%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO014-3 : TPTP v9.3.1. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:06:58 PM UTC 2026
% Result : Unsatisfiable 9.80s 1.78s
% Output : CNFRefutation 9.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 24
% Syntax : Number of clauses : 162 ( 90 unt; 0 nHn; 115 RR)
% Number of literals : 322 ( 50 equ; 165 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 337 ( 14 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(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(multiplicative_identity2,axiom,
product(X1,multiplicative_identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_identity2) ).
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(additive_inverse1,axiom,
sum(inverse(X1),X1,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_inverse1) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
cnf(inverse_is_self_cancelling,axiom,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_is_self_cancelling) ).
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(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(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(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity2) ).
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(x_inverse_times_y_inverse,hypothesis,
product(inverse(x),inverse(y),x_inverse_times_y_inverse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_inverse_times_y_inverse) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
cnf(additive_inverse2,axiom,
sum(X1,inverse(X1),multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_inverse2) ).
cnf(x_plus_y,hypothesis,
sum(x,y,x_plus_y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_plus_y) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse1) ).
cnf(distributivity6,axiom,
( ~ 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(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_inverse2,axiom,
product(X1,inverse(X1),additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse2) ).
cnf(inverse_is_unique,axiom,
( ~ product(X1,X3,additive_identity)
| ~ product(X1,X2,additive_identity)
| ~ sum(X1,X3,multiplicative_identity)
| ~ sum(X1,X2,multiplicative_identity)
| X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_is_unique) ).
cnf(prove_equation,negated_conjecture,
inverse(x_plus_y) != x_inverse_times_y_inverse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
cnf(c_0_24,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(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[addition_is_well_defined]) ).
cnf(c_0_28,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_29,axiom,
product(X1,multiplicative_identity,X1),
multiplicative_identity2 ).
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(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
c_0_27 ).
cnf(c_0_32,axiom,
sum(inverse(X1),X1,multiplicative_identity),
additive_inverse1 ).
cnf(c_0_33,plain,
( ~ sum(multiplicative_identity,X2,X3)
| ~ sum(X1,X2,multiplicative_identity)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_35,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
c_0_30 ).
cnf(c_0_36,plain,
( ~ sum(inverse(X2),X2,X1)
| X1 = multiplicative_identity ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
( ~ sum(multiplicative_identity,X1,X2)
| sum(inverse(X1),X1,X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_32]) ).
cnf(c_0_38,plain,
( ~ sum(X2,X3,X1)
| X1 = add(X2,X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_34]) ).
cnf(c_0_39,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_35,c_0_34]) ).
cnf(c_0_40,plain,
add(inverse(X1),X1) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
cnf(c_0_41,axiom,
inverse(inverse(X1)) = X1,
inverse_is_self_cancelling ).
cnf(c_0_42,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_43,plain,
sum(inverse(X1),X1,add(multiplicative_identity,X1)),
inference(spm,[status(thm)],[c_0_37,c_0_34]) ).
cnf(c_0_44,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
c_0_42 ).
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_38,c_0_43]),c_0_44]),c_0_45]) ).
cnf(c_0_48,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[multiplication_is_well_defined]) ).
cnf(c_0_49,plain,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_multiplication]) ).
cnf(c_0_50,plain,
( ~ sum(X5,X4,multiplicative_identity)
| ~ product(X3,X5,X1)
| ~ product(X3,X4,X2)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_46,c_0_29]) ).
cnf(c_0_51,plain,
sum(X1,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_39,c_0_47]) ).
cnf(c_0_52,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_48 ).
cnf(c_0_53,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_54,plain,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
c_0_49 ).
cnf(c_0_55,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_56,plain,
( ~ product(X2,X3,X1)
| sum(X1,X2,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_29]),c_0_51])]) ).
cnf(c_0_57,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_58,plain,
( ~ product(X2,X3,X1)
| X1 = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,plain,
product(X1,X2,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_54,c_0_53]) ).
cnf(c_0_60,plain,
( ~ sum(X2,additive_identity,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_31,c_0_55]) ).
cnf(c_0_61,plain,
sum(multiply(X1,X2),X1,X1),
inference(spm,[status(thm)],[c_0_56,c_0_53]) ).
cnf(c_0_62,hypothesis,
product(inverse(x),inverse(y),x_inverse_times_y_inverse),
x_inverse_times_y_inverse ).
cnf(c_0_63,plain,
( ~ sum(X6,X2,X7)
| ~ product(X1,X4,X6)
| ~ sum(X4,X2,X5)
| ~ sum(X1,X2,X3)
| product(X3,X5,X7) ),
c_0_57 ).
cnf(c_0_64,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,plain,
multiply(additive_identity,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_66,hypothesis,
product(inverse(y),inverse(x),x_inverse_times_y_inverse),
inference(spm,[status(thm)],[c_0_54,c_0_62]) ).
cnf(c_0_67,plain,
( ~ sum(X4,X6,X1)
| ~ sum(X5,X6,X2)
| ~ sum(multiply(X4,X5),X6,X3)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_63,c_0_53]) ).
cnf(c_0_68,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_69,plain,
multiply(X1,additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_70,hypothesis,
sum(x_inverse_times_y_inverse,inverse(y),inverse(y)),
inference(spm,[status(thm)],[c_0_56,c_0_66]) ).
cnf(c_0_71,plain,
( ~ sum(X4,X2,X1)
| ~ sum(additive_identity,X2,X3)
| product(X1,X2,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]) ).
cnf(c_0_72,hypothesis,
sum(inverse(y),x_inverse_times_y_inverse,inverse(y)),
inference(spm,[status(thm)],[c_0_35,c_0_70]) ).
cnf(c_0_73,plain,
( ~ sum(additive_identity,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_31,c_0_68]) ).
cnf(c_0_74,hypothesis,
( ~ sum(additive_identity,x_inverse_times_y_inverse,X1)
| product(inverse(y),x_inverse_times_y_inverse,X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_75,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_73,c_0_34]) ).
cnf(c_0_76,plain,
( ~ sum(X4,X2,X3)
| ~ sum(X5,X2,multiplicative_identity)
| ~ product(X4,X5,X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_29]) ).
cnf(c_0_77,hypothesis,
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_34]),c_0_75]) ).
cnf(c_0_78,hypothesis,
( ~ sum(x_inverse_times_y_inverse,X1,multiplicative_identity)
| ~ sum(inverse(y),X1,X2)
| sum(x_inverse_times_y_inverse,X1,X2) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_79,axiom,
sum(X1,inverse(X1),multiplicative_identity),
additive_inverse2 ).
cnf(c_0_80,hypothesis,
( ~ sum(inverse(y),inverse(x_inverse_times_y_inverse),X1)
| sum(x_inverse_times_y_inverse,inverse(x_inverse_times_y_inverse),X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_81,hypothesis,
sum(x_inverse_times_y_inverse,inverse(x_inverse_times_y_inverse),add(inverse(y),inverse(x_inverse_times_y_inverse))),
inference(spm,[status(thm)],[c_0_80,c_0_34]) ).
cnf(c_0_82,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_53]) ).
cnf(c_0_83,hypothesis,
add(inverse(y),inverse(x_inverse_times_y_inverse)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_81]),c_0_45]) ).
cnf(c_0_84,plain,
( ~ product(X2,multiplicative_identity,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_52,c_0_29]) ).
cnf(c_0_85,hypothesis,
( ~ sum(inverse(x),X1,X2)
| ~ sum(inverse(y),X1,X3)
| sum(x_inverse_times_y_inverse,X1,multiply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_82,c_0_62]) ).
cnf(c_0_86,hypothesis,
sum(inverse(y),inverse(x_inverse_times_y_inverse),multiplicative_identity),
inference(spm,[status(thm)],[c_0_34,c_0_83]) ).
cnf(c_0_87,plain,
multiply(X1,multiplicative_identity) = X1,
inference(spm,[status(thm)],[c_0_84,c_0_53]) ).
cnf(c_0_88,hypothesis,
( ~ sum(inverse(x),inverse(x_inverse_times_y_inverse),X1)
| sum(x_inverse_times_y_inverse,inverse(x_inverse_times_y_inverse),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]) ).
cnf(c_0_89,hypothesis,
sum(x,y,x_plus_y),
x_plus_y ).
cnf(c_0_90,plain,
( ~ sum(additive_identity,X2,X3)
| product(add(X1,X2),X2,X3) ),
inference(spm,[status(thm)],[c_0_71,c_0_34]) ).
cnf(c_0_91,axiom,
product(inverse(X1),X1,additive_identity),
multiplicative_inverse1 ).
cnf(c_0_92,hypothesis,
sum(x_inverse_times_y_inverse,inverse(x_inverse_times_y_inverse),add(inverse(x),inverse(x_inverse_times_y_inverse))),
inference(spm,[status(thm)],[c_0_88,c_0_34]) ).
cnf(c_0_93,hypothesis,
sum(y,x,x_plus_y),
inference(spm,[status(thm)],[c_0_35,c_0_89]) ).
cnf(c_0_94,plain,
add(X1,multiply(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_61]),c_0_44]) ).
cnf(c_0_95,plain,
product(add(X1,X2),X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_34]),c_0_75]) ).
cnf(c_0_96,plain,
( ~ sum(X3,X1,X2)
| ~ sum(inverse(X3),X1,multiplicative_identity)
| sum(additive_identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_91]) ).
cnf(c_0_97,hypothesis,
add(inverse(x),inverse(x_inverse_times_y_inverse)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_92]),c_0_45]) ).
cnf(c_0_98,hypothesis,
( ~ sum(additive_identity,x,X1)
| product(x_plus_y,x,X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_93]) ).
cnf(c_0_99,plain,
add(X1,multiply(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_94,c_0_64]) ).
cnf(c_0_100,plain,
multiply(X1,add(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_95]),c_0_64]) ).
cnf(c_0_101,plain,
( ~ sum(inverse(X2),X1,multiplicative_identity)
| sum(additive_identity,X1,add(X2,X1)) ),
inference(spm,[status(thm)],[c_0_96,c_0_34]) ).
cnf(c_0_102,hypothesis,
sum(inverse(x),inverse(x_inverse_times_y_inverse),multiplicative_identity),
inference(spm,[status(thm)],[c_0_34,c_0_97]) ).
cnf(c_0_103,hypothesis,
product(x_plus_y,x,x),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_34]),c_0_75]) ).
cnf(c_0_104,plain,
sum(X1,multiply(X2,X1),X1),
inference(spm,[status(thm)],[c_0_34,c_0_99]) ).
cnf(c_0_105,plain,
multiply(X1,add(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_100,c_0_44]) ).
cnf(c_0_106,hypothesis,
sum(additive_identity,inverse(x_inverse_times_y_inverse),add(x,inverse(x_inverse_times_y_inverse))),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_107,hypothesis,
sum(additive_identity,inverse(x_inverse_times_y_inverse),add(y,inverse(x_inverse_times_y_inverse))),
inference(spm,[status(thm)],[c_0_101,c_0_86]) ).
cnf(c_0_108,hypothesis,
( ~ sum(x_plus_y,X1,X2)
| ~ sum(x,X1,X3)
| sum(x,X1,multiply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_82,c_0_103]) ).
cnf(c_0_109,plain,
sum(add(X1,X2),X1,add(X1,X2)),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_110,hypothesis,
add(x,inverse(x_inverse_times_y_inverse)) = inverse(x_inverse_times_y_inverse),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_106]),c_0_75]) ).
cnf(c_0_111,hypothesis,
add(y,inverse(x_inverse_times_y_inverse)) = inverse(x_inverse_times_y_inverse),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_107]),c_0_75]) ).
cnf(c_0_112,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_113,hypothesis,
( ~ sum(x_plus_y,inverse(x),X1)
| sum(x,inverse(x),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_79]),c_0_87]) ).
cnf(c_0_114,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_115,hypothesis,
( ~ sum(X3,x,X1)
| ~ sum(multiply(X3,y),x,X2)
| product(X1,x_plus_y,X2) ),
inference(spm,[status(thm)],[c_0_67,c_0_93]) ).
cnf(c_0_116,hypothesis,
sum(inverse(x_inverse_times_y_inverse),x,inverse(x_inverse_times_y_inverse)),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_117,hypothesis,
multiply(y,inverse(x_inverse_times_y_inverse)) = y,
inference(spm,[status(thm)],[c_0_105,c_0_111]) ).
cnf(c_0_118,hypothesis,
( ~ sum(x,y,X1)
| X1 = x_plus_y ),
inference(spm,[status(thm)],[c_0_31,c_0_89]) ).
cnf(c_0_119,plain,
( ~ product(X3,X5,X7)
| ~ product(X2,X4,X6)
| ~ sum(X1,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X6,X7) ),
c_0_112 ).
cnf(c_0_120,hypothesis,
sum(x,inverse(x),add(x_plus_y,inverse(x))),
inference(spm,[status(thm)],[c_0_113,c_0_34]) ).
cnf(c_0_121,plain,
( ~ sum(X3,X5,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| product(X6,X2,X7) ),
c_0_114 ).
cnf(c_0_122,axiom,
product(X1,inverse(X1),additive_identity),
multiplicative_inverse2 ).
cnf(c_0_123,hypothesis,
( ~ sum(y,x,X1)
| product(inverse(x_inverse_times_y_inverse),x_plus_y,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_64]),c_0_117]) ).
cnf(c_0_124,hypothesis,
add(x,y) = x_plus_y,
inference(spm,[status(thm)],[c_0_118,c_0_34]) ).
cnf(c_0_125,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_119,c_0_53]) ).
cnf(c_0_126,hypothesis,
add(x_plus_y,inverse(x)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_120]),c_0_45]) ).
cnf(c_0_127,plain,
( ~ sum(X4,X2,X1)
| ~ sum(X5,additive_identity,X3)
| ~ product(X4,inverse(X2),X5)
| product(X1,inverse(X2),X3) ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_128,hypothesis,
product(inverse(x_inverse_times_y_inverse),x_plus_y,x_plus_y),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_34]),c_0_44]),c_0_124]) ).
cnf(c_0_129,hypothesis,
( ~ sum(X1,inverse(y),X2)
| ~ sum(X1,inverse(x),X3)
| sum(X1,x_inverse_times_y_inverse,multiply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_125,c_0_66]) ).
cnf(c_0_130,hypothesis,
sum(x_plus_y,inverse(x),multiplicative_identity),
inference(spm,[status(thm)],[c_0_34,c_0_126]) ).
cnf(c_0_131,plain,
( ~ sum(X4,X2,X1)
| ~ sum(multiply(X4,inverse(X2)),additive_identity,X3)
| product(X1,inverse(X2),X3) ),
inference(spm,[status(thm)],[c_0_127,c_0_53]) ).
cnf(c_0_132,hypothesis,
sum(x_plus_y,inverse(x_inverse_times_y_inverse),inverse(x_inverse_times_y_inverse)),
inference(spm,[status(thm)],[c_0_56,c_0_128]) ).
cnf(c_0_133,plain,
( ~ product(inverse(X2),X2,X1)
| X1 = additive_identity ),
inference(spm,[status(thm)],[c_0_52,c_0_91]) ).
cnf(c_0_134,hypothesis,
( ~ sum(x_plus_y,inverse(y),X1)
| sum(x_plus_y,x_inverse_times_y_inverse,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_87]) ).
cnf(c_0_135,hypothesis,
( ~ sum(multiply(x_plus_y,x_inverse_times_y_inverse),additive_identity,X1)
| product(inverse(x_inverse_times_y_inverse),x_inverse_times_y_inverse,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_41]),c_0_41]) ).
cnf(c_0_136,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_60,c_0_34]) ).
cnf(c_0_137,plain,
multiply(inverse(X1),X1) = additive_identity,
inference(spm,[status(thm)],[c_0_133,c_0_53]) ).
cnf(c_0_138,hypothesis,
sum(x_plus_y,x_inverse_times_y_inverse,add(x_plus_y,inverse(y))),
inference(spm,[status(thm)],[c_0_134,c_0_34]) ).
cnf(c_0_139,hypothesis,
( ~ sum(additive_identity,y,X1)
| product(x_plus_y,y,X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_89]) ).
cnf(c_0_140,plain,
( ~ product(X1,X3,additive_identity)
| ~ product(X1,X2,additive_identity)
| ~ sum(X1,X3,multiplicative_identity)
| ~ sum(X1,X2,multiplicative_identity)
| X2 = X3 ),
inference(fof_simplification,[status(thm)],[inverse_is_unique]) ).
cnf(c_0_141,hypothesis,
product(inverse(x_inverse_times_y_inverse),x_inverse_times_y_inverse,multiply(x_plus_y,x_inverse_times_y_inverse)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_34]),c_0_136]) ).
cnf(c_0_142,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_137,c_0_41]) ).
cnf(c_0_143,plain,
( ~ sum(X1,X3,X4)
| ~ sum(X2,X3,X5)
| sum(multiply(X1,X2),X3,multiply(X4,X5)) ),
inference(spm,[status(thm)],[c_0_82,c_0_53]) ).
cnf(c_0_144,hypothesis,
add(x_plus_y,inverse(y)) = add(x_plus_y,x_inverse_times_y_inverse),
inference(spm,[status(thm)],[c_0_38,c_0_138]) ).
cnf(c_0_145,hypothesis,
product(x_plus_y,y,y),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_34]),c_0_75]) ).
cnf(c_0_146,plain,
( ~ product(X1,X3,additive_identity)
| ~ product(X1,X2,additive_identity)
| ~ sum(X1,X3,multiplicative_identity)
| ~ sum(X1,X2,multiplicative_identity)
| X2 = X3 ),
c_0_140 ).
cnf(c_0_147,hypothesis,
multiply(x_plus_y,x_inverse_times_y_inverse) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_141]),c_0_64]),c_0_142]) ).
cnf(c_0_148,negated_conjecture,
inverse(x_plus_y) != x_inverse_times_y_inverse,
inference(fof_simplification,[status(thm)],[prove_equation]) ).
cnf(c_0_149,plain,
( ~ sum(X1,X2,X3)
| sum(multiply(X1,inverse(X2)),X2,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_32]),c_0_87]) ).
cnf(c_0_150,hypothesis,
sum(x_plus_y,inverse(y),add(x_plus_y,x_inverse_times_y_inverse)),
inference(spm,[status(thm)],[c_0_34,c_0_144]) ).
cnf(c_0_151,hypothesis,
multiply(y,x_plus_y) = y,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_145]),c_0_64]) ).
cnf(c_0_152,plain,
( ~ sum(X1,X5,X3)
| ~ sum(X1,X4,multiplicative_identity)
| ~ product(X4,X5,X2)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_119,c_0_26]) ).
cnf(c_0_153,plain,
( ~ sum(X2,X1,multiplicative_identity)
| ~ product(X2,X1,additive_identity)
| X1 = inverse(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_122]),c_0_79])]) ).
cnf(c_0_154,hypothesis,
product(x_plus_y,x_inverse_times_y_inverse,additive_identity),
inference(spm,[status(thm)],[c_0_53,c_0_147]) ).
cnf(c_0_155,negated_conjecture,
inverse(x_plus_y) != x_inverse_times_y_inverse,
c_0_148 ).
cnf(c_0_156,hypothesis,
sum(y,inverse(y),add(x_plus_y,x_inverse_times_y_inverse)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_41]),c_0_64]),c_0_151]) ).
cnf(c_0_157,hypothesis,
( ~ sum(X1,inverse(x),X2)
| ~ sum(X1,inverse(y),multiplicative_identity)
| sum(X1,x_inverse_times_y_inverse,X2) ),
inference(spm,[status(thm)],[c_0_152,c_0_66]) ).
cnf(c_0_158,hypothesis,
~ sum(x_plus_y,x_inverse_times_y_inverse,multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_155]) ).
cnf(c_0_159,hypothesis,
add(x_plus_y,x_inverse_times_y_inverse) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_156]),c_0_45]) ).
cnf(c_0_160,hypothesis,
~ sum(x_plus_y,inverse(y),multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_130]),c_0_158]) ).
cnf(c_0_161,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_159]),c_0_160]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO014-3 : TPTP v9.3.1. Bugfixed v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 13:46:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 Running first-order theorem proving
% 0.16/0.43 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
% 9.80/1.78 % Version: 3.5.1
% 9.80/1.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 9.80/1.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.80/1.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 9.80/1.78 % Starting new_bool_3 with 300s (1) cores
% 9.80/1.78 % Starting new_bool_1 with 300s (1) cores
% 9.80/1.78 % Starting sh5l with 300s (1) cores
% 9.80/1.78 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1244697 completed with status 0
% 9.80/1.78 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 9.80/1.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 9.80/1.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.80/1.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 9.80/1.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.80/1.78 % No SInE strategy applied
% 9.80/1.78 % Search class: FHUSM-FFMF21-SFFFFFNN
% 9.80/1.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 9.80/1.78 % Starting SubtermCWHack with 136s (1) cores
% 9.80/1.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 9.80/1.78 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 9.80/1.78 % Starting new_bool_3 with 136s (1) cores
% 9.80/1.78 % Starting new_bool_1 with 136s (1) cores
% 9.80/1.78 % new_bool_3 with pid 1244705 completed with status 0
% 9.80/1.78 % Result found by new_bool_3
% 9.80/1.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 9.80/1.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.80/1.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 9.80/1.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.80/1.78 % No SInE strategy applied
% 9.80/1.78 % Search class: FHUSM-FFMF21-SFFFFFNN
% 9.80/1.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 9.80/1.78 % Starting SubtermCWHack with 136s (1) cores
% 9.80/1.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 9.80/1.78 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 9.80/1.78 % Starting new_bool_3 with 136s (1) cores
% 9.80/1.78 % Preprocessing time : 0.002 s
% 9.80/1.78 % Presaturation interreduction done
% 9.80/1.78
% 9.80/1.78 % Proof found!
% 9.80/1.78 % SZS status Unsatisfiable
% 9.80/1.78 % SZS output start CNFRefutation
% See solution above
% 9.80/1.78 % Parsed axioms : 27
% 9.80/1.78 % Removed by relevancy pruning/SinE : 0
% 9.80/1.78 % Initial clauses : 27
% 9.80/1.78 % Removed in clause preprocessing : 0
% 9.80/1.78 % Initial clauses in saturation : 27
% 9.80/1.78 % Processed clauses : 14044
% 9.80/1.78 % ...of these trivial : 551
% 9.80/1.78 % ...subsumed : 9798
% 9.80/1.78 % ...remaining for further processing : 3695
% 9.80/1.78 % Other redundant clauses eliminated : 0
% 9.80/1.78 % Clauses deleted for lack of memory : 0
% 9.80/1.78 % Backward-subsumed : 123
% 9.80/1.78 % Backward-rewritten : 282
% 9.80/1.78 % Generated clauses : 57860
% 9.80/1.78 % ...of the previous two non-redundant : 46817
% 9.80/1.78 % ...aggressively subsumed : 0
% 9.80/1.78 % Contextual simplify-reflections : 0
% 9.80/1.78 % Paramodulations : 57860
% 9.80/1.78 % Factorizations : 0
% 9.80/1.78 % NegExts : 0
% 9.80/1.78 % Equation resolutions : 0
% 9.80/1.78 % Disequality decompositions : 0
% 9.80/1.78 % Total rewrite steps : 30739
% 9.80/1.78 % ...of those cached : 29284
% 9.80/1.78 % Propositional unsat checks : 0
% 9.80/1.78 % Propositional check models : 0
% 9.80/1.78 % Propositional check unsatisfiable : 0
% 9.80/1.78 % Propositional clauses : 0
% 9.80/1.78 % Propositional clauses after purity: 0
% 9.80/1.78 % Propositional unsat core size : 0
% 9.80/1.78 % Propositional preprocessing time : 0.000
% 9.80/1.78 % Propositional encoding time : 0.000
% 9.80/1.78 % Propositional solver time : 0.000
% 9.80/1.78 % Success case prop preproc time : 0.000
% 9.80/1.78 % Success case prop encoding time : 0.000
% 9.80/1.78 % Success case prop solver time : 0.000
% 9.80/1.78 % Current number of processed clauses : 3263
% 9.80/1.78 % Positive orientable unit clauses : 264
% 9.80/1.78 % Positive unorientable unit clauses: 2
% 9.80/1.78 % Negative unit clauses : 3
% 9.80/1.78 % Non-unit-clauses : 2994
% 9.80/1.78 % Current number of unprocessed clauses: 32155
% 9.80/1.78 % ...number of literals in the above : 74197
% 9.80/1.78 % Current number of archived formulas : 0
% 9.80/1.78 % Current number of archived clauses : 432
% 9.80/1.78 % Clause-clause subsumption calls (NU) : 1677107
% 9.80/1.78 % Rec. Clause-clause subsumption calls : 1174979
% 9.80/1.78 % Non-unit clause-clause subsumptions : 9913
% 9.80/1.78 % Unit Clause-clause subsumption calls : 4059
% 9.80/1.78 % Rewrite failures with RHS unbound : 0
% 9.80/1.78 % BW rewrite match attempts : 1083
% 9.80/1.78 % BW rewrite match successes : 91
% 9.80/1.78 % Condensation attempts : 0
% 9.80/1.78 % Condensation successes : 0
% 9.80/1.78 % Termbank termtop insertions : 854004
% 9.80/1.78 % Search garbage collected termcells : 80
% 9.80/1.78
% 9.80/1.78 % -------------------------------------------------
% 9.80/1.78 % User time : 1.257 s
% 9.80/1.78 % System time : 0.043 s
% 9.80/1.78 % Total time : 1.300 s
% 9.80/1.78 % Maximum resident set size: 3652 pages
% 9.80/1.78
% 9.80/1.78 % -------------------------------------------------
% 9.80/1.78 % User time : 6.174 s
% 9.80/1.78 % System time : 0.200 s
% 9.80/1.78 % Total time : 6.374 s
% 9.80/1.78 % Maximum resident set size: 4864 pages
% 9.80/1.78 % E exiting
%------------------------------------------------------------------------------