TSTP Solution File: BOO008-1 by E---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : BOO008-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n014.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 17:18:06 EDT 2023
% Result : Unsatisfiable 3.93s 0.97s
% Output : CNFRefutation 3.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 24
% Syntax : Number of clauses : 157 ( 91 unt; 0 nHn; 108 RR)
% Number of literals : 304 ( 47 equ; 149 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% 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 : 322 ( 22 sgn)
% Comments :
%------------------------------------------------------------------------------
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/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',distributivity8) ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X1,X1),
file('/export/starexec/sandbox2/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',multiplicative_identity1) ).
cnf(additive_inverse1,axiom,
sum(inverse(X1),X1,multiplicative_identity),
file('/export/starexec/sandbox2/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',additive_inverse1) ).
cnf(multiplicative_identity2,axiom,
product(X1,multiplicative_identity,X1),
file('/export/starexec/sandbox2/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',multiplicative_identity2) ).
cnf(addition_is_well_defined,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox2/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',addition_is_well_defined) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',closure_of_addition) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',commutativity_of_addition) ).
cnf(additive_inverse2,axiom,
sum(X1,inverse(X1),multiplicative_identity),
file('/export/starexec/sandbox2/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',additive_inverse2) ).
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/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',distributivity4) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',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/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',distributivity7) ).
cnf(x_plus_y__plus_z,hypothesis,
sum(x_plus_y,z,x_plus_y__plus_z),
file('/export/starexec/sandbox2/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',x_plus_y__plus_z) ).
cnf(multiplication_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',multiplication_is_well_defined) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',closure_of_multiplication) ).
cnf(commutativity_of_multiplication,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox2/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',commutativity_of_multiplication) ).
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/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',distributivity6) ).
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/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',distributivity3) ).
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/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',distributivity1) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox2/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',additive_identity2) ).
cnf(x_plus__y_plus_z,hypothesis,
sum(x,y_plus_z,x__plus_y_plus_z),
file('/export/starexec/sandbox2/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',x_plus__y_plus_z) ).
cnf(x_plus_y,hypothesis,
sum(x,y,x_plus_y),
file('/export/starexec/sandbox2/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',x_plus_y) ).
cnf(y_plus_z,hypothesis,
sum(y,z,y_plus_z),
file('/export/starexec/sandbox2/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',y_plus_z) ).
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/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',distributivity5) ).
cnf(prove_equality,negated_conjecture,
x__plus_y_plus_z != x_plus_y__plus_z,
file('/export/starexec/sandbox2/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p',prove_equality) ).
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,
sum(inverse(X1),X1,multiplicative_identity),
additive_inverse1 ).
cnf(c_0_28,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_29,axiom,
product(X1,multiplicative_identity,X1),
multiplicative_identity2 ).
cnf(c_0_30,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
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,axiom,
sum(X1,inverse(X1),multiplicative_identity),
additive_inverse2 ).
cnf(c_0_34,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_35,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_36,plain,
( sum(inverse(X1),X1,X2)
| ~ sum(multiplicative_identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
cnf(c_0_39,plain,
( X1 = multiplicative_identity
| ~ sum(X2,inverse(X2),X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_33]) ).
cnf(c_0_40,plain,
( product(X1,X2,X3)
| ~ product(X4,X2,additive_identity)
| ~ product(X5,X2,X3)
| ~ sum(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
sum(inverse(X1),X1,add(multiplicative_identity,X1)),
inference(spm,[status(thm)],[c_0_36,c_0_31]) ).
cnf(c_0_42,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_39,c_0_31]) ).
cnf(c_0_44,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_45,hypothesis,
sum(x_plus_y,z,x_plus_y__plus_z),
x_plus_y__plus_z ).
cnf(c_0_46,plain,
( product(X1,additive_identity,X2)
| ~ product(X3,additive_identity,X2)
| ~ sum(multiplicative_identity,X3,X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_25]) ).
cnf(c_0_47,plain,
add(multiplicative_identity,X1) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_41]),c_0_42]),c_0_43]) ).
cnf(c_0_48,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined ).
cnf(c_0_49,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_44,c_0_45]) ).
cnf(c_0_50,plain,
( sum(X1,multiplicative_identity,X2)
| ~ product(additive_identity,X3,X1)
| ~ sum(X3,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_35]) ).
cnf(c_0_51,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_52,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
commutativity_of_multiplication ).
cnf(c_0_53,plain,
( product(multiplicative_identity,additive_identity,X1)
| ~ product(X2,additive_identity,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_31]),c_0_47]) ).
cnf(c_0_54,plain,
( X1 = X2
| ~ product(multiplicative_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_25]) ).
cnf(c_0_55,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_49,c_0_45]) ).
cnf(c_0_56,plain,
( sum(multiply(additive_identity,X1),multiplicative_identity,X2)
| ~ sum(X1,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,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_58,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_51]) ).
cnf(c_0_59,plain,
product(X1,X2,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_52,c_0_51]) ).
cnf(c_0_60,plain,
product(multiplicative_identity,additive_identity,multiply(X1,additive_identity)),
inference(spm,[status(thm)],[c_0_53,c_0_51]) ).
cnf(c_0_61,plain,
multiply(multiplicative_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_54,c_0_51]) ).
cnf(c_0_62,hypothesis,
( product(add(X1,z),x_plus_y__plus_z,x_plus_y__plus_z)
| ~ product(X1,x_plus_y,x_plus_y) ),
inference(spm,[status(thm)],[c_0_55,c_0_31]) ).
cnf(c_0_63,plain,
sum(multiply(additive_identity,X1),multiplicative_identity,add(X1,multiplicative_identity)),
inference(spm,[status(thm)],[c_0_56,c_0_31]) ).
cnf(c_0_64,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_57,c_0_51]) ).
cnf(c_0_65,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_66,plain,
multiply(X1,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_60]),c_0_61]) ).
cnf(c_0_67,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_68,hypothesis,
product(add(multiplicative_identity,z),x_plus_y__plus_z,x_plus_y__plus_z),
inference(spm,[status(thm)],[c_0_62,c_0_25]) ).
cnf(c_0_69,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_70,plain,
add(multiplicative_identity,multiply(additive_identity,X1)) = add(X1,multiplicative_identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_63]),c_0_42]) ).
cnf(c_0_71,plain,
( sum(X1,multiply(X2,X3),multiply(X4,X5))
| ~ sum(X1,X2,X5)
| ~ sum(X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_64,c_0_59]) ).
cnf(c_0_72,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_73,plain,
multiply(additive_identity,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_74,hypothesis,
sum(x,y_plus_z,x__plus_y_plus_z),
x_plus__y_plus_z ).
cnf(c_0_75,hypothesis,
sum(x,y,x_plus_y),
x_plus_y ).
cnf(c_0_76,hypothesis,
( sum(X1,X2,x_plus_y__plus_z)
| ~ product(X3,x_plus_y__plus_z,X2)
| ~ product(X4,x_plus_y__plus_z,X1)
| ~ sum(X4,X3,add(multiplicative_identity,z)) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_77,plain,
( product(X1,X2,add(X3,X4))
| ~ product(X5,X6,X3)
| ~ sum(X6,X4,X2)
| ~ sum(X5,X4,X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_31]) ).
cnf(c_0_78,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_35]) ).
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_69,c_0_51]) ).
cnf(c_0_80,plain,
add(multiplicative_identity,multiply(X1,additive_identity)) = add(X1,multiplicative_identity),
inference(spm,[status(thm)],[c_0_70,c_0_65]) ).
cnf(c_0_81,plain,
( X1 = X2
| ~ product(X2,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_29]) ).
cnf(c_0_82,plain,
( sum(X1,additive_identity,multiply(X2,X1))
| ~ sum(X1,X3,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_83,hypothesis,
sum(y_plus_z,x,x__plus_y_plus_z),
inference(spm,[status(thm)],[c_0_32,c_0_74]) ).
cnf(c_0_84,plain,
( X1 = X2
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_72]) ).
cnf(c_0_85,hypothesis,
sum(y,z,y_plus_z),
y_plus_z ).
cnf(c_0_86,hypothesis,
sum(y,x,x_plus_y),
inference(spm,[status(thm)],[c_0_32,c_0_75]) ).
cnf(c_0_87,hypothesis,
( sum(X1,x_plus_y__plus_z,x_plus_y__plus_z)
| ~ product(X2,x_plus_y__plus_z,X1)
| ~ sum(X2,multiplicative_identity,add(multiplicative_identity,z)) ),
inference(spm,[status(thm)],[c_0_76,c_0_25]) ).
cnf(c_0_88,plain,
( product(X1,X2,add(X3,X2))
| ~ product(X4,additive_identity,X3)
| ~ sum(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_35]) ).
cnf(c_0_89,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_78,c_0_31]) ).
cnf(c_0_90,plain,
( sum(X1,X2,multiply(X2,X3))
| ~ product(X2,X4,X1)
| ~ sum(X4,multiplicative_identity,X3) ),
inference(spm,[status(thm)],[c_0_79,c_0_29]) ).
cnf(c_0_91,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(rw,[status(thm)],[c_0_80,c_0_47]) ).
cnf(c_0_92,plain,
multiply(X1,multiplicative_identity) = X1,
inference(spm,[status(thm)],[c_0_81,c_0_51]) ).
cnf(c_0_93,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_94,hypothesis,
sum(y_plus_z,additive_identity,multiply(y_plus_z,x__plus_y_plus_z)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_65]) ).
cnf(c_0_95,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_84,c_0_31]) ).
cnf(c_0_96,hypothesis,
( product(X1,X2,y_plus_z)
| ~ product(X3,X4,y)
| ~ sum(X4,z,X2)
| ~ sum(X3,z,X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_85]) ).
cnf(c_0_97,hypothesis,
sum(y,additive_identity,multiply(y,x_plus_y)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_86]),c_0_65]) ).
cnf(c_0_98,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_51]) ).
cnf(c_0_99,hypothesis,
( sum(multiply(X1,x_plus_y__plus_z),x_plus_y__plus_z,x_plus_y__plus_z)
| ~ sum(X1,multiplicative_identity,add(multiplicative_identity,z)) ),
inference(spm,[status(thm)],[c_0_87,c_0_51]) ).
cnf(c_0_100,plain,
sum(X1,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_38,c_0_47]) ).
cnf(c_0_101,hypothesis,
sum(x_plus_y,additive_identity,multiply(x_plus_y,x_plus_y__plus_z)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_45]),c_0_65]) ).
cnf(c_0_102,plain,
( product(X1,X2,X2)
| ~ sum(X3,X2,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_51]),c_0_66]),c_0_89]) ).
cnf(c_0_103,plain,
( sum(X1,X2,X2)
| ~ product(X2,X3,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_31]),c_0_91]),c_0_92]) ).
cnf(c_0_104,hypothesis,
( product(X1,X2,x_plus_y)
| ~ product(X3,X4,y)
| ~ sum(x,X4,X2)
| ~ sum(x,X3,X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_75]) ).
cnf(c_0_105,hypothesis,
sum(y,additive_identity,multiply(y,y_plus_z)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_85]),c_0_65]) ).
cnf(c_0_106,hypothesis,
multiply(y_plus_z,x__plus_y_plus_z) = y_plus_z,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_94]),c_0_95]) ).
cnf(c_0_107,hypothesis,
( product(X1,X2,x__plus_y_plus_z)
| ~ product(X3,X4,y_plus_z)
| ~ sum(x,X4,X2)
| ~ sum(x,X3,X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_74]) ).
cnf(c_0_108,hypothesis,
( product(X1,y_plus_z,y_plus_z)
| ~ product(X2,y,y)
| ~ sum(X2,z,X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_85]) ).
cnf(c_0_109,hypothesis,
multiply(y,x_plus_y) = y,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_97]),c_0_95]) ).
cnf(c_0_110,plain,
( sum(multiply(X1,X2),X3,multiply(X4,X5))
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_98,c_0_51]) ).
cnf(c_0_111,hypothesis,
sum(multiply(X1,x_plus_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)],[c_0_99,c_0_47]),c_0_100])]) ).
cnf(c_0_112,hypothesis,
multiply(x_plus_y,x_plus_y__plus_z) = x_plus_y,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_101]),c_0_95]) ).
cnf(c_0_113,plain,
product(add(X1,X2),X2,X2),
inference(spm,[status(thm)],[c_0_102,c_0_31]) ).
cnf(c_0_114,plain,
sum(multiply(X1,X2),X1,X1),
inference(spm,[status(thm)],[c_0_103,c_0_51]) ).
cnf(c_0_115,hypothesis,
( product(X1,x__plus_y_plus_z,x_plus_y)
| ~ product(X2,y_plus_z,y)
| ~ sum(x,X2,X1) ),
inference(spm,[status(thm)],[c_0_104,c_0_74]) ).
cnf(c_0_116,hypothesis,
multiply(y,y_plus_z) = y,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_105]),c_0_95]) ).
cnf(c_0_117,hypothesis,
product(x__plus_y_plus_z,y_plus_z,y_plus_z),
inference(spm,[status(thm)],[c_0_59,c_0_106]) ).
cnf(c_0_118,hypothesis,
( product(X1,x__plus_y_plus_z,x__plus_y_plus_z)
| ~ product(X2,y_plus_z,y_plus_z)
| ~ sum(x,X2,X1) ),
inference(spm,[status(thm)],[c_0_107,c_0_74]) ).
cnf(c_0_119,hypothesis,
( product(x_plus_y__plus_z,y_plus_z,y_plus_z)
| ~ product(x_plus_y,y,y) ),
inference(spm,[status(thm)],[c_0_108,c_0_45]) ).
cnf(c_0_120,hypothesis,
product(x_plus_y,y,y),
inference(spm,[status(thm)],[c_0_59,c_0_109]) ).
cnf(c_0_121,plain,
( sum(multiply(X1,X2),X3,multiply(X4,add(X2,X3)))
| ~ sum(X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_110,c_0_31]) ).
cnf(c_0_122,hypothesis,
sum(x_plus_y,x_plus_y__plus_z,x_plus_y__plus_z),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_123,plain,
multiply(X1,add(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_113]),c_0_65]) ).
cnf(c_0_124,plain,
add(X1,multiply(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_114]),c_0_42]) ).
cnf(c_0_125,hypothesis,
( product(X1,add(z,X2),x_plus_y__plus_z)
| ~ product(X3,X2,x_plus_y)
| ~ sum(X3,z,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_38]) ).
cnf(c_0_126,hypothesis,
( product(x_plus_y,x__plus_y_plus_z,x_plus_y)
| ~ product(y,y_plus_z,y) ),
inference(spm,[status(thm)],[c_0_115,c_0_75]) ).
cnf(c_0_127,hypothesis,
product(y,y_plus_z,y),
inference(spm,[status(thm)],[c_0_51,c_0_116]) ).
cnf(c_0_128,hypothesis,
sum(y_plus_z,x__plus_y_plus_z,x__plus_y_plus_z),
inference(spm,[status(thm)],[c_0_103,c_0_117]) ).
cnf(c_0_129,hypothesis,
( product(add(x,X1),x__plus_y_plus_z,x__plus_y_plus_z)
| ~ product(X1,y_plus_z,y_plus_z) ),
inference(spm,[status(thm)],[c_0_118,c_0_31]) ).
cnf(c_0_130,hypothesis,
product(x_plus_y__plus_z,y_plus_z,y_plus_z),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_120])]) ).
cnf(c_0_131,hypothesis,
sum(multiply(x_plus_y,X1),x_plus_y__plus_z,x_plus_y__plus_z),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123]) ).
cnf(c_0_132,plain,
add(X1,multiply(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_124,c_0_65]) ).
cnf(c_0_133,hypothesis,
( product(x_plus_y__plus_z,add(z,X1),x_plus_y__plus_z)
| ~ product(x_plus_y,X1,x_plus_y) ),
inference(spm,[status(thm)],[c_0_125,c_0_45]) ).
cnf(c_0_134,hypothesis,
product(x_plus_y,x__plus_y_plus_z,x_plus_y),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_127])]) ).
cnf(c_0_135,hypothesis,
sum(multiply(y_plus_z,X1),x__plus_y_plus_z,x__plus_y_plus_z),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_128]),c_0_123]) ).
cnf(c_0_136,hypothesis,
sum(z,y,y_plus_z),
inference(spm,[status(thm)],[c_0_32,c_0_85]) ).
cnf(c_0_137,hypothesis,
product(add(x,x_plus_y__plus_z),x__plus_y_plus_z,x__plus_y_plus_z),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_138,hypothesis,
add(x_plus_y__plus_z,multiply(x_plus_y,X1)) = x_plus_y__plus_z,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_131]),c_0_42]) ).
cnf(c_0_139,plain,
multiply(X1,multiply(X2,X1)) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_132]),c_0_65]) ).
cnf(c_0_140,hypothesis,
sum(x,additive_identity,multiply(x,x_plus_y)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_75]),c_0_65]) ).
cnf(c_0_141,hypothesis,
product(x_plus_y__plus_z,add(z,x__plus_y_plus_z),x_plus_y__plus_z),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_142,hypothesis,
add(x__plus_y_plus_z,multiply(y_plus_z,X1)) = x__plus_y_plus_z,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_135]),c_0_42]) ).
cnf(c_0_143,hypothesis,
sum(z,additive_identity,multiply(z,y_plus_z)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_136]),c_0_65]) ).
cnf(c_0_144,hypothesis,
multiply(x__plus_y_plus_z,add(x,x_plus_y__plus_z)) = x__plus_y_plus_z,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_137]),c_0_65]) ).
cnf(c_0_145,hypothesis,
add(x_plus_y__plus_z,multiply(X1,x_plus_y)) = x_plus_y__plus_z,
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_146,hypothesis,
multiply(x,x_plus_y) = x,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_140]),c_0_95]) ).
cnf(c_0_147,hypothesis,
multiply(x_plus_y__plus_z,add(z,x__plus_y_plus_z)) = x_plus_y__plus_z,
inference(spm,[status(thm)],[c_0_58,c_0_141]) ).
cnf(c_0_148,hypothesis,
add(x__plus_y_plus_z,multiply(X1,y_plus_z)) = x__plus_y_plus_z,
inference(spm,[status(thm)],[c_0_142,c_0_139]) ).
cnf(c_0_149,hypothesis,
multiply(z,y_plus_z) = z,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_143]),c_0_95]) ).
cnf(c_0_150,hypothesis,
add(x__plus_y_plus_z,add(x,x_plus_y__plus_z)) = add(x,x_plus_y__plus_z),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_144]),c_0_42]) ).
cnf(c_0_151,hypothesis,
add(x,x_plus_y__plus_z) = x_plus_y__plus_z,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_42]) ).
cnf(c_0_152,hypothesis,
add(x_plus_y__plus_z,add(z,x__plus_y_plus_z)) = add(z,x__plus_y_plus_z),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_147]),c_0_42]) ).
cnf(c_0_153,hypothesis,
add(z,x__plus_y_plus_z) = x__plus_y_plus_z,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_42]) ).
cnf(c_0_154,hypothesis,
add(x__plus_y_plus_z,x_plus_y__plus_z) = x_plus_y__plus_z,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_151]),c_0_151]) ).
cnf(c_0_155,negated_conjecture,
x__plus_y_plus_z != x_plus_y__plus_z,
prove_equality ).
cnf(c_0_156,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_152,c_0_153]),c_0_42]),c_0_154]),c_0_153]),c_0_155]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : BOO008-1 : TPTP v8.1.2. Released v1.0.0.
% 0.05/0.13 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 2400
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Oct 2 20:36:04 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.17/0.45 Running first-order theorem proving
% 0.17/0.45 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.VSbIXhZCDw/E---3.1_24433.p
% 3.93/0.97 # Version: 3.1pre001
% 3.93/0.97 # Preprocessing class: FSMSSMSMSSSNFFN.
% 3.93/0.97 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.93/0.97 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 3.93/0.97 # Starting new_bool_3 with 300s (1) cores
% 3.93/0.97 # Starting new_bool_1 with 300s (1) cores
% 3.93/0.97 # Starting sh5l with 300s (1) cores
% 3.93/0.97 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 24511 completed with status 0
% 3.93/0.97 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 3.93/0.97 # Preprocessing class: FSMSSMSMSSSNFFN.
% 3.93/0.97 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.93/0.97 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 3.93/0.97 # No SInE strategy applied
% 3.93/0.97 # Search class: FHUSM-FFMS21-SFFFFFNN
% 3.93/0.97 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 3.93/0.97 # Starting C07_19_nc_SAT001_MinMin_p005000_rr with 811s (1) cores
% 3.93/0.97 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 3.93/0.97 # Starting new_bool_3 with 136s (1) cores
% 3.93/0.97 # Starting new_bool_1 with 136s (1) cores
% 3.93/0.97 # Starting sh5l with 136s (1) cores
% 3.93/0.97 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 24516 completed with status 0
% 3.93/0.97 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 3.93/0.97 # Preprocessing class: FSMSSMSMSSSNFFN.
% 3.93/0.97 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.93/0.97 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 3.93/0.97 # No SInE strategy applied
% 3.93/0.97 # Search class: FHUSM-FFMS21-SFFFFFNN
% 3.93/0.97 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 3.93/0.97 # Starting C07_19_nc_SAT001_MinMin_p005000_rr with 811s (1) cores
% 3.93/0.97 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 3.93/0.97 # Preprocessing time : 0.001 s
% 3.93/0.97 # Presaturation interreduction done
% 3.93/0.97
% 3.93/0.97 # Proof found!
% 3.93/0.97 # SZS status Unsatisfiable
% 3.93/0.97 # SZS output start CNFRefutation
% See solution above
% 3.93/0.97 # Parsed axioms : 27
% 3.93/0.97 # Removed by relevancy pruning/SinE : 0
% 3.93/0.97 # Initial clauses : 27
% 3.93/0.97 # Removed in clause preprocessing : 0
% 3.93/0.97 # Initial clauses in saturation : 27
% 3.93/0.97 # Processed clauses : 8609
% 3.93/0.97 # ...of these trivial : 837
% 3.93/0.97 # ...subsumed : 4938
% 3.93/0.97 # ...remaining for further processing : 2834
% 3.93/0.97 # Other redundant clauses eliminated : 0
% 3.93/0.97 # Clauses deleted for lack of memory : 0
% 3.93/0.97 # Backward-subsumed : 169
% 3.93/0.97 # Backward-rewritten : 589
% 3.93/0.97 # Generated clauses : 34660
% 3.93/0.97 # ...of the previous two non-redundant : 24955
% 3.93/0.97 # ...aggressively subsumed : 0
% 3.93/0.97 # Contextual simplify-reflections : 0
% 3.93/0.97 # Paramodulations : 34660
% 3.93/0.97 # Factorizations : 0
% 3.93/0.97 # NegExts : 0
% 3.93/0.97 # Equation resolutions : 0
% 3.93/0.97 # Total rewrite steps : 21826
% 3.93/0.97 # Propositional unsat checks : 0
% 3.93/0.97 # Propositional check models : 0
% 3.93/0.97 # Propositional check unsatisfiable : 0
% 3.93/0.97 # Propositional clauses : 0
% 3.93/0.97 # Propositional clauses after purity: 0
% 3.93/0.97 # Propositional unsat core size : 0
% 3.93/0.97 # Propositional preprocessing time : 0.000
% 3.93/0.97 # Propositional encoding time : 0.000
% 3.93/0.97 # Propositional solver time : 0.000
% 3.93/0.97 # Success case prop preproc time : 0.000
% 3.93/0.97 # Success case prop encoding time : 0.000
% 3.93/0.97 # Success case prop solver time : 0.000
% 3.93/0.97 # Current number of processed clauses : 2049
% 3.93/0.97 # Positive orientable unit clauses : 338
% 3.93/0.97 # Positive unorientable unit clauses: 2
% 3.93/0.97 # Negative unit clauses : 1
% 3.93/0.97 # Non-unit-clauses : 1708
% 3.93/0.97 # Current number of unprocessed clauses: 14991
% 3.93/0.97 # ...number of literals in the above : 34173
% 3.93/0.97 # Current number of archived formulas : 0
% 3.93/0.97 # Current number of archived clauses : 785
% 3.93/0.97 # Clause-clause subsumption calls (NU) : 492550
% 3.93/0.97 # Rec. Clause-clause subsumption calls : 398268
% 3.93/0.97 # Non-unit clause-clause subsumptions : 5081
% 3.93/0.97 # Unit Clause-clause subsumption calls : 13945
% 3.93/0.97 # Rewrite failures with RHS unbound : 0
% 3.93/0.97 # BW rewrite match attempts : 2458
% 3.93/0.97 # BW rewrite match successes : 200
% 3.93/0.97 # Condensation attempts : 0
% 3.93/0.97 # Condensation successes : 0
% 3.93/0.97 # Termbank termtop insertions : 427557
% 3.93/0.97
% 3.93/0.97 # -------------------------------------------------
% 3.93/0.97 # User time : 0.501 s
% 3.93/0.97 # System time : 0.014 s
% 3.93/0.97 # Total time : 0.515 s
% 3.93/0.97 # Maximum resident set size: 1636 pages
% 3.93/0.97
% 3.93/0.97 # -------------------------------------------------
% 3.93/0.97 # User time : 2.553 s
% 3.93/0.97 # System time : 0.026 s
% 3.93/0.97 # Total time : 2.579 s
% 3.93/0.97 # Maximum resident set size: 1692 pages
% 3.93/0.97 % E---3.1 exiting
% 3.93/0.97 % E---3.1 exiting
%------------------------------------------------------------------------------