TSTP Solution File: BOO008-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : BOO008-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n011.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 18:05:44 EDT 2023
% Result : Unsatisfiable 66.26s 66.32s
% Output : CNFRefutation 66.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 36
% Syntax : Number of formulae : 180 ( 78 unt; 14 typ; 0 def)
% Number of atoms : 333 ( 47 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 339 ( 172 ~; 167 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 345 ( 29 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,
y: $i ).
tff(decl_30,type,
z: $i ).
tff(decl_31,type,
y_plus_z: $i ).
tff(decl_32,type,
x: $i ).
tff(decl_33,type,
x__plus_y_plus_z: $i ).
tff(decl_34,type,
x_plus_y: $i ).
tff(decl_35,type,
x_plus_y__plus_z: $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(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(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
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(multiplicative_identity2,axiom,
product(X1,multiplicative_identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_identity2) ).
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(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
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(distributivity3,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ product(X6,X2,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity3) ).
cnf(x_plus_y__plus_z,hypothesis,
sum(x_plus_y,z,x_plus_y__plus_z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_plus_y__plus_z) ).
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(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(x_plus_y,hypothesis,
sum(x,y,x_plus_y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_plus_y) ).
cnf(x_plus__y_plus_z,hypothesis,
sum(x,y_plus_z,x__plus_y_plus_z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_plus__y_plus_z) ).
cnf(multiplicative_inverse2,axiom,
product(X1,inverse(X1),additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse2) ).
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(y_plus_z,hypothesis,
sum(y,z,y_plus_z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',y_plus_z) ).
cnf(prove_equality,negated_conjecture,
x__plus_y_plus_z != x_plus_y__plus_z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equality) ).
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,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_25,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
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_22,c_0_23]) ).
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,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
( sum(X1,X2,X3)
| ~ product(inverse(X2),X4,X1)
| ~ sum(X4,X2,X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,axiom,
product(X1,multiplicative_identity,X1),
multiplicative_identity2 ).
cnf(c_0_32,plain,
( X1 = multiplicative_identity
| ~ sum(inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_33,plain,
( X1 = add(X2,X3)
| ~ sum(X3,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_31]) ).
cnf(c_0_35,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_32,c_0_29]) ).
cnf(c_0_36,plain,
( X1 = multiplicative_identity
| ~ sum(multiplicative_identity,X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_37,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_38,plain,
add(multiplicative_identity,X1) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_36,c_0_25]) ).
cnf(c_0_39,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined ).
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_37,c_0_31]) ).
cnf(c_0_41,plain,
sum(multiplicative_identity,X1,multiplicative_identity),
inference(spm,[status(thm)],[c_0_25,c_0_38]) ).
cnf(c_0_42,plain,
( X1 = X2
| ~ product(X2,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_31]) ).
cnf(c_0_43,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_44,plain,
( sum(X1,X2,X3)
| ~ product(X3,multiplicative_identity,X1)
| ~ product(X3,X4,X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,plain,
multiply(X1,multiplicative_identity) = X1,
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_47,plain,
( sum(X1,X2,X1)
| ~ product(X1,X3,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_43]),c_0_45]) ).
cnf(c_0_48,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_46]) ).
cnf(c_0_49,plain,
sum(X1,multiply(X1,X2),X1),
inference(spm,[status(thm)],[c_0_47,c_0_43]) ).
cnf(c_0_50,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_51,plain,
multiply(additive_identity,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_52,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ product(X6,X2,X7) ),
distributivity3 ).
cnf(c_0_53,plain,
( product(X1,X2,X3)
| ~ product(X4,X5,additive_identity)
| ~ sum(X5,X3,X2)
| ~ sum(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_46]) ).
cnf(c_0_54,plain,
product(additive_identity,X1,additive_identity),
inference(spm,[status(thm)],[c_0_43,c_0_51]) ).
cnf(c_0_55,plain,
( sum(X1,X2,X3)
| ~ product(X4,X3,X2)
| ~ product(X5,X3,X1)
| ~ sum(X5,X4,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_52,c_0_23]) ).
cnf(c_0_56,plain,
sum(X1,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_29,c_0_38]) ).
cnf(c_0_57,plain,
( X1 = X2
| ~ product(multiplicative_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_23]) ).
cnf(c_0_58,plain,
( product(X1,X2,X3)
| ~ sum(additive_identity,X3,X1)
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_48,c_0_25]) ).
cnf(c_0_60,hypothesis,
sum(x_plus_y,z,x_plus_y__plus_z),
x_plus_y__plus_z ).
cnf(c_0_61,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
commutativity_of_multiplication ).
cnf(c_0_62,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_63,plain,
( sum(X1,X2,X3)
| ~ product(multiplicative_identity,X3,X2)
| ~ product(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_64,plain,
multiply(multiplicative_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_57,c_0_43]) ).
cnf(c_0_65,plain,
( product(X1,X2,X1)
| ~ sum(X3,X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_25]),c_0_59]) ).
cnf(c_0_66,hypothesis,
sum(z,x_plus_y,x_plus_y__plus_z),
inference(spm,[status(thm)],[c_0_24,c_0_60]) ).
cnf(c_0_67,hypothesis,
sum(x,y,x_plus_y),
x_plus_y ).
cnf(c_0_68,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_43]) ).
cnf(c_0_69,plain,
product(X1,X2,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_61,c_0_43]) ).
cnf(c_0_70,hypothesis,
sum(x,y_plus_z,x__plus_y_plus_z),
x_plus__y_plus_z ).
cnf(c_0_71,axiom,
product(X1,inverse(X1),additive_identity),
multiplicative_inverse2 ).
cnf(c_0_72,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_25]) ).
cnf(c_0_73,plain,
( product(X1,X2,X3)
| ~ product(X4,X2,multiply(X3,X5))
| ~ product(X6,X2,X3)
| ~ sum(X6,X4,X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_49]) ).
cnf(c_0_74,plain,
( sum(X1,X2,X2)
| ~ product(X3,X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_43]),c_0_64]) ).
cnf(c_0_75,hypothesis,
product(x_plus_y,x_plus_y__plus_z,x_plus_y),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_76,hypothesis,
sum(y,x,x_plus_y),
inference(spm,[status(thm)],[c_0_24,c_0_67]) ).
cnf(c_0_77,plain,
( X1 = X2
| ~ sum(X2,multiply(X2,X3),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_49]) ).
cnf(c_0_78,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_79,plain,
( sum(X1,X2,multiply(X3,X4))
| ~ product(X3,X5,X2)
| ~ product(X3,X6,X1)
| ~ sum(X6,X5,X4) ),
inference(spm,[status(thm)],[c_0_37,c_0_43]) ).
cnf(c_0_80,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_81,hypothesis,
sum(y_plus_z,x,x__plus_y_plus_z),
inference(spm,[status(thm)],[c_0_24,c_0_70]) ).
cnf(c_0_82,plain,
( sum(additive_identity,X1,X2)
| ~ sum(inverse(inverse(X1)),X1,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_71]) ).
cnf(c_0_83,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_72,c_0_29]) ).
cnf(c_0_84,hypothesis,
( product(X1,X2,x__plus_y_plus_z)
| ~ product(X3,X4,x)
| ~ sum(X4,y_plus_z,X2)
| ~ sum(X3,y_plus_z,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_70]) ).
cnf(c_0_85,plain,
( product(X1,X2,X2)
| ~ product(X3,X2,X2)
| ~ sum(X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_69]) ).
cnf(c_0_86,hypothesis,
sum(x_plus_y,x_plus_y__plus_z,x_plus_y__plus_z),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_87,hypothesis,
product(x,x_plus_y,x),
inference(spm,[status(thm)],[c_0_65,c_0_76]) ).
cnf(c_0_88,plain,
( X1 = X2
| ~ sum(X2,multiply(X3,X2),X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_89,plain,
( sum(X1,multiply(X2,X3),multiply(X2,X4))
| ~ product(X2,X5,X1)
| ~ sum(X5,X3,X4) ),
inference(spm,[status(thm)],[c_0_79,c_0_43]) ).
cnf(c_0_90,hypothesis,
product(y_plus_z,x__plus_y_plus_z,y_plus_z),
inference(spm,[status(thm)],[c_0_65,c_0_70]) ).
cnf(c_0_91,hypothesis,
( product(X1,X2,x__plus_y_plus_z)
| ~ product(X3,X4,x)
| ~ sum(y_plus_z,X4,X2)
| ~ sum(y_plus_z,X3,X1) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_92,plain,
sum(additive_identity,X1,add(X1,inverse(inverse(X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_25]),c_0_83]) ).
cnf(c_0_93,hypothesis,
( product(X1,x__plus_y_plus_z,x__plus_y_plus_z)
| ~ product(X2,x,x)
| ~ sum(X2,y_plus_z,X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_70]) ).
cnf(c_0_94,hypothesis,
( product(x_plus_y__plus_z,X1,X1)
| ~ product(x_plus_y,X1,X1) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_95,hypothesis,
product(x_plus_y,x,x),
inference(spm,[status(thm)],[c_0_61,c_0_87]) ).
cnf(c_0_96,plain,
add(X1,multiply(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_88,c_0_25]) ).
cnf(c_0_97,hypothesis,
( sum(y_plus_z,multiply(y_plus_z,X1),multiply(y_plus_z,X2))
| ~ sum(x__plus_y_plus_z,X1,X2) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_98,plain,
add(X1,multiply(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_72,c_0_49]) ).
cnf(c_0_99,plain,
product(X1,add(X2,X1),X1),
inference(spm,[status(thm)],[c_0_65,c_0_25]) ).
cnf(c_0_100,hypothesis,
( product(X1,x__plus_y_plus_z,x__plus_y_plus_z)
| ~ product(X2,x,x)
| ~ sum(y_plus_z,X2,X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_81]) ).
cnf(c_0_101,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_92]),c_0_59]) ).
cnf(c_0_102,hypothesis,
( product(X1,x__plus_y_plus_z,x__plus_y_plus_z)
| ~ sum(x_plus_y__plus_z,y_plus_z,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95])]) ).
cnf(c_0_103,plain,
( product(X1,X2,X3)
| ~ product(X4,X2,X3)
| ~ sum(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_43]) ).
cnf(c_0_104,plain,
sum(multiply(X1,X2),X2,X2),
inference(spm,[status(thm)],[c_0_29,c_0_96]) ).
cnf(c_0_105,hypothesis,
( multiply(y_plus_z,X1) = y_plus_z
| ~ sum(x__plus_y_plus_z,X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_97]),c_0_98]) ).
cnf(c_0_106,plain,
sum(X1,add(X2,X1),add(X2,X1)),
inference(spm,[status(thm)],[c_0_74,c_0_99]) ).
cnf(c_0_107,hypothesis,
( product(X1,x__plus_y_plus_z,x__plus_y_plus_z)
| ~ sum(y_plus_z,x_plus_y__plus_z,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_94]),c_0_95])]) ).
cnf(c_0_108,hypothesis,
( product(X1,X2,x_plus_y__plus_z)
| ~ product(X3,X4,x_plus_y)
| ~ sum(X4,z,X2)
| ~ sum(X3,z,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_60]) ).
cnf(c_0_109,plain,
sum(inverse(inverse(X1)),X1,X1),
inference(spm,[status(thm)],[c_0_29,c_0_101]) ).
cnf(c_0_110,hypothesis,
( X1 = x__plus_y_plus_z
| ~ product(X2,x__plus_y_plus_z,X1)
| ~ sum(x_plus_y__plus_z,y_plus_z,X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_102]) ).
cnf(c_0_111,plain,
( product(X1,X2,X1)
| ~ product(multiply(X3,X1),X2,X1) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_112,plain,
multiply(X1,add(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_68,c_0_99]) ).
cnf(c_0_113,hypothesis,
multiply(y_plus_z,add(X1,x__plus_y_plus_z)) = y_plus_z,
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_114,hypothesis,
( multiply(X1,x__plus_y_plus_z) = x__plus_y_plus_z
| ~ sum(y_plus_z,x_plus_y__plus_z,X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_107]) ).
cnf(c_0_115,hypothesis,
sum(y_plus_z,x__plus_y_plus_z,x__plus_y_plus_z),
inference(spm,[status(thm)],[c_0_74,c_0_90]) ).
cnf(c_0_116,hypothesis,
sum(y,z,y_plus_z),
y_plus_z ).
cnf(c_0_117,plain,
product(add(X1,X2),X2,X2),
inference(spm,[status(thm)],[c_0_61,c_0_99]) ).
cnf(c_0_118,plain,
( product(X1,X2,add(X3,X4))
| ~ product(X5,X2,X4)
| ~ product(X6,X2,X3)
| ~ sum(X6,X5,X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_25]) ).
cnf(c_0_119,hypothesis,
( product(X1,x_plus_y__plus_z,x_plus_y__plus_z)
| ~ product(X2,x_plus_y,x_plus_y)
| ~ sum(X2,z,X1) ),
inference(spm,[status(thm)],[c_0_108,c_0_60]) ).
cnf(c_0_120,plain,
product(X1,X1,X1),
inference(spm,[status(thm)],[c_0_65,c_0_109]) ).
cnf(c_0_121,hypothesis,
( X1 = x__plus_y_plus_z
| ~ product(add(y_plus_z,x_plus_y__plus_z),x__plus_y_plus_z,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_25]),c_0_83]) ).
cnf(c_0_122,plain,
( product(add(X1,X2),X3,add(X1,X2))
| ~ product(X2,X3,add(X1,X2)) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_123,hypothesis,
add(y_plus_z,add(X1,x__plus_y_plus_z)) = add(X1,x__plus_y_plus_z),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_113]),c_0_83]) ).
cnf(c_0_124,hypothesis,
( add(X1,x__plus_y_plus_z) = X1
| ~ sum(y_plus_z,x_plus_y__plus_z,X1) ),
inference(spm,[status(thm)],[c_0_98,c_0_114]) ).
cnf(c_0_125,hypothesis,
( X1 = x_plus_y__plus_z
| ~ sum(z,x_plus_y,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_66]) ).
cnf(c_0_126,hypothesis,
( product(x__plus_y_plus_z,X1,X1)
| ~ product(y_plus_z,X1,X1) ),
inference(spm,[status(thm)],[c_0_85,c_0_115]) ).
cnf(c_0_127,hypothesis,
product(z,y_plus_z,z),
inference(spm,[status(thm)],[c_0_65,c_0_116]) ).
cnf(c_0_128,hypothesis,
sum(z,y,y_plus_z),
inference(spm,[status(thm)],[c_0_24,c_0_116]) ).
cnf(c_0_129,plain,
( X1 = X2
| ~ product(add(X3,X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_117]) ).
cnf(c_0_130,plain,
( product(add(X1,X2),X3,add(X4,X5))
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_118,c_0_25]) ).
cnf(c_0_131,hypothesis,
( product(X1,x_plus_y__plus_z,x_plus_y__plus_z)
| ~ sum(x_plus_y,z,X1) ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_132,hypothesis,
( X1 = y_plus_z
| ~ sum(y,z,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_116]) ).
cnf(c_0_133,hypothesis,
product(y,x_plus_y,y),
inference(spm,[status(thm)],[c_0_65,c_0_67]) ).
cnf(c_0_134,hypothesis,
( add(y_plus_z,x_plus_y__plus_z) = x__plus_y_plus_z
| ~ product(x_plus_y__plus_z,x__plus_y_plus_z,add(y_plus_z,x_plus_y__plus_z)) ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_135,hypothesis,
( add(y_plus_z,X1) = X1
| ~ sum(y_plus_z,x_plus_y__plus_z,X1) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_136,negated_conjecture,
x__plus_y_plus_z != x_plus_y__plus_z,
prove_equality ).
cnf(c_0_137,hypothesis,
( product(x_plus_y__plus_z,X1,add(X2,X3))
| ~ product(x_plus_y,X1,X3)
| ~ product(z,X1,X2) ),
inference(spm,[status(thm)],[c_0_118,c_0_66]) ).
cnf(c_0_138,hypothesis,
add(z,x_plus_y) = x_plus_y__plus_z,
inference(spm,[status(thm)],[c_0_125,c_0_25]) ).
cnf(c_0_139,hypothesis,
( product(X1,x__plus_y_plus_z,X1)
| ~ product(y_plus_z,X1,X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_126]) ).
cnf(c_0_140,hypothesis,
product(y_plus_z,z,z),
inference(spm,[status(thm)],[c_0_61,c_0_127]) ).
cnf(c_0_141,hypothesis,
( X1 = x_plus_y
| ~ sum(x,y,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_67]) ).
cnf(c_0_142,hypothesis,
product(y,y_plus_z,y),
inference(spm,[status(thm)],[c_0_65,c_0_128]) ).
cnf(c_0_143,plain,
( add(X1,X2) = X3
| ~ product(X3,X3,X2)
| ~ product(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_144,hypothesis,
( product(x_plus_y__plus_z,X1,x_plus_y__plus_z)
| ~ sum(x_plus_y,z,X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_131]) ).
cnf(c_0_145,hypothesis,
( product(y_plus_z,X1,add(X2,X3))
| ~ product(z,X1,X3)
| ~ product(y,X1,X2) ),
inference(spm,[status(thm)],[c_0_118,c_0_116]) ).
cnf(c_0_146,hypothesis,
add(y,z) = y_plus_z,
inference(spm,[status(thm)],[c_0_132,c_0_25]) ).
cnf(c_0_147,hypothesis,
( product(X1,x_plus_y__plus_z,X1)
| ~ product(x_plus_y,X1,X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_94]) ).
cnf(c_0_148,hypothesis,
product(x_plus_y,y,y),
inference(spm,[status(thm)],[c_0_61,c_0_133]) ).
cnf(c_0_149,hypothesis,
( ~ product(x_plus_y__plus_z,x__plus_y_plus_z,x_plus_y__plus_z)
| ~ sum(y_plus_z,x_plus_y__plus_z,x_plus_y__plus_z) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_136]) ).
cnf(c_0_150,hypothesis,
( product(x_plus_y__plus_z,X1,x_plus_y__plus_z)
| ~ product(x_plus_y,X1,x_plus_y)
| ~ product(z,X1,z) ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_151,hypothesis,
product(z,x__plus_y_plus_z,z),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_152,hypothesis,
( product(x_plus_y,X1,add(X2,X3))
| ~ product(x,X1,X3)
| ~ product(y,X1,X2) ),
inference(spm,[status(thm)],[c_0_118,c_0_76]) ).
cnf(c_0_153,hypothesis,
add(y,x) = x_plus_y,
inference(spm,[status(thm)],[c_0_141,c_0_29]) ).
cnf(c_0_154,hypothesis,
product(y_plus_z,y,y),
inference(spm,[status(thm)],[c_0_61,c_0_142]) ).
cnf(c_0_155,hypothesis,
( add(X1,x_plus_y__plus_z) = x_plus_y__plus_z
| ~ product(X2,x_plus_y__plus_z,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_60])]) ).
cnf(c_0_156,hypothesis,
( product(y_plus_z,X1,y_plus_z)
| ~ product(z,X1,z)
| ~ product(y,X1,y) ),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_157,hypothesis,
product(z,x_plus_y__plus_z,z),
inference(spm,[status(thm)],[c_0_65,c_0_60]) ).
cnf(c_0_158,hypothesis,
product(y,x_plus_y__plus_z,y),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_159,hypothesis,
( ~ product(x_plus_y,x__plus_y_plus_z,x_plus_y)
| ~ sum(y_plus_z,x_plus_y__plus_z,x_plus_y__plus_z) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_151])]) ).
cnf(c_0_160,hypothesis,
( product(x_plus_y,X1,x_plus_y)
| ~ product(x,X1,x)
| ~ product(y,X1,y) ),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_161,hypothesis,
product(x,x__plus_y_plus_z,x),
inference(spm,[status(thm)],[c_0_65,c_0_81]) ).
cnf(c_0_162,hypothesis,
product(y,x__plus_y_plus_z,y),
inference(spm,[status(thm)],[c_0_139,c_0_154]) ).
cnf(c_0_163,hypothesis,
add(y_plus_z,x_plus_y__plus_z) = x_plus_y__plus_z,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_157]),c_0_158])]) ).
cnf(c_0_164,hypothesis,
~ sum(y_plus_z,x_plus_y__plus_z,x_plus_y__plus_z),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_161]),c_0_162])]) ).
cnf(c_0_165,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_163]),c_0_164]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : BOO008-1 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 08:43:24 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.56 start to proof: theBenchmark
% 66.26/66.32 % Version : CSE_E---1.5
% 66.26/66.32 % Problem : theBenchmark.p
% 66.26/66.32 % Proof found
% 66.26/66.32 % SZS status Theorem for theBenchmark.p
% 66.26/66.32 % SZS output start Proof
% See solution above
% 66.26/66.33 % Total time : 65.740000 s
% 66.26/66.33 % SZS output end Proof
% 66.26/66.33 % Total time : 65.746000 s
%------------------------------------------------------------------------------