%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD041-3 : TPTP v9.2.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:18:21 PM UTC 2026
% Result : Unsatisfiable 14.32s 9.77s
% Output : CNFRefutation 14.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 27
% Syntax : Number of clauses : 184 ( 57 unt; 12 nHn; 184 RR)
% Number of literals : 399 ( 0 equ; 209 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 250 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(well_definedness_of_multiplicative_inverse,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(not_sum_4,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_4) ).
cnf(existence_of_inverse_addition,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
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(compatibility_of_order_relation_and_addition,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X4,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(totality_of_order_relation,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_order_relation) ).
cnf(existence_of_identity_addition,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(well_definedness_of_additive_inverse,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(antisymmetry_of_order_relation,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
cnf(associativity_addition_1,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(existence_of_inverse_multiplication,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
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(associativity_multiplication_2,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
cnf(existence_of_identity_multiplication,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(commutativity_multiplication,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(associativity_addition_2,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
cnf(associativity_multiplication_1,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(product_5,negated_conjecture,
product(a,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_5) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(totality_of_multiplication,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
cnf(transitivity_of_order_relation,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',transitivity_of_order_relation) ).
cnf(distributivity_2,axiom,
( product(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ product(X4,X2,X6)
| ~ product(X5,X2,X7)
| ~ sum(X6,X7,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_2) ).
cnf(well_definedness_of_multiplication,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplication) ).
cnf(distributivity_1,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X6)
| ~ product(X6,X7,X3)
| ~ product(X4,X7,X1)
| ~ product(X5,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
cnf(c_0_27,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_28,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_29,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
not_sum_4 ).
cnf(c_0_30,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_31,hypothesis,
defined(multiplicative_inverse(b)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_32,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_33,hypothesis,
sum(additive_inverse(multiplicative_inverse(b)),multiplicative_inverse(b),additive_identity),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_35,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X4,X5,X2) ),
compatibility_of_order_relation_and_addition ).
cnf(c_0_36,hypothesis,
sum(multiplicative_inverse(b),additive_inverse(multiplicative_inverse(b)),additive_identity),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_38,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_30,c_0_34]) ).
cnf(c_0_39,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_40,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_41,hypothesis,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X2,multiplicative_inverse(b))
| ~ sum(X2,additive_inverse(multiplicative_inverse(b)),X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_37]) ).
cnf(c_0_43,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_32,c_0_38]) ).
cnf(c_0_44,plain,
( sum(additive_identity,additive_inverse(X1),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,hypothesis,
( less_or_equal(additive_identity,additive_identity)
| ~ less_or_equal(multiplicative_inverse(b),multiplicative_inverse(b)) ),
inference(spm,[status(thm)],[c_0_41,c_0_36]) ).
cnf(c_0_46,hypothesis,
less_or_equal(multiplicative_inverse(b),multiplicative_inverse(b)),
inference(spm,[status(thm)],[c_0_42,c_0_31]) ).
cnf(c_0_47,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_48,plain,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X2,additive_identity)
| ~ sum(X2,additive_inverse(additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_43]) ).
cnf(c_0_49,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_44,c_0_34]) ).
cnf(c_0_50,hypothesis,
less_or_equal(additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
cnf(c_0_51,hypothesis,
sum(additive_identity,a,a),
inference(spm,[status(thm)],[c_0_39,c_0_47]) ).
cnf(c_0_52,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_53,plain,
less_or_equal(additive_inverse(additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50])]) ).
cnf(c_0_54,plain,
( less_or_equal(X1,additive_inverse(additive_identity))
| ~ less_or_equal(X2,additive_identity)
| ~ sum(X2,additive_inverse(additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_49]) ).
cnf(c_0_55,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1 ).
cnf(c_0_56,hypothesis,
sum(a,additive_identity,a),
inference(spm,[status(thm)],[c_0_32,c_0_51]) ).
cnf(c_0_57,plain,
( sum(additive_identity,additive_identity,additive_inverse(additive_identity))
| ~ less_or_equal(additive_identity,additive_inverse(additive_identity)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,plain,
less_or_equal(additive_identity,additive_inverse(additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_43]),c_0_50])]) ).
cnf(c_0_59,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_60,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
not_sum_3 ).
cnf(c_0_61,hypothesis,
( sum(X1,X2,a)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,plain,
sum(additive_identity,additive_identity,additive_inverse(additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).
cnf(c_0_63,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
associativity_multiplication_2 ).
cnf(c_0_64,hypothesis,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_47]),c_0_60]) ).
cnf(c_0_65,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_66,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_47]),c_0_60]) ).
cnf(c_0_67,hypothesis,
( sum(X1,additive_inverse(additive_identity),a)
| ~ sum(X1,additive_identity,a) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_68,hypothesis,
( product(X1,a,X2)
| ~ product(X3,multiplicative_inverse(a),X1)
| ~ product(X3,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_69,hypothesis,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_70,hypothesis,
( sum(X1,X2,a)
| ~ sum(X3,a,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_55,c_0_51]) ).
cnf(c_0_71,hypothesis,
( sum(additive_inverse(additive_identity),X1,a)
| ~ sum(X1,additive_identity,a) ),
inference(spm,[status(thm)],[c_0_32,c_0_67]) ).
cnf(c_0_72,plain,
( sum(X1,X2,additive_identity)
| ~ sum(X1,X3,additive_inverse(additive_identity))
| ~ sum(X3,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_38]) ).
cnf(c_0_73,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_32,c_0_49]) ).
cnf(c_0_74,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_75,hypothesis,
( product(multiplicative_inverse(a),a,X1)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_76,hypothesis,
sum(additive_inverse(a),a,additive_identity),
inference(spm,[status(thm)],[c_0_30,c_0_47]) ).
cnf(c_0_77,hypothesis,
( sum(X1,a,a)
| ~ sum(X1,additive_inverse(additive_identity),additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_56])]) ).
cnf(c_0_78,plain,
( sum(additive_inverse(additive_identity),X1,additive_identity)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_79,plain,
( sum(additive_inverse(additive_inverse(X1)),additive_inverse(X1),additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_40]) ).
cnf(c_0_80,hypothesis,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_28]),c_0_29]) ).
cnf(c_0_81,hypothesis,
( product(a,multiplicative_inverse(a),X1)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_82,hypothesis,
product(multiplicative_identity,a,a),
inference(spm,[status(thm)],[c_0_65,c_0_47]) ).
cnf(c_0_83,hypothesis,
sum(a,additive_inverse(a),additive_identity),
inference(spm,[status(thm)],[c_0_32,c_0_76]) ).
cnf(c_0_84,hypothesis,
sum(additive_inverse(additive_identity),a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_62])]) ).
cnf(c_0_85,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
associativity_addition_2 ).
cnf(c_0_86,hypothesis,
sum(additive_inverse(additive_inverse(additive_identity)),a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_79]),c_0_34])]) ).
cnf(c_0_87,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1 ).
cnf(c_0_88,hypothesis,
product(b,multiplicative_inverse(b),multiplicative_identity),
inference(spm,[status(thm)],[c_0_74,c_0_80]) ).
cnf(c_0_89,hypothesis,
( product(X1,a,X2)
| ~ product(a,multiplicative_identity,X2)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_81]) ).
cnf(c_0_90,hypothesis,
product(a,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_74,c_0_82]) ).
cnf(c_0_91,hypothesis,
( sum(X1,X2,additive_identity)
| ~ sum(X3,additive_inverse(a),X2)
| ~ sum(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_55,c_0_83]) ).
cnf(c_0_92,hypothesis,
sum(additive_identity,additive_inverse(a),additive_inverse(a)),
inference(spm,[status(thm)],[c_0_44,c_0_47]) ).
cnf(c_0_93,hypothesis,
sum(a,additive_inverse(additive_identity),a),
inference(spm,[status(thm)],[c_0_32,c_0_84]) ).
cnf(c_0_94,plain,
( sum(X1,additive_inverse(X2),X3)
| ~ defined(X2)
| ~ sum(X4,additive_inverse(additive_inverse(X2)),X1)
| ~ sum(X4,additive_identity,X3) ),
inference(spm,[status(thm)],[c_0_85,c_0_79]) ).
cnf(c_0_95,hypothesis,
sum(a,additive_inverse(additive_inverse(additive_identity)),a),
inference(spm,[status(thm)],[c_0_32,c_0_86]) ).
cnf(c_0_96,hypothesis,
( sum(X1,a,a)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_70,c_0_51]) ).
cnf(c_0_97,negated_conjecture,
product(a,b,additive_identity),
product_5 ).
cnf(c_0_98,hypothesis,
( product(X1,X2,multiplicative_identity)
| ~ product(X3,multiplicative_inverse(b),X2)
| ~ product(X1,X3,b) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_99,hypothesis,
product(multiplicative_identity,multiplicative_inverse(b),multiplicative_inverse(b)),
inference(spm,[status(thm)],[c_0_65,c_0_31]) ).
cnf(c_0_100,hypothesis,
( product(X1,a,a)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_101,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_102,hypothesis,
( sum(X1,additive_inverse(a),additive_identity)
| ~ sum(X1,additive_identity,a) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_103,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_multiplication ).
cnf(c_0_104,plain,
( product(multiplicative_identity,additive_inverse(X1),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_40]) ).
cnf(c_0_105,hypothesis,
( less_or_equal(X1,a)
| ~ less_or_equal(X2,a)
| ~ sum(X2,additive_inverse(additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_93]) ).
cnf(c_0_106,hypothesis,
( sum(a,additive_inverse(additive_identity),X1)
| ~ sum(a,additive_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_34])]) ).
cnf(c_0_107,hypothesis,
less_or_equal(a,a),
inference(spm,[status(thm)],[c_0_42,c_0_47]) ).
cnf(c_0_108,plain,
( less_or_equal(X1,additive_inverse(X2))
| less_or_equal(additive_inverse(X2),X1)
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_40]) ).
cnf(c_0_109,hypothesis,
( sum(X1,additive_inverse(a),X2)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_85,c_0_83]) ).
cnf(c_0_110,hypothesis,
( sum(a,X1,a)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_32,c_0_96]) ).
cnf(c_0_111,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_39,c_0_34]) ).
cnf(c_0_112,hypothesis,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X2,a)
| ~ sum(X2,additive_inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_83]) ).
cnf(c_0_113,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_65,c_0_34]) ).
cnf(c_0_114,hypothesis,
( product(X1,X2,a)
| ~ product(X3,a,X2)
| ~ product(X1,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_87,c_0_82]) ).
cnf(c_0_115,negated_conjecture,
product(b,a,additive_identity),
inference(spm,[status(thm)],[c_0_74,c_0_97]) ).
cnf(c_0_116,hypothesis,
( product(X1,multiplicative_inverse(b),multiplicative_identity)
| ~ product(X1,multiplicative_identity,b) ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_117,hypothesis,
product(multiplicative_identity,b,b),
inference(spm,[status(thm)],[c_0_65,c_0_28]) ).
cnf(c_0_118,hypothesis,
( product(X1,multiplicative_inverse(b),X2)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X3,b,X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_88]) ).
cnf(c_0_119,hypothesis,
( product(a,X1,a)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_100]) ).
cnf(c_0_120,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_65,c_0_101]) ).
cnf(c_0_121,hypothesis,
( sum(additive_inverse(a),X1,additive_identity)
| ~ sum(X1,additive_identity,a) ),
inference(spm,[status(thm)],[c_0_32,c_0_102]) ).
cnf(c_0_122,hypothesis,
( product(X1,b,multiply(X1,b))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_103,c_0_28]) ).
cnf(c_0_123,plain,
product(multiplicative_identity,additive_inverse(additive_identity),additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_104,c_0_34]) ).
cnf(c_0_124,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
transitivity_of_order_relation ).
cnf(c_0_125,hypothesis,
( less_or_equal(X1,a)
| ~ sum(a,additive_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107])]) ).
cnf(c_0_126,hypothesis,
( sum(X1,X2,additive_inverse(a))
| ~ sum(X3,additive_inverse(a),X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_55,c_0_92]) ).
cnf(c_0_127,hypothesis,
( less_or_equal(X1,a)
| ~ less_or_equal(X2,additive_identity)
| ~ sum(X2,a,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_51]) ).
cnf(c_0_128,plain,
( less_or_equal(additive_inverse(X1),additive_identity)
| less_or_equal(additive_identity,additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_108,c_0_34]) ).
cnf(c_0_129,hypothesis,
( sum(X1,additive_inverse(a),a)
| ~ sum(a,a,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_111])]) ).
cnf(c_0_130,hypothesis,
( less_or_equal(additive_inverse(a),additive_identity)
| ~ less_or_equal(additive_identity,a) ),
inference(spm,[status(thm)],[c_0_112,c_0_92]) ).
cnf(c_0_131,hypothesis,
( less_or_equal(X1,additive_inverse(a))
| ~ less_or_equal(X2,additive_identity)
| ~ sum(X2,additive_inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_92]) ).
cnf(c_0_132,hypothesis,
( less_or_equal(X1,a)
| less_or_equal(a,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_47]) ).
cnf(c_0_133,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(spm,[status(thm)],[c_0_74,c_0_113]) ).
cnf(c_0_134,negated_conjecture,
( product(X1,additive_identity,a)
| ~ product(X1,b,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_135,hypothesis,
( product(multiplicative_inverse(b),X1,multiplicative_identity)
| ~ product(X1,multiplicative_identity,b) ),
inference(spm,[status(thm)],[c_0_74,c_0_116]) ).
cnf(c_0_136,hypothesis,
product(b,multiplicative_identity,b),
inference(spm,[status(thm)],[c_0_74,c_0_117]) ).
cnf(c_0_137,negated_conjecture,
( product(X1,X2,additive_identity)
| ~ product(X3,b,X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_87,c_0_97]) ).
cnf(c_0_138,hypothesis,
( product(X1,multiplicative_inverse(b),a)
| ~ product(a,b,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120])]) ).
cnf(c_0_139,hypothesis,
( sum(X1,additive_identity,a)
| ~ sum(X1,additive_inverse(a),additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_121]),c_0_56])]) ).
cnf(c_0_140,axiom,
( product(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ product(X4,X2,X6)
| ~ product(X5,X2,X7)
| ~ sum(X6,X7,X3) ),
distributivity_2 ).
cnf(c_0_141,hypothesis,
product(additive_identity,b,multiply(additive_identity,b)),
inference(spm,[status(thm)],[c_0_122,c_0_34]) ).
cnf(c_0_142,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_multiplication ).
cnf(c_0_143,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X6)
| ~ product(X6,X7,X3)
| ~ product(X4,X7,X1)
| ~ product(X5,X7,X2) ),
distributivity_1 ).
cnf(c_0_144,plain,
product(additive_inverse(additive_identity),multiplicative_identity,additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_74,c_0_123]) ).
cnf(c_0_145,hypothesis,
( less_or_equal(X1,a)
| ~ less_or_equal(X1,X2)
| ~ sum(a,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_146,hypothesis,
( sum(X1,additive_identity,additive_inverse(a))
| ~ sum(X1,a,additive_identity) ),
inference(spm,[status(thm)],[c_0_126,c_0_83]) ).
cnf(c_0_147,hypothesis,
( less_or_equal(additive_identity,a)
| ~ less_or_equal(additive_inverse(a),additive_identity) ),
inference(spm,[status(thm)],[c_0_127,c_0_76]) ).
cnf(c_0_148,hypothesis,
( less_or_equal(additive_identity,additive_inverse(a))
| less_or_equal(additive_inverse(a),additive_identity) ),
inference(spm,[status(thm)],[c_0_128,c_0_47]) ).
cnf(c_0_149,hypothesis,
( sum(X1,a,X2)
| ~ sum(X3,a,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_85,c_0_51]) ).
cnf(c_0_150,hypothesis,
( sum(X1,additive_identity,a)
| ~ sum(X1,additive_inverse(additive_identity),a) ),
inference(spm,[status(thm)],[c_0_61,c_0_38]) ).
cnf(c_0_151,hypothesis,
( sum(additive_inverse(a),X1,a)
| ~ sum(a,a,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_129]) ).
cnf(c_0_152,hypothesis,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X1,additive_inverse(a))
| ~ less_or_equal(additive_identity,a) ),
inference(spm,[status(thm)],[c_0_124,c_0_130]) ).
cnf(c_0_153,hypothesis,
( less_or_equal(a,additive_inverse(a))
| ~ sum(additive_inverse(a),additive_identity,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_71]),c_0_53])]) ).
cnf(c_0_154,hypothesis,
( less_or_equal(a,additive_identity)
| less_or_equal(additive_identity,a) ),
inference(spm,[status(thm)],[c_0_132,c_0_34]) ).
cnf(c_0_155,plain,
( product(X1,multiplicative_identity,X2)
| ~ product(X3,additive_identity,X2)
| ~ product(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_133]) ).
cnf(c_0_156,hypothesis,
product(multiplicative_inverse(b),additive_identity,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_136])]) ).
cnf(c_0_157,negated_conjecture,
( product(X1,additive_identity,additive_identity)
| ~ product(X1,a,a) ),
inference(spm,[status(thm)],[c_0_137,c_0_97]) ).
cnf(c_0_158,hypothesis,
( product(multiplicative_inverse(b),X1,a)
| ~ product(a,b,X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_138]) ).
cnf(c_0_159,plain,
( sum(additive_identity,X1,additive_identity)
| ~ sum(additive_inverse(additive_identity),additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_49]) ).
cnf(c_0_160,hypothesis,
( sum(additive_inverse(additive_identity),additive_identity,a)
| ~ sum(additive_identity,additive_identity,additive_inverse(a)) ),
inference(spm,[status(thm)],[c_0_139,c_0_78]) ).
cnf(c_0_161,hypothesis,
( product(X1,b,X2)
| ~ product(X3,b,X4)
| ~ sum(X4,multiply(additive_identity,b),X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_162,plain,
( sum(additive_identity,multiply(X1,X2),multiply(X1,X2))
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_142]) ).
cnf(c_0_163,hypothesis,
( product(X1,b,X2)
| ~ product(X3,multiply(additive_identity,b),X2)
| ~ product(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_141]) ).
cnf(c_0_164,plain,
( sum(X1,X2,additive_inverse(additive_identity))
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X4,multiplicative_identity,X1)
| ~ sum(X4,X3,additive_inverse(additive_identity)) ),
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_165,hypothesis,
( less_or_equal(X1,a)
| ~ less_or_equal(X1,additive_inverse(a))
| ~ sum(a,a,additive_identity) ),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_166,hypothesis,
( less_or_equal(additive_identity,additive_inverse(a))
| less_or_equal(additive_identity,a) ),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_167,hypothesis,
( sum(X1,a,additive_identity)
| ~ sum(additive_inverse(a),additive_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_121]),c_0_56])]) ).
cnf(c_0_168,hypothesis,
( sum(additive_inverse(a),additive_identity,a)
| ~ sum(a,a,additive_inverse(additive_identity)) ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_169,hypothesis,
( less_or_equal(a,additive_identity)
| ~ sum(additive_inverse(a),additive_identity,a) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_154]) ).
cnf(c_0_170,hypothesis,
( product(X1,multiplicative_identity,a)
| ~ product(multiplicative_inverse(b),additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_171,negated_conjecture,
( product(multiplicative_inverse(b),additive_identity,additive_identity)
| ~ product(a,b,a) ),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_172,hypothesis,
( sum(additive_identity,additive_identity,additive_inverse(a))
| ~ less_or_equal(additive_identity,additive_inverse(a))
| ~ less_or_equal(additive_identity,a) ),
inference(spm,[status(thm)],[c_0_52,c_0_130]) ).
cnf(c_0_173,hypothesis,
( less_or_equal(additive_identity,additive_inverse(a))
| ~ less_or_equal(a,additive_identity) ),
inference(spm,[status(thm)],[c_0_131,c_0_83]) ).
cnf(c_0_174,hypothesis,
~ sum(additive_identity,additive_identity,additive_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_60]) ).
cnf(c_0_175,hypothesis,
( product(X1,b,multiply(additive_identity,b))
| ~ product(X2,b,additive_identity)
| ~ sum(X2,additive_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_28]),c_0_34])]) ).
cnf(c_0_176,hypothesis,
( product(X1,b,a)
| ~ product(multiplicative_inverse(b),additive_identity,X1)
| ~ product(a,b,multiply(additive_identity,b)) ),
inference(spm,[status(thm)],[c_0_163,c_0_158]) ).
cnf(c_0_177,plain,
( sum(X1,X2,additive_inverse(additive_identity))
| ~ product(additive_identity,multiplicative_identity,X2)
| ~ product(additive_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_164,c_0_62]) ).
cnf(c_0_178,hypothesis,
( less_or_equal(additive_identity,a)
| ~ sum(a,a,additive_identity) ),
inference(spm,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_179,hypothesis,
( sum(a,a,additive_identity)
| ~ sum(a,a,additive_inverse(additive_identity)) ),
inference(spm,[status(thm)],[c_0_167,c_0_168]) ).
cnf(c_0_180,hypothesis,
( less_or_equal(a,additive_identity)
| ~ sum(a,a,additive_inverse(additive_identity)) ),
inference(spm,[status(thm)],[c_0_169,c_0_168]) ).
cnf(c_0_181,hypothesis,
( product(additive_identity,multiplicative_identity,a)
| ~ product(a,b,a) ),
inference(spm,[status(thm)],[c_0_170,c_0_171]) ).
cnf(c_0_182,hypothesis,
( ~ less_or_equal(additive_identity,a)
| ~ less_or_equal(a,additive_identity) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_174]) ).
cnf(c_0_183,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_175,c_0_176,c_0_177,c_0_178,c_0_179,c_0_180,c_0_181,c_0_182,c_0_156,c_0_56,c_0_97]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD041-3 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n015.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 17:28:47 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 14.32/9.77 % Version : CSE_E---1.7
% 14.32/9.77 % Problem : theBenchmark.p
% 14.32/9.77 % SZS status Unsatisfiable for theBenchmark.p
% 14.32/9.77 % SZS output start CNFRefutation
% See solution above
% 14.42/9.82 % Total time : 7.383s
%------------------------------------------------------------------------------