%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : FLD011-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 12:23:07 PM UTC 2026
% Result : Unsatisfiable 7.31s 1.56s
% Output : CNFRefutation 7.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 19
% Syntax : Number of clauses : 131 ( 33 unt; 8 nHn; 131 RR)
% Number of literals : 319 ( 0 equ; 188 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 251 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(existence_of_inverse_multiplication,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(not_sum_2,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_2) ).
cnf(associativity_multiplication_2,axiom,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(associativity_multiplication_1,axiom,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
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/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
cnf(not_product_3,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_inverse(a)),a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_3) ).
cnf(associativity_addition_1,axiom,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(commutativity_addition,axiom,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(associativity_addition_2,axiom,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(totality_of_addition,axiom,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_addition) ).
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/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_2) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(c_0_19,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_20,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_2]) ).
cnf(c_0_21,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_22,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
c_0_19 ).
cnf(c_0_23,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_24,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
c_0_20 ).
cnf(c_0_25,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_26,plain,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
c_0_21 ).
cnf(c_0_27,hypothesis,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_28,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_29,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
c_0_25 ).
cnf(c_0_30,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_31,hypothesis,
( ~ product(X3,multiplicative_identity,X2)
| ~ product(X3,multiplicative_inverse(a),X1)
| product(X1,a,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
c_0_28 ).
cnf(c_0_33,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_23]),c_0_24]) ).
cnf(c_0_34,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
c_0_30 ).
cnf(c_0_35,hypothesis,
( ~ product(multiplicative_identity,multiplicative_identity,X1)
| product(multiplicative_inverse(a),a,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_36,hypothesis,
( ~ product(multiplicative_identity,multiplicative_identity,X1)
| product(a,multiplicative_inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_37,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_38,hypothesis,
( ~ product(multiplicative_identity,multiplicative_identity,X1)
| ~ product(a,multiplicative_identity,X2)
| product(X1,a,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_36]) ).
cnf(c_0_39,plain,
( ~ defined(X1)
| product(X1,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_32]) ).
cnf(c_0_40,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
c_0_37 ).
cnf(c_0_41,hypothesis,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(spm,[status(thm)],[c_0_34,c_0_27]) ).
cnf(c_0_42,hypothesis,
( ~ product(multiplicative_identity,multiplicative_identity,X1)
| product(X1,a,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_23])]) ).
cnf(c_0_43,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_44,hypothesis,
( ~ product(X1,X3,a)
| ~ product(X3,multiplicative_inverse(a),X2)
| product(X1,X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,hypothesis,
product(multiplicative_identity,a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_39]),c_0_43])]) ).
cnf(c_0_46,hypothesis,
( ~ product(X1,multiplicative_identity,a)
| product(X1,multiplicative_inverse(a),multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_32]),c_0_33])]) ).
cnf(c_0_47,hypothesis,
( ~ product(X1,X3,multiplicative_identity)
| ~ product(X3,a,X2)
| product(X1,X2,a) ),
inference(spm,[status(thm)],[c_0_40,c_0_45]) ).
cnf(c_0_48,hypothesis,
( ~ product(X1,multiplicative_identity,a)
| product(multiplicative_inverse(a),X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_34,c_0_46]) ).
cnf(c_0_49,hypothesis,
product(a,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_34,c_0_45]) ).
cnf(c_0_50,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_51,hypothesis,
( ~ product(X1,multiplicative_inverse(a),multiplicative_identity)
| product(X1,multiplicative_identity,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
cnf(c_0_52,hypothesis,
( sum(additive_identity,multiplicative_inverse(a),additive_identity)
| product(multiplicative_inverse(multiplicative_inverse(a)),multiplicative_inverse(a),multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_22,c_0_33]) ).
cnf(c_0_53,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_inverse(a)),a),
inference(fof_simplification,[status(thm)],[not_product_3]) ).
cnf(c_0_54,plain,
( ~ product(X5,X7,X2)
| ~ product(X4,X7,X1)
| ~ product(X6,X7,X3)
| ~ sum(X4,X5,X6)
| sum(X1,X2,X3) ),
c_0_50 ).
cnf(c_0_55,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_56,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_57,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_58,hypothesis,
( sum(additive_identity,multiplicative_inverse(a),additive_identity)
| product(multiplicative_inverse(multiplicative_inverse(a)),multiplicative_identity,a) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_inverse(a)),a),
c_0_53 ).
cnf(c_0_60,hypothesis,
( ~ sum(X4,X3,multiplicative_identity)
| ~ product(X4,a,X1)
| ~ product(X3,a,X2)
| sum(X1,X2,a) ),
inference(spm,[status(thm)],[c_0_54,c_0_45]) ).
cnf(c_0_61,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
c_0_55 ).
cnf(c_0_62,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
c_0_56 ).
cnf(c_0_63,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
c_0_57 ).
cnf(c_0_64,hypothesis,
sum(additive_identity,multiplicative_inverse(a),additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_58]),c_0_59]) ).
cnf(c_0_65,hypothesis,
( ~ sum(X2,multiplicative_identity,multiplicative_identity)
| ~ product(X2,a,X1)
| sum(X1,a,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_32]),c_0_23])]) ).
cnf(c_0_66,plain,
( ~ sum(X4,X3,X2)
| ~ sum(X1,X4,additive_identity)
| ~ defined(X3)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_67,hypothesis,
sum(multiplicative_inverse(a),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_68,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_69,hypothesis,
( ~ sum(multiplicative_inverse(a),multiplicative_identity,multiplicative_identity)
| sum(multiplicative_identity,a,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_48]),c_0_49])]) ).
cnf(c_0_70,hypothesis,
( ~ sum(additive_identity,X2,X1)
| ~ defined(X2)
| sum(multiplicative_inverse(a),X1,X2) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_71,plain,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
c_0_68 ).
cnf(c_0_72,plain,
( ~ defined(X1)
| sum(X1,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_62]) ).
cnf(c_0_73,hypothesis,
( ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| sum(multiplicative_identity,a,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_43])]) ).
cnf(c_0_74,plain,
( ~ sum(X4,X3,X1)
| ~ sum(X4,X3,X2)
| ~ defined(X3)
| sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_75,hypothesis,
sum(multiplicative_identity,a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_62]),c_0_43])]) ).
cnf(c_0_76,hypothesis,
( ~ sum(multiplicative_inverse(a),X2,X1)
| ~ defined(X2)
| sum(additive_identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_66,c_0_64]) ).
cnf(c_0_77,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_78,hypothesis,
( ~ sum(multiplicative_identity,a,X1)
| sum(X1,additive_identity,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_23])]) ).
cnf(c_0_79,hypothesis,
sum(additive_identity,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_67]),c_0_77])]) ).
cnf(c_0_80,plain,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X1,X2)) ),
inference(fof_simplification,[status(thm)],[totality_of_addition]) ).
cnf(c_0_81,hypothesis,
sum(a,additive_identity,a),
inference(spm,[status(thm)],[c_0_78,c_0_75]) ).
cnf(c_0_82,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_83,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_addition]) ).
cnf(c_0_84,hypothesis,
( ~ sum(additive_identity,X2,X1)
| ~ defined(X2)
| sum(additive_identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_66,c_0_79]) ).
cnf(c_0_85,plain,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X1,X2)) ),
c_0_80 ).
cnf(c_0_86,hypothesis,
( ~ sum(a,additive_identity,X1)
| sum(X1,additive_identity,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_81]),c_0_77])]) ).
cnf(c_0_87,plain,
( ~ sum(X6,X7,X3)
| ~ product(X5,X2,X7)
| ~ product(X4,X2,X6)
| ~ sum(X4,X5,X1)
| product(X1,X2,X3) ),
c_0_82 ).
cnf(c_0_88,hypothesis,
( ~ product(X1,a,a)
| product(X1,multiplicative_identity,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_44,c_0_41]) ).
cnf(c_0_89,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
c_0_83 ).
cnf(c_0_90,hypothesis,
( ~ sum(X1,X3,additive_identity)
| ~ sum(X3,additive_identity,X2)
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_61,c_0_79]) ).
cnf(c_0_91,hypothesis,
sum(additive_identity,additive_identity,multiplicative_inverse(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_64]),c_0_33])]) ).
cnf(c_0_92,plain,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X2,X1)) ),
inference(spm,[status(thm)],[c_0_63,c_0_85]) ).
cnf(c_0_93,hypothesis,
sum(add(a,additive_identity),additive_identity,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_85]),c_0_77]),c_0_23])]) ).
cnf(c_0_94,plain,
( ~ sum(X3,X5,X1)
| ~ sum(X4,X5,X2)
| ~ defined(X5)
| ~ product(X3,multiplicative_identity,X4)
| product(X1,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_87,c_0_39]) ).
cnf(c_0_95,hypothesis,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_32]),c_0_23])]) ).
cnf(c_0_96,plain,
( ~ defined(X1)
| sum(X1,additive_inverse(X1),additive_identity) ),
inference(spm,[status(thm)],[c_0_63,c_0_89]) ).
cnf(c_0_97,hypothesis,
( ~ sum(X1,additive_identity,additive_identity)
| sum(X1,multiplicative_inverse(a),additive_identity) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_98,plain,
( ~ sum(X5,X4,X1)
| ~ sum(X5,add(X2,X4),X3)
| ~ defined(X2)
| ~ defined(X4)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_71,c_0_92]) ).
cnf(c_0_99,hypothesis,
sum(additive_identity,add(a,additive_identity),a),
inference(spm,[status(thm)],[c_0_63,c_0_93]) ).
cnf(c_0_100,hypothesis,
( ~ sum(X3,additive_identity,X1)
| ~ sum(X3,additive_identity,X2)
| sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_79]) ).
cnf(c_0_101,hypothesis,
( ~ sum(multiplicative_identity,X3,X1)
| ~ sum(multiplicative_identity,X3,X2)
| ~ defined(X3)
| product(X1,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_102,plain,
( ~ sum(X4,X2,X1)
| ~ sum(X4,additive_identity,X3)
| ~ defined(X2)
| sum(X1,additive_inverse(X2),X3) ),
inference(spm,[status(thm)],[c_0_71,c_0_96]) ).
cnf(c_0_103,hypothesis,
( ~ sum(X1,additive_identity,additive_identity)
| sum(multiplicative_inverse(a),X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_63,c_0_97]) ).
cnf(c_0_104,hypothesis,
( ~ sum(additive_identity,additive_identity,X1)
| sum(X1,a,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_77]),c_0_23])]) ).
cnf(c_0_105,hypothesis,
( ~ sum(additive_identity,additive_identity,X1)
| sum(X1,additive_identity,multiplicative_inverse(a)) ),
inference(spm,[status(thm)],[c_0_100,c_0_91]) ).
cnf(c_0_106,plain,
( ~ defined(X3)
| ~ product(X4,X3,X2)
| ~ product(X1,X4,multiplicative_identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_40,c_0_32]) ).
cnf(c_0_107,hypothesis,
( ~ sum(multiplicative_identity,additive_identity,X1)
| product(X1,multiplicative_identity,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_72]),c_0_77]),c_0_43])]) ).
cnf(c_0_108,hypothesis,
( ~ sum(multiplicative_inverse(a),X2,X1)
| ~ defined(X2)
| sum(X1,additive_inverse(X2),additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_79])]) ).
cnf(c_0_109,hypothesis,
sum(multiplicative_inverse(a),a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_79])]) ).
cnf(c_0_110,hypothesis,
( ~ defined(X2)
| ~ product(multiplicative_inverse(a),X2,X1)
| product(a,X1,X2) ),
inference(spm,[status(thm)],[c_0_106,c_0_41]) ).
cnf(c_0_111,hypothesis,
( ~ sum(multiplicative_identity,additive_identity,X1)
| product(multiplicative_identity,X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_34,c_0_107]) ).
cnf(c_0_112,hypothesis,
( ~ sum(X1,X3,additive_identity)
| ~ sum(X3,additive_identity,X2)
| sum(X1,X2,multiplicative_inverse(a)) ),
inference(spm,[status(thm)],[c_0_61,c_0_91]) ).
cnf(c_0_113,hypothesis,
sum(a,additive_inverse(a),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_23])]) ).
cnf(c_0_114,hypothesis,
( ~ sum(X4,X3,a)
| ~ product(X4,multiplicative_identity,X1)
| ~ product(X3,multiplicative_identity,X2)
| sum(X1,X2,a) ),
inference(spm,[status(thm)],[c_0_54,c_0_49]) ).
cnf(c_0_115,hypothesis,
( ~ product(multiplicative_identity,multiplicative_identity,X1)
| product(a,X1,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_35]),c_0_23])]) ).
cnf(c_0_116,hypothesis,
( ~ sum(multiplicative_identity,additive_identity,multiplicative_inverse(a))
| product(multiplicative_identity,multiplicative_identity,a) ),
inference(spm,[status(thm)],[c_0_51,c_0_111]) ).
cnf(c_0_117,hypothesis,
( ~ sum(X1,additive_identity,additive_identity)
| sum(X1,additive_identity,multiplicative_inverse(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_62]),c_0_77])]) ).
cnf(c_0_118,hypothesis,
sum(additive_inverse(a),a,additive_identity),
inference(spm,[status(thm)],[c_0_63,c_0_113]) ).
cnf(c_0_119,hypothesis,
( ~ sum(X2,a,a)
| ~ product(X2,multiplicative_identity,X1)
| sum(X1,a,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_95])]) ).
cnf(c_0_120,hypothesis,
( ~ sum(multiplicative_identity,additive_identity,additive_identity)
| product(multiplicative_identity,multiplicative_identity,a) ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_121,hypothesis,
( ~ sum(additive_inverse(a),a,X1)
| sum(X1,additive_identity,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_118]),c_0_23])]) ).
cnf(c_0_122,plain,
( ~ sum(X1,X3,X2)
| ~ defined(X1)
| ~ defined(X3)
| sum(additive_inverse(X1),X2,X3) ),
inference(spm,[status(thm)],[c_0_66,c_0_89]) ).
cnf(c_0_123,hypothesis,
( ~ sum(multiplicative_identity,additive_identity,additive_identity)
| ~ sum(multiplicative_identity,a,a)
| sum(a,a,a) ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_124,hypothesis,
( ~ sum(a,additive_identity,additive_identity)
| sum(multiplicative_inverse(a),additive_identity,a) ),
inference(spm,[status(thm)],[c_0_86,c_0_117]) ).
cnf(c_0_125,hypothesis,
( ~ sum(a,X1,a)
| ~ defined(X1)
| sum(X1,additive_identity,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_23])]) ).
cnf(c_0_126,hypothesis,
( ~ sum(multiplicative_identity,additive_identity,additive_identity)
| sum(a,a,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_75])]) ).
cnf(c_0_127,hypothesis,
~ sum(a,additive_identity,additive_identity),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_124]),c_0_77])]),c_0_24]) ).
cnf(c_0_128,hypothesis,
sum(a,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_63,c_0_75]) ).
cnf(c_0_129,hypothesis,
~ sum(multiplicative_identity,additive_identity,additive_identity),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_23])]),c_0_127]) ).
cnf(c_0_130,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_128]),c_0_43])]),c_0_129]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD011-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.43 % Computer : n009.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 15:37:58 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.51 Running first-order theorem proving
% 0.18/0.51 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
% 7.31/1.56 % Version: 3.5.1
% 7.31/1.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.31/1.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.31/1.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.31/1.56 % Starting new_bool_3 with 300s (1) cores
% 7.31/1.56 % Starting new_bool_1 with 300s (1) cores
% 7.31/1.56 % Starting sh5l with 300s (1) cores
% 7.31/1.56 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2114745 completed with status 0
% 7.31/1.56 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 7.31/1.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.31/1.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.31/1.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.31/1.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.31/1.56 % No SInE strategy applied
% 7.31/1.56 % Search class: FGUNF-FFMS21-SFFFFFNN
% 7.31/1.56 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 7.31/1.56 % Starting SubtermCWHack with 136s (1) cores
% 7.31/1.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 7.31/1.56 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 7.31/1.56 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 7.31/1.56 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 7.31/1.56 % G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 2114753 completed with status 0
% 7.31/1.56 % Result found by G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 7.31/1.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.31/1.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.31/1.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.31/1.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.31/1.56 % No SInE strategy applied
% 7.31/1.56 % Search class: FGUNF-FFMS21-SFFFFFNN
% 7.31/1.56 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 7.31/1.56 % Starting SubtermCWHack with 136s (1) cores
% 7.31/1.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 7.31/1.56 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 7.31/1.56 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 7.31/1.56 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 7.31/1.56 % Preprocessing time : 0.002 s
% 7.31/1.56 % Presaturation interreduction done
% 7.31/1.56
% 7.31/1.56 % Proof found!
% 7.31/1.56 % SZS status Unsatisfiable
% 7.31/1.56 % SZS output start CNFRefutation
% See solution above
% 7.31/1.56 % Parsed axioms : 29
% 7.31/1.56 % Removed by relevancy pruning/SinE : 0
% 7.31/1.56 % Initial clauses : 29
% 7.31/1.56 % Removed in clause preprocessing : 0
% 7.31/1.56 % Initial clauses in saturation : 29
% 7.31/1.56 % Processed clauses : 8264
% 7.31/1.56 % ...of these trivial : 40
% 7.31/1.56 % ...subsumed : 5645
% 7.31/1.56 % ...remaining for further processing : 2578
% 7.31/1.56 % Other redundant clauses eliminated : 0
% 7.31/1.56 % Clauses deleted for lack of memory : 0
% 7.31/1.56 % Backward-subsumed : 414
% 7.31/1.56 % Backward-rewritten : 89
% 7.31/1.56 % Generated clauses : 48453
% 7.31/1.56 % ...of the previous two non-redundant : 42718
% 7.31/1.56 % ...aggressively subsumed : 0
% 7.31/1.56 % Contextual simplify-reflections : 26
% 7.31/1.56 % Paramodulations : 48453
% 7.31/1.56 % Factorizations : 0
% 7.31/1.56 % NegExts : 0
% 7.31/1.56 % Equation resolutions : 0
% 7.31/1.56 % Disequality decompositions : 0
% 7.31/1.56 % Total rewrite steps : 18562
% 7.31/1.56 % ...of those cached : 18460
% 7.31/1.56 % Propositional unsat checks : 0
% 7.31/1.56 % Propositional check models : 0
% 7.31/1.56 % Propositional check unsatisfiable : 0
% 7.31/1.56 % Propositional clauses : 0
% 7.31/1.56 % Propositional clauses after purity: 0
% 7.31/1.56 % Propositional unsat core size : 0
% 7.31/1.56 % Propositional preprocessing time : 0.000
% 7.31/1.56 % Propositional encoding time : 0.000
% 7.31/1.56 % Propositional solver time : 0.000
% 7.31/1.56 % Success case prop preproc time : 0.000
% 7.31/1.56 % Success case prop encoding time : 0.000
% 7.31/1.56 % Success case prop solver time : 0.000
% 7.31/1.56 % Current number of processed clauses : 2046
% 7.31/1.56 % Positive orientable unit clauses : 126
% 7.31/1.56 % Positive unorientable unit clauses: 0
% 7.31/1.56 % Negative unit clauses : 11
% 7.31/1.56 % Non-unit-clauses : 1909
% 7.31/1.56 % Current number of unprocessed clauses: 34261
% 7.31/1.56 % ...number of literals in the above : 133019
% 7.31/1.56 % Current number of archived formulas : 0
% 7.31/1.56 % Current number of archived clauses : 532
% 7.31/1.56 % Clause-clause subsumption calls (NU) : 541368
% 7.31/1.56 % Rec. Clause-clause subsumption calls : 416669
% 7.31/1.56 % Non-unit clause-clause subsumptions : 5832
% 7.31/1.56 % Unit Clause-clause subsumption calls : 20260
% 7.31/1.56 % Rewrite failures with RHS unbound : 0
% 7.31/1.56 % BW rewrite match attempts : 124
% 7.31/1.56 % BW rewrite match successes : 16
% 7.31/1.56 % Condensation attempts : 0
% 7.31/1.56 % Condensation successes : 0
% 7.31/1.56 % Termbank termtop insertions : 683977
% 7.31/1.56 % Search garbage collected termcells : 118
% 7.31/1.56
% 7.31/1.56 % -------------------------------------------------
% 7.31/1.56 % User time : 0.916 s
% 7.31/1.56 % System time : 0.036 s
% 7.31/1.56 % Total time : 0.952 s
% 7.31/1.56 % Maximum resident set size: 3660 pages
% 7.31/1.56
% 7.31/1.56 % -------------------------------------------------
% 7.31/1.56 % User time : 4.506 s
% 7.31/1.56 % System time : 0.166 s
% 7.31/1.56 % Total time : 4.672 s
% 7.31/1.56 % Maximum resident set size: 4864 pages
% 7.31/1.56 % E exiting
%------------------------------------------------------------------------------