0_33,c_0_133]) ).
cnf(c_0_140,negated_conjecture,
product(inverse(x_inverse_times_y_inverse),x_plus_y,x_plus_y),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_29]),c_0_135]) ).
cnf(c_0_141,negated_conjecture,
multiply(x_plus_y,inverse(x_inverse_times_y_inverse)) = inverse(x_inverse_times_y_inverse),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_52]) ).
cnf(c_0_142,negated_conjecture,
( sum(inverse(x_plus_y),additive_identity,x_inverse_times_y_inverse)
| ~ sum(inverse(x_plus_y),inverse(x_inverse_times_y_inverse),multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_143,negated_conjecture,
inverse(x_inverse_times_y_inverse) = x_plus_y,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_140]),c_0_52]),c_0_141]) ).
cnf(c_0_144,negated_conjecture,
sum(inverse(x_plus_y),additive_identity,x_inverse_times_y_inverse),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_142,c_0_143]),c_0_27])]) ).
cnf(c_0_145,negated_conjecture,
inverse(x_plus_y) != x_inverse_times_y_inverse,
prove_equation ).
cnf(c_0_146,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_144]),c_0_131]),c_0_145]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : BOO014-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.31 % Computer : n021.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sun Aug 27 08:37:27 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.16/0.55 start to proof: theBenchmark
% 1.54/1.69 % Version : CSE_E---1.5
% 1.54/1.69 % Problem : theBenchmark.p
% 1.54/1.69 % Proof found
% 1.54/1.69 % SZS status Theorem for theBenchmark.p
% 1.54/1.69 % SZS output start Proof
% See solution above
% 1.54/1.70 % Total time : 1.101000 s
% 1.54/1.70 % SZS output end Proof
% 1.54/1.70 % Total time : 1.104000 s
%------------------------------------------------------------------------------