%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD011-3 : 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 : 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 12:22:39 PM UTC 2026
% Result : Unsatisfiable 12.50s 2.28s
% Output : CNFRefutation 12.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 22
% Syntax : Number of clauses : 152 ( 44 unt; 17 nHn; 152 RR)
% Number of literals : 360 ( 0 equ; 210 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 252 ( 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/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(not_sum_2,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_2) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
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(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(totality_of_order_relation,axiom,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_order_relation) ).
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(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(antisymmetry_of_order_relation,axiom,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
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(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(not_product_3,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_inverse(a)),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_3) ).
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(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(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(different_identities,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',different_identities) ).
cnf(well_definedness_of_additive_inverse,axiom,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
cnf(well_definedness_of_addition,axiom,
( ~ defined(X2)
| ~ defined(X1)
| defined(add(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_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(c_0_22,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_23,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_2]) ).
cnf(c_0_24,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_25,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
c_0_22 ).
cnf(c_0_26,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_27,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
c_0_23 ).
cnf(c_0_28,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_29,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_30,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
c_0_24 ).
cnf(c_0_31,hypothesis,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_32,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_33,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
c_0_28 ).
cnf(c_0_34,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
c_0_29 ).
cnf(c_0_35,hypothesis,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
c_0_32 ).
cnf(c_0_37,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_26]),c_0_27]) ).
cnf(c_0_38,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_39,hypothesis,
( ~ product(X1,X3,a)
| ~ product(X3,multiplicative_inverse(a),X2)
| product(X1,X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
( ~ defined(X3)
| ~ product(X4,X3,X2)
| ~ product(X1,X4,multiplicative_identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_36]) ).
cnf(c_0_41,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_25,c_0_37]) ).
cnf(c_0_42,plain,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
c_0_38 ).
cnf(c_0_43,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_44,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_45,hypothesis,
( ~ product(X1,a,a)
| product(X1,multiplicative_identity,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_39,c_0_35]) ).
cnf(c_0_46,hypothesis,
( ~ defined(X2)
| ~ product(multiplicative_inverse(a),X2,X1)
| product(a,X1,X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_35]) ).
cnf(c_0_47,hypothesis,
( sum(additive_identity,multiplicative_inverse(a),additive_identity)
| product(multiplicative_inverse(a),multiplicative_inverse(multiplicative_inverse(a)),multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_30,c_0_41]) ).
cnf(c_0_48,hypothesis,
( sum(additive_identity,multiplicative_inverse(a),additive_identity)
| defined(multiplicative_inverse(multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_33,c_0_37]) ).
cnf(c_0_49,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_50,plain,
( ~ defined(X1)
| less_or_equal(multiplicative_identity,X1)
| less_or_equal(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_51,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_52,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_53,plain,
( ~ defined(X1)
| less_or_equal(additive_identity,X1)
| less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_42,c_0_44]) ).
cnf(c_0_54,hypothesis,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_36]),c_0_26])]) ).
cnf(c_0_55,hypothesis,
( sum(additive_identity,multiplicative_inverse(a),additive_identity)
| product(a,multiplicative_identity,multiplicative_inverse(multiplicative_inverse(a))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_56,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_inverse(a)),a),
inference(fof_simplification,[status(thm)],[not_product_3]) ).
cnf(c_0_57,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_58,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
c_0_49 ).
cnf(c_0_59,plain,
less_or_equal(multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_50,c_0_43]) ).
cnf(c_0_60,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
c_0_51 ).
cnf(c_0_61,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
c_0_52 ).
cnf(c_0_62,plain,
less_or_equal(additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_53,c_0_44]) ).
cnf(c_0_63,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_64,hypothesis,
( ~ defined(X2)
| ~ product(multiplicative_identity,X2,X1)
| product(multiplicative_identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_54]) ).
cnf(c_0_65,hypothesis,
( sum(additive_identity,multiplicative_inverse(a),additive_identity)
| product(multiplicative_identity,a,multiplicative_inverse(multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_30,c_0_55]) ).
cnf(c_0_66,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_inverse(a)),a),
c_0_56 ).
cnf(c_0_67,plain,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
c_0_57 ).
cnf(c_0_68,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_59])]) ).
cnf(c_0_69,plain,
( ~ sum(X4,X3,X2)
| ~ sum(X1,X4,additive_identity)
| ~ defined(X3)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_70,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_62]),c_0_62])]) ).
cnf(c_0_71,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
c_0_63 ).
cnf(c_0_72,hypothesis,
sum(additive_identity,multiplicative_inverse(a),additive_identity),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_26])]),c_0_66]) ).
cnf(c_0_73,plain,
( ~ sum(X3,additive_identity,X1)
| ~ sum(X3,multiplicative_identity,X2)
| sum(X1,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,plain,
( ~ sum(additive_identity,X2,X1)
| ~ defined(X2)
| sum(additive_identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_75,plain,
( ~ sum(X1,X3,additive_identity)
| ~ sum(X3,multiplicative_identity,X2)
| sum(X1,X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_60,c_0_68]) ).
cnf(c_0_76,plain,
( ~ sum(X3,additive_identity,X1)
| ~ sum(X3,additive_identity,X2)
| sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_67,c_0_70]) ).
cnf(c_0_77,hypothesis,
sum(multiplicative_inverse(a),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_78,plain,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X1,X2)) ),
inference(fof_simplification,[status(thm)],[totality_of_addition]) ).
cnf(c_0_79,plain,
sum(multiplicative_identity,additive_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_71,c_0_68]) ).
cnf(c_0_80,plain,
( ~ sum(additive_identity,additive_identity,X1)
| sum(X1,multiplicative_identity,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_61]),c_0_43])]) ).
cnf(c_0_81,hypothesis,
sum(additive_identity,additive_identity,multiplicative_inverse(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_72]),c_0_37])]) ).
cnf(c_0_82,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_addition]) ).
cnf(c_0_83,plain,
( ~ sum(X1,X3,additive_identity)
| ~ sum(X3,additive_identity,X2)
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_60,c_0_70]) ).
cnf(c_0_84,plain,
( ~ sum(X1,additive_identity,additive_identity)
| sum(X1,multiplicative_identity,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_61]),c_0_43])]) ).
cnf(c_0_85,hypothesis,
( ~ sum(multiplicative_inverse(a),additive_identity,X1)
| sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_86,plain,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X1,X2)) ),
c_0_78 ).
cnf(c_0_87,plain,
( ~ sum(X3,multiplicative_identity,X1)
| ~ sum(X3,multiplicative_identity,X2)
| sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_67,c_0_79]) ).
cnf(c_0_88,hypothesis,
sum(multiplicative_inverse(a),multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_89,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
c_0_82 ).
cnf(c_0_90,hypothesis,
( ~ sum(X1,multiplicative_inverse(a),additive_identity)
| sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_83,c_0_77]) ).
cnf(c_0_91,plain,
( ~ sum(X1,additive_identity,additive_identity)
| sum(multiplicative_identity,X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_71,c_0_84]) ).
cnf(c_0_92,hypothesis,
sum(add(multiplicative_inverse(a),additive_identity),additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_44]),c_0_37])]) ).
cnf(c_0_93,hypothesis,
( ~ sum(multiplicative_inverse(a),multiplicative_identity,X1)
| sum(X1,additive_identity,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_94,plain,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X2,X1)) ),
inference(spm,[status(thm)],[c_0_71,c_0_86]) ).
cnf(c_0_95,plain,
( ~ defined(X1)
| sum(X1,additive_inverse(X1),additive_identity) ),
inference(spm,[status(thm)],[c_0_71,c_0_89]) ).
cnf(c_0_96,hypothesis,
sum(additive_inverse(multiplicative_inverse(a)),additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_89]),c_0_37])]) ).
cnf(c_0_97,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_67,c_0_86]) ).
cnf(c_0_98,hypothesis,
sum(multiplicative_identity,add(multiplicative_inverse(a),additive_identity),multiplicative_identity),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_99,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(fof_simplification,[status(thm)],[different_identities]) ).
cnf(c_0_100,plain,
( ~ defined(X1)
| sum(X1,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_61]) ).
cnf(c_0_101,hypothesis,
sum(add(multiplicative_identity,multiplicative_inverse(a)),additive_identity,multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_37]),c_0_43])]) ).
cnf(c_0_102,plain,
( ~ sum(X1,X4,X3)
| ~ sum(X4,additive_inverse(X3),X2)
| ~ defined(X3)
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_60,c_0_95]) ).
cnf(c_0_103,plain,
( ~ sum(X4,additive_identity,X3)
| ~ sum(X4,additive_inverse(X2),X1)
| ~ defined(X2)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_67,c_0_89]) ).
cnf(c_0_104,hypothesis,
sum(multiplicative_identity,additive_inverse(multiplicative_inverse(a)),multiplicative_identity),
inference(spm,[status(thm)],[c_0_91,c_0_96]) ).
cnf(c_0_105,hypothesis,
( ~ sum(multiplicative_identity,multiplicative_inverse(a),X1)
| sum(X1,additive_identity,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_44]),c_0_37])]) ).
cnf(c_0_106,hypothesis,
( ~ sum(X1,additive_identity,additive_identity)
| sum(X1,multiplicative_inverse(a),additive_identity) ),
inference(spm,[status(thm)],[c_0_83,c_0_81]) ).
cnf(c_0_107,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
c_0_99 ).
cnf(c_0_108,plain,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_additive_inverse]) ).
cnf(c_0_109,plain,
( ~ sum(X4,X3,X1)
| ~ sum(X4,X3,X2)
| ~ defined(X3)
| sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_67,c_0_100]) ).
cnf(c_0_110,hypothesis,
sum(additive_identity,add(multiplicative_identity,multiplicative_inverse(a)),multiplicative_identity),
inference(spm,[status(thm)],[c_0_71,c_0_101]) ).
cnf(c_0_111,plain,
( ~ sum(X1,X2,X2)
| ~ defined(X2)
| sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_102,c_0_95]) ).
cnf(c_0_112,hypothesis,
( ~ sum(multiplicative_identity,additive_identity,X1)
| sum(multiplicative_identity,multiplicative_inverse(a),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_37])]) ).
cnf(c_0_113,hypothesis,
~ sum(multiplicative_identity,additive_identity,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]) ).
cnf(c_0_114,plain,
( ~ sum(X4,X3,X2)
| ~ sum(X1,X4,additive_inverse(X3))
| ~ defined(X3)
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_60,c_0_89]) ).
cnf(c_0_115,plain,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
c_0_108 ).
cnf(c_0_116,plain,
( ~ sum(X1,X3,multiplicative_identity)
| ~ sum(X3,additive_identity,X2)
| sum(X1,X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_60,c_0_79]) ).
cnf(c_0_117,plain,
( ~ sum(additive_identity,X2,X1)
| ~ defined(X2)
| sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_109,c_0_61]) ).
cnf(c_0_118,hypothesis,
( ~ sum(additive_identity,multiplicative_identity,X1)
| sum(X1,multiplicative_inverse(a),multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_110]),c_0_37]),c_0_43])]) ).
cnf(c_0_119,hypothesis,
~ sum(multiplicative_identity,additive_identity,multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_37])]),c_0_113]) ).
cnf(c_0_120,plain,
( ~ sum(additive_inverse(X2),X2,X1)
| ~ defined(X2)
| sum(additive_identity,X1,additive_identity) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_61]),c_0_115]) ).
cnf(c_0_121,plain,
( ~ sum(X1,X2,multiplicative_identity)
| ~ defined(X2)
| sum(X1,add(X2,additive_identity),multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_86]),c_0_44])]) ).
cnf(c_0_122,hypothesis,
~ sum(additive_identity,multiplicative_identity,additive_identity),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_37])]),c_0_119]) ).
cnf(c_0_123,hypothesis,
( ~ defined(X1)
| less_or_equal(a,X1)
| less_or_equal(X1,a) ),
inference(spm,[status(thm)],[c_0_42,c_0_26]) ).
cnf(c_0_124,plain,
( ~ sum(additive_inverse(add(X1,additive_identity)),X1,multiplicative_identity)
| ~ defined(X1)
| ~ defined(add(X1,additive_identity)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_122]) ).
cnf(c_0_125,plain,
( ~ sum(X1,X3,X2)
| ~ defined(X1)
| ~ defined(X3)
| sum(additive_inverse(X1),X2,X3) ),
inference(spm,[status(thm)],[c_0_69,c_0_89]) ).
cnf(c_0_126,plain,
( ~ sum(X4,X2,X3)
| ~ sum(X4,additive_identity,X1)
| ~ defined(X2)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_67,c_0_61]) ).
cnf(c_0_127,hypothesis,
less_or_equal(a,a),
inference(spm,[status(thm)],[c_0_123,c_0_26]) ).
cnf(c_0_128,plain,
( ~ sum(add(X1,additive_identity),multiplicative_identity,X1)
| ~ defined(X1)
| ~ defined(add(X1,additive_identity)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_43])]) ).
cnf(c_0_129,plain,
( ~ sum(X1,X2,X3)
| ~ defined(X1)
| ~ defined(X2)
| sum(add(X1,additive_identity),X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_86]),c_0_44])]) ).
cnf(c_0_130,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(add(X1,X2)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_addition]) ).
cnf(c_0_131,hypothesis,
sum(additive_identity,a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_127]),c_0_127])]) ).
cnf(c_0_132,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_133,plain,
( ~ sum(X1,multiplicative_identity,X1)
| ~ defined(X1)
| ~ defined(add(X1,additive_identity)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_43])]) ).
cnf(c_0_134,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(add(X1,X2)) ),
c_0_130 ).
cnf(c_0_135,hypothesis,
sum(a,additive_identity,a),
inference(spm,[status(thm)],[c_0_71,c_0_131]) ).
cnf(c_0_136,plain,
( ~ product(X5,X7,X2)
| ~ product(X4,X7,X1)
| ~ product(X6,X7,X3)
| ~ sum(X4,X5,X6)
| sum(X1,X2,X3) ),
c_0_132 ).
cnf(c_0_137,hypothesis,
product(a,multiplicative_identity,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_31]),c_0_26])]) ).
cnf(c_0_138,plain,
( ~ sum(X1,multiplicative_identity,X1)
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_44])]) ).
cnf(c_0_139,plain,
( ~ sum(X2,additive_identity,X1)
| ~ defined(X2)
| sum(X1,multiplicative_identity,add(X2,multiplicative_identity)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_86]),c_0_43])]) ).
cnf(c_0_140,hypothesis,
( ~ sum(X3,a,X1)
| ~ sum(X3,a,X2)
| sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_67,c_0_135]) ).
cnf(c_0_141,plain,
( ~ sum(X5,X4,multiplicative_identity)
| ~ defined(X3)
| ~ product(X5,X3,X1)
| ~ product(X4,X3,X2)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_136,c_0_36]) ).
cnf(c_0_142,hypothesis,
product(multiplicative_identity,a,a),
inference(spm,[status(thm)],[c_0_30,c_0_137]) ).
cnf(c_0_143,plain,
( ~ sum(X1,additive_identity,add(X1,multiplicative_identity))
| ~ defined(X1)
| ~ defined(add(X1,multiplicative_identity)) ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_144,hypothesis,
( ~ sum(X2,a,X1)
| ~ defined(X2)
| sum(X1,additive_identity,add(a,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_94]),c_0_26])]) ).
cnf(c_0_145,hypothesis,
( ~ defined(X3)
| ~ product(multiplicative_identity,X3,X2)
| ~ product(multiplicative_inverse(a),X3,X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_141,c_0_88]) ).
cnf(c_0_146,hypothesis,
( ~ product(X1,X3,multiplicative_identity)
| ~ product(X3,a,X2)
| product(X1,X2,a) ),
inference(spm,[status(thm)],[c_0_34,c_0_142]) ).
cnf(c_0_147,hypothesis,
( ~ sum(multiplicative_identity,a,a)
| ~ defined(add(a,multiplicative_identity)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_26]),c_0_43])]) ).
cnf(c_0_148,hypothesis,
( ~ product(multiplicative_identity,a,X1)
| sum(multiplicative_identity,X1,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_31]),c_0_26])]) ).
cnf(c_0_149,hypothesis,
( ~ product(X1,multiplicative_identity,multiplicative_identity)
| product(X1,a,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_36]),c_0_26])]) ).
cnf(c_0_150,hypothesis,
~ sum(multiplicative_identity,a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_134]),c_0_43]),c_0_26])]) ).
cnf(c_0_151,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_54])]),c_0_150]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : FLD011-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.47 % Computer : n011.cluster.edu
% 0.18/0.47 % Model : x86_64 x86_64
% 0.18/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.47 % Memory : 8046.5625MB
% 0.18/0.47 % OS : Linux 6.8.0-71-generic
% 0.18/0.47 % CPULimit : 300
% 0.18/0.47 % WCLimit : 300
% 0.18/0.47 % DateTime : Mon Sep 21 15:37:56 UTC 2026
% 0.18/0.47 % CPUTime :
% 0.18/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.54 Running first-order theorem proving
% 0.21/0.54 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
% 12.50/2.28 % Version: 3.5.1
% 12.50/2.28 % Preprocessing class: FSMSSMSSSSSNFFN.
% 12.50/2.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.50/2.28 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 12.50/2.28 % Starting new_bool_3 with 300s (1) cores
% 12.50/2.28 % Starting new_bool_1 with 300s (1) cores
% 12.50/2.28 % Starting sh5l with 300s (1) cores
% 12.50/2.28 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2263179 completed with status 0
% 12.50/2.28 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 12.50/2.28 % Preprocessing class: FSMSSMSSSSSNFFN.
% 12.50/2.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.50/2.28 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 12.50/2.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 12.50/2.28 % No SInE strategy applied
% 12.50/2.28 % Search class: FGUNF-FFMS21-SFFFFFNN
% 12.50/2.28 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 12.50/2.28 % Starting SubtermCWHack with 136s (1) cores
% 12.50/2.28 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 12.50/2.28 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 12.50/2.28 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 12.50/2.28 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 12.50/2.28 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2263185 completed with status 0
% 12.50/2.28 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 12.50/2.28 % Preprocessing class: FSMSSMSSSSSNFFN.
% 12.50/2.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.50/2.28 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 12.50/2.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 12.50/2.28 % No SInE strategy applied
% 12.50/2.28 % Search class: FGUNF-FFMS21-SFFFFFNN
% 12.50/2.28 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 12.50/2.28 % Starting SubtermCWHack with 136s (1) cores
% 12.50/2.28 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 12.50/2.28 % Preprocessing time : 0.002 s
% 12.50/2.28 % Presaturation interreduction done
% 12.50/2.28
% 12.50/2.28 % Proof found!
% 12.50/2.28 % SZS status Unsatisfiable
% 12.50/2.28 % SZS output start CNFRefutation
% See solution above
% 12.50/2.28 % Parsed axioms : 29
% 12.50/2.28 % Removed by relevancy pruning/SinE : 0
% 12.50/2.28 % Initial clauses : 29
% 12.50/2.28 % Removed in clause preprocessing : 0
% 12.50/2.28 % Initial clauses in saturation : 29
% 12.50/2.28 % Processed clauses : 8456
% 12.50/2.28 % ...of these trivial : 117
% 12.50/2.28 % ...subsumed : 5668
% 12.50/2.28 % ...remaining for further processing : 2671
% 12.50/2.28 % Other redundant clauses eliminated : 0
% 12.50/2.28 % Clauses deleted for lack of memory : 0
% 12.50/2.28 % Backward-subsumed : 452
% 12.50/2.28 % Backward-rewritten : 28
% 12.50/2.28 % Generated clauses : 44848
% 12.50/2.28 % ...of the previous two non-redundant : 39942
% 12.50/2.28 % ...aggressively subsumed : 0
% 12.50/2.28 % Contextual simplify-reflections : 43
% 12.50/2.28 % Paramodulations : 44804
% 12.50/2.28 % Factorizations : 0
% 12.50/2.28 % NegExts : 0
% 12.50/2.28 % Equation resolutions : 0
% 12.50/2.28 % Disequality decompositions : 0
% 12.50/2.28 % Total rewrite steps : 23505
% 12.50/2.28 % ...of those cached : 23249
% 12.50/2.28 % Propositional unsat checks : 0
% 12.50/2.28 % Propositional check models : 0
% 12.50/2.28 % Propositional check unsatisfiable : 0
% 12.50/2.28 % Propositional clauses : 0
% 12.50/2.28 % Propositional clauses after purity: 0
% 12.50/2.28 % Propositional unsat core size : 0
% 12.50/2.28 % Propositional preprocessing time : 0.000
% 12.50/2.28 % Propositional encoding time : 0.000
% 12.50/2.28 % Propositional solver time : 0.000
% 12.50/2.28 % Success case prop preproc time : 0.000
% 12.50/2.28 % Success case prop encoding time : 0.000
% 12.50/2.28 % Success case prop solver time : 0.000
% 12.50/2.28 % Current number of processed clauses : 2118
% 12.50/2.28 % Positive orientable unit clauses : 298
% 12.50/2.28 % Positive unorientable unit clauses: 0
% 12.50/2.28 % Negative unit clauses : 97
% 12.50/2.28 % Non-unit-clauses : 1723
% 12.50/2.28 % Current number of unprocessed clauses: 30991
% 12.50/2.28 % ...number of literals in the above : 116626
% 12.50/2.28 % Current number of archived formulas : 0
% 12.50/2.28 % Current number of archived clauses : 553
% 12.50/2.28 % Clause-clause subsumption calls (NU) : 255501
% 12.50/2.28 % Rec. Clause-clause subsumption calls : 207427
% 12.50/2.28 % Non-unit clause-clause subsumptions : 4284
% 12.50/2.28 % Unit Clause-clause subsumption calls : 38581
% 12.50/2.28 % Rewrite failures with RHS unbound : 0
% 12.50/2.28 % BW rewrite match attempts : 553
% 12.50/2.28 % BW rewrite match successes : 15
% 12.50/2.28 % Condensation attempts : 0
% 12.50/2.28 % Condensation successes : 0
% 12.50/2.28 % Termbank termtop insertions : 631674
% 12.50/2.28 % Search garbage collected termcells : 118
% 12.50/2.28
% 12.50/2.28 % -------------------------------------------------
% 12.50/2.28 % User time : 1.532 s
% 12.50/2.28 % System time : 0.043 s
% 12.50/2.28 % Total time : 1.575 s
% 12.50/2.28 % Maximum resident set size: 3404 pages
% 12.50/2.28
% 12.50/2.28 % -------------------------------------------------
% 12.50/2.28 % User time : 7.388 s
% 12.50/2.28 % System time : 0.229 s
% 12.50/2.28 % Total time : 7.617 s
% 12.50/2.28 % Maximum resident set size: 4608 pages
% 12.50/2.28 % E exiting
%------------------------------------------------------------------------------