%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD041-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:22:48 PM UTC 2026
% Result : Unsatisfiable 8.25s 1.65s
% Output : CNFRefutation 8.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 24
% Syntax : Number of clauses : 125 ( 52 unt; 8 nHn; 125 RR)
% Number of literals : 272 ( 0 equ; 145 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 215 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(existence_of_identity_addition,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(distributivity_1,axiom,
( ~ product(X5,X7,X2)
| ~ product(X4,X7,X1)
| ~ product(X6,X7,X3)
| ~ sum(X4,X5,X6)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(existence_of_inverse_multiplication,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(distributivity_2,axiom,
( ~ sum(X6,X7,X3)
| ~ product(X5,X2,X7)
| ~ product(X4,X2,X6)
| ~ sum(X4,X5,X1)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_2) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(not_sum_5,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_5) ).
cnf(sum_7,negated_conjecture,
sum(additive_identity,c,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_7) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(totality_of_multiplication,axiom,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(associativity_addition_2,axiom,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
cnf(commutativity_addition,axiom,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(associativity_multiplication_2,axiom,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
cnf(totality_of_addition,axiom,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_addition) ).
cnf(product_6,negated_conjecture,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_6) ).
cnf(associativity_multiplication_1,axiom,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(associativity_addition_1,axiom,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(not_sum_4,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_4) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(c_0_24,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_25,plain,
( ~ product(X5,X7,X2)
| ~ product(X4,X7,X1)
| ~ product(X6,X7,X3)
| ~ sum(X4,X5,X6)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[distributivity_1]) ).
cnf(c_0_26,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
c_0_24 ).
cnf(c_0_27,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_28,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_29,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_multiplication]) ).
cnf(c_0_30,plain,
( ~ sum(X6,X7,X3)
| ~ product(X5,X2,X7)
| ~ product(X4,X2,X6)
| ~ sum(X4,X5,X1)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[distributivity_2]) ).
cnf(c_0_31,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_32,plain,
( ~ product(X5,X7,X2)
| ~ product(X4,X7,X1)
| ~ product(X6,X7,X3)
| ~ sum(X4,X5,X6)
| sum(X1,X2,X3) ),
c_0_25 ).
cnf(c_0_33,hypothesis,
sum(additive_identity,b,b),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
c_0_28 ).
cnf(c_0_35,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
c_0_29 ).
cnf(c_0_36,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_5]) ).
cnf(c_0_37,plain,
( ~ sum(X6,X7,X3)
| ~ product(X5,X2,X7)
| ~ product(X4,X2,X6)
| ~ sum(X4,X5,X1)
| product(X1,X2,X3) ),
c_0_30 ).
cnf(c_0_38,negated_conjecture,
sum(additive_identity,c,additive_identity),
sum_7 ).
cnf(c_0_39,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_40,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
c_0_31 ).
cnf(c_0_41,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_42,hypothesis,
( ~ product(additive_identity,X4,X1)
| ~ product(b,X4,X2)
| ~ product(b,X4,X3)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_43,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(X1,multiplicative_inverse(X1),multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_44,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
c_0_36 ).
cnf(c_0_45,plain,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
inference(fof_simplification,[status(thm)],[totality_of_multiplication]) ).
cnf(c_0_46,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_multiplicative_inverse]) ).
cnf(c_0_47,negated_conjecture,
( ~ sum(X4,X3,X1)
| ~ product(X4,X2,additive_identity)
| ~ product(X3,X2,c)
| product(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_48,hypothesis,
sum(additive_identity,c,c),
inference(spm,[status(thm)],[c_0_26,c_0_39]) ).
cnf(c_0_49,hypothesis,
product(multiplicative_identity,c,c),
inference(spm,[status(thm)],[c_0_40,c_0_39]) ).
cnf(c_0_50,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_51,plain,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[associativity_addition_2]) ).
cnf(c_0_52,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_53,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_54,hypothesis,
( ~ product(additive_identity,multiplicative_inverse(b),X1)
| ~ product(b,multiplicative_inverse(b),X2)
| sum(X1,X2,multiplicative_identity) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_27])]),c_0_44]) ).
cnf(c_0_55,plain,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
c_0_45 ).
cnf(c_0_56,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
c_0_46 ).
cnf(c_0_57,plain,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[associativity_multiplication_2]) ).
cnf(c_0_58,hypothesis,
( ~ product(additive_identity,X1,additive_identity)
| ~ product(c,X1,c)
| product(c,X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_59,hypothesis,
product(c,multiplicative_identity,c),
inference(spm,[status(thm)],[c_0_34,c_0_49]) ).
cnf(c_0_60,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(spm,[status(thm)],[c_0_34,c_0_50]) ).
cnf(c_0_61,plain,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
c_0_51 ).
cnf(c_0_62,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
c_0_52 ).
cnf(c_0_63,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_26,c_0_53]) ).
cnf(c_0_64,hypothesis,
( ~ product(additive_identity,multiplicative_inverse(b),X1)
| sum(X1,multiplicative_identity,multiplicative_identity) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_43]),c_0_27])]),c_0_44]) ).
cnf(c_0_65,plain,
( ~ defined(X2)
| ~ defined(X1)
| sum(additive_identity,X2,additive_identity)
| product(X1,multiplicative_inverse(X2),multiply(X1,multiplicative_inverse(X2))) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_66,plain,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X1,X2)) ),
inference(fof_simplification,[status(thm)],[totality_of_addition]) ).
cnf(c_0_67,plain,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
c_0_57 ).
cnf(c_0_68,negated_conjecture,
product(a,b,c),
product_6 ).
cnf(c_0_69,hypothesis,
product(c,multiplicative_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60])]) ).
cnf(c_0_70,negated_conjecture,
( ~ sum(X3,additive_identity,X1)
| ~ sum(X3,additive_identity,X2)
| sum(X1,c,X2) ),
inference(spm,[status(thm)],[c_0_61,c_0_38]) ).
cnf(c_0_71,plain,
sum(multiplicative_identity,additive_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_72,hypothesis,
sum(multiply(additive_identity,multiplicative_inverse(b)),multiplicative_identity,multiplicative_identity),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_41]),c_0_27])]),c_0_44]) ).
cnf(c_0_73,plain,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X1,X2)) ),
c_0_66 ).
cnf(c_0_74,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[associativity_multiplication_1]) ).
cnf(c_0_75,negated_conjecture,
( ~ product(X3,a,X1)
| ~ product(X3,c,X2)
| product(X1,b,X2) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_76,hypothesis,
product(multiplicative_identity,c,additive_identity),
inference(spm,[status(thm)],[c_0_34,c_0_69]) ).
cnf(c_0_77,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_78,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[associativity_addition_1]) ).
cnf(c_0_79,negated_conjecture,
( ~ sum(multiplicative_identity,additive_identity,X1)
| sum(X1,c,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_80,hypothesis,
sum(multiplicative_identity,multiply(additive_identity,multiplicative_inverse(b)),multiplicative_identity),
inference(spm,[status(thm)],[c_0_62,c_0_72]) ).
cnf(c_0_81,hypothesis,
( ~ defined(X1)
| sum(c,X1,add(c,X1)) ),
inference(spm,[status(thm)],[c_0_73,c_0_39]) ).
cnf(c_0_82,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
c_0_74 ).
cnf(c_0_83,hypothesis,
product(multiplicative_identity,b,b),
inference(spm,[status(thm)],[c_0_40,c_0_27]) ).
cnf(c_0_84,negated_conjecture,
( ~ product(multiplicative_identity,a,X1)
| product(X1,b,additive_identity) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_85,hypothesis,
product(multiplicative_identity,a,a),
inference(spm,[status(thm)],[c_0_40,c_0_77]) ).
cnf(c_0_86,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
c_0_78 ).
cnf(c_0_87,negated_conjecture,
sum(multiplicative_identity,c,multiplicative_identity),
inference(spm,[status(thm)],[c_0_79,c_0_71]) ).
cnf(c_0_88,hypothesis,
( ~ sum(X3,multiplicative_identity,X1)
| ~ sum(X3,multiplicative_identity,X2)
| sum(X1,multiply(additive_identity,multiplicative_inverse(b)),X2) ),
inference(spm,[status(thm)],[c_0_61,c_0_80]) ).
cnf(c_0_89,hypothesis,
sum(c,multiplicative_identity,add(c,multiplicative_identity)),
inference(spm,[status(thm)],[c_0_81,c_0_53]) ).
cnf(c_0_90,hypothesis,
sum(additive_identity,a,a),
inference(spm,[status(thm)],[c_0_26,c_0_77]) ).
cnf(c_0_91,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_4]) ).
cnf(c_0_92,hypothesis,
( ~ product(X1,X3,multiplicative_identity)
| ~ product(X3,b,X2)
| product(X1,X2,b) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_93,hypothesis,
product(a,b,additive_identity),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_94,hypothesis,
( ~ sum(X1,X3,multiplicative_identity)
| ~ sum(X3,multiply(additive_identity,multiplicative_inverse(b)),X2)
| sum(X1,X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_86,c_0_80]) ).
cnf(c_0_95,negated_conjecture,
sum(c,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_62,c_0_87]) ).
cnf(c_0_96,hypothesis,
( ~ sum(c,multiplicative_identity,X1)
| sum(X1,multiply(additive_identity,multiplicative_inverse(b)),add(c,multiplicative_identity)) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_97,hypothesis,
( ~ product(additive_identity,X4,X1)
| ~ product(a,X4,X2)
| ~ product(a,X4,X3)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_32,c_0_90]) ).
cnf(c_0_98,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
c_0_91 ).
cnf(c_0_99,hypothesis,
( ~ product(X1,a,multiplicative_identity)
| product(X1,additive_identity,b) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_100,negated_conjecture,
( ~ sum(multiplicative_identity,multiply(additive_identity,multiplicative_inverse(b)),X1)
| sum(c,X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_101,negated_conjecture,
sum(multiplicative_identity,multiply(additive_identity,multiplicative_inverse(b)),add(c,multiplicative_identity)),
inference(spm,[status(thm)],[c_0_96,c_0_95]) ).
cnf(c_0_102,hypothesis,
( ~ product(additive_identity,multiplicative_inverse(a),X1)
| ~ product(a,multiplicative_inverse(a),X2)
| sum(X1,X2,multiplicative_identity) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_43]),c_0_77])]),c_0_98]) ).
cnf(c_0_103,hypothesis,
product(multiplicative_inverse(a),additive_identity,b),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_35]),c_0_77])]),c_0_98]) ).
cnf(c_0_104,negated_conjecture,
sum(c,add(c,multiplicative_identity),multiplicative_identity),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_105,negated_conjecture,
( ~ sum(X1,X3,additive_identity)
| ~ sum(X3,c,X2)
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_86,c_0_38]) ).
cnf(c_0_106,hypothesis,
sum(multiplicative_identity,c,add(c,multiplicative_identity)),
inference(spm,[status(thm)],[c_0_62,c_0_89]) ).
cnf(c_0_107,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_addition]) ).
cnf(c_0_108,hypothesis,
( ~ product(additive_identity,multiplicative_inverse(a),X1)
| sum(X1,multiplicative_identity,multiplicative_identity) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_43]),c_0_77])]),c_0_98]) ).
cnf(c_0_109,hypothesis,
product(additive_identity,multiplicative_inverse(a),b),
inference(spm,[status(thm)],[c_0_34,c_0_103]) ).
cnf(c_0_110,negated_conjecture,
sum(add(c,multiplicative_identity),c,multiplicative_identity),
inference(spm,[status(thm)],[c_0_62,c_0_104]) ).
cnf(c_0_111,negated_conjecture,
( ~ sum(X1,multiplicative_identity,additive_identity)
| sum(X1,add(c,multiplicative_identity),additive_identity) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_112,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
c_0_107 ).
cnf(c_0_113,hypothesis,
sum(b,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_114,negated_conjecture,
( ~ sum(X1,add(c,multiplicative_identity),additive_identity)
| sum(X1,multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_105,c_0_110]) ).
cnf(c_0_115,negated_conjecture,
sum(additive_inverse(multiplicative_identity),add(c,multiplicative_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_53])]) ).
cnf(c_0_116,hypothesis,
( ~ sum(X1,X3,additive_identity)
| ~ sum(X3,b,X2)
| sum(X1,X2,b) ),
inference(spm,[status(thm)],[c_0_86,c_0_33]) ).
cnf(c_0_117,hypothesis,
sum(multiplicative_identity,b,multiplicative_identity),
inference(spm,[status(thm)],[c_0_62,c_0_113]) ).
cnf(c_0_118,plain,
( ~ sum(X3,multiplicative_identity,X1)
| ~ sum(X3,multiplicative_identity,X2)
| sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_61,c_0_71]) ).
cnf(c_0_119,negated_conjecture,
sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_120,hypothesis,
( ~ sum(X1,multiplicative_identity,additive_identity)
| sum(X1,multiplicative_identity,b) ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_121,negated_conjecture,
( ~ sum(additive_inverse(multiplicative_identity),multiplicative_identity,X1)
| sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_122,hypothesis,
sum(additive_inverse(multiplicative_identity),multiplicative_identity,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_112]),c_0_53])]) ).
cnf(c_0_123,hypothesis,
sum(b,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_124,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_123]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD041-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 15:42:01 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 8.25/1.65 % Version: 3.5.1
% 8.25/1.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 8.25/1.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.25/1.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.25/1.65 % Starting new_bool_3 with 300s (1) cores
% 8.25/1.65 % Starting new_bool_1 with 300s (1) cores
% 8.25/1.65 % Starting sh5l with 300s (1) cores
% 8.25/1.65 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2244907 completed with status 0
% 8.25/1.65 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 8.25/1.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 8.25/1.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.25/1.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.25/1.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.25/1.65 % No SInE strategy applied
% 8.25/1.65 % Search class: FGUNF-FFMM21-SFFFFFNN
% 8.25/1.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 8.25/1.65 % Starting SubtermCWHack with 136s (1) cores
% 8.25/1.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 8.25/1.65 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 296s (1) cores
% 8.25/1.65 % Starting new_bool_3 with 269s (1) cores
% 8.25/1.65 % Starting G-E--_107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S08BN with 136s (1) cores
% 8.25/1.65 % G-E--_107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S08BN with pid 2244925 completed with status 0
% 8.25/1.65 % Result found by G-E--_107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S08BN
% 8.25/1.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 8.25/1.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.25/1.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.25/1.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.25/1.65 % No SInE strategy applied
% 8.25/1.65 % Search class: FGUNF-FFMM21-SFFFFFNN
% 8.25/1.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 8.25/1.65 % Starting SubtermCWHack with 136s (1) cores
% 8.25/1.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 8.25/1.65 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 296s (1) cores
% 8.25/1.65 % Starting new_bool_3 with 269s (1) cores
% 8.25/1.65 % Starting G-E--_107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S08BN with 136s (1) cores
% 8.25/1.65 % Preprocessing time : 0.002 s
% 8.25/1.65 % Presaturation interreduction done
% 8.25/1.65
% 8.25/1.65 % Proof found!
% 8.25/1.65 % SZS status Unsatisfiable
% 8.25/1.65 % SZS output start CNFRefutation
% See solution above
% 8.25/1.65 % Parsed axioms : 33
% 8.25/1.65 % Removed by relevancy pruning/SinE : 0
% 8.25/1.65 % Initial clauses : 33
% 8.25/1.65 % Removed in clause preprocessing : 0
% 8.25/1.65 % Initial clauses in saturation : 33
% 8.25/1.65 % Processed clauses : 3812
% 8.25/1.65 % ...of these trivial : 366
% 8.25/1.65 % ...subsumed : 246
% 8.25/1.65 % ...remaining for further processing : 3200
% 8.25/1.65 % Other redundant clauses eliminated : 0
% 8.25/1.65 % Clauses deleted for lack of memory : 0
% 8.25/1.65 % Backward-subsumed : 3
% 8.25/1.65 % Backward-rewritten : 2
% 8.25/1.65 % Generated clauses : 85166
% 8.25/1.65 % ...of the previous two non-redundant : 79001
% 8.25/1.65 % ...aggressively subsumed : 0
% 8.25/1.65 % Contextual simplify-reflections : 2
% 8.25/1.65 % Paramodulations : 85166
% 8.25/1.65 % Factorizations : 0
% 8.25/1.65 % NegExts : 0
% 8.25/1.65 % Equation resolutions : 0
% 8.25/1.65 % Disequality decompositions : 0
% 8.25/1.65 % Total rewrite steps : 10395
% 8.25/1.65 % ...of those cached : 9431
% 8.25/1.65 % Propositional unsat checks : 0
% 8.25/1.65 % Propositional check models : 0
% 8.25/1.65 % Propositional check unsatisfiable : 0
% 8.25/1.65 % Propositional clauses : 0
% 8.25/1.65 % Propositional clauses after purity: 0
% 8.25/1.65 % Propositional unsat core size : 0
% 8.25/1.65 % Propositional preprocessing time : 0.000
% 8.25/1.65 % Propositional encoding time : 0.000
% 8.25/1.65 % Propositional solver time : 0.000
% 8.25/1.65 % Success case prop preproc time : 0.000
% 8.25/1.65 % Success case prop encoding time : 0.000
% 8.25/1.65 % Success case prop solver time : 0.000
% 8.25/1.65 % Current number of processed clauses : 3162
% 8.25/1.65 % Positive orientable unit clauses : 1286
% 8.25/1.65 % Positive unorientable unit clauses: 0
% 8.25/1.65 % Negative unit clauses : 3
% 8.25/1.65 % Non-unit-clauses : 1873
% 8.25/1.65 % Current number of unprocessed clauses: 75255
% 8.25/1.65 % ...number of literals in the above : 231046
% 8.25/1.65 % Current number of archived formulas : 0
% 8.25/1.65 % Current number of archived clauses : 38
% 8.25/1.65 % Clause-clause subsumption calls (NU) : 147823
% 8.25/1.65 % Rec. Clause-clause subsumption calls : 114840
% 8.25/1.65 % Non-unit clause-clause subsumptions : 251
% 8.25/1.65 % Unit Clause-clause subsumption calls : 20212
% 8.25/1.65 % Rewrite failures with RHS unbound : 0
% 8.25/1.65 % BW rewrite match attempts : 1233
% 8.25/1.65 % BW rewrite match successes : 2
% 8.25/1.65 % Condensation attempts : 0
% 8.25/1.65 % Condensation successes : 0
% 8.25/1.65 % Termbank termtop insertions : 1430857
% 8.25/1.65 % Search garbage collected termcells : 118
% 8.25/1.65
% 8.25/1.65 % -------------------------------------------------
% 8.25/1.65 % User time : 1.126 s
% 8.25/1.65 % System time : 0.071 s
% 8.25/1.65 % Total time : 1.197 s
% 8.25/1.65 % Maximum resident set size: 3652 pages
% 8.25/1.65
% 8.25/1.65 % -------------------------------------------------
% 8.25/1.65 % User time : 5.751 s
% 8.25/1.65 % System time : 0.255 s
% 8.25/1.65 % Total time : 6.006 s
% 8.25/1.65 % Maximum resident set size: 4608 pages
% 8.25/1.65 % E exiting
%------------------------------------------------------------------------------