%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD040-3 : 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 : n011.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 1.97s 0.77s
% Output : CNFRefutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 24
% Syntax : Number of clauses : 129 ( 34 unt; 10 nHn; 129 RR)
% Number of literals : 313 ( 0 equ; 182 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 245 ( 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(commutativity_multiplication,axiom,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
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(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(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(commutativity_addition,axiom,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
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(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_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(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(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(sum_3,negated_conjecture,
sum(additive_identity,additive_identity,multiplicative_inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_3) ).
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(totality_of_multiplication,axiom,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
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(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(well_definedness_of_additive_inverse,axiom,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
cnf(totality_of_order_relation,axiom,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_order_relation) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ less_or_equal(X3,X4)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(different_identities,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',different_identities) ).
cnf(antisymmetry_of_order_relation,axiom,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
cnf(c_0_24,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_25,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_2]) ).
cnf(c_0_26,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_27,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
c_0_24 ).
cnf(c_0_28,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_29,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
c_0_25 ).
cnf(c_0_30,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_31,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
c_0_26 ).
cnf(c_0_32,hypothesis,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_33,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
c_0_30 ).
cnf(c_0_34,hypothesis,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,hypothesis,
( ~ product(X1,X3,a)
| ~ product(X3,multiplicative_inverse(a),X2)
| product(X1,X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_36,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_37,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_38,hypothesis,
( ~ product(X1,a,a)
| product(X1,multiplicative_identity,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_35,c_0_34]) ).
cnf(c_0_39,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
c_0_36 ).
cnf(c_0_40,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_41,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_42,plain,
( ~ product(X5,X7,X2)
| ~ product(X4,X7,X1)
| ~ product(X6,X7,X3)
| ~ sum(X4,X5,X6)
| sum(X1,X2,X3) ),
c_0_37 ).
cnf(c_0_43,hypothesis,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_28])]) ).
cnf(c_0_44,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_45,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_46,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_47,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
c_0_40 ).
cnf(c_0_48,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
c_0_41 ).
cnf(c_0_49,hypothesis,
( ~ sum(X4,X3,multiplicative_identity)
| ~ product(X4,multiplicative_identity,X1)
| ~ product(X3,multiplicative_identity,X2)
| sum(X1,X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_51,plain,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
c_0_44 ).
cnf(c_0_52,negated_conjecture,
sum(additive_identity,additive_identity,multiplicative_inverse(a)),
sum_3 ).
cnf(c_0_53,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_addition]) ).
cnf(c_0_54,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
c_0_45 ).
cnf(c_0_55,plain,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
c_0_46 ).
cnf(c_0_56,plain,
( ~ defined(X1)
| sum(X1,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_57,hypothesis,
( ~ sum(X2,multiplicative_identity,multiplicative_identity)
| ~ product(X2,multiplicative_identity,X1)
| sum(X1,multiplicative_identity,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_39]),c_0_50])]) ).
cnf(c_0_58,negated_conjecture,
( ~ sum(X3,additive_identity,X1)
| ~ sum(X3,multiplicative_inverse(a),X2)
| sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
c_0_53 ).
cnf(c_0_60,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_28]),c_0_29]) ).
cnf(c_0_61,hypothesis,
( ~ product(X3,multiplicative_identity,X1)
| ~ product(X3,multiplicative_identity,X2)
| product(X1,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_43]) ).
cnf(c_0_62,plain,
( ~ defined(X1)
| product(X1,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_39]) ).
cnf(c_0_63,plain,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
inference(fof_simplification,[status(thm)],[totality_of_multiplication]) ).
cnf(c_0_64,plain,
( ~ sum(X4,X3,X1)
| ~ sum(X4,X3,X2)
| ~ defined(X3)
| sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_56]) ).
cnf(c_0_65,hypothesis,
( ~ product(additive_identity,multiplicative_identity,X1)
| sum(X1,multiplicative_identity,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_48]),c_0_50])]) ).
cnf(c_0_66,negated_conjecture,
( ~ sum(additive_inverse(multiplicative_inverse(a)),additive_identity,X1)
| sum(X1,additive_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_67,hypothesis,
( ~ product(X3,multiplicative_identity,X2)
| ~ product(X3,multiplicative_inverse(a),X1)
| product(X1,a,X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_32]) ).
cnf(c_0_68,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_35,c_0_39]),c_0_60])]) ).
cnf(c_0_69,hypothesis,
( ~ defined(X2)
| ~ product(X2,multiplicative_identity,X1)
| product(X1,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_70,plain,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
c_0_63 ).
cnf(c_0_71,hypothesis,
( ~ sum(X2,multiplicative_identity,X1)
| ~ product(additive_identity,multiplicative_identity,X2)
| sum(X1,additive_identity,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_50])]) ).
cnf(c_0_72,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_73,plain,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X1,X2)) ),
inference(fof_simplification,[status(thm)],[totality_of_addition]) ).
cnf(c_0_74,negated_conjecture,
( ~ defined(additive_inverse(multiplicative_inverse(a)))
| sum(additive_inverse(multiplicative_inverse(a)),additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_66,c_0_56]) ).
cnf(c_0_75,hypothesis,
( ~ product(X2,multiplicative_identity,X1)
| ~ product(X2,multiplicative_identity,a)
| product(multiplicative_identity,a,X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_76,hypothesis,
( ~ defined(X1)
| product(multiply(X1,multiplicative_identity),multiplicative_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_50])]) ).
cnf(c_0_77,hypothesis,
( ~ sum(additive_identity,multiplicative_identity,X1)
| sum(X1,additive_identity,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_62]),c_0_72])]) ).
cnf(c_0_78,plain,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X1,X2)) ),
c_0_73 ).
cnf(c_0_79,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_80,negated_conjecture,
( ~ defined(additive_inverse(multiplicative_inverse(a)))
| sum(additive_identity,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_66,c_0_74]) ).
cnf(c_0_81,plain,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_additive_inverse]) ).
cnf(c_0_82,hypothesis,
( ~ product(multiply(a,multiplicative_identity),multiplicative_identity,X1)
| product(multiplicative_identity,a,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_28])]) ).
cnf(c_0_83,hypothesis,
sum(add(additive_identity,multiplicative_identity),additive_identity,multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_50]),c_0_72])]) ).
cnf(c_0_84,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
c_0_79 ).
cnf(c_0_85,negated_conjecture,
( ~ sum(additive_identity,additive_identity,X1)
| ~ defined(additive_inverse(multiplicative_inverse(a)))
| sum(X1,additive_identity,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_80]),c_0_72])]) ).
cnf(c_0_86,plain,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
c_0_81 ).
cnf(c_0_87,hypothesis,
product(multiplicative_identity,a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_76]),c_0_28])]) ).
cnf(c_0_88,plain,
( ~ sum(X5,X4,X1)
| ~ sum(X5,add(X4,X2),X3)
| ~ defined(X4)
| ~ defined(X2)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_51,c_0_78]) ).
cnf(c_0_89,hypothesis,
sum(additive_identity,add(additive_identity,multiplicative_identity),multiplicative_identity),
inference(spm,[status(thm)],[c_0_47,c_0_83]) ).
cnf(c_0_90,negated_conjecture,
( ~ sum(X1,X3,additive_identity)
| ~ sum(X3,additive_identity,X2)
| sum(X1,X2,multiplicative_inverse(a)) ),
inference(spm,[status(thm)],[c_0_84,c_0_52]) ).
cnf(c_0_91,negated_conjecture,
( ~ sum(additive_identity,additive_identity,X1)
| sum(X1,additive_identity,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_60])]) ).
cnf(c_0_92,hypothesis,
( ~ sum(X4,X3,multiplicative_identity)
| ~ product(X4,a,X1)
| ~ product(X3,a,X2)
| sum(X1,X2,a) ),
inference(spm,[status(thm)],[c_0_42,c_0_87]) ).
cnf(c_0_93,hypothesis,
( ~ sum(additive_identity,additive_identity,X1)
| sum(X1,multiplicative_identity,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_50]),c_0_72])]) ).
cnf(c_0_94,negated_conjecture,
( ~ 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_90,c_0_48]),c_0_72])]) ).
cnf(c_0_95,negated_conjecture,
sum(additive_identity,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_56]),c_0_72])]) ).
cnf(c_0_96,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_92,c_0_39]),c_0_28])]) ).
cnf(c_0_97,negated_conjecture,
sum(multiplicative_inverse(a),multiplicative_identity,multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95])]) ).
cnf(c_0_98,hypothesis,
( ~ product(X3,a,X2)
| ~ product(X1,X3,multiplicative_inverse(a))
| product(X1,X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_33,c_0_32]) ).
cnf(c_0_99,hypothesis,
sum(multiplicative_identity,additive_identity,multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_48]),c_0_50])]) ).
cnf(c_0_100,negated_conjecture,
( ~ product(multiplicative_inverse(a),a,X1)
| sum(X1,a,a) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_101,hypothesis,
( ~ product(multiplicative_identity,a,X1)
| product(multiplicative_inverse(a),X1,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_62]),c_0_60])]) ).
cnf(c_0_102,hypothesis,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_47,c_0_99]) ).
cnf(c_0_103,hypothesis,
sum(multiplicative_identity,a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_87])]) ).
cnf(c_0_104,hypothesis,
( ~ sum(X1,X3,additive_identity)
| ~ sum(X3,multiplicative_identity,X2)
| sum(X1,X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_84,c_0_102]) ).
cnf(c_0_105,hypothesis,
sum(a,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_47,c_0_103]) ).
cnf(c_0_106,plain,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[totality_of_order_relation]) ).
cnf(c_0_107,hypothesis,
( ~ sum(X1,a,additive_identity)
| sum(X1,a,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_108,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ less_or_equal(X3,X4)
| less_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[compatibility_of_order_relation_and_addition]) ).
cnf(c_0_109,plain,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
c_0_106 ).
cnf(c_0_110,plain,
( ~ defined(X1)
| sum(X1,additive_inverse(X1),additive_identity) ),
inference(spm,[status(thm)],[c_0_47,c_0_59]) ).
cnf(c_0_111,hypothesis,
sum(additive_inverse(a),a,multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_59]),c_0_28])]) ).
cnf(c_0_112,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(fof_simplification,[status(thm)],[different_identities]) ).
cnf(c_0_113,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
inference(fof_simplification,[status(thm)],[antisymmetry_of_order_relation]) ).
cnf(c_0_114,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ less_or_equal(X3,X4)
| less_or_equal(X1,X2) ),
c_0_108 ).
cnf(c_0_115,hypothesis,
( ~ defined(X1)
| less_or_equal(a,X1)
| less_or_equal(X1,a) ),
inference(spm,[status(thm)],[c_0_109,c_0_28]) ).
cnf(c_0_116,plain,
( ~ sum(X1,X4,X3)
| ~ sum(X4,additive_inverse(X3),X2)
| ~ defined(X3)
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_84,c_0_110]) ).
cnf(c_0_117,hypothesis,
sum(a,additive_inverse(a),multiplicative_identity),
inference(spm,[status(thm)],[c_0_47,c_0_111]) ).
cnf(c_0_118,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
c_0_112 ).
cnf(c_0_119,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
c_0_113 ).
cnf(c_0_120,plain,
( ~ sum(X2,additive_inverse(X3),X1)
| ~ defined(X3)
| ~ less_or_equal(X2,X3)
| less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_114,c_0_110]) ).
cnf(c_0_121,hypothesis,
less_or_equal(a,a),
inference(spm,[status(thm)],[c_0_115,c_0_28]) ).
cnf(c_0_122,hypothesis,
( ~ sum(X1,a,a)
| sum(X1,multiplicative_identity,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_28])]) ).
cnf(c_0_123,plain,
( ~ less_or_equal(additive_identity,multiplicative_identity)
| ~ less_or_equal(multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_124,hypothesis,
less_or_equal(multiplicative_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_117]),c_0_121]),c_0_28])]) ).
cnf(c_0_125,plain,
( ~ sum(X3,X2,X1)
| ~ defined(X2)
| ~ less_or_equal(X3,additive_identity)
| less_or_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_114,c_0_48]) ).
cnf(c_0_126,hypothesis,
sum(multiplicative_identity,multiplicative_identity,additive_identity),
inference(spm,[status(thm)],[c_0_122,c_0_103]) ).
cnf(c_0_127,plain,
~ less_or_equal(additive_identity,multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_124])]) ).
cnf(c_0_128,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_124]),c_0_50])]),c_0_127]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD040-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n011.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 21 15:39:57 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 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
% 1.97/0.77 % Version: 3.5.1
% 1.97/0.77 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.97/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.97/0.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.97/0.77 % Starting new_bool_3 with 300s (1) cores
% 1.97/0.77 % Starting new_bool_1 with 300s (1) cores
% 1.97/0.77 % Starting sh5l with 300s (1) cores
% 1.97/0.77 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2267675 completed with status 0
% 1.97/0.77 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.97/0.77 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.97/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.97/0.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.97/0.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.97/0.77 % No SInE strategy applied
% 1.97/0.77 % Search class: FGUNF-FFMS21-SFFFFFNN
% 1.97/0.77 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 1.97/0.77 % Starting SubtermCWHack with 136s (1) cores
% 1.97/0.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.97/0.77 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 1.97/0.77 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.97/0.77 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.97/0.77 % G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 2267685 completed with status 0
% 1.97/0.77 % Result found by G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 1.97/0.77 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.97/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.97/0.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.97/0.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.97/0.77 % No SInE strategy applied
% 1.97/0.77 % Search class: FGUNF-FFMS21-SFFFFFNN
% 1.97/0.77 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 1.97/0.77 % Starting SubtermCWHack with 136s (1) cores
% 1.97/0.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.97/0.77 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 1.97/0.77 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.97/0.77 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.97/0.77 % Preprocessing time : 0.001 s
% 1.97/0.77 % Presaturation interreduction done
% 1.97/0.77
% 1.97/0.77 % Proof found!
% 1.97/0.77 % SZS status Unsatisfiable
% 1.97/0.77 % SZS output start CNFRefutation
% See solution above
% 1.97/0.77 % Parsed axioms : 29
% 1.97/0.77 % Removed by relevancy pruning/SinE : 0
% 1.97/0.77 % Initial clauses : 29
% 1.97/0.77 % Removed in clause preprocessing : 0
% 1.97/0.77 % Initial clauses in saturation : 29
% 1.97/0.77 % Processed clauses : 2726
% 1.97/0.77 % ...of these trivial : 66
% 1.97/0.77 % ...subsumed : 1365
% 1.97/0.77 % ...remaining for further processing : 1295
% 1.97/0.77 % Other redundant clauses eliminated : 0
% 1.97/0.77 % Clauses deleted for lack of memory : 0
% 1.97/0.77 % Backward-subsumed : 129
% 1.97/0.77 % Backward-rewritten : 144
% 1.97/0.77 % Generated clauses : 14681
% 1.97/0.77 % ...of the previous two non-redundant : 11306
% 1.97/0.77 % ...aggressively subsumed : 0
% 1.97/0.77 % Contextual simplify-reflections : 6
% 1.97/0.77 % Paramodulations : 14677
% 1.97/0.77 % Factorizations : 0
% 1.97/0.77 % NegExts : 0
% 1.97/0.77 % Equation resolutions : 0
% 1.97/0.77 % Disequality decompositions : 0
% 1.97/0.77 % Total rewrite steps : 8036
% 1.97/0.77 % ...of those cached : 7921
% 1.97/0.77 % Propositional unsat checks : 0
% 1.97/0.77 % Propositional check models : 0
% 1.97/0.77 % Propositional check unsatisfiable : 0
% 1.97/0.77 % Propositional clauses : 0
% 1.97/0.77 % Propositional clauses after purity: 0
% 1.97/0.77 % Propositional unsat core size : 0
% 1.97/0.77 % Propositional preprocessing time : 0.000
% 1.97/0.77 % Propositional encoding time : 0.000
% 1.97/0.77 % Propositional solver time : 0.000
% 1.97/0.77 % Success case prop preproc time : 0.000
% 1.97/0.77 % Success case prop encoding time : 0.000
% 1.97/0.77 % Success case prop solver time : 0.000
% 1.97/0.77 % Current number of processed clauses : 989
% 1.97/0.77 % Positive orientable unit clauses : 142
% 1.97/0.77 % Positive unorientable unit clauses: 0
% 1.97/0.77 % Negative unit clauses : 22
% 1.97/0.77 % Non-unit-clauses : 825
% 1.97/0.77 % Current number of unprocessed clauses: 8361
% 1.97/0.77 % ...number of literals in the above : 29770
% 1.97/0.77 % Current number of archived formulas : 0
% 1.97/0.77 % Current number of archived clauses : 306
% 1.97/0.77 % Clause-clause subsumption calls (NU) : 69840
% 1.97/0.77 % Rec. Clause-clause subsumption calls : 48804
% 1.97/0.77 % Non-unit clause-clause subsumptions : 1325
% 1.97/0.77 % Unit Clause-clause subsumption calls : 7739
% 1.97/0.77 % Rewrite failures with RHS unbound : 0
% 1.97/0.77 % BW rewrite match attempts : 117
% 1.97/0.77 % BW rewrite match successes : 35
% 1.97/0.77 % Condensation attempts : 0
% 1.97/0.77 % Condensation successes : 0
% 1.97/0.77 % Termbank termtop insertions : 209973
% 1.97/0.77 % Search garbage collected termcells : 116
% 1.97/0.77
% 1.97/0.77 % -------------------------------------------------
% 1.97/0.77 % User time : 0.297 s
% 1.97/0.77 % System time : 0.010 s
% 1.97/0.77 % Total time : 0.307 s
% 1.97/0.77 % Maximum resident set size: 3660 pages
% 1.97/0.77
% 1.97/0.77 % -------------------------------------------------
% 1.97/0.77 % User time : 1.358 s
% 1.97/0.77 % System time : 0.059 s
% 1.97/0.77 % Total time : 1.417 s
% 1.97/0.77 % Maximum resident set size: 4608 pages
% 1.97/0.77 % E exiting
%------------------------------------------------------------------------------