%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD009-1 : 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 12:22:38 PM UTC 2026
% Result : Unsatisfiable 25.59s 4.19s
% Output : CNFRefutation 25.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 24
% Syntax : Number of clauses : 129 ( 36 unt; 11 nHn; 129 RR)
% Number of literals : 305 ( 0 equ; 171 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 188 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
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/FLD001-0.ax',totality_of_order_relation) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(transitivity_of_equality,axiom,
( ~ equalish(X3,X2)
| ~ equalish(X1,X3)
| equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X1)
| equalish(add(additive_identity,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).
cnf(compatibility_of_equality_and_order_relation,axiom,
( ~ equalish(X3,X1)
| ~ less_or_equal(X3,X2)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_order_relation) ).
cnf(commutativity_addition,axiom,
( ~ defined(X2)
| ~ defined(X1)
| equalish(add(X1,X2),add(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_addition) ).
cnf(symmetry_of_equality,axiom,
( ~ equalish(X2,X1)
| equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( ~ less_or_equal(X1,X3)
| ~ defined(X2)
| less_or_equal(add(X1,X2),add(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(antisymmetry_of_order_relation,axiom,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',antisymmetry_of_order_relation) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X1)
| equalish(multiply(multiplicative_identity,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_multiplication) ).
cnf(commutativity_multiplication,axiom,
( ~ defined(X2)
| ~ defined(X1)
| equalish(multiply(X1,X2),multiply(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_multiplication) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(well_definedness_of_addition,axiom,
( ~ defined(X2)
| ~ defined(X1)
| defined(add(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_addition) ).
cnf(compatibility_of_equality_and_addition,axiom,
( ~ equalish(X1,X3)
| ~ defined(X2)
| equalish(add(X1,X2),add(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_addition) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X1)
| equalish(add(X1,additive_inverse(X1)),additive_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_addition) ).
cnf(compatibility_of_equality_and_multiplication,axiom,
( ~ equalish(X1,X3)
| ~ defined(X2)
| equalish(multiply(X1,X2),multiply(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_multiplication) ).
cnf(existence_of_inverse_multiplication,axiom,
( ~ defined(X1)
| equalish(X1,additive_identity)
| equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_multiplication) ).
cnf(a_not_equal_to_additive_identity_3,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_equal_to_additive_identity_3) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(associativity_multiplication,axiom,
( ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1)
| equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',associativity_multiplication) ).
cnf(well_definedness_of_multiplication,axiom,
( ~ defined(X2)
| ~ defined(X1)
| defined(multiply(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplication) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( ~ defined(X1)
| equalish(X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(multiply_not_equal_to_b_4,negated_conjecture,
~ equalish(multiply(a,X1),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_not_equal_to_b_4) ).
cnf(c_0_24,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_25,plain,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
c_0_24 ).
cnf(c_0_26,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_27,plain,
( ~ equalish(X3,X2)
| ~ equalish(X1,X3)
| equalish(X1,X2) ),
inference(fof_simplification,[status(thm)],[transitivity_of_equality]) ).
cnf(c_0_28,plain,
( ~ defined(X1)
| equalish(add(additive_identity,X1),X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_29,plain,
( ~ equalish(X3,X1)
| ~ less_or_equal(X3,X2)
| less_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[compatibility_of_equality_and_order_relation]) ).
cnf(c_0_30,hypothesis,
( ~ defined(X1)
| less_or_equal(b,X1)
| less_or_equal(X1,b) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
( ~ equalish(X3,X2)
| ~ equalish(X1,X3)
| equalish(X1,X2) ),
c_0_27 ).
cnf(c_0_32,plain,
( ~ defined(X1)
| equalish(add(additive_identity,X1),X1) ),
c_0_28 ).
cnf(c_0_33,plain,
( ~ defined(X2)
| ~ defined(X1)
| equalish(add(X1,X2),add(X2,X1)) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_34,plain,
( ~ equalish(X3,X1)
| ~ less_or_equal(X3,X2)
| less_or_equal(X1,X2) ),
c_0_29 ).
cnf(c_0_35,hypothesis,
less_or_equal(b,b),
inference(spm,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_36,plain,
( ~ equalish(X2,X1)
| equalish(X1,X2) ),
inference(fof_simplification,[status(thm)],[symmetry_of_equality]) ).
cnf(c_0_37,plain,
( ~ equalish(X1,add(additive_identity,X2))
| ~ defined(X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,plain,
( ~ defined(X2)
| ~ defined(X1)
| equalish(add(X1,X2),add(X2,X1)) ),
c_0_33 ).
cnf(c_0_39,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_40,hypothesis,
( ~ equalish(b,X1)
| less_or_equal(X1,b) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
( ~ equalish(X2,X1)
| equalish(X1,X2) ),
c_0_36 ).
cnf(c_0_42,plain,
( ~ defined(X1)
| equalish(add(X1,additive_identity),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_43,hypothesis,
( ~ equalish(X2,X1)
| ~ equalish(b,X2)
| less_or_equal(X1,b) ),
inference(spm,[status(thm)],[c_0_34,c_0_40]) ).
cnf(c_0_44,plain,
( ~ defined(X1)
| equalish(X1,add(X1,additive_identity)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,plain,
( ~ less_or_equal(X1,X3)
| ~ defined(X2)
| less_or_equal(add(X1,X2),add(X3,X2)) ),
inference(fof_simplification,[status(thm)],[compatibility_of_order_relation_and_addition]) ).
cnf(c_0_46,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| equalish(X1,X2) ),
inference(fof_simplification,[status(thm)],[antisymmetry_of_order_relation]) ).
cnf(c_0_47,hypothesis,
( ~ equalish(add(b,additive_identity),X1)
| less_or_equal(X1,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_26])]) ).
cnf(c_0_48,plain,
( ~ less_or_equal(X1,X3)
| ~ defined(X2)
| less_or_equal(add(X1,X2),add(X3,X2)) ),
c_0_45 ).
cnf(c_0_49,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| equalish(X1,X2) ),
c_0_46 ).
cnf(c_0_50,hypothesis,
less_or_equal(add(additive_identity,b),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_38]),c_0_39]),c_0_26])]) ).
cnf(c_0_51,plain,
( ~ equalish(add(X4,X3),X1)
| ~ defined(X3)
| ~ less_or_equal(X4,X2)
| less_or_equal(X1,add(X2,X3)) ),
inference(spm,[status(thm)],[c_0_34,c_0_48]) ).
cnf(c_0_52,plain,
( ~ defined(X1)
| less_or_equal(additive_identity,X1)
| less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_25,c_0_39]) ).
cnf(c_0_53,hypothesis,
( ~ less_or_equal(b,add(additive_identity,b))
| equalish(b,add(additive_identity,b)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,plain,
( ~ defined(X1)
| ~ less_or_equal(additive_identity,X2)
| less_or_equal(X1,add(X2,X1)) ),
inference(spm,[status(thm)],[c_0_51,c_0_32]) ).
cnf(c_0_55,plain,
less_or_equal(additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_52,c_0_39]) ).
cnf(c_0_56,plain,
( ~ defined(X1)
| equalish(multiply(multiplicative_identity,X1),X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_57,plain,
( ~ equalish(X1,add(X3,X2))
| ~ defined(X3)
| ~ defined(X2)
| equalish(X1,add(X2,X3)) ),
inference(spm,[status(thm)],[c_0_31,c_0_38]) ).
cnf(c_0_58,hypothesis,
equalish(b,add(additive_identity,b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]),c_0_26])]) ).
cnf(c_0_59,plain,
( ~ defined(X1)
| equalish(multiply(multiplicative_identity,X1),X1) ),
c_0_56 ).
cnf(c_0_60,plain,
( ~ defined(X2)
| ~ defined(X1)
| equalish(multiply(X1,X2),multiply(X2,X1)) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_61,hypothesis,
equalish(b,add(b,additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_26]),c_0_39])]) ).
cnf(c_0_62,plain,
( ~ equalish(X1,multiply(multiplicative_identity,X2))
| ~ defined(X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_59]) ).
cnf(c_0_63,plain,
( ~ defined(X2)
| ~ defined(X1)
| equalish(multiply(X1,X2),multiply(X2,X1)) ),
c_0_60 ).
cnf(c_0_64,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_65,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(add(X1,X2)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_addition]) ).
cnf(c_0_66,hypothesis,
equalish(add(b,additive_identity),b),
inference(spm,[status(thm)],[c_0_41,c_0_61]) ).
cnf(c_0_67,plain,
( ~ defined(X1)
| equalish(multiply(X1,multiplicative_identity),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64])]) ).
cnf(c_0_68,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(add(X1,X2)) ),
c_0_65 ).
cnf(c_0_69,plain,
( ~ equalish(X1,X3)
| ~ defined(X2)
| equalish(add(X1,X2),add(X3,X2)) ),
inference(fof_simplification,[status(thm)],[compatibility_of_equality_and_addition]) ).
cnf(c_0_70,plain,
( ~ defined(X1)
| equalish(add(X1,additive_inverse(X1)),additive_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_addition]) ).
cnf(c_0_71,plain,
( ~ equalish(X1,X3)
| ~ defined(X2)
| equalish(multiply(X1,X2),multiply(X3,X2)) ),
inference(fof_simplification,[status(thm)],[compatibility_of_equality_and_multiplication]) ).
cnf(c_0_72,hypothesis,
( ~ equalish(X1,add(b,additive_identity))
| equalish(X1,b) ),
inference(spm,[status(thm)],[c_0_31,c_0_66]) ).
cnf(c_0_73,plain,
( ~ defined(X1)
| ~ defined(X2)
| equalish(multiply(add(X1,X2),multiplicative_identity),add(X2,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_67]),c_0_68]) ).
cnf(c_0_74,plain,
( ~ equalish(X1,X3)
| ~ defined(X2)
| equalish(add(X1,X2),add(X3,X2)) ),
c_0_69 ).
cnf(c_0_75,plain,
( ~ defined(X1)
| equalish(add(X1,additive_inverse(X1)),additive_identity) ),
c_0_70 ).
cnf(c_0_76,plain,
( ~ defined(X1)
| equalish(X1,additive_identity)
| equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_multiplication]) ).
cnf(c_0_77,negated_conjecture,
~ equalish(a,additive_identity),
inference(fof_simplification,[status(thm)],[a_not_equal_to_additive_identity_3]) ).
cnf(c_0_78,plain,
( ~ equalish(X1,X3)
| ~ defined(X2)
| equalish(multiply(X1,X2),multiply(X3,X2)) ),
c_0_71 ).
cnf(c_0_79,hypothesis,
equalish(multiply(add(additive_identity,b),multiplicative_identity),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_26]),c_0_39])]) ).
cnf(c_0_80,plain,
( ~ equalish(X4,X2)
| ~ equalish(X1,add(X4,X3))
| ~ defined(X3)
| equalish(X1,add(X2,X3)) ),
inference(spm,[status(thm)],[c_0_31,c_0_74]) ).
cnf(c_0_81,plain,
( ~ equalish(X1,add(X2,additive_inverse(X2)))
| ~ defined(X2)
| equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_31,c_0_75]) ).
cnf(c_0_82,plain,
( ~ defined(X1)
| equalish(additive_identity,add(X1,additive_inverse(X1))) ),
inference(spm,[status(thm)],[c_0_41,c_0_75]) ).
cnf(c_0_83,plain,
( ~ defined(X1)
| equalish(X1,additive_identity)
| equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity) ),
c_0_76 ).
cnf(c_0_84,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_85,negated_conjecture,
~ equalish(a,additive_identity),
c_0_77 ).
cnf(c_0_86,plain,
( ~ equalish(X4,X2)
| ~ equalish(X1,multiply(X4,X3))
| ~ defined(X3)
| equalish(X1,multiply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_31,c_0_78]) ).
cnf(c_0_87,hypothesis,
equalish(b,multiply(add(additive_identity,b),multiplicative_identity)),
inference(spm,[status(thm)],[c_0_41,c_0_79]) ).
cnf(c_0_88,hypothesis,
( ~ equalish(additive_identity,X1)
| equalish(b,add(X1,b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_58]),c_0_26])]) ).
cnf(c_0_89,plain,
( ~ defined(X1)
| equalish(additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_90,hypothesis,
equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]) ).
cnf(c_0_91,plain,
( ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1)
| equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3)) ),
inference(fof_simplification,[status(thm)],[associativity_multiplication]) ).
cnf(c_0_92,hypothesis,
( ~ equalish(add(additive_identity,b),X1)
| equalish(b,multiply(X1,multiplicative_identity)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_64])]) ).
cnf(c_0_93,hypothesis,
( ~ equalish(additive_identity,X1)
| equalish(add(X1,b),b) ),
inference(spm,[status(thm)],[c_0_41,c_0_88]) ).
cnf(c_0_94,hypothesis,
equalish(additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_89,c_0_26]) ).
cnf(c_0_95,hypothesis,
equalish(multiplicative_identity,multiply(a,multiplicative_inverse(a))),
inference(spm,[status(thm)],[c_0_41,c_0_90]) ).
cnf(c_0_96,plain,
( ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1)
| equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3)) ),
c_0_91 ).
cnf(c_0_97,hypothesis,
equalish(b,multiply(b,multiplicative_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94])]) ).
cnf(c_0_98,hypothesis,
( ~ equalish(X1,multiplicative_identity)
| equalish(X1,multiply(a,multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_31,c_0_95]) ).
cnf(c_0_99,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(multiply(X1,X2)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_multiplication]) ).
cnf(c_0_100,plain,
( ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3)
| equalish(multiply(multiply(X1,X2),X3),multiply(X1,multiply(X2,X3))) ),
inference(spm,[status(thm)],[c_0_41,c_0_96]) ).
cnf(c_0_101,hypothesis,
( ~ equalish(X1,b)
| equalish(X1,multiply(b,multiplicative_identity)) ),
inference(spm,[status(thm)],[c_0_31,c_0_97]) ).
cnf(c_0_102,hypothesis,
equalish(add(additive_identity,b),b),
inference(spm,[status(thm)],[c_0_41,c_0_58]) ).
cnf(c_0_103,hypothesis,
( ~ equalish(X1,multiplicative_identity)
| equalish(multiply(a,multiplicative_inverse(a)),X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_98]) ).
cnf(c_0_104,plain,
( ~ equalish(X1,multiply(X3,X2))
| ~ defined(X3)
| ~ defined(X2)
| equalish(X1,multiply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_31,c_0_63]) ).
cnf(c_0_105,plain,
( ~ equalish(X1,multiply(X2,multiply(X3,X4)))
| ~ defined(X2)
| ~ defined(X3)
| ~ defined(X4)
| equalish(X1,multiply(multiply(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_31,c_0_96]) ).
cnf(c_0_106,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(multiply(X1,X2)) ),
c_0_99 ).
cnf(c_0_107,plain,
( ~ equalish(X1,multiply(multiply(X2,X3),X4))
| ~ defined(X2)
| ~ defined(X3)
| ~ defined(X4)
| equalish(X1,multiply(X2,multiply(X3,X4))) ),
inference(spm,[status(thm)],[c_0_31,c_0_100]) ).
cnf(c_0_108,hypothesis,
equalish(b,multiply(multiply(b,multiplicative_identity),multiplicative_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_101]),c_0_102])]) ).
cnf(c_0_109,hypothesis,
( ~ equalish(X2,multiplicative_identity)
| ~ equalish(X1,multiply(a,multiplicative_inverse(a)))
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_103]) ).
cnf(c_0_110,plain,
( ~ equalish(X1,multiply(X3,multiply(X4,X2)))
| ~ defined(X3)
| ~ defined(X4)
| ~ defined(X2)
| equalish(X1,multiply(X2,multiply(X3,X4))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106]) ).
cnf(c_0_111,hypothesis,
equalish(b,multiply(b,multiply(multiplicative_identity,multiplicative_identity))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_64]),c_0_26])]) ).
cnf(c_0_112,hypothesis,
( ~ equalish(X1,multiplicative_identity)
| ~ equalish(X2,multiplicative_identity)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_109,c_0_98]) ).
cnf(c_0_113,hypothesis,
equalish(b,multiply(multiplicative_identity,multiply(b,multiplicative_identity))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_64]),c_0_26])]) ).
cnf(c_0_114,hypothesis,
( ~ equalish(X1,multiplicative_identity)
| equalish(X1,multiply(multiplicative_identity,multiplicative_identity)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_59]),c_0_64])]) ).
cnf(c_0_115,plain,
( ~ equalish(multiply(X5,X4),X2)
| ~ equalish(X1,multiply(X5,multiply(X4,X3)))
| ~ defined(X5)
| ~ defined(X4)
| ~ defined(X3)
| equalish(X1,multiply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_86,c_0_105]) ).
cnf(c_0_116,hypothesis,
equalish(b,multiply(multiplicative_identity,multiply(multiplicative_identity,b))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_113]),c_0_64]),c_0_26])]) ).
cnf(c_0_117,hypothesis,
( ~ equalish(X1,multiply(a,multiplicative_inverse(a)))
| equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_31,c_0_90]) ).
cnf(c_0_118,hypothesis,
( ~ equalish(X1,multiplicative_identity)
| equalish(multiply(multiplicative_identity,multiplicative_identity),X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_114]) ).
cnf(c_0_119,plain,
( ~ defined(X1)
| equalish(X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_multiplicative_inverse]) ).
cnf(c_0_120,hypothesis,
( ~ equalish(multiply(multiplicative_identity,multiplicative_identity),X1)
| equalish(b,multiply(X1,b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_26]),c_0_64])]) ).
cnf(c_0_121,hypothesis,
equalish(multiply(multiplicative_identity,multiplicative_identity),multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_90])]) ).
cnf(c_0_122,plain,
( ~ defined(X1)
| equalish(X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
c_0_119 ).
cnf(c_0_123,hypothesis,
equalish(b,multiply(multiply(a,multiplicative_inverse(a)),b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_98]),c_0_121])]) ).
cnf(c_0_124,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_84]),c_0_85]) ).
cnf(c_0_125,negated_conjecture,
~ equalish(multiply(a,X1),b),
inference(fof_simplification,[status(thm)],[multiply_not_equal_to_b_4]) ).
cnf(c_0_126,hypothesis,
equalish(b,multiply(a,multiply(multiplicative_inverse(a),b))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_123]),c_0_26]),c_0_124]),c_0_84])]) ).
cnf(c_0_127,negated_conjecture,
~ equalish(multiply(a,X1),b),
c_0_125 ).
cnf(c_0_128,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_126]),c_0_127]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD009-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n011.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 15:36:56 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 25.59/4.19 % Version: 3.5.1
% 25.59/4.19 % Preprocessing class: FSMSSMSSSSSNFFN.
% 25.59/4.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 25.59/4.19 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 25.59/4.19 % Starting new_bool_3 with 300s (1) cores
% 25.59/4.19 % Starting new_bool_1 with 300s (1) cores
% 25.59/4.19 % Starting sh5l with 300s (1) cores
% 25.59/4.19 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2260295 completed with status 0
% 25.59/4.19 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 25.59/4.19 % Preprocessing class: FSMSSMSSSSSNFFN.
% 25.59/4.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 25.59/4.19 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 25.59/4.19 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 25.59/4.19 % No SInE strategy applied
% 25.59/4.19 % Search class: FGUNF-FFMS21-SFFFFFNN
% 25.59/4.19 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 25.59/4.19 % Starting SubtermCWHack with 136s (1) cores
% 25.59/4.19 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 25.59/4.19 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 25.59/4.19 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 25.59/4.19 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 25.59/4.19 % U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 2260304 completed with status 0
% 25.59/4.19 % Result found by U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 25.59/4.19 % Preprocessing class: FSMSSMSSSSSNFFN.
% 25.59/4.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 25.59/4.19 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 25.59/4.19 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 25.59/4.19 % No SInE strategy applied
% 25.59/4.19 % Search class: FGUNF-FFMS21-SFFFFFNN
% 25.59/4.19 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 25.59/4.19 % Starting SubtermCWHack with 136s (1) cores
% 25.59/4.19 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 25.59/4.19 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 25.59/4.19 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 25.59/4.19 % Preprocessing time : 0.001 s
% 25.59/4.19 % Presaturation interreduction done
% 25.59/4.19
% 25.59/4.19 % Proof found!
% 25.59/4.19 % SZS status Unsatisfiable
% 25.59/4.19 % SZS output start CNFRefutation
% See solution above
% 25.59/4.19 % Parsed axioms : 31
% 25.59/4.19 % Removed by relevancy pruning/SinE : 0
% 25.59/4.19 % Initial clauses : 31
% 25.59/4.19 % Removed in clause preprocessing : 0
% 25.59/4.19 % Initial clauses in saturation : 31
% 25.59/4.19 % Processed clauses : 20277
% 25.59/4.19 % ...of these trivial : 888
% 25.59/4.19 % ...subsumed : 13768
% 25.59/4.19 % ...remaining for further processing : 5621
% 25.59/4.19 % Other redundant clauses eliminated : 0
% 25.59/4.19 % Clauses deleted for lack of memory : 0
% 25.59/4.19 % Backward-subsumed : 516
% 25.59/4.19 % Backward-rewritten : 33
% 25.59/4.19 % Generated clauses : 196180
% 25.59/4.19 % ...of the previous two non-redundant : 171457
% 25.59/4.19 % ...aggressively subsumed : 0
% 25.59/4.19 % Contextual simplify-reflections : 58
% 25.59/4.19 % Paramodulations : 196163
% 25.59/4.19 % Factorizations : 0
% 25.59/4.19 % NegExts : 0
% 25.59/4.19 % Equation resolutions : 0
% 25.59/4.19 % Disequality decompositions : 0
% 25.59/4.19 % Total rewrite steps : 72290
% 25.59/4.19 % ...of those cached : 71022
% 25.59/4.19 % Propositional unsat checks : 0
% 25.59/4.19 % Propositional check models : 0
% 25.59/4.19 % Propositional check unsatisfiable : 0
% 25.59/4.19 % Propositional clauses : 0
% 25.59/4.19 % Propositional clauses after purity: 0
% 25.59/4.19 % Propositional unsat core size : 0
% 25.59/4.19 % Propositional preprocessing time : 0.000
% 25.59/4.19 % Propositional encoding time : 0.000
% 25.59/4.19 % Propositional solver time : 0.000
% 25.59/4.19 % Success case prop preproc time : 0.000
% 25.59/4.19 % Success case prop encoding time : 0.000
% 25.59/4.19 % Success case prop solver time : 0.000
% 25.59/4.19 % Current number of processed clauses : 5024
% 25.59/4.19 % Positive orientable unit clauses : 1387
% 25.59/4.19 % Positive unorientable unit clauses: 0
% 25.59/4.19 % Negative unit clauses : 605
% 25.59/4.19 % Non-unit-clauses : 3032
% 25.59/4.19 % Current number of unprocessed clauses: 150568
% 25.59/4.19 % ...number of literals in the above : 501789
% 25.59/4.19 % Current number of archived formulas : 0
% 25.59/4.19 % Current number of archived clauses : 597
% 25.59/4.19 % Clause-clause subsumption calls (NU) : 697663
% 25.59/4.19 % Rec. Clause-clause subsumption calls : 442096
% 25.59/4.19 % Non-unit clause-clause subsumptions : 5784
% 25.59/4.19 % Unit Clause-clause subsumption calls : 310210
% 25.59/4.19 % Rewrite failures with RHS unbound : 0
% 25.59/4.19 % BW rewrite match attempts : 9401
% 25.59/4.19 % BW rewrite match successes : 188
% 25.59/4.19 % Condensation attempts : 0
% 25.59/4.19 % Condensation successes : 0
% 25.59/4.19 % Termbank termtop insertions : 3473851
% 25.59/4.19 % Search garbage collected termcells : 73
% 25.59/4.19
% 25.59/4.19 % -------------------------------------------------
% 25.59/4.19 % User time : 3.484 s
% 25.59/4.19 % System time : 0.141 s
% 25.59/4.19 % Total time : 3.624 s
% 25.59/4.19 % Maximum resident set size: 3660 pages
% 25.59/4.19
% 25.59/4.19 % -------------------------------------------------
% 25.59/4.19 % User time : 17.319 s
% 25.59/4.19 % System time : 0.724 s
% 25.59/4.19 % Total time : 18.043 s
% 25.59/4.19 % Maximum resident set size: 4864 pages
% 25.59/4.19 % E exiting
%------------------------------------------------------------------------------