TSTP Solution File: FLD012-3 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : FLD012-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n008.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 : Wed Aug 30 22:32:51 EDT 2023
% Result : Unsatisfiable 181.05s 24.99s
% Output : CNFRefutation 181.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 21
% Syntax : Number of clauses : 136 ( 10 unt; 9 nHn; 136 RR)
% Number of literals : 436 ( 0 equ; 295 neg)
% Maximal clause size : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 218 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_49,plain,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(c_50,plain,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(c_51,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_3) ).
cnf(c_52,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_4) ).
cnf(c_53,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(multiply(a,b)),multiply(multiplicative_inverse(a),multiplicative_inverse(b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_5) ).
cnf(c_54,plain,
( ~ sum(X0,X1,X2)
| ~ sum(X1,X3,X4)
| ~ sum(X2,X3,X5)
| sum(X0,X4,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(c_56,plain,
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(c_58,plain,
( ~ sum(X0,X1,X2)
| sum(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(c_59,plain,
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| ~ product(X2,X3,X5)
| product(X0,X4,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(c_60,plain,
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ product(X3,X5,X1)
| product(X4,X5,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
cnf(c_61,plain,
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(c_62,plain,
( ~ defined(X0)
| product(multiplicative_inverse(X0),X0,multiplicative_identity)
| sum(additive_identity,X0,additive_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(c_63,plain,
( ~ product(X0,X1,X2)
| product(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(c_64,plain,
( ~ sum(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ product(X1,X3,X5)
| ~ product(X2,X3,X6)
| sum(X4,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
cnf(c_65,plain,
( ~ sum(X0,X1,X2)
| ~ sum(X3,X4,X5)
| ~ product(X0,X6,X3)
| ~ product(X1,X6,X4)
| product(X2,X6,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_2) ).
cnf(c_67,plain,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(c_69,plain,
( ~ defined(X0)
| ~ defined(X1)
| defined(multiply(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplication) ).
cnf(c_70,plain,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(c_71,plain,
( ~ defined(X0)
| sum(additive_identity,X0,additive_identity)
| defined(multiplicative_inverse(X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(c_73,plain,
( ~ defined(X0)
| ~ defined(X1)
| product(X0,X1,multiply(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
cnf(c_79,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',different_identities) ).
cnf(c_82,plain,
( ~ defined(additive_identity)
| sum(additive_identity,additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_84,plain,
( ~ defined(additive_identity)
| defined(multiply(additive_identity,additive_identity)) ),
inference(instantiation,[status(thm)],[c_69]) ).
cnf(c_88,plain,
( ~ defined(additive_identity)
| product(additive_identity,additive_identity,multiply(additive_identity,additive_identity)) ),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_255,plain,
( ~ defined(X0)
| product(X0,multiplicative_identity,X0) ),
inference(superposition,[status(thm)],[c_61,c_63]) ).
cnf(c_256,plain,
( ~ defined(additive_identity)
| product(additive_identity,multiplicative_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_255]) ).
cnf(c_257,plain,
( ~ defined(a)
| defined(multiplicative_inverse(a)) ),
inference(superposition,[status(thm)],[c_71,c_51]) ).
cnf(c_258,plain,
( ~ defined(b)
| defined(multiplicative_inverse(b)) ),
inference(superposition,[status(thm)],[c_71,c_52]) ).
cnf(c_277,plain,
( ~ defined(a)
| product(multiplicative_inverse(a),a,multiplicative_identity)
| sum(additive_identity,a,additive_identity) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_278,plain,
( ~ defined(b)
| product(multiplicative_inverse(b),b,multiplicative_identity)
| sum(additive_identity,b,additive_identity) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_290,plain,
( ~ product(multiplicative_identity,X0,X0)
| product(X0,multiplicative_identity,X0) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_296,plain,
( ~ product(X0,X1,multiply(X0,X1))
| product(X1,X0,multiply(X0,X1)) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_320,plain,
( ~ product(X0,X1,X2)
| ~ product(X3,X0,multiplicative_identity)
| ~ product(multiplicative_identity,X1,X1)
| product(X3,X2,X1) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_321,plain,
( ~ product(X0,X1,multiply(X0,X1))
| ~ product(X2,X3,X0)
| ~ product(X3,X1,X4)
| product(X2,X4,multiply(X0,X1)) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_322,plain,
( ~ product(X0,X1,X2)
| ~ product(X0,multiplicative_identity,X3)
| ~ product(multiplicative_identity,X1,X1)
| product(X3,X1,X2) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_328,plain,
( ~ sum(X0,X1,X2)
| ~ product(X0,X3,additive_identity)
| ~ product(X1,X3,additive_identity)
| ~ product(X2,X3,multiplicative_identity)
| sum(additive_identity,additive_identity,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_64]) ).
cnf(c_335,plain,
( ~ sum(X0,multiply(X1,X2),X3)
| ~ product(X1,X2,multiply(X1,X2))
| ~ sum(X4,X1,X5)
| ~ product(X4,X2,X0)
| product(X5,X2,X3) ),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_346,plain,
( ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| product(a,multiplicative_inverse(a),multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_365,plain,
( ~ product(X0,multiplicative_inverse(b),X1)
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ product(X0,multiplicative_identity,X2)
| product(X1,b,X2) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_433,plain,
( ~ sum(X0,X1,X2)
| ~ sum(X3,X1,X4)
| ~ product(X0,multiplicative_identity,X3)
| ~ product(X1,multiplicative_identity,X1)
| product(X2,multiplicative_identity,X4) ),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_507,plain,
( ~ defined(X0)
| product(X0,multiplicative_identity,X0) ),
inference(resolution,[status(thm)],[c_63,c_61]) ).
cnf(c_568,plain,
( ~ defined(X0)
| product(X0,multiplicative_inverse(X0),multiplicative_identity)
| sum(additive_identity,X0,additive_identity) ),
inference(resolution,[status(thm)],[c_62,c_63]) ).
cnf(c_613,plain,
( ~ sum(X0,X1,X2)
| ~ sum(X3,X0,additive_identity)
| ~ defined(X1)
| sum(X3,X2,X1) ),
inference(resolution,[status(thm)],[c_54,c_56]) ).
cnf(c_735,plain,
( ~ sum(additive_identity,X0,X1)
| ~ defined(X0)
| ~ defined(additive_identity)
| sum(additive_identity,X1,X0) ),
inference(resolution,[status(thm)],[c_613,c_56]) ).
cnf(c_740,plain,
( ~ defined(multiplicative_identity)
| product(multiplicative_identity,multiplicative_identity,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_742,plain,
( ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ product(a,X0,X1)
| ~ product(multiplicative_identity,X0,X0)
| product(multiplicative_inverse(a),X1,X0) ),
inference(instantiation,[status(thm)],[c_320]) ).
cnf(c_744,plain,
( ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ product(b,X0,X1)
| ~ product(multiplicative_identity,X0,X0)
| product(multiplicative_inverse(b),X1,X0) ),
inference(instantiation,[status(thm)],[c_320]) ).
cnf(c_762,plain,
( ~ product(X0,multiplicative_identity,X0)
| ~ product(X0,multiplicative_identity,X1)
| ~ product(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| product(X1,multiplicative_identity,X0) ),
inference(instantiation,[status(thm)],[c_322]) ).
cnf(c_768,plain,
( ~ defined(X0)
| ~ sum(additive_identity,X0,X1)
| sum(additive_identity,X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_735,c_67,c_735]) ).
cnf(c_769,plain,
( ~ sum(additive_identity,X0,X1)
| ~ defined(X0)
| sum(additive_identity,X1,X0) ),
inference(renaming,[status(thm)],[c_768]) ).
cnf(c_872,plain,
( ~ product(X0,a,multiply(X0,a))
| ~ product(X1,multiplicative_inverse(a),X0)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| product(X1,multiplicative_identity,multiply(X0,a)) ),
inference(instantiation,[status(thm)],[c_321]) ).
cnf(c_942,plain,
( ~ sum(multiply(X0,X1),multiply(X2,X1),X3)
| ~ product(X0,X1,multiply(X0,X1))
| ~ product(X2,X1,multiply(X2,X1))
| ~ sum(X0,X2,X4)
| product(X4,X1,X3) ),
inference(instantiation,[status(thm)],[c_335]) ).
cnf(c_943,plain,
( ~ sum(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity),additive_identity)
| ~ product(additive_identity,additive_identity,multiply(additive_identity,additive_identity))
| ~ sum(additive_identity,additive_identity,additive_identity)
| product(additive_identity,additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_942]) ).
cnf(c_1127,plain,
( ~ product(X0,X1,X2)
| ~ product(X3,X0,multiplicative_identity)
| ~ defined(X1)
| product(X3,X2,X1) ),
inference(resolution,[status(thm)],[c_59,c_61]) ).
cnf(c_1193,plain,
( ~ sum(X0,additive_identity,X1)
| ~ product(X0,multiplicative_identity,additive_identity)
| ~ product(X1,multiplicative_identity,multiplicative_identity)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| sum(additive_identity,additive_identity,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_328]) ).
cnf(c_1194,plain,
( ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(additive_identity,multiplicative_identity,multiplicative_identity)
| sum(additive_identity,additive_identity,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_1193]) ).
cnf(c_1261,plain,
( ~ product(X0,X1,X2)
| ~ product(X0,multiplicative_identity,X3)
| ~ defined(X1)
| product(X2,multiplicative_inverse(X1),X3)
| sum(additive_identity,X1,additive_identity) ),
inference(resolution,[status(thm)],[c_60,c_568]) ).
cnf(c_1362,plain,
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X4)
| ~ sum(X0,X3,multiplicative_identity)
| ~ defined(X1)
| sum(X2,X4,X1) ),
inference(resolution,[status(thm)],[c_64,c_61]) ).
cnf(c_1414,plain,
( ~ defined(a)
| product(multiplicative_identity,a,a) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_1415,plain,
( ~ defined(b)
| product(multiplicative_identity,b,b) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_1424,plain,
( ~ product(multiplicative_inverse(a),X0,multiply(multiplicative_inverse(a),X0))
| product(X0,multiplicative_inverse(a),multiply(multiplicative_inverse(a),X0)) ),
inference(instantiation,[status(thm)],[c_296]) ).
cnf(c_1471,plain,
( ~ defined(multiplicative_inverse(b))
| product(multiplicative_identity,multiplicative_inverse(b),multiplicative_inverse(b)) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_1474,plain,
( ~ defined(multiplicative_inverse(b))
| ~ defined(X0)
| product(X0,multiplicative_inverse(b),multiply(X0,multiplicative_inverse(b))) ),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_1527,plain,
( ~ product(a,X0,multiply(a,X0))
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ product(multiplicative_identity,X0,X0)
| product(multiplicative_inverse(a),multiply(a,X0),X0) ),
inference(instantiation,[status(thm)],[c_742]) ).
cnf(c_1532,plain,
( ~ product(a,X0,multiply(X0,a))
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ product(multiplicative_identity,X0,X0)
| product(multiplicative_inverse(a),multiply(X0,a),X0) ),
inference(instantiation,[status(thm)],[c_742]) ).
cnf(c_1533,plain,
( ~ product(X0,a,multiply(X0,a))
| product(a,X0,multiply(X0,a)) ),
inference(instantiation,[status(thm)],[c_296]) ).
cnf(c_1546,plain,
( ~ product(b,X0,multiply(b,X0))
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ product(multiplicative_identity,X0,X0)
| product(multiplicative_inverse(b),multiply(b,X0),X0) ),
inference(instantiation,[status(thm)],[c_744]) ).
cnf(c_1551,plain,
( ~ product(b,X0,multiply(X0,b))
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ product(multiplicative_identity,X0,X0)
| product(multiplicative_inverse(b),multiply(X0,b),X0) ),
inference(instantiation,[status(thm)],[c_744]) ).
cnf(c_1552,plain,
( ~ product(X0,b,multiply(X0,b))
| product(b,X0,multiply(X0,b)) ),
inference(instantiation,[status(thm)],[c_296]) ).
cnf(c_1595,plain,
( ~ defined(X0)
| ~ defined(a)
| product(X0,a,multiply(X0,a)) ),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_1599,plain,
( ~ defined(X0)
| ~ defined(b)
| product(X0,b,multiply(X0,b)) ),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_1759,plain,
( ~ product(multiplicative_identity,b,b)
| product(b,multiplicative_identity,b) ),
inference(instantiation,[status(thm)],[c_290]) ).
cnf(c_2179,plain,
( ~ product(X0,X1,X2)
| ~ defined(X0)
| ~ defined(X1)
| product(multiplicative_inverse(X0),X2,X1)
| sum(additive_identity,X0,additive_identity) ),
inference(resolution,[status(thm)],[c_1127,c_62]) ).
cnf(c_4336,plain,
( ~ product(additive_identity,X0,X1)
| ~ product(multiplicative_identity,X0,X2)
| ~ defined(X0)
| ~ defined(multiplicative_identity)
| sum(X1,X2,X0) ),
inference(resolution,[status(thm)],[c_1362,c_56]) ).
cnf(c_6851,plain,
( ~ product(multiplicative_inverse(a),multiplicative_inverse(b),multiply(multiplicative_inverse(a),multiplicative_inverse(b)))
| product(multiplicative_inverse(b),multiplicative_inverse(a),multiply(multiplicative_inverse(a),multiplicative_inverse(b))) ),
inference(instantiation,[status(thm)],[c_1424]) ).
cnf(c_6852,plain,
( ~ defined(multiplicative_inverse(a))
| ~ defined(multiplicative_inverse(b))
| product(multiplicative_inverse(a),multiplicative_inverse(b),multiply(multiplicative_inverse(a),multiplicative_inverse(b))) ),
inference(instantiation,[status(thm)],[c_1474]) ).
cnf(c_6978,plain,
( ~ product(b,a,multiply(b,a))
| product(a,b,multiply(b,a)) ),
inference(instantiation,[status(thm)],[c_1533]) ).
cnf(c_7054,plain,
( ~ product(a,b,multiply(a,b))
| product(b,a,multiply(a,b)) ),
inference(instantiation,[status(thm)],[c_1552]) ).
cnf(c_9483,plain,
( ~ product(a,b,multiply(a,b))
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ product(multiplicative_identity,b,b)
| product(multiplicative_inverse(a),multiply(a,b),b) ),
inference(instantiation,[status(thm)],[c_1527]) ).
cnf(c_9565,plain,
( ~ product(a,b,multiply(b,a))
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ product(multiplicative_identity,b,b)
| product(multiplicative_inverse(a),multiply(b,a),b) ),
inference(instantiation,[status(thm)],[c_1532]) ).
cnf(c_9691,plain,
( ~ product(b,a,multiply(b,a))
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ product(multiplicative_identity,a,a)
| product(multiplicative_inverse(b),multiply(b,a),a) ),
inference(instantiation,[status(thm)],[c_1546]) ).
cnf(c_9936,plain,
( ~ product(b,a,multiply(a,b))
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ product(multiplicative_identity,a,a)
| product(multiplicative_inverse(b),multiply(a,b),a) ),
inference(instantiation,[status(thm)],[c_1551]) ).
cnf(c_14973,plain,
( ~ product(X0,X1,a)
| product(X1,X0,a) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_14974,plain,
( ~ product(X0,X1,b)
| product(X1,X0,b) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_16294,plain,
( ~ product(X0,X1,a)
| ~ product(X0,multiplicative_identity,X2)
| ~ product(multiplicative_identity,X1,X1)
| product(X2,X1,a) ),
inference(instantiation,[status(thm)],[c_322]) ).
cnf(c_17501,plain,
( ~ defined(a)
| ~ defined(b)
| product(b,a,multiply(b,a)) ),
inference(instantiation,[status(thm)],[c_1595]) ).
cnf(c_17560,plain,
( ~ defined(a)
| ~ defined(b)
| product(a,b,multiply(a,b)) ),
inference(instantiation,[status(thm)],[c_1599]) ).
cnf(c_20967,plain,
( ~ product(X0,X1,X2)
| ~ defined(X0)
| ~ defined(X1)
| product(X2,multiplicative_inverse(X0),X1)
| sum(additive_identity,X0,additive_identity) ),
inference(resolution,[status(thm)],[c_2179,c_63]) ).
cnf(c_30258,plain,
( ~ product(multiplicative_inverse(a),multiply(b,a),b)
| product(multiply(b,a),multiplicative_inverse(a),b) ),
inference(instantiation,[status(thm)],[c_14974]) ).
cnf(c_30293,plain,
( ~ product(multiplicative_inverse(b),multiply(b,a),a)
| product(multiply(b,a),multiplicative_inverse(b),a) ),
inference(instantiation,[status(thm)],[c_14973]) ).
cnf(c_30301,plain,
( ~ defined(X0)
| ~ product(multiplicative_identity,X0,X2)
| ~ product(additive_identity,X0,X1)
| sum(X1,X2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_4336,c_70,c_4336]) ).
cnf(c_30302,plain,
( ~ product(additive_identity,X0,X1)
| ~ product(multiplicative_identity,X0,X2)
| ~ defined(X0)
| sum(X1,X2,X0) ),
inference(renaming,[status(thm)],[c_30301]) ).
cnf(c_30812,plain,
( ~ product(multiplicative_inverse(b),multiply(a,b),a)
| product(multiply(a,b),multiplicative_inverse(b),a) ),
inference(instantiation,[status(thm)],[c_14973]) ).
cnf(c_46008,plain,
( ~ product(X0,X1,X2)
| ~ defined(X0)
| ~ defined(X1)
| product(X2,multiplicative_inverse(X1),X0)
| sum(additive_identity,X1,additive_identity) ),
inference(resolution,[status(thm)],[c_1261,c_507]) ).
cnf(c_47162,plain,
( ~ product(multiply(b,a),multiplicative_inverse(a),b)
| ~ product(b,a,multiply(b,a))
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| product(multiply(b,a),multiplicative_identity,multiply(b,a)) ),
inference(instantiation,[status(thm)],[c_872]) ).
cnf(c_47544,plain,
( ~ product(multiply(a,b),multiplicative_inverse(b),a)
| ~ product(multiply(a,b),multiplicative_identity,X0)
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| product(a,b,X0) ),
inference(instantiation,[status(thm)],[c_365]) ).
cnf(c_47545,plain,
( ~ product(multiply(a,b),multiplicative_inverse(b),a)
| ~ product(multiply(a,b),multiplicative_identity,additive_identity)
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| product(a,b,additive_identity) ),
inference(instantiation,[status(thm)],[c_47544]) ).
cnf(c_47557,plain,
( ~ product(multiply(a,b),multiplicative_inverse(b),a)
| ~ product(multiply(a,b),multiplicative_identity,X0)
| ~ product(multiplicative_identity,multiplicative_inverse(b),multiplicative_inverse(b))
| product(X0,multiplicative_inverse(b),a) ),
inference(instantiation,[status(thm)],[c_16294]) ).
cnf(c_47561,plain,
( ~ product(multiply(a,b),multiplicative_inverse(b),a)
| ~ product(multiply(a,b),multiplicative_identity,additive_identity)
| ~ product(multiplicative_identity,multiplicative_inverse(b),multiplicative_inverse(b))
| product(additive_identity,multiplicative_inverse(b),a) ),
inference(instantiation,[status(thm)],[c_47557]) ).
cnf(c_58515,plain,
( ~ sum(X0,X1,multiply(a,b))
| ~ sum(X2,X1,X3)
| ~ product(X0,multiplicative_identity,X2)
| ~ product(X1,multiplicative_identity,X1)
| product(multiply(a,b),multiplicative_identity,X3) ),
inference(instantiation,[status(thm)],[c_433]) ).
cnf(c_58516,plain,
( ~ sum(additive_identity,additive_identity,multiply(a,b))
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| product(multiply(a,b),multiplicative_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_58515]) ).
cnf(c_75990,plain,
( ~ product(multiply(b,a),multiplicative_identity,multiply(b,a))
| ~ product(multiply(b,a),multiplicative_identity,additive_identity)
| ~ product(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| product(additive_identity,multiplicative_identity,multiply(b,a)) ),
inference(instantiation,[status(thm)],[c_762]) ).
cnf(c_150715,plain,
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| ~ product(X1,multiplicative_identity,X1)
| product(X3,multiplicative_identity,X2) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_151190,plain,
( ~ product(X0,X1,X2)
| ~ product(X1,multiplicative_identity,X3)
| ~ product(X2,multiplicative_identity,X4)
| product(X0,X3,X4) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_151293,plain,
( ~ product(X0,X1,multiply(X1,X0))
| ~ product(X0,X1,X2)
| ~ product(X1,multiplicative_identity,X1)
| product(multiply(X1,X0),multiplicative_identity,X2) ),
inference(instantiation,[status(thm)],[c_150715]) ).
cnf(c_151777,plain,
( ~ sum(multiply(X0,X1),X2,X3)
| ~ sum(X2,X4,multiply(X5,X1))
| ~ sum(X3,X4,X6)
| sum(multiply(X0,X1),multiply(X5,X1),X6) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_151778,plain,
( ~ sum(multiply(additive_identity,additive_identity),additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,multiply(additive_identity,additive_identity))
| ~ sum(additive_identity,additive_identity,additive_identity)
| sum(multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity),additive_identity) ),
inference(instantiation,[status(thm)],[c_151777]) ).
cnf(c_155040,plain,
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| ~ product(X2,X3,multiplicative_identity)
| product(X0,X4,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_155564,plain,
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| ~ product(X0,X4,multiplicative_identity)
| product(X2,X3,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_158238,plain,
( ~ product(multiplicative_inverse(b),X0,X1)
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ product(X0,X2,b)
| product(X1,X2,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_155564]) ).
cnf(c_165042,plain,
( ~ product(multiplicative_inverse(a),multiply(a,b),b)
| ~ product(multiplicative_inverse(b),multiplicative_inverse(a),X0)
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| product(X0,multiply(a,b),multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_158238]) ).
cnf(c_172614,plain,
( ~ defined(multiplicative_inverse(a))
| ~ defined(multiplicative_inverse(b))
| defined(multiply(multiplicative_inverse(a),multiplicative_inverse(b))) ),
inference(instantiation,[status(thm)],[c_69]) ).
cnf(c_175063,plain,
( ~ product(multiplicative_inverse(b),multiplicative_inverse(a),multiply(multiplicative_inverse(a),multiplicative_inverse(b)))
| ~ product(multiplicative_inverse(a),multiply(a,b),b)
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| product(multiply(multiplicative_inverse(a),multiplicative_inverse(b)),multiply(a,b),multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_165042]) ).
cnf(c_177869,plain,
( ~ product(X0,multiplicative_identity,multiply(b,a))
| ~ product(X1,X2,X0)
| ~ product(X2,multiplicative_identity,X3)
| product(X1,X3,multiply(b,a)) ),
inference(instantiation,[status(thm)],[c_151190]) ).
cnf(c_177870,plain,
( ~ product(additive_identity,multiplicative_identity,multiply(b,a))
| ~ product(additive_identity,additive_identity,additive_identity)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| product(additive_identity,additive_identity,multiply(b,a)) ),
inference(instantiation,[status(thm)],[c_177869]) ).
cnf(c_182235,plain,
( ~ defined(a)
| ~ defined(b)
| defined(multiply(a,b)) ),
inference(instantiation,[status(thm)],[c_69]) ).
cnf(c_205224,plain,
( ~ product(a,b,multiply(b,a))
| ~ product(a,b,X0)
| ~ product(b,multiplicative_identity,b)
| product(multiply(b,a),multiplicative_identity,X0) ),
inference(instantiation,[status(thm)],[c_151293]) ).
cnf(c_205225,plain,
( ~ product(a,b,multiply(b,a))
| ~ product(a,b,additive_identity)
| ~ product(b,multiplicative_identity,b)
| product(multiply(b,a),multiplicative_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_205224]) ).
cnf(c_212338,plain,
( ~ product(X0,multiplicative_inverse(a),multiplicative_identity)
| ~ product(a,multiplicative_inverse(a),multiplicative_identity)
| ~ product(X1,a,X0)
| product(X1,multiplicative_identity,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_155040]) ).
cnf(c_241538,plain,
( ~ product(additive_identity,X0,X1)
| ~ defined(X0)
| sum(X1,X0,X0) ),
inference(resolution,[status(thm)],[c_30302,c_61]) ).
cnf(c_251209,plain,
( ~ defined(X0)
| ~ defined(additive_identity)
| sum(multiply(additive_identity,X0),X0,X0) ),
inference(resolution,[status(thm)],[c_241538,c_73]) ).
cnf(c_251210,plain,
( ~ defined(additive_identity)
| sum(multiply(additive_identity,additive_identity),additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_251209]) ).
cnf(c_255133,plain,
( ~ defined(X0)
| sum(multiply(additive_identity,X0),X0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_251209,c_67,c_251209]) ).
cnf(c_255144,plain,
( ~ defined(X0)
| sum(X0,multiply(additive_identity,X0),X0) ),
inference(resolution,[status(thm)],[c_255133,c_58]) ).
cnf(c_256011,plain,
( ~ defined(multiply(additive_identity,additive_identity))
| ~ defined(additive_identity)
| sum(additive_identity,additive_identity,multiply(additive_identity,additive_identity)) ),
inference(resolution,[status(thm)],[c_255144,c_769]) ).
cnf(c_256348,plain,
( ~ product(a,multiplicative_inverse(a),multiplicative_identity)
| ~ product(X0,a,a)
| product(X0,multiplicative_identity,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_212338]) ).
cnf(c_256349,plain,
( ~ product(a,multiplicative_inverse(a),multiplicative_identity)
| ~ product(additive_identity,a,a)
| product(additive_identity,multiplicative_identity,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_256348]) ).
cnf(c_284990,plain,
( ~ product(multiply(a,b),multiply(multiplicative_inverse(a),multiplicative_inverse(b)),multiplicative_identity)
| ~ defined(multiply(multiplicative_inverse(a),multiplicative_inverse(b)))
| ~ defined(multiply(a,b))
| sum(additive_identity,multiply(a,b),additive_identity) ),
inference(resolution,[status(thm)],[c_20967,c_53]) ).
cnf(c_287843,plain,
( ~ product(multiply(multiplicative_inverse(a),multiplicative_inverse(b)),multiply(a,b),multiplicative_identity)
| ~ defined(multiply(multiplicative_inverse(a),multiplicative_inverse(b)))
| ~ defined(multiply(a,b))
| sum(additive_identity,multiply(a,b),additive_identity) ),
inference(resolution,[status(thm)],[c_46008,c_53]) ).
cnf(c_288539,plain,
sum(additive_identity,multiply(a,b),additive_identity),
inference(global_subsumption_just,[status(thm)],[c_284990,c_50,c_49,c_52,c_51,c_258,c_257,c_277,c_278,c_1415,c_6851,c_6852,c_9483,c_17560,c_172614,c_175063,c_182235,c_287843]) ).
cnf(c_288554,plain,
( ~ defined(multiply(a,b))
| sum(additive_identity,additive_identity,multiply(a,b)) ),
inference(resolution,[status(thm)],[c_288539,c_769]) ).
cnf(c_302658,plain,
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| ~ product(X2,X3,a)
| product(X0,X4,a) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_317671,plain,
( ~ product(multiply(b,a),multiplicative_inverse(b),a)
| ~ product(X0,X1,multiply(b,a))
| ~ product(X1,multiplicative_inverse(b),X2)
| product(X0,X2,a) ),
inference(instantiation,[status(thm)],[c_302658]) ).
cnf(c_331443,plain,
( ~ product(multiply(b,a),multiplicative_inverse(b),a)
| ~ product(X0,X1,multiply(b,a))
| ~ product(X1,multiplicative_inverse(b),a)
| product(X0,a,a) ),
inference(instantiation,[status(thm)],[c_317671]) ).
cnf(c_331444,plain,
( ~ product(multiply(b,a),multiplicative_inverse(b),a)
| ~ product(additive_identity,additive_identity,multiply(b,a))
| ~ product(additive_identity,multiplicative_inverse(b),a)
| product(additive_identity,a,a) ),
inference(instantiation,[status(thm)],[c_331443]) ).
cnf(c_331445,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_331444,c_288554,c_256349,c_256011,c_251210,c_205225,c_182235,c_177870,c_151778,c_75990,c_58516,c_47561,c_47545,c_47162,c_30812,c_30293,c_30258,c_17560,c_17501,c_9936,c_9691,c_9565,c_7054,c_6978,c_1759,c_1471,c_1415,c_1414,c_1194,c_943,c_740,c_346,c_278,c_277,c_258,c_256,c_88,c_84,c_82,c_79,c_51,c_52,c_49,c_50,c_67,c_70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : FLD012-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 23:50:02 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 181.05/24.99 % SZS status Started for theBenchmark.p
% 181.05/24.99 % SZS status Unsatisfiable for theBenchmark.p
% 181.05/24.99
% 181.05/24.99 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 181.05/24.99
% 181.05/24.99 ------ iProver source info
% 181.05/24.99
% 181.05/24.99 git: date: 2023-05-31 18:12:56 +0000
% 181.05/24.99 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 181.05/24.99 git: non_committed_changes: false
% 181.05/24.99 git: last_make_outside_of_git: false
% 181.05/24.99
% 181.05/24.99 ------ Parsing...successful
% 181.05/24.99
% 181.05/24.99
% 181.05/24.99
% 181.05/24.99 ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e
% 181.05/24.99
% 181.05/24.99 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 181.05/24.99 ------ Proving...
% 181.05/24.99 ------ Problem Properties
% 181.05/24.99
% 181.05/24.99
% 181.05/24.99 clauses 31
% 181.05/24.99 conjectures 3
% 181.05/24.99 EPR 22
% 181.05/24.99 Horn 28
% 181.05/24.99 unary 8
% 181.05/24.99 binary 6
% 181.05/24.99 lits 82
% 181.05/24.99 lits eq 0
% 181.05/24.99 fd_pure 0
% 181.05/24.99 fd_pseudo 0
% 181.05/24.99 fd_cond 0
% 181.05/24.99 fd_pseudo_cond 0
% 181.05/24.99 AC symbols 0
% 181.05/24.99
% 181.05/24.99 ------ Input Options Time Limit: Unbounded
% 181.05/24.99
% 181.05/24.99
% 181.05/24.99 ------
% 181.05/24.99 Current options:
% 181.05/24.99 ------
% 181.05/24.99
% 181.05/24.99
% 181.05/24.99
% 181.05/24.99
% 181.05/24.99 ------ Proving...
% 181.05/24.99
% 181.05/24.99
% 181.05/24.99 ------ Proving...
% 181.05/24.99
% 181.05/24.99
% 181.05/24.99 % SZS status Unsatisfiable for theBenchmark.p
% 181.05/24.99
% 181.05/24.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 181.05/24.99
% 181.05/25.00
%------------------------------------------------------------------------------