TSTP Solution File: FLD065-1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : FLD065-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n003.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 22:33:21 EDT 2023
% Result : Unsatisfiable 92.41s 13.25s
% Output : CNFRefutation 92.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 23
% Syntax : Number of clauses : 267 ( 49 unt; 10 nHn; 267 RR)
% Number of literals : 627 ( 0 equ; 353 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 204 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_49,plain,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(c_50,negated_conjecture,
less_or_equal(additive_inverse(a),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_2) ).
cnf(c_51,negated_conjecture,
~ less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_3) ).
cnf(c_53,plain,
( ~ defined(X0)
| equalish(add(additive_identity,X0),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).
cnf(c_54,plain,
( ~ defined(X0)
| equalish(add(X0,additive_inverse(X0)),additive_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_addition) ).
cnf(c_55,plain,
( ~ defined(X0)
| ~ defined(X1)
| equalish(add(X0,X1),add(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_addition) ).
cnf(c_57,plain,
( ~ defined(X0)
| equalish(multiply(multiplicative_identity,X0),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_multiplication) ).
cnf(c_59,plain,
( ~ defined(X0)
| ~ defined(X1)
| equalish(multiply(X0,X1),multiply(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_multiplication) ).
cnf(c_61,plain,
( ~ defined(X0)
| ~ defined(X1)
| defined(add(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_addition) ).
cnf(c_62,plain,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
cnf(c_63,plain,
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_inverse) ).
cnf(c_64,plain,
( ~ defined(X0)
| ~ defined(X1)
| defined(multiply(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplication) ).
cnf(c_65,plain,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(c_66,plain,
( ~ defined(X0)
| defined(multiplicative_inverse(X0))
| equalish(X0,additive_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(c_67,plain,
( ~ less_or_equal(X0,X1)
| ~ less_or_equal(X1,X0)
| equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',antisymmetry_of_order_relation) ).
cnf(c_68,plain,
( ~ less_or_equal(X0,X1)
| ~ less_or_equal(X1,X2)
| less_or_equal(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',transitivity_of_order_relation) ).
cnf(c_69,plain,
( ~ defined(X0)
| ~ defined(X1)
| less_or_equal(X0,X1)
| less_or_equal(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',totality_of_order_relation) ).
cnf(c_70,plain,
( ~ less_or_equal(X0,X1)
| ~ defined(X2)
| less_or_equal(add(X0,X2),add(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(c_71,plain,
( ~ less_or_equal(additive_identity,X0)
| ~ less_or_equal(additive_identity,X1)
| less_or_equal(additive_identity,multiply(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_order_relation_and_multiplication) ).
cnf(c_72,plain,
( ~ defined(X0)
| equalish(X0,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',reflexivity_of_equality) ).
cnf(c_73,plain,
( ~ equalish(X0,X1)
| equalish(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
cnf(c_74,plain,
( ~ equalish(X0,X1)
| ~ equalish(X1,X2)
| equalish(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
cnf(c_77,plain,
( ~ less_or_equal(X0,X1)
| ~ equalish(X0,X2)
| less_or_equal(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_order_relation) ).
cnf(c_79,plain,
( ~ defined(additive_identity)
| equalish(additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_80,plain,
( ~ defined(additive_identity)
| defined(additive_inverse(additive_identity)) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_81,plain,
( ~ defined(additive_identity)
| equalish(multiply(multiplicative_identity,additive_identity),additive_identity) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_82,plain,
( ~ defined(additive_identity)
| equalish(add(additive_identity,additive_identity),additive_identity) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_85,plain,
( ~ defined(additive_identity)
| defined(add(additive_identity,additive_identity)) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_87,plain,
( ~ defined(additive_identity)
| less_or_equal(additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_69]) ).
cnf(c_252,plain,
( ~ less_or_equal(X0,a)
| ~ equalish(X0,additive_identity)
| less_or_equal(additive_identity,a) ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_255,plain,
( ~ defined(X0)
| ~ defined(a)
| less_or_equal(X0,a)
| less_or_equal(a,X0) ),
inference(instantiation,[status(thm)],[c_69]) ).
cnf(c_284,plain,
( ~ defined(X0)
| equalish(X0,add(additive_identity,X0)) ),
inference(superposition,[status(thm)],[c_53,c_73]) ).
cnf(c_285,plain,
( ~ defined(additive_identity)
| equalish(additive_identity,add(additive_identity,additive_identity)) ),
inference(instantiation,[status(thm)],[c_284]) ).
cnf(c_292,plain,
( ~ defined(X0)
| equalish(additive_identity,add(X0,additive_inverse(X0))) ),
inference(superposition,[status(thm)],[c_54,c_73]) ).
cnf(c_293,plain,
( ~ defined(additive_identity)
| equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity))) ),
inference(instantiation,[status(thm)],[c_292]) ).
cnf(c_300,plain,
( ~ defined(a)
| less_or_equal(a,a) ),
inference(instantiation,[status(thm)],[c_255]) ).
cnf(c_301,plain,
( ~ less_or_equal(a,a)
| ~ equalish(a,additive_identity)
| less_or_equal(additive_identity,a) ),
inference(instantiation,[status(thm)],[c_252]) ).
cnf(c_428,plain,
( ~ equalish(additive_identity,a)
| equalish(a,additive_identity) ),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_439,plain,
( ~ defined(a)
| ~ defined(additive_identity)
| less_or_equal(a,additive_identity) ),
inference(superposition,[status(thm)],[c_69,c_51]) ).
cnf(c_446,plain,
less_or_equal(a,additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_439,c_62,c_49]) ).
cnf(c_454,plain,
( ~ equalish(a,X0)
| less_or_equal(X0,additive_identity) ),
inference(superposition,[status(thm)],[c_446,c_77]) ).
cnf(c_472,plain,
( ~ defined(a)
| less_or_equal(add(additive_identity,a),additive_identity) ),
inference(superposition,[status(thm)],[c_284,c_454]) ).
cnf(c_475,plain,
less_or_equal(add(additive_identity,a),additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_472,c_49]) ).
cnf(c_492,plain,
( ~ defined(X0)
| equalish(X0,add(additive_identity,X0)) ),
inference(superposition,[status(thm)],[c_53,c_73]) ).
cnf(c_495,plain,
( ~ defined(X0)
| equalish(X0,multiply(multiplicative_identity,X0)) ),
inference(superposition,[status(thm)],[c_57,c_73]) ).
cnf(c_548,plain,
( ~ equalish(add(additive_identity,X0),X1)
| ~ defined(X0)
| equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_492,c_74]) ).
cnf(c_549,plain,
( ~ equalish(multiply(multiplicative_identity,X0),X1)
| ~ defined(X0)
| equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_495,c_74]) ).
cnf(c_669,plain,
( ~ less_or_equal(add(X0,additive_inverse(X0)),X1)
| ~ defined(X0)
| less_or_equal(additive_identity,X1) ),
inference(resolution,[status(thm)],[c_77,c_54]) ).
cnf(c_776,plain,
( ~ less_or_equal(multiply(multiplicative_identity,X0),X1)
| ~ defined(X0)
| less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[c_57,c_77]) ).
cnf(c_838,plain,
( ~ equalish(add(X0,X1),X2)
| ~ less_or_equal(X0,X3)
| ~ defined(X1)
| less_or_equal(X2,add(X3,X1)) ),
inference(superposition,[status(thm)],[c_70,c_77]) ).
cnf(c_841,plain,
( ~ equalish(add(additive_identity,additive_identity),additive_identity)
| ~ less_or_equal(additive_identity,additive_identity)
| ~ defined(additive_identity)
| less_or_equal(additive_identity,add(additive_identity,additive_identity)) ),
inference(instantiation,[status(thm)],[c_838]) ).
cnf(c_909,plain,
( ~ defined(additive_inverse(additive_identity))
| ~ defined(additive_identity)
| equalish(additive_inverse(additive_identity),additive_identity) ),
inference(superposition,[status(thm)],[c_54,c_548]) ).
cnf(c_915,plain,
( ~ defined(add(additive_identity,X0))
| ~ defined(X0)
| equalish(X0,multiply(multiplicative_identity,add(additive_identity,X0))) ),
inference(superposition,[status(thm)],[c_495,c_548]) ).
cnf(c_918,plain,
( ~ defined(additive_inverse(additive_identity))
| equalish(additive_inverse(additive_identity),additive_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[c_909,c_62]) ).
cnf(c_919,plain,
( ~ defined(add(additive_identity,additive_identity))
| ~ defined(additive_identity)
| equalish(additive_identity,multiply(multiplicative_identity,add(additive_identity,additive_identity))) ),
inference(instantiation,[status(thm)],[c_915]) ).
cnf(c_954,plain,
( ~ defined(X0)
| less_or_equal(X0,X0) ),
inference(factoring,[status(thm)],[c_69]) ).
cnf(c_961,plain,
( ~ equalish(X0,a)
| ~ equalish(additive_identity,X0)
| equalish(additive_identity,a) ),
inference(instantiation,[status(thm)],[c_74]) ).
cnf(c_968,plain,
( ~ defined(X0)
| ~ defined(multiplicative_identity)
| equalish(X0,multiply(X0,multiplicative_identity)) ),
inference(superposition,[status(thm)],[c_59,c_549]) ).
cnf(c_973,plain,
( ~ defined(X0)
| equalish(X0,multiply(X0,multiplicative_identity)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_968,c_65]) ).
cnf(c_975,plain,
( ~ defined(additive_identity)
| equalish(additive_identity,multiply(additive_identity,multiplicative_identity)) ),
inference(instantiation,[status(thm)],[c_973]) ).
cnf(c_1224,plain,
( ~ defined(X0)
| equalish(additive_identity,add(X0,additive_inverse(X0))) ),
inference(superposition,[status(thm)],[c_54,c_73]) ).
cnf(c_1276,plain,
( ~ equalish(add(X0,additive_inverse(X0)),X1)
| ~ defined(X0)
| equalish(additive_identity,X1) ),
inference(superposition,[status(thm)],[c_1224,c_74]) ).
cnf(c_1347,plain,
( ~ defined(additive_inverse(additive_identity))
| ~ defined(additive_identity)
| equalish(additive_identity,additive_inverse(additive_identity)) ),
inference(superposition,[status(thm)],[c_53,c_1276]) ).
cnf(c_1354,plain,
( ~ defined(additive_inverse(additive_identity))
| equalish(additive_identity,additive_inverse(additive_identity)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1347,c_62]) ).
cnf(c_1602,plain,
( ~ less_or_equal(add(X0,X1),X2)
| ~ defined(X0)
| ~ defined(X1)
| less_or_equal(add(X1,X0),X2) ),
inference(resolution,[status(thm)],[c_55,c_77]) ).
cnf(c_1622,plain,
( ~ less_or_equal(multiply(X0,X1),X2)
| ~ defined(X0)
| ~ defined(X1)
| less_or_equal(multiply(X1,X0),X2) ),
inference(resolution,[status(thm)],[c_59,c_77]) ).
cnf(c_2088,plain,
( ~ less_or_equal(X0,add(X1,X2))
| ~ less_or_equal(X1,X3)
| ~ defined(X2)
| less_or_equal(X0,add(X3,X2)) ),
inference(resolution,[status(thm)],[c_70,c_68]) ).
cnf(c_2407,plain,
( ~ equalish(add(additive_identity,a),a)
| ~ equalish(additive_identity,add(additive_identity,a))
| equalish(additive_identity,a) ),
inference(instantiation,[status(thm)],[c_961]) ).
cnf(c_2408,plain,
( ~ defined(a)
| equalish(add(additive_identity,a),a) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_2584,plain,
( ~ defined(X0)
| equalish(X0,add(additive_identity,X0)) ),
inference(superposition,[status(thm)],[c_53,c_73]) ).
cnf(c_2587,plain,
( ~ defined(X0)
| equalish(X0,multiply(multiplicative_identity,X0)) ),
inference(superposition,[status(thm)],[c_57,c_73]) ).
cnf(c_2640,plain,
( ~ equalish(add(additive_identity,X0),X1)
| ~ defined(X0)
| equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_2584,c_74]) ).
cnf(c_2641,plain,
( ~ equalish(multiply(multiplicative_identity,X0),X1)
| ~ defined(X0)
| equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_2587,c_74]) ).
cnf(c_2666,plain,
( ~ defined(X0)
| less_or_equal(X0,X0) ),
inference(equality_factoring,[status(thm)],[c_69]) ).
cnf(c_2686,plain,
( ~ defined(additive_inverse(additive_identity))
| ~ defined(additive_identity)
| equalish(additive_inverse(additive_identity),additive_identity) ),
inference(superposition,[status(thm)],[c_54,c_2640]) ).
cnf(c_2692,plain,
( ~ defined(additive_inverse(additive_identity))
| equalish(additive_inverse(additive_identity),additive_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2686,c_62]) ).
cnf(c_2782,plain,
( ~ defined(X0)
| ~ defined(multiplicative_identity)
| equalish(X0,multiply(X0,multiplicative_identity)) ),
inference(superposition,[status(thm)],[c_59,c_2641]) ).
cnf(c_2787,plain,
( ~ defined(X0)
| equalish(X0,multiply(X0,multiplicative_identity)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2782,c_65]) ).
cnf(c_2953,plain,
( ~ equalish(X0,X1)
| ~ defined(X0)
| less_or_equal(X1,X0) ),
inference(superposition,[status(thm)],[c_2666,c_77]) ).
cnf(c_2968,plain,
equalish(additive_inverse(additive_identity),additive_identity),
inference(global_subsumption_just,[status(thm)],[c_2692,c_62,c_80,c_918]) ).
cnf(c_2970,plain,
( ~ equalish(additive_identity,X0)
| equalish(additive_inverse(additive_identity),X0) ),
inference(superposition,[status(thm)],[c_2968,c_74]) ).
cnf(c_3020,plain,
( ~ defined(multiply(X0,X1))
| ~ defined(X0)
| ~ defined(X1)
| less_or_equal(multiply(X1,X0),multiply(X0,X1)) ),
inference(superposition,[status(thm)],[c_59,c_2953]) ).
cnf(c_3035,plain,
( ~ defined(additive_inverse(additive_identity))
| less_or_equal(additive_identity,additive_inverse(additive_identity)) ),
inference(superposition,[status(thm)],[c_2968,c_2953]) ).
cnf(c_3124,plain,
( ~ defined(add(additive_identity,X0))
| ~ defined(X0)
| equalish(X0,multiply(add(additive_identity,X0),multiplicative_identity)) ),
inference(superposition,[status(thm)],[c_2787,c_2640]) ).
cnf(c_3132,plain,
( ~ defined(add(additive_identity,additive_identity))
| ~ defined(additive_identity)
| equalish(additive_identity,multiply(add(additive_identity,additive_identity),multiplicative_identity)) ),
inference(instantiation,[status(thm)],[c_3124]) ).
cnf(c_3578,plain,
( ~ equalish(X0,X1)
| ~ equalish(additive_identity,X0)
| equalish(additive_inverse(additive_identity),X1) ),
inference(superposition,[status(thm)],[c_2970,c_74]) ).
cnf(c_3757,plain,
( ~ equalish(additive_identity,X0)
| ~ defined(X0)
| equalish(additive_inverse(additive_identity),multiply(multiplicative_identity,X0)) ),
inference(superposition,[status(thm)],[c_2587,c_3578]) ).
cnf(c_3768,plain,
( ~ equalish(additive_identity,X0)
| ~ defined(X0)
| equalish(additive_inverse(additive_identity),multiply(X0,multiplicative_identity)) ),
inference(superposition,[status(thm)],[c_2787,c_3578]) ).
cnf(c_3779,plain,
( ~ equalish(additive_identity,additive_identity)
| ~ defined(additive_identity)
| equalish(additive_inverse(additive_identity),multiply(additive_identity,multiplicative_identity)) ),
inference(instantiation,[status(thm)],[c_3768]) ).
cnf(c_3781,plain,
( ~ equalish(additive_identity,additive_identity)
| ~ defined(additive_identity)
| equalish(additive_inverse(additive_identity),multiply(multiplicative_identity,additive_identity)) ),
inference(instantiation,[status(thm)],[c_3757]) ).
cnf(c_4969,plain,
( ~ less_or_equal(X0,X1)
| ~ defined(additive_inverse(X0))
| ~ defined(X0)
| less_or_equal(additive_identity,add(X1,additive_inverse(X0))) ),
inference(resolution,[status(thm)],[c_669,c_70]) ).
cnf(c_4970,plain,
( ~ defined(additive_inverse(additive_identity))
| ~ less_or_equal(additive_identity,additive_identity)
| ~ defined(additive_identity)
| less_or_equal(additive_identity,add(additive_identity,additive_inverse(additive_identity))) ),
inference(instantiation,[status(thm)],[c_4969]) ).
cnf(c_5380,plain,
( ~ defined(X0)
| equalish(X0,add(additive_identity,X0)) ),
inference(superposition,[status(thm)],[c_53,c_73]) ).
cnf(c_5383,plain,
( ~ defined(X0)
| equalish(X0,multiply(multiplicative_identity,X0)) ),
inference(superposition,[status(thm)],[c_57,c_73]) ).
cnf(c_5425,plain,
( ~ less_or_equal(additive_identity,X0)
| less_or_equal(additive_inverse(a),X0) ),
inference(superposition,[status(thm)],[c_50,c_68]) ).
cnf(c_5442,plain,
( ~ equalish(additive_inverse(a),X0)
| less_or_equal(X0,additive_identity) ),
inference(superposition,[status(thm)],[c_50,c_77]) ).
cnf(c_5501,plain,
( ~ less_or_equal(X0,additive_inverse(a))
| ~ less_or_equal(additive_identity,X0)
| equalish(additive_inverse(a),X0) ),
inference(superposition,[status(thm)],[c_5425,c_67]) ).
cnf(c_5504,plain,
( ~ defined(additive_inverse(a))
| defined(multiplicative_inverse(additive_inverse(a)))
| less_or_equal(additive_identity,additive_identity) ),
inference(superposition,[status(thm)],[c_66,c_5442]) ).
cnf(c_5518,plain,
less_or_equal(additive_identity,additive_identity),
inference(global_subsumption_just,[status(thm)],[c_5504,c_62,c_87]) ).
cnf(c_5520,plain,
( ~ equalish(additive_identity,X0)
| less_or_equal(X0,additive_identity) ),
inference(superposition,[status(thm)],[c_5518,c_77]) ).
cnf(c_5611,plain,
( ~ defined(additive_identity)
| less_or_equal(add(additive_identity,additive_identity),additive_identity) ),
inference(superposition,[status(thm)],[c_5380,c_5520]) ).
cnf(c_5612,plain,
( ~ defined(additive_identity)
| less_or_equal(multiply(multiplicative_identity,additive_identity),additive_identity) ),
inference(superposition,[status(thm)],[c_5383,c_5520]) ).
cnf(c_5614,plain,
less_or_equal(multiply(multiplicative_identity,additive_identity),additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_5612,c_62]) ).
cnf(c_5615,plain,
less_or_equal(add(additive_identity,additive_identity),additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_5611,c_62]) ).
cnf(c_5704,plain,
( ~ less_or_equal(additive_identity,X0)
| less_or_equal(add(additive_identity,additive_identity),X0) ),
inference(superposition,[status(thm)],[c_5615,c_68]) ).
cnf(c_5713,plain,
( ~ equalish(multiply(multiplicative_identity,additive_identity),X0)
| less_or_equal(X0,additive_identity) ),
inference(superposition,[status(thm)],[c_5614,c_77]) ).
cnf(c_6161,plain,
( ~ less_or_equal(additive_identity,add(additive_identity,additive_identity))
| ~ less_or_equal(additive_identity,additive_inverse(a))
| equalish(additive_inverse(a),add(additive_identity,additive_identity)) ),
inference(superposition,[status(thm)],[c_5704,c_5501]) ).
cnf(c_6321,plain,
( ~ defined(additive_identity)
| ~ defined(multiplicative_identity)
| less_or_equal(multiply(additive_identity,multiplicative_identity),additive_identity) ),
inference(superposition,[status(thm)],[c_59,c_5713]) ).
cnf(c_6327,plain,
less_or_equal(multiply(additive_identity,multiplicative_identity),additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_6321,c_65,c_62]) ).
cnf(c_6333,plain,
( ~ less_or_equal(additive_identity,X0)
| less_or_equal(multiply(additive_identity,multiplicative_identity),X0) ),
inference(superposition,[status(thm)],[c_6327,c_68]) ).
cnf(c_6845,plain,
( ~ less_or_equal(additive_identity,multiply(additive_identity,multiplicative_identity))
| ~ less_or_equal(additive_identity,additive_inverse(a))
| equalish(additive_inverse(a),multiply(additive_identity,multiplicative_identity)) ),
inference(superposition,[status(thm)],[c_6333,c_5501]) ).
cnf(c_8086,plain,
( ~ less_or_equal(add(additive_identity,a),additive_identity)
| ~ less_or_equal(additive_identity,add(additive_identity,a))
| equalish(additive_identity,add(additive_identity,a)) ),
inference(instantiation,[status(thm)],[c_67]) ).
cnf(c_11036,plain,
( ~ defined(multiply(X0,X1))
| ~ defined(X0)
| ~ defined(X1)
| less_or_equal(multiply(X1,X0),multiply(X0,X1)) ),
inference(resolution,[status(thm)],[c_1622,c_954]) ).
cnf(c_15227,plain,
( ~ less_or_equal(X0,X1)
| ~ less_or_equal(X2,X0)
| ~ defined(X3)
| less_or_equal(add(X2,X3),add(X1,X3)) ),
inference(resolution,[status(thm)],[c_2088,c_70]) ).
cnf(c_24010,plain,
( ~ defined(X0)
| equalish(X0,add(additive_identity,X0)) ),
inference(superposition,[status(thm)],[c_53,c_73]) ).
cnf(c_24013,plain,
( ~ defined(X0)
| equalish(X0,multiply(multiplicative_identity,X0)) ),
inference(superposition,[status(thm)],[c_57,c_73]) ).
cnf(c_24016,plain,
( ~ defined(X0)
| equalish(additive_identity,add(X0,additive_inverse(X0))) ),
inference(superposition,[status(thm)],[c_54,c_73]) ).
cnf(c_24068,plain,
( ~ equalish(add(X0,additive_inverse(X0)),X1)
| ~ defined(X0)
| equalish(additive_identity,X1) ),
inference(superposition,[status(thm)],[c_24016,c_74]) ).
cnf(c_24072,plain,
( ~ equalish(additive_inverse(a),X0)
| less_or_equal(X0,additive_identity) ),
inference(superposition,[status(thm)],[c_50,c_77]) ).
cnf(c_24093,plain,
( ~ defined(X0)
| less_or_equal(X0,X0) ),
inference(equality_factoring,[status(thm)],[c_69]) ).
cnf(c_24133,plain,
( ~ defined(additive_inverse(additive_identity))
| ~ defined(additive_identity)
| equalish(additive_identity,additive_inverse(additive_identity)) ),
inference(superposition,[status(thm)],[c_53,c_24068]) ).
cnf(c_24139,plain,
( ~ defined(additive_inverse(additive_identity))
| equalish(additive_identity,additive_inverse(additive_identity)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24133,c_62]) ).
cnf(c_24147,plain,
( ~ defined(additive_inverse(a))
| defined(multiplicative_inverse(additive_inverse(a)))
| less_or_equal(additive_identity,additive_identity) ),
inference(superposition,[status(thm)],[c_66,c_24072]) ).
cnf(c_24161,plain,
less_or_equal(additive_identity,additive_identity),
inference(global_subsumption_just,[status(thm)],[c_24147,c_62,c_87]) ).
cnf(c_24163,plain,
( ~ equalish(additive_identity,X0)
| less_or_equal(X0,additive_identity) ),
inference(superposition,[status(thm)],[c_24161,c_77]) ).
cnf(c_24165,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| equalish(additive_identity,additive_identity) ),
inference(superposition,[status(thm)],[c_24161,c_67]) ).
cnf(c_24166,plain,
equalish(additive_identity,additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_24165,c_24161]) ).
cnf(c_24257,plain,
( ~ defined(additive_identity)
| less_or_equal(multiply(multiplicative_identity,additive_identity),additive_identity) ),
inference(superposition,[status(thm)],[c_24013,c_24163]) ).
cnf(c_24259,plain,
less_or_equal(multiply(multiplicative_identity,additive_identity),additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_24257,c_62]) ).
cnf(c_24393,plain,
( ~ equalish(X0,X1)
| ~ defined(X0)
| less_or_equal(X1,X0) ),
inference(superposition,[status(thm)],[c_24093,c_77]) ).
cnf(c_24400,plain,
equalish(additive_identity,additive_inverse(additive_identity)),
inference(global_subsumption_just,[status(thm)],[c_24139,c_62,c_80,c_1354]) ).
cnf(c_24403,plain,
( ~ equalish(additive_inverse(additive_identity),X0)
| equalish(additive_identity,X0) ),
inference(superposition,[status(thm)],[c_24400,c_74]) ).
cnf(c_24404,plain,
equalish(additive_inverse(additive_identity),additive_identity),
inference(superposition,[status(thm)],[c_24400,c_73]) ).
cnf(c_24405,plain,
less_or_equal(additive_inverse(additive_identity),additive_identity),
inference(superposition,[status(thm)],[c_24400,c_24163]) ).
cnf(c_24408,plain,
( ~ equalish(additive_identity,X0)
| equalish(additive_inverse(additive_identity),X0) ),
inference(superposition,[status(thm)],[c_24404,c_74]) ).
cnf(c_24412,plain,
( ~ less_or_equal(additive_identity,X0)
| less_or_equal(additive_inverse(additive_identity),X0) ),
inference(superposition,[status(thm)],[c_24405,c_68]) ).
cnf(c_24486,plain,
( ~ defined(additive_inverse(additive_identity))
| equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity))) ),
inference(superposition,[status(thm)],[c_24010,c_24403]) ).
cnf(c_24493,plain,
( ~ equalish(additive_identity,X0)
| equalish(X0,additive_inverse(additive_identity)) ),
inference(superposition,[status(thm)],[c_24408,c_73]) ).
cnf(c_24507,plain,
( ~ less_or_equal(X0,X1)
| ~ less_or_equal(additive_identity,X0)
| less_or_equal(additive_inverse(additive_identity),X1) ),
inference(superposition,[status(thm)],[c_24412,c_68]) ).
cnf(c_24519,plain,
( ~ less_or_equal(additive_identity,X0)
| less_or_equal(multiply(multiplicative_identity,additive_identity),X0) ),
inference(superposition,[status(thm)],[c_24259,c_68]) ).
cnf(c_24521,plain,
equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity))),
inference(global_subsumption_just,[status(thm)],[c_24486,c_62,c_293]) ).
cnf(c_24525,plain,
equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity),
inference(superposition,[status(thm)],[c_24521,c_73]) ).
cnf(c_24596,plain,
( ~ equalish(additive_identity,X0)
| equalish(add(additive_identity,additive_inverse(additive_identity)),X0) ),
inference(superposition,[status(thm)],[c_24525,c_74]) ).
cnf(c_24602,plain,
( ~ equalish(additive_inverse(additive_identity),X0)
| ~ equalish(additive_identity,X1)
| equalish(X1,X0) ),
inference(superposition,[status(thm)],[c_24493,c_74]) ).
cnf(c_24843,plain,
( ~ less_or_equal(additive_identity,X0)
| ~ less_or_equal(additive_identity,X1)
| ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(additive_inverse(additive_identity),multiply(X0,X1)) ),
inference(superposition,[status(thm)],[c_71,c_24507]) ).
cnf(c_24879,plain,
( ~ less_or_equal(additive_identity,X0)
| ~ less_or_equal(additive_identity,X1)
| less_or_equal(additive_inverse(additive_identity),multiply(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24843,c_24161]) ).
cnf(c_24889,plain,
( ~ less_or_equal(multiply(X0,X1),additive_inverse(additive_identity))
| ~ less_or_equal(additive_identity,X0)
| ~ less_or_equal(additive_identity,X1)
| equalish(additive_inverse(additive_identity),multiply(X0,X1)) ),
inference(superposition,[status(thm)],[c_24879,c_67]) ).
cnf(c_25507,plain,
( ~ less_or_equal(additive_identity,additive_inverse(additive_identity))
| ~ less_or_equal(additive_identity,additive_identity)
| ~ less_or_equal(additive_identity,multiplicative_identity)
| equalish(additive_inverse(additive_identity),multiply(multiplicative_identity,additive_identity)) ),
inference(superposition,[status(thm)],[c_24519,c_24889]) ).
cnf(c_25510,plain,
( ~ less_or_equal(additive_identity,additive_inverse(additive_identity))
| ~ less_or_equal(additive_identity,multiplicative_identity)
| equalish(additive_inverse(additive_identity),multiply(multiplicative_identity,additive_identity)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25507,c_24161]) ).
cnf(c_25512,plain,
equalish(additive_inverse(additive_identity),multiply(multiplicative_identity,additive_identity)),
inference(global_subsumption_just,[status(thm)],[c_25510,c_62,c_79,c_3781]) ).
cnf(c_25515,plain,
( ~ equalish(multiply(multiplicative_identity,additive_identity),X0)
| equalish(additive_inverse(additive_identity),X0) ),
inference(superposition,[status(thm)],[c_25512,c_74]) ).
cnf(c_25654,plain,
( ~ defined(additive_identity)
| ~ defined(multiplicative_identity)
| equalish(additive_inverse(additive_identity),multiply(additive_identity,multiplicative_identity)) ),
inference(superposition,[status(thm)],[c_59,c_25515]) ).
cnf(c_25667,plain,
equalish(additive_inverse(additive_identity),multiply(additive_identity,multiplicative_identity)),
inference(forward_subsumption_resolution,[status(thm)],[c_25654,c_65,c_62]) ).
cnf(c_25711,plain,
( ~ equalish(additive_identity,X0)
| equalish(X0,multiply(additive_identity,multiplicative_identity)) ),
inference(superposition,[status(thm)],[c_25667,c_24602]) ).
cnf(c_26650,plain,
( ~ defined(add(additive_identity,additive_inverse(additive_identity)))
| less_or_equal(additive_identity,add(additive_identity,additive_inverse(additive_identity))) ),
inference(superposition,[status(thm)],[c_24525,c_24393]) ).
cnf(c_27758,plain,
( ~ equalish(additive_identity,X0)
| equalish(X0,add(additive_identity,additive_inverse(additive_identity))) ),
inference(superposition,[status(thm)],[c_24596,c_73]) ).
cnf(c_28194,plain,
less_or_equal(additive_identity,add(additive_identity,additive_inverse(additive_identity))),
inference(global_subsumption_just,[status(thm)],[c_26650,c_62,c_80,c_87,c_4970]) ).
cnf(c_28210,plain,
( ~ less_or_equal(add(additive_identity,additive_inverse(additive_identity)),X0)
| less_or_equal(additive_identity,X0) ),
inference(superposition,[status(thm)],[c_28194,c_68]) ).
cnf(c_29582,plain,
( ~ equalish(additive_identity,X0)
| ~ defined(X0)
| less_or_equal(add(additive_identity,additive_inverse(additive_identity)),X0) ),
inference(superposition,[status(thm)],[c_27758,c_24393]) ).
cnf(c_30520,plain,
( ~ equalish(additive_identity,X0)
| ~ defined(X0)
| less_or_equal(additive_identity,X0) ),
inference(superposition,[status(thm)],[c_29582,c_28210]) ).
cnf(c_30651,plain,
( ~ defined(multiply(additive_identity,multiplicative_identity))
| ~ equalish(additive_identity,additive_identity)
| less_or_equal(additive_identity,multiply(additive_identity,multiplicative_identity)) ),
inference(superposition,[status(thm)],[c_25711,c_30520]) ).
cnf(c_30654,plain,
( ~ defined(multiply(additive_identity,multiplicative_identity))
| less_or_equal(additive_identity,multiply(additive_identity,multiplicative_identity)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30651,c_24166]) ).
cnf(c_39049,plain,
( ~ defined(X0)
| ~ defined(multiplicative_identity)
| defined(multiply(X0,multiplicative_identity)) ),
inference(instantiation,[status(thm)],[c_64]) ).
cnf(c_39050,plain,
( ~ defined(additive_identity)
| ~ defined(multiplicative_identity)
| defined(multiply(additive_identity,multiplicative_identity)) ),
inference(instantiation,[status(thm)],[c_39049]) ).
cnf(c_127099,plain,
( ~ defined(X0)
| equalish(X0,add(additive_identity,X0)) ),
inference(superposition,[status(thm)],[c_53,c_73]) ).
cnf(c_127111,plain,
( ~ defined(X0)
| equalish(additive_identity,add(X0,additive_inverse(X0))) ),
inference(superposition,[status(thm)],[c_54,c_73]) ).
cnf(c_127114,plain,
( ~ defined(X0)
| equalish(X0,multiply(multiplicative_identity,X0)) ),
inference(superposition,[status(thm)],[c_57,c_73]) ).
cnf(c_127124,plain,
( ~ defined(X0)
| defined(multiplicative_inverse(X0))
| equalish(additive_identity,X0) ),
inference(superposition,[status(thm)],[c_66,c_73]) ).
cnf(c_127142,plain,
( ~ less_or_equal(additive_identity,X0)
| less_or_equal(additive_inverse(a),X0) ),
inference(superposition,[status(thm)],[c_50,c_68]) ).
cnf(c_127152,plain,
( ~ equalish(X0,X1)
| ~ defined(X0)
| defined(multiplicative_inverse(X0))
| equalish(additive_identity,X1) ),
inference(superposition,[status(thm)],[c_127124,c_74]) ).
cnf(c_127154,plain,
( ~ equalish(multiply(multiplicative_identity,X0),X1)
| ~ defined(X0)
| equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_127114,c_74]) ).
cnf(c_127155,plain,
( ~ equalish(add(X0,additive_inverse(X0)),X1)
| ~ defined(X0)
| equalish(additive_identity,X1) ),
inference(superposition,[status(thm)],[c_127111,c_74]) ).
cnf(c_127159,plain,
( ~ equalish(additive_inverse(a),X0)
| less_or_equal(X0,additive_identity) ),
inference(superposition,[status(thm)],[c_50,c_77]) ).
cnf(c_127170,plain,
( ~ less_or_equal(X0,additive_inverse(a))
| ~ less_or_equal(additive_identity,X0)
| equalish(additive_inverse(a),X0) ),
inference(superposition,[status(thm)],[c_127142,c_67]) ).
cnf(c_127205,plain,
( ~ defined(additive_inverse(additive_identity))
| ~ defined(additive_identity)
| equalish(additive_identity,additive_inverse(additive_identity)) ),
inference(superposition,[status(thm)],[c_53,c_127155]) ).
cnf(c_127211,plain,
( ~ defined(additive_inverse(additive_identity))
| equalish(additive_identity,additive_inverse(additive_identity)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_127205,c_62]) ).
cnf(c_127214,plain,
( ~ defined(additive_inverse(a))
| defined(multiplicative_inverse(additive_inverse(a)))
| less_or_equal(additive_identity,additive_identity) ),
inference(superposition,[status(thm)],[c_66,c_127159]) ).
cnf(c_127216,plain,
( ~ defined(additive_inverse(a))
| less_or_equal(add(additive_identity,additive_inverse(a)),additive_identity) ),
inference(superposition,[status(thm)],[c_127099,c_127159]) ).
cnf(c_127223,plain,
( ~ less_or_equal(additive_identity,X0)
| ~ defined(additive_inverse(a))
| less_or_equal(add(additive_identity,additive_inverse(a)),X0) ),
inference(superposition,[status(thm)],[c_127216,c_68]) ).
cnf(c_127230,plain,
less_or_equal(additive_identity,additive_identity),
inference(global_subsumption_just,[status(thm)],[c_127214,c_62,c_87]) ).
cnf(c_127232,plain,
( ~ equalish(additive_identity,X0)
| less_or_equal(X0,additive_identity) ),
inference(superposition,[status(thm)],[c_127230,c_77]) ).
cnf(c_127234,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| equalish(additive_identity,additive_identity) ),
inference(superposition,[status(thm)],[c_127230,c_67]) ).
cnf(c_127235,plain,
equalish(additive_identity,additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_127234,c_127230]) ).
cnf(c_127275,plain,
( ~ defined(X0)
| less_or_equal(X0,X0) ),
inference(equality_factoring,[status(thm)],[c_69]) ).
cnf(c_127328,plain,
( ~ defined(additive_identity)
| less_or_equal(add(additive_identity,additive_identity),additive_identity) ),
inference(superposition,[status(thm)],[c_127099,c_127232]) ).
cnf(c_127329,plain,
( ~ defined(additive_identity)
| less_or_equal(multiply(multiplicative_identity,additive_identity),additive_identity) ),
inference(superposition,[status(thm)],[c_127114,c_127232]) ).
cnf(c_127331,plain,
less_or_equal(multiply(multiplicative_identity,additive_identity),additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_127329,c_62]) ).
cnf(c_127332,plain,
less_or_equal(add(additive_identity,additive_identity),additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_127328,c_62]) ).
cnf(c_127363,plain,
( ~ less_or_equal(X0,X1)
| ~ less_or_equal(additive_identity,X0)
| ~ defined(additive_inverse(a))
| less_or_equal(add(additive_identity,additive_inverse(a)),X1) ),
inference(superposition,[status(thm)],[c_127223,c_68]) ).
cnf(c_127414,plain,
( ~ equalish(multiply(multiplicative_identity,additive_identity),X0)
| less_or_equal(X0,additive_identity) ),
inference(superposition,[status(thm)],[c_127331,c_77]) ).
cnf(c_127415,plain,
( ~ less_or_equal(additive_identity,X0)
| less_or_equal(multiply(multiplicative_identity,additive_identity),X0) ),
inference(superposition,[status(thm)],[c_127331,c_68]) ).
cnf(c_127416,plain,
( ~ less_or_equal(additive_identity,multiply(multiplicative_identity,additive_identity))
| equalish(multiply(multiplicative_identity,additive_identity),additive_identity) ),
inference(superposition,[status(thm)],[c_127331,c_67]) ).
cnf(c_127419,plain,
( ~ less_or_equal(additive_identity,X0)
| less_or_equal(add(additive_identity,additive_identity),X0) ),
inference(superposition,[status(thm)],[c_127332,c_68]) ).
cnf(c_127486,plain,
( ~ equalish(X0,X1)
| ~ defined(X0)
| less_or_equal(X1,X0) ),
inference(superposition,[status(thm)],[c_127275,c_77]) ).
cnf(c_127493,plain,
equalish(additive_identity,additive_inverse(additive_identity)),
inference(global_subsumption_just,[status(thm)],[c_127211,c_62,c_80,c_1354]) ).
cnf(c_127497,plain,
equalish(additive_inverse(additive_identity),additive_identity),
inference(superposition,[status(thm)],[c_127493,c_73]) ).
cnf(c_127498,plain,
less_or_equal(additive_inverse(additive_identity),additive_identity),
inference(superposition,[status(thm)],[c_127493,c_127232]) ).
cnf(c_127502,plain,
( ~ less_or_equal(additive_identity,X0)
| less_or_equal(additive_inverse(additive_identity),X0) ),
inference(superposition,[status(thm)],[c_127498,c_68]) ).
cnf(c_127581,plain,
( ~ less_or_equal(X0,X1)
| ~ less_or_equal(additive_identity,X0)
| less_or_equal(additive_inverse(additive_identity),X1) ),
inference(superposition,[status(thm)],[c_127502,c_68]) ).
cnf(c_127624,plain,
( ~ less_or_equal(X0,X1)
| ~ less_or_equal(additive_identity,X0)
| less_or_equal(multiply(multiplicative_identity,additive_identity),X1) ),
inference(superposition,[status(thm)],[c_127415,c_68]) ).
cnf(c_127753,plain,
( ~ defined(additive_identity)
| ~ defined(multiplicative_identity)
| less_or_equal(multiply(additive_identity,multiplicative_identity),additive_identity) ),
inference(superposition,[status(thm)],[c_59,c_127414]) ).
cnf(c_127760,plain,
less_or_equal(multiply(additive_identity,multiplicative_identity),additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_127753,c_65,c_62]) ).
cnf(c_127765,plain,
( ~ less_or_equal(additive_identity,X0)
| less_or_equal(multiply(additive_identity,multiplicative_identity),X0) ),
inference(superposition,[status(thm)],[c_127760,c_68]) ).
cnf(c_127775,plain,
( ~ less_or_equal(additive_identity,add(additive_identity,additive_identity))
| ~ less_or_equal(additive_identity,additive_inverse(a))
| equalish(additive_inverse(a),add(additive_identity,additive_identity)) ),
inference(superposition,[status(thm)],[c_127419,c_127170]) ).
cnf(c_127791,plain,
( ~ less_or_equal(additive_identity,multiply(additive_identity,multiplicative_identity))
| ~ less_or_equal(additive_identity,additive_inverse(a))
| equalish(additive_inverse(a),multiply(additive_identity,multiplicative_identity)) ),
inference(superposition,[status(thm)],[c_127765,c_127170]) ).
cnf(c_127792,plain,
( ~ less_or_equal(additive_identity,additive_inverse(a))
| equalish(additive_inverse(a),add(additive_identity,additive_identity)) ),
inference(global_subsumption_just,[status(thm)],[c_127775,c_62,c_82,c_87,c_841,c_6161]) ).
cnf(c_127796,plain,
( ~ less_or_equal(additive_identity,additive_inverse(a))
| ~ defined(additive_inverse(a))
| equalish(additive_identity,add(additive_identity,additive_identity))
| defined(multiplicative_inverse(additive_inverse(a))) ),
inference(superposition,[status(thm)],[c_127792,c_127152]) ).
cnf(c_127802,plain,
( ~ less_or_equal(additive_identity,additive_inverse(a))
| equalish(additive_inverse(a),multiply(additive_identity,multiplicative_identity)) ),
inference(global_subsumption_just,[status(thm)],[c_127791,c_65,c_62,c_6845,c_30654,c_39050]) ).
cnf(c_127806,plain,
( ~ less_or_equal(additive_identity,additive_inverse(a))
| ~ defined(additive_inverse(a))
| equalish(additive_identity,multiply(additive_identity,multiplicative_identity))
| defined(multiplicative_inverse(additive_inverse(a))) ),
inference(superposition,[status(thm)],[c_127802,c_127152]) ).
cnf(c_128103,plain,
( ~ less_or_equal(additive_identity,X0)
| ~ less_or_equal(additive_identity,X1)
| ~ defined(additive_inverse(a))
| ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(add(additive_identity,additive_inverse(a)),multiply(X0,X1)) ),
inference(superposition,[status(thm)],[c_71,c_127363]) ).
cnf(c_128150,plain,
( ~ less_or_equal(additive_identity,X0)
| ~ less_or_equal(additive_identity,X1)
| ~ defined(additive_inverse(a))
| less_or_equal(add(additive_identity,additive_inverse(a)),multiply(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_128103,c_127230]) ).
cnf(c_128159,plain,
( ~ less_or_equal(multiply(X0,X1),X2)
| ~ less_or_equal(additive_identity,X0)
| ~ less_or_equal(additive_identity,X1)
| ~ defined(additive_inverse(a))
| less_or_equal(add(additive_identity,additive_inverse(a)),X2) ),
inference(superposition,[status(thm)],[c_128150,c_68]) ).
cnf(c_128226,plain,
equalish(multiply(multiplicative_identity,additive_identity),additive_identity),
inference(global_subsumption_just,[status(thm)],[c_127416,c_62,c_81]) ).
cnf(c_128230,plain,
equalish(additive_identity,multiply(multiplicative_identity,additive_identity)),
inference(superposition,[status(thm)],[c_128226,c_73]) ).
cnf(c_128326,plain,
equalish(additive_identity,add(additive_identity,additive_identity)),
inference(global_subsumption_just,[status(thm)],[c_127796,c_62,c_285]) ).
cnf(c_128329,plain,
( ~ equalish(add(additive_identity,additive_identity),X0)
| equalish(additive_identity,X0) ),
inference(superposition,[status(thm)],[c_128326,c_74]) ).
cnf(c_128330,plain,
equalish(add(additive_identity,additive_identity),additive_identity),
inference(superposition,[status(thm)],[c_128326,c_73]) ).
cnf(c_128333,plain,
equalish(additive_identity,multiply(additive_identity,multiplicative_identity)),
inference(global_subsumption_just,[status(thm)],[c_127806,c_62,c_975]) ).
cnf(c_128506,plain,
( ~ less_or_equal(additive_identity,X0)
| ~ less_or_equal(additive_identity,X1)
| ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(additive_inverse(additive_identity),multiply(X0,X1)) ),
inference(superposition,[status(thm)],[c_71,c_127581]) ).
cnf(c_128563,plain,
( ~ less_or_equal(additive_identity,X0)
| ~ less_or_equal(additive_identity,X1)
| less_or_equal(additive_inverse(additive_identity),multiply(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_128506,c_127230]) ).
cnf(c_128574,plain,
( ~ less_or_equal(multiply(X0,X1),additive_inverse(additive_identity))
| ~ less_or_equal(additive_identity,X0)
| ~ less_or_equal(additive_identity,X1)
| equalish(additive_inverse(additive_identity),multiply(X0,X1)) ),
inference(superposition,[status(thm)],[c_128563,c_67]) ).
cnf(c_128660,plain,
( ~ defined(add(additive_identity,additive_identity))
| equalish(additive_identity,multiply(multiplicative_identity,add(additive_identity,additive_identity))) ),
inference(superposition,[status(thm)],[c_127114,c_128329]) ).
cnf(c_128860,plain,
( ~ less_or_equal(additive_identity,additive_inverse(additive_identity))
| ~ less_or_equal(additive_identity,additive_identity)
| ~ less_or_equal(additive_identity,multiplicative_identity)
| equalish(additive_inverse(additive_identity),multiply(additive_identity,multiplicative_identity)) ),
inference(superposition,[status(thm)],[c_127765,c_128574]) ).
cnf(c_128862,plain,
( ~ less_or_equal(additive_identity,additive_inverse(additive_identity))
| ~ less_or_equal(additive_identity,multiplicative_identity)
| equalish(additive_inverse(additive_identity),multiply(additive_identity,multiplicative_identity)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_128860,c_127230]) ).
cnf(c_128864,plain,
equalish(additive_inverse(additive_identity),multiply(additive_identity,multiplicative_identity)),
inference(global_subsumption_just,[status(thm)],[c_128862,c_62,c_79,c_3779]) ).
cnf(c_128867,plain,
( ~ equalish(multiply(additive_identity,multiplicative_identity),X0)
| equalish(additive_inverse(additive_identity),X0) ),
inference(superposition,[status(thm)],[c_128864,c_74]) ).
cnf(c_129188,plain,
equalish(additive_identity,multiply(multiplicative_identity,add(additive_identity,additive_identity))),
inference(global_subsumption_just,[status(thm)],[c_128660,c_62,c_85,c_919]) ).
cnf(c_129191,plain,
( ~ equalish(multiply(multiplicative_identity,add(additive_identity,additive_identity)),X0)
| equalish(additive_identity,X0) ),
inference(superposition,[status(thm)],[c_129188,c_74]) ).
cnf(c_129317,plain,
( ~ defined(add(additive_identity,additive_identity))
| less_or_equal(additive_identity,add(additive_identity,additive_identity)) ),
inference(superposition,[status(thm)],[c_128330,c_127486]) ).
cnf(c_129330,plain,
( ~ defined(additive_inverse(additive_identity))
| less_or_equal(additive_identity,additive_inverse(additive_identity)) ),
inference(superposition,[status(thm)],[c_127497,c_127486]) ).
cnf(c_129440,plain,
less_or_equal(additive_identity,additive_inverse(additive_identity)),
inference(global_subsumption_just,[status(thm)],[c_129330,c_62,c_80,c_3035]) ).
cnf(c_129801,plain,
less_or_equal(additive_identity,add(additive_identity,additive_identity)),
inference(global_subsumption_just,[status(thm)],[c_129317,c_62,c_82,c_87,c_841]) ).
cnf(c_129813,plain,
( ~ equalish(additive_identity,X0)
| less_or_equal(X0,add(additive_identity,additive_identity)) ),
inference(superposition,[status(thm)],[c_129801,c_77]) ).
cnf(c_129887,plain,
( ~ equalish(X0,X1)
| ~ equalish(additive_identity,X0)
| less_or_equal(X1,add(additive_identity,additive_identity)) ),
inference(superposition,[status(thm)],[c_129813,c_77]) ).
cnf(c_135744,plain,
( ~ defined(add(additive_identity,additive_identity))
| ~ defined(multiplicative_identity)
| equalish(additive_identity,multiply(add(additive_identity,additive_identity),multiplicative_identity)) ),
inference(superposition,[status(thm)],[c_59,c_129191]) ).
cnf(c_135764,plain,
( ~ defined(add(additive_identity,additive_identity))
| equalish(additive_identity,multiply(add(additive_identity,additive_identity),multiplicative_identity)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_135744,c_65]) ).
cnf(c_135803,plain,
equalish(additive_identity,multiply(add(additive_identity,additive_identity),multiplicative_identity)),
inference(global_subsumption_just,[status(thm)],[c_135764,c_62,c_85,c_3132]) ).
cnf(c_135810,plain,
equalish(multiply(add(additive_identity,additive_identity),multiplicative_identity),additive_identity),
inference(superposition,[status(thm)],[c_135803,c_73]) ).
cnf(c_136139,plain,
( ~ equalish(additive_identity,X0)
| equalish(multiply(add(additive_identity,additive_identity),multiplicative_identity),X0) ),
inference(superposition,[status(thm)],[c_135810,c_74]) ).
cnf(c_136988,plain,
( ~ equalish(additive_identity,additive_identity)
| less_or_equal(multiply(multiplicative_identity,additive_identity),add(additive_identity,additive_identity)) ),
inference(superposition,[status(thm)],[c_128230,c_129887]) ).
cnf(c_137137,plain,
less_or_equal(multiply(multiplicative_identity,additive_identity),add(additive_identity,additive_identity)),
inference(forward_subsumption_resolution,[status(thm)],[c_136988,c_127235]) ).
cnf(c_137215,plain,
( ~ less_or_equal(add(additive_identity,additive_identity),X0)
| less_or_equal(multiply(multiplicative_identity,additive_identity),X0) ),
inference(superposition,[status(thm)],[c_137137,c_68]) ).
cnf(c_139975,plain,
( ~ equalish(additive_identity,X0)
| equalish(X0,multiply(add(additive_identity,additive_identity),multiplicative_identity)) ),
inference(superposition,[status(thm)],[c_136139,c_73]) ).
cnf(c_142420,plain,
( ~ equalish(additive_identity,multiply(additive_identity,multiplicative_identity))
| equalish(additive_inverse(additive_identity),multiply(add(additive_identity,additive_identity),multiplicative_identity)) ),
inference(superposition,[status(thm)],[c_139975,c_128867]) ).
cnf(c_142458,plain,
equalish(additive_inverse(additive_identity),multiply(add(additive_identity,additive_identity),multiplicative_identity)),
inference(forward_subsumption_resolution,[status(thm)],[c_142420,c_128333]) ).
cnf(c_142501,plain,
equalish(multiply(add(additive_identity,additive_identity),multiplicative_identity),additive_inverse(additive_identity)),
inference(superposition,[status(thm)],[c_142458,c_73]) ).
cnf(c_142807,plain,
( ~ defined(multiply(add(additive_identity,additive_identity),multiplicative_identity))
| less_or_equal(additive_inverse(additive_identity),multiply(add(additive_identity,additive_identity),multiplicative_identity)) ),
inference(superposition,[status(thm)],[c_142501,c_127486]) ).
cnf(c_145358,plain,
( ~ defined(X0)
| ~ defined(multiplicative_identity)
| equalish(X0,multiply(X0,multiplicative_identity)) ),
inference(superposition,[status(thm)],[c_59,c_127154]) ).
cnf(c_145421,plain,
( ~ defined(X0)
| equalish(X0,multiply(X0,multiplicative_identity)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_145358,c_65]) ).
cnf(c_145575,plain,
( ~ defined(X0)
| equalish(multiply(X0,multiplicative_identity),X0) ),
inference(superposition,[status(thm)],[c_145421,c_73]) ).
cnf(c_146088,plain,
( ~ defined(multiply(X0,multiplicative_identity))
| ~ defined(X0)
| less_or_equal(X0,multiply(X0,multiplicative_identity)) ),
inference(superposition,[status(thm)],[c_145575,c_127486]) ).
cnf(c_234821,plain,
( ~ defined(X0)
| ~ defined(X1)
| less_or_equal(multiply(X1,X0),multiply(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_11036,c_64,c_3020]) ).
cnf(c_236168,plain,
( ~ defined(X0)
| ~ defined(multiplicative_identity)
| less_or_equal(X0,multiply(X0,multiplicative_identity)) ),
inference(resolution,[status(thm)],[c_234821,c_776]) ).
cnf(c_236758,plain,
( ~ less_or_equal(additive_identity,X0)
| ~ defined(X1)
| less_or_equal(add(additive_inverse(a),X1),add(X0,X1)) ),
inference(resolution,[status(thm)],[c_15227,c_50]) ).
cnf(c_237319,plain,
( ~ defined(X0)
| less_or_equal(X0,multiply(X0,multiplicative_identity)) ),
inference(global_subsumption_just,[status(thm)],[c_146088,c_65,c_236168]) ).
cnf(c_237354,plain,
( ~ defined(add(additive_identity,additive_identity))
| less_or_equal(multiply(multiplicative_identity,additive_identity),multiply(add(additive_identity,additive_identity),multiplicative_identity)) ),
inference(superposition,[status(thm)],[c_237319,c_137215]) ).
cnf(c_245774,plain,
( ~ less_or_equal(additive_identity,X0)
| ~ defined(additive_inverse(a))
| ~ defined(X1)
| less_or_equal(add(X1,additive_inverse(a)),add(X0,X1)) ),
inference(resolution,[status(thm)],[c_236758,c_1602]) ).
cnf(c_248633,plain,
( ~ less_or_equal(additive_identity,X0)
| ~ defined(additive_inverse(a))
| ~ defined(a)
| less_or_equal(additive_identity,add(X0,a)) ),
inference(resolution,[status(thm)],[c_245774,c_669]) ).
cnf(c_248634,plain,
( ~ defined(additive_inverse(a))
| ~ less_or_equal(additive_identity,additive_identity)
| ~ defined(a)
| less_or_equal(additive_identity,add(additive_identity,a)) ),
inference(instantiation,[status(thm)],[c_248633]) ).
cnf(c_249735,plain,
( ~ defined(multiply(add(additive_identity,additive_identity),multiplicative_identity))
| ~ less_or_equal(additive_identity,additive_inverse(additive_identity))
| less_or_equal(multiply(multiplicative_identity,additive_identity),multiply(add(additive_identity,additive_identity),multiplicative_identity)) ),
inference(superposition,[status(thm)],[c_142807,c_127624]) ).
cnf(c_249974,plain,
( ~ defined(multiply(add(additive_identity,additive_identity),multiplicative_identity))
| less_or_equal(multiply(multiplicative_identity,additive_identity),multiply(add(additive_identity,additive_identity),multiplicative_identity)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_249735,c_129440]) ).
cnf(c_250689,plain,
less_or_equal(multiply(multiplicative_identity,additive_identity),multiply(add(additive_identity,additive_identity),multiplicative_identity)),
inference(global_subsumption_just,[status(thm)],[c_249974,c_62,c_85,c_237354]) ).
cnf(c_250711,plain,
( ~ defined(additive_inverse(a))
| ~ less_or_equal(additive_identity,additive_identity)
| ~ less_or_equal(additive_identity,multiplicative_identity)
| less_or_equal(add(additive_identity,additive_inverse(a)),multiply(add(additive_identity,additive_identity),multiplicative_identity)) ),
inference(superposition,[status(thm)],[c_250689,c_128159]) ).
cnf(c_250717,plain,
( ~ defined(additive_inverse(a))
| ~ less_or_equal(additive_identity,multiplicative_identity)
| less_or_equal(add(additive_identity,additive_inverse(a)),multiply(add(additive_identity,additive_identity),multiplicative_identity)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_250711,c_127230]) ).
cnf(c_250966,plain,
~ defined(additive_inverse(a)),
inference(global_subsumption_just,[status(thm)],[c_250717,c_62,c_49,c_51,c_87,c_300,c_301,c_428,c_475,c_2407,c_2408,c_8086,c_248634]) ).
cnf(c_250968,plain,
~ defined(a),
inference(superposition,[status(thm)],[c_63,c_250966]) ).
cnf(c_250969,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_250968,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD065-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 : Mon Aug 28 00:51:55 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.46 Running first-order theorem proving
% 0.20/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 92.41/13.25 % SZS status Started for theBenchmark.p
% 92.41/13.25 % SZS status Unsatisfiable for theBenchmark.p
% 92.41/13.25
% 92.41/13.25 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 92.41/13.25
% 92.41/13.25 ------ iProver source info
% 92.41/13.25
% 92.41/13.25 git: date: 2023-05-31 18:12:56 +0000
% 92.41/13.25 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 92.41/13.25 git: non_committed_changes: false
% 92.41/13.25 git: last_make_outside_of_git: false
% 92.41/13.25
% 92.41/13.25 ------ Parsing...successful
% 92.41/13.25
% 92.41/13.25
% 92.41/13.25
% 92.41/13.25 ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e
% 92.41/13.25
% 92.41/13.25 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 92.41/13.25 ------ Proving...
% 92.41/13.25 ------ Problem Properties
% 92.41/13.25
% 92.41/13.25
% 92.41/13.25 clauses 30
% 92.41/13.25 conjectures 2
% 92.41/13.25 EPR 12
% 92.41/13.25 Horn 27
% 92.41/13.25 unary 6
% 92.41/13.25 binary 6
% 92.41/13.25 lits 76
% 92.41/13.25 lits eq 0
% 92.41/13.25 fd_pure 0
% 92.41/13.25 fd_pseudo 0
% 92.41/13.25 fd_cond 0
% 92.41/13.25 fd_pseudo_cond 0
% 92.41/13.25 AC symbols 0
% 92.41/13.25
% 92.41/13.25 ------ Input Options Time Limit: Unbounded
% 92.41/13.25
% 92.41/13.25
% 92.41/13.25 ------
% 92.41/13.25 Current options:
% 92.41/13.25 ------
% 92.41/13.25
% 92.41/13.25
% 92.41/13.25
% 92.41/13.25
% 92.41/13.25 ------ Proving...
% 92.41/13.25
% 92.41/13.25
% 92.41/13.25 % SZS status Unsatisfiable for theBenchmark.p
% 92.41/13.25
% 92.41/13.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 92.41/13.26
% 92.41/13.27
%------------------------------------------------------------------------------