%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO008-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:06:55 PM UTC 2026
% Result : Unsatisfiable 6.24s 1.73s
% Output : CNFRefutation 6.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 24
% Syntax : Number of clauses : 169 ( 92 unt; 0 nHn; 120 RR)
% Number of literals : 350 ( 50 equ; 184 neg)
% Maximal clause size : 5 ( 2 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 : 385 ( 22 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity8,axiom,
( ~ product(X3,X5,X7)
| ~ product(X1,X4,X6)
| ~ sum(X4,X2,X5)
| ~ sum(X1,X2,X3)
| sum(X6,X2,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(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,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',addition_is_well_defined) ).
cnf(commutativity_of_addition,axiom,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',commutativity_of_addition) ).
cnf(distributivity4,axiom,
( ~ sum(X3,X5,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| product(X6,X2,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity4) ).
cnf(multiplicative_identity2,axiom,
product(X1,multiplicative_identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_identity2) ).
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_inverse2,axiom,
sum(X1,inverse(X1),multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_inverse2) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
cnf(distributivity7,axiom,
( ~ sum(X6,X2,X7)
| ~ product(X1,X4,X6)
| ~ sum(X4,X2,X5)
| ~ sum(X1,X2,X3)
| product(X3,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity7) ).
cnf(multiplication_is_well_defined,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplication_is_well_defined) ).
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(X1,X2,X3)
| product(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',commutativity_of_multiplication) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',closure_of_multiplication) ).
cnf(distributivity6,axiom,
( ~ product(X3,X5,X7)
| ~ product(X2,X4,X6)
| ~ sum(X1,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X6,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity6) ).
cnf(distributivity3,axiom,
( ~ product(X6,X2,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity3) ).
cnf(distributivity1,axiom,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity1) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity2) ).
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(x_plus_y,hypothesis,
sum(x,y,x_plus_y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_plus_y) ).
cnf(distributivity5,axiom,
( ~ sum(X1,X6,X7)
| ~ product(X2,X4,X6)
| ~ sum(X1,X4,X5)
| ~ sum(X1,X2,X3)
| product(X3,X5,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_24,plain,
( ~ product(X3,X5,X7)
| ~ product(X1,X4,X6)
| ~ sum(X4,X2,X5)
| ~ sum(X1,X2,X3)
| sum(X6,X2,X7) ),
inference(fof_simplification,[status(thm)],[distributivity8]) ).
cnf(c_0_25,plain,
( ~ product(X3,X5,X7)
| ~ product(X1,X4,X6)
| ~ sum(X4,X2,X5)
| ~ sum(X1,X2,X3)
| sum(X6,X2,X7) ),
c_0_24 ).
cnf(c_0_26,axiom,
product(multiplicative_identity,X1,X1),
multiplicative_identity1 ).
cnf(c_0_27,plain,
( ~ sum(X5,X2,X3)
| ~ sum(X4,X2,multiplicative_identity)
| ~ product(X4,X5,X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,axiom,
sum(inverse(X1),X1,multiplicative_identity),
additive_inverse1 ).
cnf(c_0_29,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[addition_is_well_defined]) ).
cnf(c_0_30,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_addition]) ).
cnf(c_0_31,plain,
( ~ sum(X3,X5,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| product(X6,X2,X7) ),
inference(fof_simplification,[status(thm)],[distributivity4]) ).
cnf(c_0_32,plain,
( ~ sum(X4,X2,X3)
| ~ product(inverse(X2),X4,X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,axiom,
product(X1,multiplicative_identity,X1),
multiplicative_identity2 ).
cnf(c_0_34,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
c_0_29 ).
cnf(c_0_35,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_36,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
c_0_30 ).
cnf(c_0_37,axiom,
sum(X1,inverse(X1),multiplicative_identity),
additive_inverse2 ).
cnf(c_0_38,plain,
( ~ sum(X3,X5,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| product(X6,X2,X7) ),
c_0_31 ).
cnf(c_0_39,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_40,plain,
( ~ sum(multiplicative_identity,X1,X2)
| sum(inverse(X1),X1,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_41,plain,
( ~ sum(X2,X3,X1)
| X1 = add(X2,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_43,plain,
( ~ sum(X2,inverse(X2),X1)
| X1 = multiplicative_identity ),
inference(spm,[status(thm)],[c_0_34,c_0_37]) ).
cnf(c_0_44,plain,
( ~ sum(X6,X2,X7)
| ~ product(X1,X4,X6)
| ~ sum(X4,X2,X5)
| ~ sum(X1,X2,X3)
| product(X3,X5,X7) ),
inference(fof_simplification,[status(thm)],[distributivity7]) ).
cnf(c_0_45,plain,
( ~ sum(X4,X5,X1)
| ~ product(X5,X2,X3)
| ~ product(X4,X2,additive_identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,plain,
sum(inverse(X1),X1,add(multiplicative_identity,X1)),
inference(spm,[status(thm)],[c_0_40,c_0_35]) ).
cnf(c_0_47,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_43,c_0_35]) ).
cnf(c_0_49,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[multiplication_is_well_defined]) ).
cnf(c_0_50,plain,
( ~ sum(X6,X2,X7)
| ~ product(X1,X4,X6)
| ~ sum(X4,X2,X5)
| ~ sum(X1,X2,X3)
| product(X3,X5,X7) ),
c_0_44 ).
cnf(c_0_51,hypothesis,
sum(x_plus_y,z,x_plus_y__plus_z),
x_plus_y__plus_z ).
cnf(c_0_52,plain,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_multiplication]) ).
cnf(c_0_53,plain,
( ~ sum(multiplicative_identity,X3,X1)
| ~ product(X3,additive_identity,X2)
| product(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_45,c_0_26]) ).
cnf(c_0_54,plain,
add(multiplicative_identity,X1) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_46]),c_0_47]),c_0_48]) ).
cnf(c_0_55,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_49 ).
cnf(c_0_56,hypothesis,
( ~ sum(X3,z,X1)
| ~ sum(X4,z,X2)
| ~ product(X3,X4,x_plus_y)
| product(X1,X2,x_plus_y__plus_z) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,plain,
( ~ sum(X3,multiplicative_identity,X2)
| ~ product(additive_identity,X3,X1)
| sum(X1,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_39]) ).
cnf(c_0_58,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_59,plain,
( ~ product(X3,X5,X7)
| ~ product(X2,X4,X6)
| ~ sum(X1,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X6,X7) ),
inference(fof_simplification,[status(thm)],[distributivity6]) ).
cnf(c_0_60,plain,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
c_0_52 ).
cnf(c_0_61,plain,
( ~ product(X2,additive_identity,X1)
| product(multiplicative_identity,additive_identity,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_35]),c_0_54]) ).
cnf(c_0_62,plain,
( ~ product(multiplicative_identity,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_55,c_0_26]) ).
cnf(c_0_63,hypothesis,
( ~ sum(X2,z,X1)
| ~ product(X2,x_plus_y,x_plus_y)
| product(X1,x_plus_y__plus_z,x_plus_y__plus_z) ),
inference(spm,[status(thm)],[c_0_56,c_0_51]) ).
cnf(c_0_64,plain,
( ~ sum(X1,multiplicative_identity,X2)
| sum(multiply(additive_identity,X1),multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_65,plain,
( ~ product(X3,X5,X7)
| ~ product(X2,X4,X6)
| ~ sum(X1,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X6,X7) ),
c_0_59 ).
cnf(c_0_66,plain,
( ~ product(X2,X3,X1)
| X1 = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_55,c_0_58]) ).
cnf(c_0_67,plain,
product(X1,X2,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_60,c_0_58]) ).
cnf(c_0_68,plain,
product(multiplicative_identity,additive_identity,multiply(X1,additive_identity)),
inference(spm,[status(thm)],[c_0_61,c_0_58]) ).
cnf(c_0_69,plain,
multiply(multiplicative_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_62,c_0_58]) ).
cnf(c_0_70,plain,
( ~ product(X6,X2,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
inference(fof_simplification,[status(thm)],[distributivity3]) ).
cnf(c_0_71,hypothesis,
( ~ product(X1,x_plus_y,x_plus_y)
| product(add(X1,z),x_plus_y__plus_z,x_plus_y__plus_z) ),
inference(spm,[status(thm)],[c_0_63,c_0_35]) ).
cnf(c_0_72,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
inference(fof_simplification,[status(thm)],[distributivity1]) ).
cnf(c_0_73,plain,
sum(multiply(additive_identity,X1),multiplicative_identity,add(X1,multiplicative_identity)),
inference(spm,[status(thm)],[c_0_64,c_0_35]) ).
cnf(c_0_74,plain,
( ~ sum(X1,X5,X3)
| ~ sum(X1,X6,X4)
| ~ product(X5,X6,X2)
| sum(X1,X2,multiply(X3,X4)) ),
inference(spm,[status(thm)],[c_0_65,c_0_58]) ).
cnf(c_0_75,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_76,plain,
multiply(X1,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_68]),c_0_69]) ).
cnf(c_0_77,plain,
( ~ product(X6,X2,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
c_0_70 ).
cnf(c_0_78,hypothesis,
product(add(multiplicative_identity,z),x_plus_y__plus_z,x_plus_y__plus_z),
inference(spm,[status(thm)],[c_0_71,c_0_26]) ).
cnf(c_0_79,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
c_0_72 ).
cnf(c_0_80,plain,
add(multiplicative_identity,multiply(additive_identity,X1)) = add(X1,multiplicative_identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_73]),c_0_47]) ).
cnf(c_0_81,plain,
( ~ sum(X1,X3,X4)
| ~ sum(X1,X2,X5)
| sum(X1,multiply(X2,X3),multiply(X4,X5)) ),
inference(spm,[status(thm)],[c_0_74,c_0_67]) ).
cnf(c_0_82,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_83,plain,
multiply(additive_identity,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_84,hypothesis,
sum(x,y_plus_z,x__plus_y_plus_z),
x_plus__y_plus_z ).
cnf(c_0_85,hypothesis,
sum(x,y,x_plus_y),
x_plus_y ).
cnf(c_0_86,hypothesis,
( ~ sum(X4,X3,add(multiplicative_identity,z))
| ~ product(X4,x_plus_y__plus_z,X1)
| ~ product(X3,x_plus_y__plus_z,X2)
| sum(X1,X2,x_plus_y__plus_z) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_87,plain,
( ~ sum(X5,X4,X1)
| ~ sum(X6,X4,X2)
| ~ product(X5,X6,X3)
| product(X1,X2,add(X3,X4)) ),
inference(spm,[status(thm)],[c_0_50,c_0_35]) ).
cnf(c_0_88,plain,
( ~ sum(additive_identity,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_34,c_0_39]) ).
cnf(c_0_89,plain,
( ~ sum(X6,X5,X4)
| ~ product(X3,X6,X1)
| ~ product(X3,X5,X2)
| sum(X1,X2,multiply(X3,X4)) ),
inference(spm,[status(thm)],[c_0_79,c_0_58]) ).
cnf(c_0_90,plain,
add(multiplicative_identity,multiply(X1,additive_identity)) = add(X1,multiplicative_identity),
inference(spm,[status(thm)],[c_0_80,c_0_75]) ).
cnf(c_0_91,plain,
( ~ product(X2,multiplicative_identity,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_55,c_0_33]) ).
cnf(c_0_92,plain,
( ~ sum(X1,X6,X7)
| ~ product(X2,X4,X6)
| ~ sum(X1,X4,X5)
| ~ sum(X1,X2,X3)
| product(X3,X5,X7) ),
inference(fof_simplification,[status(thm)],[distributivity5]) ).
cnf(c_0_93,plain,
( ~ sum(X1,X3,X2)
| sum(X1,additive_identity,multiply(X2,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]) ).
cnf(c_0_94,hypothesis,
sum(y_plus_z,x,x__plus_y_plus_z),
inference(spm,[status(thm)],[c_0_36,c_0_84]) ).
cnf(c_0_95,plain,
( ~ sum(X2,additive_identity,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_34,c_0_82]) ).
cnf(c_0_96,hypothesis,
sum(y,z,y_plus_z),
y_plus_z ).
cnf(c_0_97,hypothesis,
sum(y,x,x_plus_y),
inference(spm,[status(thm)],[c_0_36,c_0_85]) ).
cnf(c_0_98,hypothesis,
( ~ sum(X2,multiplicative_identity,add(multiplicative_identity,z))
| ~ product(X2,x_plus_y__plus_z,X1)
| sum(X1,x_plus_y__plus_z,x_plus_y__plus_z) ),
inference(spm,[status(thm)],[c_0_86,c_0_26]) ).
cnf(c_0_99,plain,
( ~ sum(X4,X2,X1)
| ~ product(X4,additive_identity,X3)
| product(X1,X2,add(X3,X2)) ),
inference(spm,[status(thm)],[c_0_87,c_0_39]) ).
cnf(c_0_100,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_88,c_0_35]) ).
cnf(c_0_101,plain,
( ~ sum(X4,multiplicative_identity,X3)
| ~ product(X2,X4,X1)
| sum(X1,X2,multiply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_89,c_0_33]) ).
cnf(c_0_102,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(rw,[status(thm)],[c_0_90,c_0_54]) ).
cnf(c_0_103,plain,
multiply(X1,multiplicative_identity) = X1,
inference(spm,[status(thm)],[c_0_91,c_0_58]) ).
cnf(c_0_104,plain,
( ~ sum(X1,X6,X7)
| ~ product(X2,X4,X6)
| ~ sum(X1,X4,X5)
| ~ sum(X1,X2,X3)
| product(X3,X5,X7) ),
c_0_92 ).
cnf(c_0_105,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_93,c_0_94]),c_0_75]) ).
cnf(c_0_106,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_95,c_0_35]) ).
cnf(c_0_107,hypothesis,
( ~ sum(X3,z,X1)
| ~ sum(X4,z,X2)
| ~ product(X3,X4,y)
| product(X1,X2,y_plus_z) ),
inference(spm,[status(thm)],[c_0_50,c_0_96]) ).
cnf(c_0_108,hypothesis,
sum(y,additive_identity,multiply(y,x_plus_y)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_97]),c_0_75]) ).
cnf(c_0_109,plain,
( ~ sum(X5,X2,X3)
| ~ sum(X6,X2,X4)
| ~ product(X5,X6,X1)
| sum(X1,X2,multiply(X3,X4)) ),
inference(spm,[status(thm)],[c_0_25,c_0_58]) ).
cnf(c_0_110,hypothesis,
( ~ sum(X1,multiplicative_identity,add(multiplicative_identity,z))
| sum(multiply(X1,x_plus_y__plus_z),x_plus_y__plus_z,x_plus_y__plus_z) ),
inference(spm,[status(thm)],[c_0_98,c_0_58]) ).
cnf(c_0_111,plain,
sum(X1,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_42,c_0_54]) ).
cnf(c_0_112,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_93,c_0_51]),c_0_75]) ).
cnf(c_0_113,plain,
( ~ sum(X3,X2,X1)
| product(X1,X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_58]),c_0_76]),c_0_100]) ).
cnf(c_0_114,plain,
( ~ product(X2,X3,X1)
| sum(X1,X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_35]),c_0_102]),c_0_103]) ).
cnf(c_0_115,hypothesis,
( ~ sum(x,X3,X1)
| ~ sum(x,X4,X2)
| ~ product(X3,X4,y)
| product(X1,X2,x_plus_y) ),
inference(spm,[status(thm)],[c_0_104,c_0_85]) ).
cnf(c_0_116,hypothesis,
sum(y,additive_identity,multiply(y,y_plus_z)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_96]),c_0_75]) ).
cnf(c_0_117,hypothesis,
multiply(y_plus_z,x__plus_y_plus_z) = y_plus_z,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_105]),c_0_106]) ).
cnf(c_0_118,hypothesis,
( ~ sum(x,X3,X1)
| ~ sum(x,X4,X2)
| ~ product(X3,X4,y_plus_z)
| product(X1,X2,x__plus_y_plus_z) ),
inference(spm,[status(thm)],[c_0_104,c_0_84]) ).
cnf(c_0_119,hypothesis,
( ~ sum(X2,z,X1)
| ~ product(X2,y,y)
| product(X1,y_plus_z,y_plus_z) ),
inference(spm,[status(thm)],[c_0_107,c_0_96]) ).
cnf(c_0_120,hypothesis,
multiply(y,x_plus_y) = y,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_108]),c_0_106]) ).
cnf(c_0_121,plain,
( ~ sum(X1,X3,X4)
| ~ sum(X2,X3,X5)
| sum(multiply(X1,X2),X3,multiply(X4,X5)) ),
inference(spm,[status(thm)],[c_0_109,c_0_58]) ).
cnf(c_0_122,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_110,c_0_54]),c_0_111])]) ).
cnf(c_0_123,hypothesis,
multiply(x_plus_y,x_plus_y__plus_z) = x_plus_y,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_112]),c_0_106]) ).
cnf(c_0_124,plain,
product(add(X1,X2),X2,X2),
inference(spm,[status(thm)],[c_0_113,c_0_35]) ).
cnf(c_0_125,plain,
sum(multiply(X1,X2),X1,X1),
inference(spm,[status(thm)],[c_0_114,c_0_58]) ).
cnf(c_0_126,hypothesis,
( ~ sum(x,X2,X1)
| ~ product(X2,y_plus_z,y)
| product(X1,x__plus_y_plus_z,x_plus_y) ),
inference(spm,[status(thm)],[c_0_115,c_0_84]) ).
cnf(c_0_127,hypothesis,
multiply(y,y_plus_z) = y,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_116]),c_0_106]) ).
cnf(c_0_128,hypothesis,
product(x__plus_y_plus_z,y_plus_z,y_plus_z),
inference(spm,[status(thm)],[c_0_67,c_0_117]) ).
cnf(c_0_129,hypothesis,
( ~ sum(x,X2,X1)
| ~ product(X2,y_plus_z,y_plus_z)
| product(X1,x__plus_y_plus_z,x__plus_y_plus_z) ),
inference(spm,[status(thm)],[c_0_118,c_0_84]) ).
cnf(c_0_130,hypothesis,
( ~ product(x_plus_y,y,y)
| product(x_plus_y__plus_z,y_plus_z,y_plus_z) ),
inference(spm,[status(thm)],[c_0_119,c_0_51]) ).
cnf(c_0_131,hypothesis,
product(x_plus_y,y,y),
inference(spm,[status(thm)],[c_0_67,c_0_120]) ).
cnf(c_0_132,plain,
( ~ sum(X1,X3,X4)
| sum(multiply(X1,X2),X3,multiply(X4,add(X2,X3))) ),
inference(spm,[status(thm)],[c_0_121,c_0_35]) ).
cnf(c_0_133,hypothesis,
sum(x_plus_y,x_plus_y__plus_z,x_plus_y__plus_z),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_134,plain,
multiply(X1,add(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_124]),c_0_75]) ).
cnf(c_0_135,plain,
add(X1,multiply(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_125]),c_0_47]) ).
cnf(c_0_136,hypothesis,
( ~ sum(X3,z,X1)
| ~ product(X3,X2,x_plus_y)
| product(X1,add(z,X2),x_plus_y__plus_z) ),
inference(spm,[status(thm)],[c_0_56,c_0_42]) ).
cnf(c_0_137,hypothesis,
( ~ product(y,y_plus_z,y)
| product(x_plus_y,x__plus_y_plus_z,x_plus_y) ),
inference(spm,[status(thm)],[c_0_126,c_0_85]) ).
cnf(c_0_138,hypothesis,
product(y,y_plus_z,y),
inference(spm,[status(thm)],[c_0_58,c_0_127]) ).
cnf(c_0_139,hypothesis,
sum(y_plus_z,x__plus_y_plus_z,x__plus_y_plus_z),
inference(spm,[status(thm)],[c_0_114,c_0_128]) ).
cnf(c_0_140,hypothesis,
( ~ product(X1,y_plus_z,y_plus_z)
| product(add(x,X1),x__plus_y_plus_z,x__plus_y_plus_z) ),
inference(spm,[status(thm)],[c_0_129,c_0_35]) ).
cnf(c_0_141,hypothesis,
product(x_plus_y__plus_z,y_plus_z,y_plus_z),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_131])]) ).
cnf(c_0_142,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_132,c_0_133]),c_0_134]) ).
cnf(c_0_143,plain,
add(X1,multiply(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_135,c_0_75]) ).
cnf(c_0_144,hypothesis,
( ~ product(x_plus_y,X1,x_plus_y)
| product(x_plus_y__plus_z,add(z,X1),x_plus_y__plus_z) ),
inference(spm,[status(thm)],[c_0_136,c_0_51]) ).
cnf(c_0_145,hypothesis,
product(x_plus_y,x__plus_y_plus_z,x_plus_y),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_138])]) ).
cnf(c_0_146,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_132,c_0_139]),c_0_134]) ).
cnf(c_0_147,hypothesis,
sum(z,y,y_plus_z),
inference(spm,[status(thm)],[c_0_36,c_0_96]) ).
cnf(c_0_148,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_140,c_0_141]) ).
cnf(c_0_149,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_41,c_0_142]),c_0_47]) ).
cnf(c_0_150,plain,
multiply(X1,multiply(X2,X1)) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_143]),c_0_75]) ).
cnf(c_0_151,hypothesis,
sum(x,additive_identity,multiply(x,x_plus_y)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_85]),c_0_75]) ).
cnf(c_0_152,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_144,c_0_145]) ).
cnf(c_0_153,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_41,c_0_146]),c_0_47]) ).
cnf(c_0_154,hypothesis,
sum(z,additive_identity,multiply(z,y_plus_z)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_147]),c_0_75]) ).
cnf(c_0_155,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_66,c_0_148]),c_0_75]) ).
cnf(c_0_156,hypothesis,
add(x_plus_y__plus_z,multiply(X1,x_plus_y)) = x_plus_y__plus_z,
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_157,hypothesis,
multiply(x,x_plus_y) = x,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_151]),c_0_106]) ).
cnf(c_0_158,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_66,c_0_152]) ).
cnf(c_0_159,hypothesis,
add(x__plus_y_plus_z,multiply(X1,y_plus_z)) = x__plus_y_plus_z,
inference(spm,[status(thm)],[c_0_153,c_0_150]) ).
cnf(c_0_160,hypothesis,
multiply(z,y_plus_z) = z,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_154]),c_0_106]) ).
cnf(c_0_161,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_143,c_0_155]),c_0_47]) ).
cnf(c_0_162,hypothesis,
add(x,x_plus_y__plus_z) = x_plus_y__plus_z,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_47]) ).
cnf(c_0_163,negated_conjecture,
x__plus_y_plus_z != x_plus_y__plus_z,
inference(fof_simplification,[status(thm)],[prove_equality]) ).
cnf(c_0_164,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_143,c_0_158]),c_0_47]) ).
cnf(c_0_165,hypothesis,
add(z,x__plus_y_plus_z) = x__plus_y_plus_z,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_47]) ).
cnf(c_0_166,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_161,c_0_162]),c_0_162]) ).
cnf(c_0_167,negated_conjecture,
x__plus_y_plus_z != x_plus_y__plus_z,
c_0_163 ).
cnf(c_0_168,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_164,c_0_165]),c_0_47]),c_0_166]),c_0_165]),c_0_167]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 % Computer : n006.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Mon Sep 21 13:46:42 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.49 Running first-order theorem proving
% 0.19/0.49 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/benchmark/theBenchmark.p
% 6.24/1.73 % Version: 3.5.1
% 6.24/1.73 % Preprocessing class: FSMSSMSMSSSNFFN.
% 6.24/1.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.24/1.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 6.24/1.73 % Starting new_bool_3 with 300s (1) cores
% 6.24/1.73 % Starting new_bool_1 with 300s (1) cores
% 6.24/1.73 % Starting sh5l with 300s (1) cores
% 6.24/1.73 % new_bool_1 with pid 2998298 completed with status 9
% 6.24/1.73 % new_bool_3 with pid 2998297 completed with status 9
% 6.24/1.73 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 2998296 completed with status 0
% 6.24/1.73 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 6.24/1.73 % Preprocessing class: FSMSSMSMSSSNFFN.
% 6.24/1.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.24/1.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 6.24/1.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.24/1.73 % No SInE strategy applied
% 6.24/1.73 % Search class: FHUSM-FFMS21-SFFFFFNN
% 6.24/1.73 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.24/1.73 % Starting SubtermCWHack with 136s (1) cores
% 6.24/1.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 6.24/1.73 % Starting G-E--_301_C18_F1_URBAN_S0Y with 136s (1) cores
% 6.24/1.73 % Starting new_bool_3 with 136s (1) cores
% 6.24/1.73 % Starting new_bool_1 with 136s (1) cores
% 6.24/1.73 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 2998301 completed with status 0
% 6.24/1.73 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 6.24/1.73 % Preprocessing class: FSMSSMSMSSSNFFN.
% 6.24/1.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.24/1.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 6.24/1.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.24/1.73 % No SInE strategy applied
% 6.24/1.73 % Search class: FHUSM-FFMS21-SFFFFFNN
% 6.24/1.73 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.24/1.73 % Starting SubtermCWHack with 136s (1) cores
% 6.24/1.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 6.24/1.73 % Preprocessing time : 0.002 s
% 6.24/1.73 % Presaturation interreduction done
% 6.24/1.73
% 6.24/1.73 % Proof found!
% 6.24/1.73 % SZS status Unsatisfiable
% 6.24/1.73 % SZS output start CNFRefutation
% See solution above
% 6.24/1.73 % Parsed axioms : 27
% 6.24/1.73 % Removed by relevancy pruning/SinE : 0
% 6.24/1.73 % Initial clauses : 27
% 6.24/1.73 % Removed in clause preprocessing : 0
% 6.24/1.73 % Initial clauses in saturation : 27
% 6.24/1.73 % Processed clauses : 8609
% 6.24/1.73 % ...of these trivial : 837
% 6.24/1.73 % ...subsumed : 4938
% 6.24/1.73 % ...remaining for further processing : 2834
% 6.24/1.73 % Other redundant clauses eliminated : 0
% 6.24/1.73 % Clauses deleted for lack of memory : 0
% 6.24/1.73 % Backward-subsumed : 169
% 6.24/1.73 % Backward-rewritten : 589
% 6.24/1.73 % Generated clauses : 34660
% 6.24/1.73 % ...of the previous two non-redundant : 24955
% 6.24/1.73 % ...aggressively subsumed : 0
% 6.24/1.73 % Contextual simplify-reflections : 0
% 6.24/1.73 % Paramodulations : 34660
% 6.24/1.73 % Factorizations : 0
% 6.24/1.73 % NegExts : 0
% 6.24/1.73 % Equation resolutions : 0
% 6.24/1.73 % Disequality decompositions : 0
% 6.24/1.73 % Total rewrite steps : 21826
% 6.24/1.73 % ...of those cached : 20010
% 6.24/1.73 % Propositional unsat checks : 0
% 6.24/1.73 % Propositional check models : 0
% 6.24/1.73 % Propositional check unsatisfiable : 0
% 6.24/1.73 % Propositional clauses : 0
% 6.24/1.73 % Propositional clauses after purity: 0
% 6.24/1.73 % Propositional unsat core size : 0
% 6.24/1.73 % Propositional preprocessing time : 0.000
% 6.24/1.73 % Propositional encoding time : 0.000
% 6.24/1.73 % Propositional solver time : 0.000
% 6.24/1.73 % Success case prop preproc time : 0.000
% 6.24/1.73 % Success case prop encoding time : 0.000
% 6.24/1.73 % Success case prop solver time : 0.000
% 6.24/1.73 % Current number of processed clauses : 2049
% 6.24/1.73 % Positive orientable unit clauses : 338
% 6.24/1.73 % Positive unorientable unit clauses: 2
% 6.24/1.73 % Negative unit clauses : 1
% 6.24/1.73 % Non-unit-clauses : 1708
% 6.24/1.73 % Current number of unprocessed clauses: 14991
% 6.24/1.73 % ...number of literals in the above : 34173
% 6.24/1.73 % Current number of archived formulas : 0
% 6.24/1.73 % Current number of archived clauses : 785
% 6.24/1.73 % Clause-clause subsumption calls (NU) : 317551
% 6.24/1.73 % Rec. Clause-clause subsumption calls : 274727
% 6.24/1.73 % Non-unit clause-clause subsumptions : 5081
% 6.24/1.73 % Unit Clause-clause subsumption calls : 17156
% 6.24/1.73 % Rewrite failures with RHS unbound : 0
% 6.24/1.73 % BW rewrite match attempts : 2458
% 6.24/1.73 % BW rewrite match successes : 200
% 6.24/1.73 % Condensation attempts : 0
% 6.24/1.73 % Condensation successes : 0
% 6.24/1.73 % Termbank termtop insertions : 427853
% 6.24/1.73 % Search garbage collected termcells : 68
% 6.24/1.73
% 6.24/1.73 % -------------------------------------------------
% 6.24/1.73 % User time : 1.130 s
% 6.24/1.73 % System time : 0.033 s
% 6.24/1.73 % Total time : 1.163 s
% 6.24/1.73 % Maximum resident set size: 3652 pages
% 6.24/1.73
% 6.24/1.73 % -------------------------------------------------
% 6.24/1.73 % User time : 5.893 s
% 6.24/1.73 % System time : 0.235 s
% 6.24/1.73 % Total time : 6.128 s
% 6.24/1.73 % Maximum resident set size: 4608 pages
% 6.24/1.73 % E exiting
%------------------------------------------------------------------------------