%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD043-5 : TPTP v9.2.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n016.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 26.04s 15.68s
% Output : CNFRefutation 26.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 24
% Syntax : Number of clauses : 188 ( 64 unt; 11 nHn; 188 RR)
% Number of literals : 405 ( 0 equ; 211 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 : 269 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(existence_of_identity_multiplication,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
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(associativity_multiplication_2,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
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/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_2) ).
cnf(commutativity_multiplication,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(existence_of_identity_addition,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
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/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(totality_of_multiplication,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
cnf(different_identities,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',different_identities) ).
cnf(existence_of_inverse_multiplication,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(associativity_multiplication_1,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(existence_of_inverse_addition,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(associativity_addition_1,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(well_definedness_of_additive_inverse,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
cnf(totality_of_order_relation,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_order_relation) ).
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/sandbox/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
cnf(well_definedness_of_multiplication,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_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/sandbox/benchmark/Axioms/FLD002-0.ax',transitivity_of_order_relation) ).
cnf(not_product_2,negated_conjecture,
~ product(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_2) ).
cnf(c_0_24,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_25,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_26,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_27,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
associativity_multiplication_2 ).
cnf(c_0_28,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,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_30,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_31,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_24,c_0_26]) ).
cnf(c_0_32,plain,
( product(X1,multiplicative_identity,X2)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X3,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
( product(X1,multiplicative_identity,X2)
| ~ product(X3,multiplicative_identity,X4)
| ~ sum(X4,multiplicative_identity,X2)
| ~ sum(X3,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_34,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_36,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_37,plain,
( product(X1,multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_28]) ).
cnf(c_0_38,plain,
( product(X1,multiplicative_identity,X2)
| ~ sum(additive_identity,multiplicative_identity,X2)
| ~ sum(additive_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_35,c_0_25]) ).
cnf(c_0_40,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_41,plain,
( sum(X1,X2,multiplicative_identity)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X4,multiplicative_identity,X1)
| ~ sum(X4,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_36,c_0_28]) ).
cnf(c_0_42,plain,
( product(X1,multiplicative_identity,additive_identity)
| ~ product(additive_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_34]) ).
cnf(c_0_43,plain,
( product(X1,multiplicative_identity,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_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_44,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_45,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_multiplication ).
cnf(c_0_46,plain,
( defined(multiplicative_inverse(multiplicative_identity))
| sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_40,c_0_25]) ).
cnf(c_0_47,plain,
( sum(X1,additive_identity,multiplicative_identity)
| ~ product(X2,multiplicative_identity,X1)
| ~ sum(X2,additive_identity,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_41,c_0_34]) ).
cnf(c_0_48,plain,
( product(multiplicative_identity,multiplicative_identity,additive_identity)
| ~ sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,plain,
sum(multiplicative_identity,additive_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_44,c_0_39]) ).
cnf(c_0_50,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
different_identities ).
cnf(c_0_51,plain,
( product(X1,multiplicative_identity,multiply(X1,multiplicative_identity))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_25]) ).
cnf(c_0_52,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_53,plain,
( product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_24,c_0_46]) ).
cnf(c_0_54,plain,
~ 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_47,c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_55,plain,
product(multiplicative_identity,multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity)),
inference(spm,[status(thm)],[c_0_51,c_0_25]) ).
cnf(c_0_56,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1 ).
cnf(c_0_57,plain,
( product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_52,c_0_25]) ).
cnf(c_0_58,plain,
product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)),
inference(sr,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,plain,
product(multiply(multiplicative_identity,multiplicative_identity),multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_37,c_0_55]) ).
cnf(c_0_60,plain,
( product(X1,X2,multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ product(X1,X3,multiplicative_inverse(multiplicative_identity))
| ~ product(X3,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_61,plain,
product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_inverse(multiplicative_identity)),
inference(spm,[status(thm)],[c_0_30,c_0_58]) ).
cnf(c_0_62,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_63,plain,
( product(X1,multiplicative_identity,X2)
| ~ product(X3,multiply(multiplicative_identity,multiplicative_identity),X1)
| ~ product(X3,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_59]) ).
cnf(c_0_64,plain,
( product(multiplicative_inverse(multiplicative_identity),X1,multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_54]) ).
cnf(c_0_65,plain,
sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity),
inference(spm,[status(thm)],[c_0_62,c_0_25]) ).
cnf(c_0_66,plain,
( product(X1,additive_identity,multiply(X1,additive_identity))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_26]) ).
cnf(c_0_67,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1 ).
cnf(c_0_68,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_35,c_0_26]) ).
cnf(c_0_69,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_70,plain,
( product(X1,additive_identity,X2)
| ~ product(X3,additive_identity,X2)
| ~ product(X3,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_31]) ).
cnf(c_0_71,plain,
( product(multiplicative_identity,multiplicative_identity,X1)
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_55])]) ).
cnf(c_0_72,plain,
( product(X1,multiplicative_identity,X2)
| ~ product(X3,additive_identity,X2)
| ~ product(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_34]) ).
cnf(c_0_73,plain,
sum(multiplicative_identity,additive_inverse(multiplicative_identity),additive_identity),
inference(spm,[status(thm)],[c_0_44,c_0_65]) ).
cnf(c_0_74,plain,
product(multiplicative_identity,additive_identity,multiply(multiplicative_identity,additive_identity)),
inference(spm,[status(thm)],[c_0_66,c_0_25]) ).
cnf(c_0_75,plain,
( sum(X1,X2,additive_identity)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_76,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_62,c_0_26]) ).
cnf(c_0_77,plain,
( sum(additive_inverse(additive_inverse(X1)),additive_inverse(X1),additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_69]) ).
cnf(c_0_78,plain,
( product(X1,additive_identity,additive_identity)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_31]) ).
cnf(c_0_79,plain,
( product(X1,multiplicative_identity,X2)
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ product(X3,multiplicative_inverse(multiplicative_identity),X1)
| ~ product(X3,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_57]) ).
cnf(c_0_80,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity)),
inference(spm,[status(thm)],[c_0_71,c_0_61]) ).
cnf(c_0_81,plain,
( product(X1,multiplicative_identity,additive_identity)
| ~ product(multiplicative_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_31]) ).
cnf(c_0_82,plain,
( sum(X1,X2,additive_identity)
| ~ sum(X3,additive_inverse(multiplicative_identity),X2)
| ~ sum(X1,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_67,c_0_73]) ).
cnf(c_0_83,plain,
( sum(X1,multiplicative_identity,multiplicative_identity)
| ~ product(X2,multiplicative_identity,X1)
| ~ sum(X2,multiplicative_identity,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_41,c_0_28]) ).
cnf(c_0_84,plain,
product(additive_identity,multiplicative_identity,multiply(multiplicative_identity,additive_identity)),
inference(spm,[status(thm)],[c_0_30,c_0_74]) ).
cnf(c_0_85,plain,
( sum(X1,additive_identity,additive_identity)
| ~ sum(X1,additive_inverse(additive_identity),additive_identity) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_86,plain,
sum(additive_inverse(additive_inverse(additive_identity)),additive_inverse(additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_77,c_0_26]) ).
cnf(c_0_87,plain,
product(multiply(multiplicative_identity,multiplicative_identity),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_78,c_0_55]) ).
cnf(c_0_88,plain,
( product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,X1)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_58]),c_0_54]) ).
cnf(c_0_89,plain,
( product(X1,multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_80]) ).
cnf(c_0_90,plain,
( product(X1,multiplicative_identity,X2)
| ~ product(X3,multiplicative_identity,X4)
| ~ sum(X4,additive_identity,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_34]) ).
cnf(c_0_91,plain,
product(multiply(multiplicative_identity,additive_identity),multiplicative_identity,additive_identity),
inference(spm,[status(thm)],[c_0_81,c_0_74]) ).
cnf(c_0_92,plain,
( sum(X1,additive_identity,additive_identity)
| ~ sum(X1,multiplicative_identity,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_82,c_0_73]) ).
cnf(c_0_93,plain,
sum(multiply(multiplicative_identity,additive_identity),multiplicative_identity,multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_39])]) ).
cnf(c_0_94,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_95,plain,
sum(additive_inverse(additive_inverse(additive_identity)),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_96,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_44,c_0_76]) ).
cnf(c_0_97,plain,
( sum(additive_identity,additive_inverse(X1),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_69]) ).
cnf(c_0_98,plain,
( product(X1,X2,additive_identity)
| ~ product(X1,X3,multiply(multiplicative_identity,multiplicative_identity))
| ~ product(X3,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_87]) ).
cnf(c_0_99,plain,
( product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),X1)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_88]) ).
cnf(c_0_100,plain,
( product(X1,additive_identity,X2)
| ~ product(X3,multiply(multiplicative_identity,multiplicative_identity),X1)
| ~ product(X3,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_87]) ).
cnf(c_0_101,plain,
( product(multiplicative_identity,X1,multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_89]) ).
cnf(c_0_102,plain,
( product(X1,multiplicative_identity,X2)
| ~ sum(multiply(multiplicative_identity,additive_identity),additive_identity,X1)
| ~ sum(additive_identity,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_103,plain,
sum(multiply(multiplicative_identity,additive_identity),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_104,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_105,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_94]) ).
cnf(c_0_106,plain,
sum(additive_identity,additive_inverse(additive_inverse(additive_identity)),additive_identity),
inference(spm,[status(thm)],[c_0_44,c_0_95]) ).
cnf(c_0_107,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_108,plain,
( sum(X1,X2,additive_identity)
| ~ sum(X3,additive_inverse(additive_identity),X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_67,c_0_96]) ).
cnf(c_0_109,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_97,c_0_26]) ).
cnf(c_0_110,plain,
( product(multiplicative_identity,additive_inverse(X1),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_69]) ).
cnf(c_0_111,plain,
( product(multiplicative_identity,X1,additive_identity)
| ~ product(multiplicative_inverse(multiplicative_identity),additive_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_55])]) ).
cnf(c_0_112,plain,
( product(multiplicative_inverse(multiplicative_identity),additive_identity,X1)
| ~ product(multiplicative_identity,additive_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_55])]) ).
cnf(c_0_113,plain,
( product(additive_identity,multiplicative_identity,X1)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_114,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_104,c_0_96]) ).
cnf(c_0_115,plain,
less_or_equal(additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_105,c_0_26]) ).
cnf(c_0_116,plain,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X2,additive_identity)
| ~ sum(X2,additive_inverse(additive_inverse(additive_identity)),X1) ),
inference(spm,[status(thm)],[c_0_104,c_0_106]) ).
cnf(c_0_117,plain,
( sum(additive_identity,additive_inverse(additive_inverse(X1)),additive_inverse(additive_inverse(X1)))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_97,c_0_69]) ).
cnf(c_0_118,hypothesis,
product(multiplicative_identity,a,a),
inference(spm,[status(thm)],[c_0_24,c_0_107]) ).
cnf(c_0_119,plain,
( sum(X1,X2,multiplicative_identity)
| ~ sum(X3,multiplicative_identity,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_67,c_0_39]) ).
cnf(c_0_120,plain,
( sum(X1,additive_inverse(additive_identity),additive_identity)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_121,plain,
product(multiplicative_identity,additive_inverse(additive_identity),additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_110,c_0_26]) ).
cnf(c_0_122,plain,
( product(multiplicative_identity,X1,additive_identity)
| ~ product(multiplicative_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_123,plain,
( product(multiplicative_identity,additive_identity,X1)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_113]) ).
cnf(c_0_124,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_125,plain,
less_or_equal(additive_inverse(additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_109]),c_0_115])]) ).
cnf(c_0_126,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_104,c_0_109]) ).
cnf(c_0_127,plain,
less_or_equal(additive_inverse(additive_inverse(additive_identity)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_115]),c_0_26])]) ).
cnf(c_0_128,hypothesis,
( sum(X1,X2,a)
| ~ product(X3,a,X2)
| ~ product(X4,a,X1)
| ~ sum(X4,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_36,c_0_118]) ).
cnf(c_0_129,plain,
( sum(X1,multiplicative_identity,multiplicative_identity)
| ~ sum(X1,multiply(multiplicative_identity,additive_identity),additive_identity) ),
inference(spm,[status(thm)],[c_0_119,c_0_93]) ).
cnf(c_0_130,plain,
( sum(additive_inverse(additive_identity),X1,additive_identity)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_44,c_0_120]) ).
cnf(c_0_131,hypothesis,
product(a,additive_identity,multiply(a,additive_identity)),
inference(spm,[status(thm)],[c_0_66,c_0_107]) ).
cnf(c_0_132,plain,
product(additive_inverse(additive_identity),multiplicative_identity,additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_30,c_0_121]) ).
cnf(c_0_133,plain,
( product(multiplicative_identity,X1,additive_identity)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_134,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_124,c_0_125]) ).
cnf(c_0_135,plain,
less_or_equal(additive_identity,additive_inverse(additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_86]),c_0_127])]) ).
cnf(c_0_136,hypothesis,
( sum(X1,a,a)
| ~ product(X2,a,X1)
| ~ sum(X2,multiplicative_identity,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_128,c_0_118]) ).
cnf(c_0_137,plain,
sum(additive_inverse(additive_identity),multiplicative_identity,multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_103])]) ).
cnf(c_0_138,hypothesis,
( product(X1,a,X2)
| ~ product(X3,a,X2)
| ~ product(X3,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_118]) ).
cnf(c_0_139,hypothesis,
product(additive_identity,a,multiply(a,additive_identity)),
inference(spm,[status(thm)],[c_0_30,c_0_131]) ).
cnf(c_0_140,plain,
( product(X1,multiplicative_identity,additive_inverse(additive_identity))
| ~ product(additive_inverse(additive_identity),multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_132]) ).
cnf(c_0_141,plain,
( product(X1,multiplicative_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_133]) ).
cnf(c_0_142,plain,
sum(additive_identity,additive_identity,additive_inverse(additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_135])]) ).
cnf(c_0_143,hypothesis,
sum(additive_inverse(a),a,additive_identity),
inference(spm,[status(thm)],[c_0_62,c_0_107]) ).
cnf(c_0_144,hypothesis,
sum(additive_identity,a,a),
inference(spm,[status(thm)],[c_0_35,c_0_107]) ).
cnf(c_0_145,hypothesis,
( sum(X1,a,a)
| ~ product(additive_inverse(additive_identity),a,X1) ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_146,hypothesis,
( product(X1,a,multiply(a,additive_identity))
| ~ product(additive_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_147,plain,
product(additive_identity,multiplicative_identity,additive_inverse(additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_142])]) ).
cnf(c_0_148,hypothesis,
sum(a,additive_inverse(a),additive_identity),
inference(spm,[status(thm)],[c_0_44,c_0_143]) ).
cnf(c_0_149,hypothesis,
( sum(X1,X2,a)
| ~ sum(X3,a,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_67,c_0_144]) ).
cnf(c_0_150,hypothesis,
sum(multiply(a,additive_identity),a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_147])]) ).
cnf(c_0_151,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_multiplication ).
cnf(c_0_152,hypothesis,
( sum(X1,X2,additive_identity)
| ~ sum(X3,additive_inverse(a),X2)
| ~ sum(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_67,c_0_148]) ).
cnf(c_0_153,hypothesis,
( sum(X1,a,a)
| ~ sum(X1,multiply(a,additive_identity),additive_identity) ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_154,plain,
( sum(additive_inverse(multiply(X1,X2)),multiply(X1,X2),additive_identity)
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_151]) ).
cnf(c_0_155,hypothesis,
( sum(X1,additive_identity,additive_identity)
| ~ sum(X1,a,a) ),
inference(spm,[status(thm)],[c_0_152,c_0_148]) ).
cnf(c_0_156,hypothesis,
sum(additive_inverse(multiply(a,additive_identity)),a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_26]),c_0_107])]) ).
cnf(c_0_157,plain,
( sum(additive_identity,multiply(X1,X2),multiply(X1,X2))
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_151]) ).
cnf(c_0_158,plain,
( sum(additive_identity,additive_inverse(multiply(X1,X2)),additive_inverse(multiply(X1,X2)))
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_97,c_0_151]) ).
cnf(c_0_159,hypothesis,
sum(additive_inverse(multiply(a,additive_identity)),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_160,plain,
( sum(additive_identity,multiply(X1,additive_identity),multiply(X1,additive_identity))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_157,c_0_26]) ).
cnf(c_0_161,plain,
( sum(X1,X2,additive_inverse(additive_identity))
| ~ sum(X3,additive_inverse(additive_identity),X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_67,c_0_109]) ).
cnf(c_0_162,hypothesis,
( sum(X1,a,a)
| ~ product(additive_identity,a,X1) ),
inference(spm,[status(thm)],[c_0_136,c_0_39]) ).
cnf(c_0_163,plain,
( less_or_equal(X1,additive_inverse(multiply(X2,X3)))
| ~ less_or_equal(X4,additive_identity)
| ~ defined(X3)
| ~ defined(X2)
| ~ sum(X4,additive_inverse(multiply(X2,X3)),X1) ),
inference(spm,[status(thm)],[c_0_104,c_0_158]) ).
cnf(c_0_164,hypothesis,
sum(additive_identity,additive_inverse(multiply(a,additive_identity)),additive_identity),
inference(spm,[status(thm)],[c_0_44,c_0_159]) ).
cnf(c_0_165,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
transitivity_of_order_relation ).
cnf(c_0_166,hypothesis,
sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity)),
inference(spm,[status(thm)],[c_0_160,c_0_107]) ).
cnf(c_0_167,plain,
( sum(X1,additive_identity,additive_inverse(additive_identity))
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_161,c_0_96]) ).
cnf(c_0_168,hypothesis,
( sum(X1,additive_identity,additive_identity)
| ~ product(additive_identity,a,X1) ),
inference(spm,[status(thm)],[c_0_155,c_0_162]) ).
cnf(c_0_169,plain,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X2,additive_inverse(multiply(X3,X4)))
| ~ defined(X4)
| ~ defined(X3)
| ~ sum(X2,multiply(X3,X4),X1) ),
inference(spm,[status(thm)],[c_0_104,c_0_154]) ).
cnf(c_0_170,hypothesis,
less_or_equal(additive_identity,additive_inverse(multiply(a,additive_identity))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_115]),c_0_26]),c_0_107])]) ).
cnf(c_0_171,plain,
( less_or_equal(X1,additive_inverse(additive_identity))
| ~ less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_165,c_0_135]) ).
cnf(c_0_172,hypothesis,
( less_or_equal(X1,multiply(a,additive_identity))
| ~ less_or_equal(X2,additive_identity)
| ~ sum(X2,multiply(a,additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_104,c_0_166]) ).
cnf(c_0_173,plain,
( sum(additive_identity,X1,additive_inverse(additive_identity))
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_44,c_0_167]) ).
cnf(c_0_174,hypothesis,
sum(multiply(a,additive_identity),additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_146]),c_0_34])]) ).
cnf(c_0_175,hypothesis,
( less_or_equal(X1,additive_identity)
| ~ sum(additive_identity,multiply(a,additive_identity),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_26]),c_0_107])]) ).
cnf(c_0_176,plain,
( product(X1,multiplicative_identity,X2)
| ~ product(X3,multiplicative_identity,X4)
| ~ sum(X4,additive_inverse(additive_identity),X2)
| ~ sum(X3,additive_inverse(additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_132]) ).
cnf(c_0_177,plain,
( sum(additive_identity,additive_inverse(additive_identity),X1)
| ~ less_or_equal(additive_inverse(additive_identity),X1)
| ~ less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_124,c_0_171]) ).
cnf(c_0_178,hypothesis,
less_or_equal(additive_inverse(additive_identity),multiply(a,additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_115]),c_0_174])]) ).
cnf(c_0_179,hypothesis,
less_or_equal(multiply(a,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_175,c_0_166]) ).
cnf(c_0_180,plain,
( product(X1,multiplicative_identity,additive_identity)
| ~ product(X2,multiplicative_identity,additive_identity)
| ~ sum(X2,additive_inverse(additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_176,c_0_96]) ).
cnf(c_0_181,hypothesis,
sum(additive_identity,additive_inverse(additive_identity),multiply(a,additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_179])]) ).
cnf(c_0_182,hypothesis,
product(multiply(a,additive_identity),multiplicative_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_34])]) ).
cnf(c_0_183,hypothesis,
( product(X1,a,X2)
| ~ product(X3,multiply(a,additive_identity),X2)
| ~ product(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_139]) ).
cnf(c_0_184,hypothesis,
product(multiplicative_identity,multiply(a,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_30,c_0_182]) ).
cnf(c_0_185,negated_conjecture,
~ product(additive_identity,a,additive_identity),
not_product_2 ).
cnf(c_0_186,hypothesis,
( product(X1,a,additive_identity)
| ~ product(multiplicative_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_187,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : FLD043-5 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n016.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 17:29:06 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 26.04/15.68 % Version : CSE_E---1.7
% 26.04/15.68 % Problem : theBenchmark.p
% 26.04/15.68 % SZS status Unsatisfiable for theBenchmark.p
% 26.04/15.68 % SZS output start CNFRefutation
% See solution above
% 26.14/15.78 % Total time : 11.392s
%------------------------------------------------------------------------------