%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD011-3 : 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 : n010.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 04:18:11 PM UTC 2026
% Result : Unsatisfiable 18.18s 11.12s
% Output : CNFRefutation 18.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 19
% Syntax : Number of clauses : 136 ( 50 unt; 6 nHn; 136 RR)
% Number of literals : 273 ( 0 equ; 142 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 177 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(not_sum_2,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_2) ).
cnf(commutativity_multiplication,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
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(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_identity_multiplication,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_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(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_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(associativity_addition_2,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
cnf(totality_of_addition,axiom,
( sum(X1,X2,add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_addition) ).
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(not_product_3,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_inverse(a)),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_3) ).
cnf(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_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(different_identities,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',different_identities) ).
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(c_0_19,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_20,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_21,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
not_sum_2 ).
cnf(c_0_22,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_23,hypothesis,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_24,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_25,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1 ).
cnf(c_0_26,hypothesis,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_28,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_20]),c_0_21]) ).
cnf(c_0_29,hypothesis,
( product(X1,X2,multiplicative_identity)
| ~ product(X3,multiplicative_inverse(a),X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,hypothesis,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_32,hypothesis,
product(multiplicative_identity,a,a),
inference(spm,[status(thm)],[c_0_27,c_0_20]) ).
cnf(c_0_33,hypothesis,
( product(X1,multiplicative_inverse(a),multiplicative_identity)
| ~ product(X1,multiplicative_identity,a) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_35,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_36,hypothesis,
sum(additive_identity,multiplicative_inverse(a),multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_31,c_0_28]) ).
cnf(c_0_37,hypothesis,
( product(X1,X2,a)
| ~ product(X3,a,X2)
| ~ product(X1,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_25,c_0_32]) ).
cnf(c_0_38,hypothesis,
( product(multiplicative_inverse(a),X1,multiplicative_identity)
| ~ product(X1,multiplicative_identity,a) ),
inference(spm,[status(thm)],[c_0_22,c_0_33]) ).
cnf(c_0_39,hypothesis,
product(a,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_22,c_0_32]) ).
cnf(c_0_40,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1 ).
cnf(c_0_41,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_31,c_0_34]) ).
cnf(c_0_42,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
associativity_addition_2 ).
cnf(c_0_43,hypothesis,
sum(multiplicative_inverse(a),additive_identity,multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,hypothesis,
( product(X1,multiplicative_identity,a)
| ~ product(X1,multiplicative_inverse(a),multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_45,hypothesis,
( product(multiplicative_inverse(multiplicative_inverse(a)),multiplicative_inverse(a),multiplicative_identity)
| sum(additive_identity,multiplicative_inverse(a),additive_identity) ),
inference(spm,[status(thm)],[c_0_19,c_0_28]) ).
cnf(c_0_46,plain,
( sum(X1,X2,multiplicative_identity)
| ~ sum(X3,multiplicative_identity,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,hypothesis,
( sum(X1,additive_identity,X2)
| ~ sum(X3,multiplicative_inverse(a),X2)
| ~ sum(X3,multiplicative_inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,axiom,
( sum(X1,X2,add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_addition ).
cnf(c_0_49,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_50,hypothesis,
( product(multiplicative_inverse(multiplicative_inverse(a)),multiplicative_identity,a)
| sum(additive_identity,multiplicative_inverse(a),additive_identity) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_inverse(a)),a),
not_product_3 ).
cnf(c_0_52,plain,
( sum(X1,multiplicative_identity,multiplicative_identity)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_46,c_0_41]) ).
cnf(c_0_53,hypothesis,
sum(additive_identity,a,a),
inference(spm,[status(thm)],[c_0_31,c_0_20]) ).
cnf(c_0_54,plain,
sum(multiplicative_identity,additive_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_35,c_0_41]) ).
cnf(c_0_55,hypothesis,
( sum(X1,additive_identity,multiplicative_inverse(a))
| ~ sum(additive_identity,multiplicative_inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_36]) ).
cnf(c_0_56,hypothesis,
( sum(X1,multiplicative_inverse(a),add(X1,multiplicative_inverse(a)))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_28]) ).
cnf(c_0_57,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_31,c_0_49]) ).
cnf(c_0_58,hypothesis,
sum(additive_identity,multiplicative_inverse(a),additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_50]),c_0_51]) ).
cnf(c_0_59,plain,
( sum(multiplicative_identity,X1,multiplicative_identity)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_35,c_0_52]) ).
cnf(c_0_60,hypothesis,
( sum(X1,X2,multiplicative_inverse(a))
| ~ sum(X3,multiplicative_inverse(a),X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_40,c_0_36]) ).
cnf(c_0_61,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_62,hypothesis,
sum(a,additive_identity,a),
inference(spm,[status(thm)],[c_0_35,c_0_53]) ).
cnf(c_0_63,hypothesis,
( sum(X1,X2,a)
| ~ sum(X3,a,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_40,c_0_53]) ).
cnf(c_0_64,plain,
( sum(X1,X2,multiplicative_identity)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X1,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_40,c_0_54]) ).
cnf(c_0_65,hypothesis,
sum(add(additive_identity,multiplicative_inverse(a)),additive_identity,multiplicative_inverse(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_49])]) ).
cnf(c_0_66,plain,
( sum(X1,X2,additive_identity)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_40,c_0_57]) ).
cnf(c_0_67,hypothesis,
sum(multiplicative_inverse(a),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_35,c_0_58]) ).
cnf(c_0_68,hypothesis,
( sum(X1,additive_identity,multiplicative_identity)
| ~ sum(multiplicative_inverse(a),additive_identity,additive_identity)
| ~ sum(multiplicative_identity,multiplicative_inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_59]) ).
cnf(c_0_69,hypothesis,
( sum(X1,multiplicative_inverse(a),multiplicative_inverse(a))
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_60,c_0_36]) ).
cnf(c_0_70,hypothesis,
sum(additive_inverse(a),a,additive_identity),
inference(spm,[status(thm)],[c_0_61,c_0_20]) ).
cnf(c_0_71,hypothesis,
( sum(X1,X2,a)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_40,c_0_62]) ).
cnf(c_0_72,hypothesis,
( sum(X1,a,a)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_63,c_0_53]) ).
cnf(c_0_73,hypothesis,
( sum(X1,multiplicative_inverse(a),multiplicative_identity)
| ~ sum(X1,add(additive_identity,multiplicative_inverse(a)),multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_74,hypothesis,
( sum(X1,additive_identity,additive_identity)
| ~ sum(additive_identity,multiplicative_inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_58]) ).
cnf(c_0_75,hypothesis,
( sum(X1,multiplicative_inverse(a),X2)
| ~ sum(X3,multiplicative_inverse(a),X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_36]) ).
cnf(c_0_76,hypothesis,
sum(additive_inverse(multiplicative_inverse(a)),multiplicative_inverse(a),additive_identity),
inference(spm,[status(thm)],[c_0_61,c_0_28]) ).
cnf(c_0_77,hypothesis,
( sum(X1,additive_identity,additive_identity)
| ~ sum(X1,multiplicative_inverse(a),additive_identity) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_78,hypothesis,
( sum(multiplicative_inverse(a),additive_identity,multiplicative_identity)
| ~ sum(multiplicative_inverse(a),additive_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_79,hypothesis,
sum(a,additive_inverse(a),additive_identity),
inference(spm,[status(thm)],[c_0_35,c_0_70]) ).
cnf(c_0_80,hypothesis,
( sum(X1,additive_identity,multiplicative_identity)
| ~ sum(multiplicative_identity,multiplicative_inverse(a),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_67])]) ).
cnf(c_0_81,hypothesis,
( sum(X1,a,add(X1,a))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_20]) ).
cnf(c_0_82,hypothesis,
( sum(X1,multiplicative_inverse(a),a)
| ~ sum(X1,add(additive_identity,multiplicative_inverse(a)),a) ),
inference(spm,[status(thm)],[c_0_71,c_0_65]) ).
cnf(c_0_83,hypothesis,
( sum(a,X1,a)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_35,c_0_72]) ).
cnf(c_0_84,hypothesis,
( sum(multiplicative_identity,multiplicative_inverse(a),multiplicative_identity)
| ~ sum(add(additive_identity,multiplicative_inverse(a)),additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_73,c_0_59]) ).
cnf(c_0_85,hypothesis,
sum(add(additive_identity,multiplicative_inverse(a)),additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_56]),c_0_49])]) ).
cnf(c_0_86,hypothesis,
( sum(X1,multiplicative_inverse(a),additive_identity)
| ~ sum(additive_inverse(multiplicative_inverse(a)),additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_87,hypothesis,
( sum(X1,additive_identity,multiplicative_inverse(a))
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_60,c_0_58]) ).
cnf(c_0_88,hypothesis,
sum(additive_inverse(multiplicative_inverse(a)),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_77,c_0_76]) ).
cnf(c_0_89,hypothesis,
( sum(additive_identity,multiplicative_inverse(a),multiplicative_identity)
| ~ sum(multiplicative_inverse(a),additive_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_35,c_0_78]) ).
cnf(c_0_90,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
associativity_multiplication_2 ).
cnf(c_0_91,hypothesis,
( sum(X1,additive_inverse(a),X2)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_79]) ).
cnf(c_0_92,hypothesis,
sum(add(multiplicative_identity,multiplicative_inverse(a)),additive_identity,multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_56]),c_0_34])]) ).
cnf(c_0_93,hypothesis,
( sum(X1,a,X2)
| ~ sum(X3,a,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_53]) ).
cnf(c_0_94,hypothesis,
sum(multiplicative_identity,a,add(multiplicative_identity,a)),
inference(spm,[status(thm)],[c_0_81,c_0_34]) ).
cnf(c_0_95,hypothesis,
( sum(X1,additive_identity,add(X2,multiplicative_inverse(a)))
| ~ defined(X2)
| ~ sum(X2,multiplicative_inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_56]) ).
cnf(c_0_96,hypothesis,
( sum(a,multiplicative_inverse(a),a)
| ~ sum(add(additive_identity,multiplicative_inverse(a)),additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_97,hypothesis,
sum(multiplicative_identity,multiplicative_inverse(a),multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85])]) ).
cnf(c_0_98,hypothesis,
sum(multiplicative_inverse(a),multiplicative_inverse(a),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88])]) ).
cnf(c_0_99,hypothesis,
sum(additive_identity,additive_identity,multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_55,c_0_58]) ).
cnf(c_0_100,hypothesis,
( sum(X1,additive_identity,multiplicative_identity)
| ~ sum(X1,multiplicative_inverse(a),multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_64,c_0_67]) ).
cnf(c_0_101,hypothesis,
( sum(additive_identity,multiplicative_inverse(a),multiplicative_identity)
| ~ sum(multiplicative_identity,additive_identity,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_67])]) ).
cnf(c_0_102,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
different_identities ).
cnf(c_0_103,hypothesis,
( product(X1,a,X2)
| ~ product(X3,multiplicative_inverse(a),X1)
| ~ product(X3,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_90,c_0_23]) ).
cnf(c_0_104,hypothesis,
( sum(X1,additive_inverse(a),multiplicative_identity)
| ~ sum(add(multiplicative_identity,multiplicative_inverse(a)),a,X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_105,hypothesis,
( sum(X1,a,add(multiplicative_identity,a))
| ~ sum(multiplicative_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_106,hypothesis,
sum(multiplicative_identity,additive_identity,add(multiplicative_identity,multiplicative_inverse(a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_59]),c_0_34]),c_0_67])]) ).
cnf(c_0_107,hypothesis,
sum(a,multiplicative_inverse(a),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_85])]) ).
cnf(c_0_108,plain,
( sum(X1,additive_identity,X2)
| ~ sum(X3,multiplicative_identity,X2)
| ~ sum(X3,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_54]) ).
cnf(c_0_109,hypothesis,
sum(multiplicative_inverse(a),multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_35,c_0_97]) ).
cnf(c_0_110,hypothesis,
( sum(X1,additive_identity,additive_identity)
| ~ sum(multiplicative_inverse(a),multiplicative_inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_98]) ).
cnf(c_0_111,hypothesis,
( sum(X1,multiplicative_inverse(a),multiplicative_identity)
| ~ sum(X1,additive_identity,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_64,c_0_99]) ).
cnf(c_0_112,hypothesis,
~ sum(multiplicative_identity,additive_identity,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102]) ).
cnf(c_0_113,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_114,hypothesis,
( product(multiplicative_inverse(a),a,X1)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_103,c_0_30]) ).
cnf(c_0_115,hypothesis,
( sum(X1,X2,additive_identity)
| ~ sum(X3,additive_inverse(a),X2)
| ~ sum(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_40,c_0_79]) ).
cnf(c_0_116,hypothesis,
sum(add(multiplicative_identity,a),additive_inverse(a),multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106])]) ).
cnf(c_0_117,hypothesis,
( sum(X1,multiplicative_inverse(a),a)
| ~ sum(a,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_75,c_0_107]) ).
cnf(c_0_118,hypothesis,
( sum(X1,additive_identity,multiplicative_identity)
| ~ sum(multiplicative_inverse(a),multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_119,hypothesis,
( sum(X1,multiplicative_identity,multiplicative_inverse(a))
| ~ sum(X1,multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_60,c_0_97]) ).
cnf(c_0_120,hypothesis,
~ sum(multiplicative_inverse(a),additive_identity,multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112]) ).
cnf(c_0_121,hypothesis,
( sum(X1,X2,a)
| ~ product(X3,a,X2)
| ~ product(X4,a,X1)
| ~ sum(X4,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_113,c_0_32]) ).
cnf(c_0_122,hypothesis,
( product(a,multiplicative_inverse(a),X1)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_114]) ).
cnf(c_0_123,hypothesis,
( sum(X1,multiplicative_identity,additive_identity)
| ~ sum(X1,add(multiplicative_identity,a),a) ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_124,hypothesis,
( sum(multiplicative_inverse(a),X1,a)
| ~ sum(a,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_117]) ).
cnf(c_0_125,hypothesis,
~ sum(multiplicative_inverse(a),multiplicative_identity,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120]) ).
cnf(c_0_126,hypothesis,
sum(a,multiplicative_identity,add(multiplicative_identity,a)),
inference(spm,[status(thm)],[c_0_35,c_0_94]) ).
cnf(c_0_127,hypothesis,
( sum(X1,multiplicative_identity,a)
| ~ product(X2,a,X1)
| ~ sum(X2,multiplicative_inverse(a),multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_38]),c_0_39])]) ).
cnf(c_0_128,hypothesis,
( product(X1,a,X2)
| ~ product(a,multiplicative_identity,X2)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_103,c_0_122]) ).
cnf(c_0_129,hypothesis,
~ sum(a,additive_identity,add(multiplicative_identity,a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_125]) ).
cnf(c_0_130,hypothesis,
( sum(X1,additive_identity,add(multiplicative_identity,a))
| ~ sum(a,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_108,c_0_126]) ).
cnf(c_0_131,hypothesis,
( sum(X1,multiplicative_identity,a)
| ~ product(multiplicative_identity,a,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_59]),c_0_67])]) ).
cnf(c_0_132,hypothesis,
( product(X1,a,a)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_128,c_0_39]) ).
cnf(c_0_133,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_27,c_0_34]) ).
cnf(c_0_134,hypothesis,
~ sum(a,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_135,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_133])]),c_0_134]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD011-3 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n010.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 17:26:21 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 18.18/11.12 % Version : CSE_E---1.7
% 18.18/11.12 % Problem : theBenchmark.p
% 18.18/11.12 % SZS status Unsatisfiable for theBenchmark.p
% 18.18/11.12 % SZS output start CNFRefutation
% See solution above
% 18.18/11.19 % Total time : 8.383s
%------------------------------------------------------------------------------