%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD041-3 : 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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:22:48 PM UTC 2026
% Result : Unsatisfiable 0.71s 0.58s
% Output : CNFRefutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 25
% Syntax : Number of clauses : 128 ( 36 unt; 7 nHn; 128 RR)
% Number of literals : 317 ( 0 equ; 188 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 263 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(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_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(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
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(transitivity_of_order_relation,axiom,
( ~ less_or_equal(X3,X2)
| ~ less_or_equal(X1,X3)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',transitivity_of_order_relation) ).
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_multiplication,axiom,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
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(product_5,negated_conjecture,
product(a,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_5) ).
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(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(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
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(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(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_multiplication,axiom,
( ~ defined(X2)
| ~ defined(X1)
| defined(multiply(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplication) ).
cnf(existence_of_inverse_multiplication,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(not_sum_3,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).
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(not_sum_4,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_4) ).
cnf(c_0_25,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_26,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_27,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_28,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
c_0_25 ).
cnf(c_0_29,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
c_0_26 ).
cnf(c_0_30,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ less_or_equal(X3,X4)
| less_or_equal(X1,X2) ),
c_0_27 ).
cnf(c_0_31,plain,
( ~ defined(X1)
| sum(X1,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_addition]) ).
cnf(c_0_33,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_34,plain,
( ~ sum(X3,additive_identity,X1)
| ~ defined(X2)
| ~ less_or_equal(X3,X2)
| less_or_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
c_0_32 ).
cnf(c_0_36,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_37,plain,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
c_0_33 ).
cnf(c_0_38,plain,
( ~ defined(X1)
| ~ less_or_equal(additive_inverse(additive_identity),X1)
| less_or_equal(additive_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_39,plain,
( ~ defined(X1)
| less_or_equal(X1,X1) ),
inference(ef,[status(thm)],[c_0_37]) ).
cnf(c_0_40,plain,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_additive_inverse]) ).
cnf(c_0_41,plain,
( ~ less_or_equal(X3,X2)
| ~ less_or_equal(X1,X3)
| less_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[transitivity_of_order_relation]) ).
cnf(c_0_42,plain,
( ~ defined(additive_inverse(additive_identity))
| less_or_equal(additive_identity,additive_inverse(additive_identity)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
c_0_40 ).
cnf(c_0_44,plain,
( ~ less_or_equal(X3,X2)
| ~ less_or_equal(X1,X3)
| less_or_equal(X1,X2) ),
c_0_41 ).
cnf(c_0_45,plain,
less_or_equal(additive_identity,additive_inverse(additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_36])]) ).
cnf(c_0_46,plain,
( ~ sum(X2,X3,X1)
| ~ defined(X3)
| ~ less_or_equal(X2,additive_inverse(X3))
| less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_30,c_0_35]) ).
cnf(c_0_47,plain,
( ~ less_or_equal(X1,additive_identity)
| less_or_equal(X1,additive_inverse(additive_identity)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,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_49,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_50,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_51,plain,
( ~ defined(X1)
| ~ less_or_equal(additive_identity,additive_inverse(X1))
| less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_46,c_0_29]) ).
cnf(c_0_52,plain,
( ~ defined(X1)
| less_or_equal(additive_identity,X1)
| less_or_equal(X1,additive_inverse(additive_identity)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_37]),c_0_36])]) ).
cnf(c_0_53,plain,
( ~ product(X5,X7,X2)
| ~ product(X4,X7,X1)
| ~ product(X6,X7,X3)
| ~ sum(X4,X5,X6)
| sum(X1,X2,X3) ),
c_0_48 ).
cnf(c_0_54,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
c_0_49 ).
cnf(c_0_55,negated_conjecture,
product(a,b,additive_identity),
product_5 ).
cnf(c_0_56,plain,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
inference(fof_simplification,[status(thm)],[totality_of_multiplication]) ).
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_50 ).
cnf(c_0_59,plain,
less_or_equal(additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_36])]) ).
cnf(c_0_60,plain,
( ~ defined(X5)
| ~ product(X5,X4,X2)
| ~ product(X5,X4,X3)
| ~ product(additive_identity,X4,X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_53,c_0_29]) ).
cnf(c_0_61,negated_conjecture,
product(b,a,additive_identity),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_62,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_63,plain,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
c_0_56 ).
cnf(c_0_64,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_65,plain,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
c_0_57 ).
cnf(c_0_66,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_59]),c_0_59])]) ).
cnf(c_0_67,negated_conjecture,
( ~ product(b,a,X2)
| ~ product(additive_identity,a,X1)
| sum(X1,X2,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62])]) ).
cnf(c_0_68,plain,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X2,X1)) ),
inference(spm,[status(thm)],[c_0_54,c_0_63]) ).
cnf(c_0_69,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_70,plain,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
c_0_64 ).
cnf(c_0_71,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_72,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_73,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_74,plain,
( ~ sum(X3,additive_identity,X1)
| ~ sum(X3,additive_identity,X2)
| sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_75,negated_conjecture,
( ~ product(b,a,X1)
| sum(multiply(a,additive_identity),X1,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_36]),c_0_69])]) ).
cnf(c_0_76,negated_conjecture,
( ~ product(X3,b,X1)
| ~ product(X3,additive_identity,X2)
| product(X1,a,X2) ),
inference(spm,[status(thm)],[c_0_70,c_0_61]) ).
cnf(c_0_77,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
c_0_71 ).
cnf(c_0_78,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
c_0_72 ).
cnf(c_0_79,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
c_0_73 ).
cnf(c_0_80,plain,
( ~ sum(X2,additive_identity,X1)
| ~ defined(X2)
| sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_74,c_0_31]) ).
cnf(c_0_81,negated_conjecture,
sum(multiply(a,additive_identity),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_75,c_0_61]) ).
cnf(c_0_82,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(multiply(X1,X2)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_multiplication]) ).
cnf(c_0_83,negated_conjecture,
( ~ defined(X2)
| ~ product(X2,b,X1)
| product(X1,a,multiply(X2,additive_identity)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_63]),c_0_36])]) ).
cnf(c_0_84,plain,
( ~ defined(X3)
| ~ product(X4,X3,X2)
| ~ product(X1,X4,multiplicative_identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_85,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_86,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_3]) ).
cnf(c_0_87,negated_conjecture,
( ~ product(X1,X3,b)
| ~ product(X3,a,X2)
| product(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_77,c_0_61]) ).
cnf(c_0_88,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_89,plain,
( ~ sum(X1,X4,X3)
| ~ sum(X4,additive_identity,X2)
| ~ defined(X3)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_79,c_0_31]) ).
cnf(c_0_90,negated_conjecture,
( ~ defined(multiply(a,additive_identity))
| sum(additive_identity,additive_identity,multiply(a,additive_identity)) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_91,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(multiply(X1,X2)) ),
c_0_82 ).
cnf(c_0_92,negated_conjecture,
product(additive_identity,a,multiply(a,additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_55]),c_0_69])]) ).
cnf(c_0_93,negated_conjecture,
( ~ product(X1,a,multiplicative_identity)
| product(X1,additive_identity,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_55]),c_0_62])]) ).
cnf(c_0_94,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
c_0_85 ).
cnf(c_0_95,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
c_0_86 ).
cnf(c_0_96,negated_conjecture,
( ~ product(X1,b,b)
| product(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_87,c_0_61]) ).
cnf(c_0_97,plain,
( ~ sum(X6,X7,X3)
| ~ product(X5,X2,X7)
| ~ product(X4,X2,X6)
| ~ sum(X4,X5,X1)
| product(X1,X2,X3) ),
c_0_88 ).
cnf(c_0_98,negated_conjecture,
( ~ sum(additive_identity,additive_identity,X1)
| sum(multiply(a,additive_identity),X1,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_81]),c_0_36])]) ).
cnf(c_0_99,negated_conjecture,
sum(additive_identity,additive_identity,multiply(a,additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_36]),c_0_69])]) ).
cnf(c_0_100,negated_conjecture,
( ~ product(X1,additive_identity,b)
| product(X1,multiply(a,additive_identity),additive_identity) ),
inference(spm,[status(thm)],[c_0_87,c_0_92]) ).
cnf(c_0_101,negated_conjecture,
product(multiplicative_inverse(a),additive_identity,b),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_69])]),c_0_95]) ).
cnf(c_0_102,negated_conjecture,
product(multiplicative_identity,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_78]),c_0_62])]) ).
cnf(c_0_103,plain,
( ~ sum(X4,X3,X1)
| ~ product(X4,X2,additive_identity)
| ~ product(X3,X2,additive_identity)
| product(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_97,c_0_66]) ).
cnf(c_0_104,negated_conjecture,
sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_105,negated_conjecture,
product(multiplicative_inverse(a),multiply(a,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_106,negated_conjecture,
product(additive_identity,multiplicative_identity,additive_identity),
inference(spm,[status(thm)],[c_0_54,c_0_102]) ).
cnf(c_0_107,negated_conjecture,
( ~ product(multiply(a,additive_identity),X1,additive_identity)
| product(additive_identity,X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_108,negated_conjecture,
product(multiply(a,additive_identity),multiplicative_inverse(a),additive_identity),
inference(spm,[status(thm)],[c_0_54,c_0_105]) ).
cnf(c_0_109,plain,
( ~ defined(X1)
| product(X1,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_78]) ).
cnf(c_0_110,negated_conjecture,
( ~ product(X3,additive_identity,X1)
| ~ product(X3,additive_identity,X2)
| product(X1,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_70,c_0_106]) ).
cnf(c_0_111,negated_conjecture,
product(additive_identity,multiplicative_inverse(a),additive_identity),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_112,plain,
( ~ defined(X3)
| ~ product(X1,X4,X3)
| ~ product(X4,multiplicative_identity,X2)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_77,c_0_109]) ).
cnf(c_0_113,negated_conjecture,
( ~ product(multiplicative_inverse(a),additive_identity,X1)
| product(X1,multiplicative_identity,b) ),
inference(spm,[status(thm)],[c_0_110,c_0_101]) ).
cnf(c_0_114,negated_conjecture,
product(multiplicative_inverse(a),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_54,c_0_111]) ).
cnf(c_0_115,negated_conjecture,
( ~ product(additive_identity,multiplicative_identity,X1)
| product(multiplicative_inverse(a),X1,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_101]),c_0_62])]) ).
cnf(c_0_116,negated_conjecture,
product(additive_identity,multiplicative_identity,b),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_117,negated_conjecture,
( ~ product(multiplicative_inverse(a),b,X1)
| product(X1,a,b) ),
inference(spm,[status(thm)],[c_0_76,c_0_101]) ).
cnf(c_0_118,negated_conjecture,
product(multiplicative_inverse(a),b,b),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_119,negated_conjecture,
product(b,a,b),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_120,plain,
( ~ sum(X4,X3,X2)
| ~ sum(X1,X4,additive_identity)
| ~ defined(X3)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_79,c_0_29]) ).
cnf(c_0_121,negated_conjecture,
sum(multiply(a,additive_identity),b,additive_identity),
inference(spm,[status(thm)],[c_0_75,c_0_119]) ).
cnf(c_0_122,negated_conjecture,
( ~ sum(X1,multiply(a,additive_identity),additive_identity)
| sum(X1,additive_identity,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_81]),c_0_36])]) ).
cnf(c_0_123,negated_conjecture,
sum(b,multiply(a,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_28,c_0_121]) ).
cnf(c_0_124,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_4]) ).
cnf(c_0_125,negated_conjecture,
sum(b,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_126,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
c_0_124 ).
cnf(c_0_127,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_125]),c_0_126]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD041-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 15:41:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.71/0.58 % Version: 3.5.1
% 0.71/0.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.71/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.71/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.71/0.58 % Starting new_bool_3 with 300s (1) cores
% 0.71/0.58 % Starting new_bool_1 with 300s (1) cores
% 0.71/0.58 % Starting sh5l with 300s (1) cores
% 0.71/0.58 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2244087 completed with status 0
% 0.71/0.58 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.71/0.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.71/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.71/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.71/0.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.71/0.58 % No SInE strategy applied
% 0.71/0.58 % Search class: FGUNF-FFMS21-SFFFFFNN
% 0.71/0.58 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.71/0.58 % Starting SubtermCWHack with 136s (1) cores
% 0.71/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.71/0.58 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 0.71/0.58 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.71/0.58 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.71/0.58 % G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with pid 2244095 completed with status 0
% 0.71/0.58 % Result found by G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c
% 0.71/0.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.71/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.71/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.71/0.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.71/0.58 % No SInE strategy applied
% 0.71/0.58 % Search class: FGUNF-FFMS21-SFFFFFNN
% 0.71/0.58 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.71/0.58 % Starting SubtermCWHack with 136s (1) cores
% 0.71/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.71/0.58 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 0.71/0.58 % Preprocessing time : 0.002 s
% 0.71/0.58 % Presaturation interreduction done
% 0.71/0.58
% 0.71/0.58 % Proof found!
% 0.71/0.58 % SZS status Unsatisfiable
% 0.71/0.58 % SZS output start CNFRefutation
% See solution above
% 0.71/0.58 % Parsed axioms : 31
% 0.71/0.58 % Removed by relevancy pruning/SinE : 0
% 0.71/0.58 % Initial clauses : 31
% 0.71/0.58 % Removed in clause preprocessing : 0
% 0.71/0.58 % Initial clauses in saturation : 31
% 0.71/0.58 % Processed clauses : 992
% 0.71/0.58 % ...of these trivial : 144
% 0.71/0.58 % ...subsumed : 217
% 0.71/0.58 % ...remaining for further processing : 631
% 0.71/0.58 % Other redundant clauses eliminated : 0
% 0.71/0.58 % Clauses deleted for lack of memory : 0
% 0.71/0.58 % Backward-subsumed : 1
% 0.71/0.58 % Backward-rewritten : 20
% 0.71/0.58 % Generated clauses : 8415
% 0.71/0.58 % ...of the previous two non-redundant : 6620
% 0.71/0.58 % ...aggressively subsumed : 0
% 0.71/0.58 % Contextual simplify-reflections : 2
% 0.71/0.58 % Paramodulations : 8405
% 0.71/0.58 % Factorizations : 10
% 0.71/0.58 % NegExts : 0
% 0.71/0.58 % Equation resolutions : 0
% 0.71/0.58 % Disequality decompositions : 0
% 0.71/0.58 % Total rewrite steps : 5075
% 0.71/0.58 % ...of those cached : 4883
% 0.71/0.58 % Propositional unsat checks : 0
% 0.71/0.58 % Propositional check models : 0
% 0.71/0.58 % Propositional check unsatisfiable : 0
% 0.71/0.58 % Propositional clauses : 0
% 0.71/0.58 % Propositional clauses after purity: 0
% 0.71/0.58 % Propositional unsat core size : 0
% 0.71/0.58 % Propositional preprocessing time : 0.000
% 0.71/0.58 % Propositional encoding time : 0.000
% 0.71/0.58 % Propositional solver time : 0.000
% 0.71/0.58 % Success case prop preproc time : 0.000
% 0.71/0.58 % Success case prop encoding time : 0.000
% 0.71/0.58 % Success case prop solver time : 0.000
% 0.71/0.58 % Current number of processed clauses : 579
% 0.71/0.58 % Positive orientable unit clauses : 227
% 0.71/0.58 % Positive unorientable unit clauses: 0
% 0.71/0.58 % Negative unit clauses : 4
% 0.71/0.58 % Non-unit-clauses : 348
% 0.71/0.58 % Current number of unprocessed clauses: 5686
% 0.71/0.58 % ...number of literals in the above : 18406
% 0.71/0.58 % Current number of archived formulas : 0
% 0.71/0.58 % Current number of archived clauses : 52
% 0.71/0.58 % Clause-clause subsumption calls (NU) : 10669
% 0.71/0.58 % Rec. Clause-clause subsumption calls : 7144
% 0.71/0.58 % Non-unit clause-clause subsumptions : 220
% 0.71/0.58 % Unit Clause-clause subsumption calls : 959
% 0.71/0.58 % Rewrite failures with RHS unbound : 0
% 0.71/0.58 % BW rewrite match attempts : 258
% 0.71/0.58 % BW rewrite match successes : 15
% 0.71/0.58 % Condensation attempts : 0
% 0.71/0.58 % Condensation successes : 0
% 0.71/0.58 % Termbank termtop insertions : 130660
% 0.71/0.58 % Search garbage collected termcells : 118
% 0.71/0.58
% 0.71/0.58 % -------------------------------------------------
% 0.71/0.58 % User time : 0.140 s
% 0.71/0.58 % System time : 0.008 s
% 0.71/0.58 % Total time : 0.148 s
% 0.71/0.58 % Maximum resident set size: 3660 pages
% 0.71/0.58
% 0.71/0.58 % -------------------------------------------------
% 0.71/0.58 % User time : 0.686 s
% 0.71/0.58 % System time : 0.041 s
% 0.71/0.58 % Total time : 0.726 s
% 0.71/0.58 % Maximum resident set size: 4608 pages
% 0.71/0.58 % E exiting
%------------------------------------------------------------------------------