TSTP Solution File: FLD054-4 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : FLD054-4 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n014.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 : Mon May 20 19:52:36 EDT 2024
% Result : Unsatisfiable 3.08s 0.87s
% Output : CNFRefutation 3.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 24
% Syntax : Number of clauses : 122 ( 53 unt; 8 nHn; 122 RR)
% Number of literals : 263 ( 0 equ; 142 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-1 aty)
% Number of variables : 197 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(existence_of_identity_addition,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(distributivity_2,axiom,
( product(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ product(X4,X2,X6)
| ~ product(X5,X2,X7)
| ~ sum(X6,X7,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_2) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(commutativity_multiplication,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(existence_of_identity_multiplication,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(associativity_multiplication_2,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
cnf(existence_of_inverse_multiplication,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(not_sum_7,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_7) ).
cnf(associativity_multiplication_1,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(product_10,negated_conjecture,
product(a,b,l),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_10) ).
cnf(not_sum_6,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_6) ).
cnf(sum_9,negated_conjecture,
sum(a,b,k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_9) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(sum_8,negated_conjecture,
sum(multiplicative_inverse(a),multiplicative_inverse(b),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_8) ).
cnf(l_is_defined,hypothesis,
defined(l),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l_is_defined) ).
cnf(u_is_defined,hypothesis,
defined(u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_is_defined) ).
cnf(not_product_11,negated_conjecture,
~ product(k,multiplicative_inverse(l),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_11) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(distributivity_1,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X6)
| ~ product(X6,X7,X3)
| ~ product(X4,X7,X1)
| ~ product(X5,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
cnf(existence_of_inverse_addition,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(associativity_addition_1,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(c_0_24,plain,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_25,plain,
( product(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ product(X4,X2,X6)
| ~ product(X5,X2,X7)
| ~ sum(X6,X7,X3) ),
inference(fof_simplification,[status(thm)],[distributivity_2]) ).
cnf(c_0_26,plain,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
c_0_24 ).
cnf(c_0_27,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_28,plain,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_29,plain,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_30,plain,
( product(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ product(X4,X2,X6)
| ~ product(X5,X2,X7)
| ~ sum(X6,X7,X3) ),
c_0_25 ).
cnf(c_0_31,hypothesis,
sum(additive_identity,b,b),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
c_0_28 ).
cnf(c_0_33,plain,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
c_0_29 ).
cnf(c_0_34,hypothesis,
( product(X1,X2,b)
| ~ product(X3,X2,b)
| ~ product(X4,X2,additive_identity)
| ~ sum(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
( product(X1,multiplicative_identity,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,hypothesis,
( product(X1,multiplicative_identity,b)
| ~ product(X2,multiplicative_identity,additive_identity)
| ~ sum(X2,b,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_27])]) ).
cnf(c_0_37,hypothesis,
( product(b,multiplicative_identity,b)
| ~ product(additive_identity,multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_36,c_0_31]) ).
cnf(c_0_38,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_39,plain,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
inference(fof_simplification,[status(thm)],[associativity_multiplication_2]) ).
cnf(c_0_40,hypothesis,
product(b,multiplicative_identity,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_35]),c_0_38])]) ).
cnf(c_0_41,plain,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
c_0_39 ).
cnf(c_0_42,hypothesis,
product(multiplicative_identity,b,b),
inference(spm,[status(thm)],[c_0_32,c_0_40]) ).
cnf(c_0_43,plain,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_multiplication]) ).
cnf(c_0_44,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_7]) ).
cnf(c_0_45,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
inference(fof_simplification,[status(thm)],[associativity_multiplication_1]) ).
cnf(c_0_46,hypothesis,
( product(X1,b,X2)
| ~ product(X3,b,X2)
| ~ product(X3,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,plain,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
c_0_43 ).
cnf(c_0_48,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
c_0_44 ).
cnf(c_0_49,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
c_0_45 ).
cnf(c_0_50,hypothesis,
( product(X1,b,multiplicative_identity)
| ~ product(multiplicative_inverse(b),multiplicative_identity,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_27])]),c_0_48]) ).
cnf(c_0_51,plain,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_multiplicative_inverse]) ).
cnf(c_0_52,hypothesis,
( product(X1,X2,b)
| ~ product(X3,b,X2)
| ~ product(X1,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_49,c_0_42]) ).
cnf(c_0_53,negated_conjecture,
product(a,b,l),
product_10 ).
cnf(c_0_54,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_6]) ).
cnf(c_0_55,hypothesis,
( product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ defined(multiplicative_inverse(b)) ),
inference(spm,[status(thm)],[c_0_50,c_0_35]) ).
cnf(c_0_56,plain,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
c_0_51 ).
cnf(c_0_57,negated_conjecture,
sum(a,b,k),
sum_9 ).
cnf(c_0_58,negated_conjecture,
( product(X1,l,b)
| ~ product(X1,a,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_60,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
c_0_54 ).
cnf(c_0_61,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,multiplicative_identity)
| ~ product(X4,X3,X2)
| ~ defined(X3) ),
inference(spm,[status(thm)],[c_0_49,c_0_33]) ).
cnf(c_0_62,hypothesis,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_27])]),c_0_48]) ).
cnf(c_0_63,negated_conjecture,
( product(X1,X2,k)
| ~ product(X3,X2,b)
| ~ product(X4,X2,a)
| ~ sum(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_57]) ).
cnf(c_0_64,negated_conjecture,
product(multiplicative_inverse(a),l,b),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_47]),c_0_59])]),c_0_60]) ).
cnf(c_0_65,hypothesis,
( product(multiplicative_inverse(b),X1,X2)
| ~ product(b,X2,X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,negated_conjecture,
product(b,a,l),
inference(spm,[status(thm)],[c_0_32,c_0_53]) ).
cnf(c_0_67,plain,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_68,negated_conjecture,
( product(X1,l,k)
| ~ product(X2,l,a)
| ~ sum(X2,multiplicative_inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_69,negated_conjecture,
product(multiplicative_inverse(b),l,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_59])]) ).
cnf(c_0_70,plain,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
c_0_67 ).
cnf(c_0_71,negated_conjecture,
sum(multiplicative_inverse(a),multiplicative_inverse(b),u),
sum_8 ).
cnf(c_0_72,negated_conjecture,
( product(X1,X2,l)
| ~ product(X3,b,X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_49,c_0_53]) ).
cnf(c_0_73,negated_conjecture,
( product(X1,l,k)
| ~ sum(multiplicative_inverse(b),multiplicative_inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_74,negated_conjecture,
sum(multiplicative_inverse(b),multiplicative_inverse(a),u),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_75,hypothesis,
defined(l),
l_is_defined ).
cnf(c_0_76,negated_conjecture,
( product(X1,l,l)
| ~ product(X1,a,a) ),
inference(spm,[status(thm)],[c_0_72,c_0_53]) ).
cnf(c_0_77,negated_conjecture,
product(u,l,k),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_78,hypothesis,
sum(additive_identity,l,l),
inference(spm,[status(thm)],[c_0_26,c_0_75]) ).
cnf(c_0_79,negated_conjecture,
product(multiplicative_identity,l,l),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_33]),c_0_59])]) ).
cnf(c_0_80,plain,
( product(multiplicative_inverse(X1),X2,X3)
| sum(additive_identity,X1,additive_identity)
| ~ product(X1,X3,X2)
| ~ defined(X3)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_47]) ).
cnf(c_0_81,negated_conjecture,
product(l,u,k),
inference(spm,[status(thm)],[c_0_32,c_0_77]) ).
cnf(c_0_82,hypothesis,
defined(u),
u_is_defined ).
cnf(c_0_83,negated_conjecture,
~ product(k,multiplicative_inverse(l),u),
inference(fof_simplification,[status(thm)],[not_product_11]) ).
cnf(c_0_84,hypothesis,
( product(X1,X2,l)
| ~ product(X3,X2,l)
| ~ product(X4,X2,additive_identity)
| ~ sum(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_78]) ).
cnf(c_0_85,negated_conjecture,
product(l,multiplicative_identity,l),
inference(spm,[status(thm)],[c_0_32,c_0_79]) ).
cnf(c_0_86,negated_conjecture,
( product(multiplicative_inverse(l),k,u)
| sum(additive_identity,l,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]),c_0_75])]) ).
cnf(c_0_87,negated_conjecture,
~ product(k,multiplicative_inverse(l),u),
c_0_83 ).
cnf(c_0_88,negated_conjecture,
( product(X1,multiplicative_identity,l)
| ~ product(X2,multiplicative_identity,additive_identity)
| ~ sum(X2,l,X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_89,negated_conjecture,
sum(additive_identity,l,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_86]),c_0_87]) ).
cnf(c_0_90,negated_conjecture,
( product(additive_identity,multiplicative_identity,l)
| ~ product(additive_identity,multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_91,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_92,negated_conjecture,
product(additive_identity,multiplicative_identity,l),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_35]),c_0_38])]) ).
cnf(c_0_93,plain,
( product(multiplicative_identity,X1,X2)
| ~ product(multiplicative_identity,X2,X1)
| ~ defined(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_33]),c_0_91])]) ).
cnf(c_0_94,negated_conjecture,
product(multiplicative_identity,additive_identity,l),
inference(spm,[status(thm)],[c_0_32,c_0_92]) ).
cnf(c_0_95,negated_conjecture,
( product(X1,b,X2)
| ~ product(X3,l,X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_53]) ).
cnf(c_0_96,negated_conjecture,
product(multiplicative_identity,l,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_38])]) ).
cnf(c_0_97,plain,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X6)
| ~ product(X6,X7,X3)
| ~ product(X4,X7,X1)
| ~ product(X5,X7,X2) ),
inference(fof_simplification,[status(thm)],[distributivity_1]) ).
cnf(c_0_98,negated_conjecture,
( product(X1,b,additive_identity)
| ~ product(multiplicative_identity,a,X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_99,plain,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X6)
| ~ product(X6,X7,X3)
| ~ product(X4,X7,X1)
| ~ product(X5,X7,X2) ),
c_0_97 ).
cnf(c_0_100,negated_conjecture,
product(a,b,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_33]),c_0_59])]) ).
cnf(c_0_101,plain,
( sum(X1,X2,X3)
| ~ product(X4,X3,X2)
| ~ product(X5,X3,X1)
| ~ defined(X3)
| ~ sum(X5,X4,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_99,c_0_33]) ).
cnf(c_0_102,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_26,c_0_91]) ).
cnf(c_0_103,negated_conjecture,
product(b,a,additive_identity),
inference(spm,[status(thm)],[c_0_32,c_0_100]) ).
cnf(c_0_104,plain,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_addition]) ).
cnf(c_0_105,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
inference(fof_simplification,[status(thm)],[associativity_addition_1]) ).
cnf(c_0_106,plain,
( sum(X1,X2,X3)
| ~ product(multiplicative_identity,X3,X2)
| ~ product(additive_identity,X3,X1)
| ~ defined(X3) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_107,negated_conjecture,
product(multiplicative_inverse(b),additive_identity,a),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_103]),c_0_59]),c_0_27])]),c_0_48]) ).
cnf(c_0_108,plain,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
c_0_104 ).
cnf(c_0_109,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
c_0_105 ).
cnf(c_0_110,plain,
( sum(X1,X2,X2)
| ~ product(additive_identity,X2,X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_106,c_0_33]) ).
cnf(c_0_111,negated_conjecture,
product(additive_identity,multiplicative_inverse(b),a),
inference(spm,[status(thm)],[c_0_32,c_0_107]) ).
cnf(c_0_112,plain,
( sum(X1,additive_inverse(X1),additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_108]) ).
cnf(c_0_113,negated_conjecture,
( sum(X1,X2,u)
| ~ sum(X3,multiplicative_inverse(a),X2)
| ~ sum(X1,X3,multiplicative_inverse(b)) ),
inference(spm,[status(thm)],[c_0_109,c_0_74]) ).
cnf(c_0_114,negated_conjecture,
( sum(a,multiplicative_inverse(b),multiplicative_inverse(b))
| ~ defined(multiplicative_inverse(b)) ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_115,plain,
( sum(X1,X2,additive_identity)
| ~ defined(X3)
| ~ sum(X4,additive_inverse(X3),X2)
| ~ sum(X1,X4,X3) ),
inference(spm,[status(thm)],[c_0_109,c_0_112]) ).
cnf(c_0_116,negated_conjecture,
( sum(X1,u,u)
| ~ sum(X1,multiplicative_inverse(b),multiplicative_inverse(b)) ),
inference(spm,[status(thm)],[c_0_113,c_0_74]) ).
cnf(c_0_117,negated_conjecture,
sum(a,multiplicative_inverse(b),multiplicative_inverse(b)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_56]),c_0_27])]),c_0_48]) ).
cnf(c_0_118,plain,
( sum(X1,additive_identity,additive_identity)
| ~ defined(X2)
| ~ sum(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_115,c_0_112]) ).
cnf(c_0_119,negated_conjecture,
sum(a,u,u),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_120,negated_conjecture,
sum(a,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_82])]) ).
cnf(c_0_121,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_120]),c_0_60]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : FLD054-4 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.06/0.14 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat May 18 21:25:53 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.17/0.46 Running first-order theorem proving
% 0.17/0.46 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.08/0.87 # Version: 3.1.0
% 3.08/0.87 # Preprocessing class: FSMSSMSSSSSNFFN.
% 3.08/0.87 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.08/0.87 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.08/0.87 # Starting new_bool_3 with 300s (1) cores
% 3.08/0.87 # Starting new_bool_1 with 300s (1) cores
% 3.08/0.87 # Starting sh5l with 300s (1) cores
% 3.08/0.87 # sh5l with pid 17964 completed with status 0
% 3.08/0.87 # Result found by sh5l
% 3.08/0.87 # Preprocessing class: FSMSSMSSSSSNFFN.
% 3.08/0.87 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.08/0.87 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.08/0.87 # Starting new_bool_3 with 300s (1) cores
% 3.08/0.87 # Starting new_bool_1 with 300s (1) cores
% 3.08/0.87 # Starting sh5l with 300s (1) cores
% 3.08/0.87 # SinE strategy is gf500_gu_R04_F100_L20000
% 3.08/0.87 # Search class: FGUNF-FFMM11-SFFFFFNN
% 3.08/0.87 # partial match(1): FGUNF-FFMM21-SFFFFFNN
% 3.08/0.87 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 3.08/0.87 # Starting G-E--_006_C18_F1_PI_AE_Q4_CS_SP_S2S with 118s (1) cores
% 3.08/0.87 # G-E--_006_C18_F1_PI_AE_Q4_CS_SP_S2S with pid 17971 completed with status 0
% 3.08/0.87 # Result found by G-E--_006_C18_F1_PI_AE_Q4_CS_SP_S2S
% 3.08/0.87 # Preprocessing class: FSMSSMSSSSSNFFN.
% 3.08/0.87 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.08/0.87 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.08/0.87 # Starting new_bool_3 with 300s (1) cores
% 3.08/0.87 # Starting new_bool_1 with 300s (1) cores
% 3.08/0.87 # Starting sh5l with 300s (1) cores
% 3.08/0.87 # SinE strategy is gf500_gu_R04_F100_L20000
% 3.08/0.87 # Search class: FGUNF-FFMM11-SFFFFFNN
% 3.08/0.87 # partial match(1): FGUNF-FFMM21-SFFFFFNN
% 3.08/0.87 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 3.08/0.87 # Starting G-E--_006_C18_F1_PI_AE_Q4_CS_SP_S2S with 118s (1) cores
% 3.08/0.87 # Preprocessing time : 0.001 s
% 3.08/0.87
% 3.08/0.87 # Proof found!
% 3.08/0.87 # SZS status Unsatisfiable
% 3.08/0.87 # SZS output start CNFRefutation
% See solution above
% 3.08/0.87 # Parsed axioms : 37
% 3.08/0.87 # Removed by relevancy pruning/SinE : 4
% 3.08/0.87 # Initial clauses : 33
% 3.08/0.87 # Removed in clause preprocessing : 0
% 3.08/0.87 # Initial clauses in saturation : 33
% 3.08/0.87 # Processed clauses : 5326
% 3.08/0.87 # ...of these trivial : 806
% 3.08/0.87 # ...subsumed : 1119
% 3.08/0.87 # ...remaining for further processing : 3401
% 3.08/0.87 # Other redundant clauses eliminated : 0
% 3.08/0.87 # Clauses deleted for lack of memory : 0
% 3.08/0.87 # Backward-subsumed : 27
% 3.08/0.87 # Backward-rewritten : 85
% 3.08/0.87 # Generated clauses : 23278
% 3.08/0.87 # ...of the previous two non-redundant : 14263
% 3.08/0.87 # ...aggressively subsumed : 0
% 3.08/0.87 # Contextual simplify-reflections : 18
% 3.08/0.87 # Paramodulations : 23236
% 3.08/0.87 # Factorizations : 42
% 3.08/0.87 # NegExts : 0
% 3.08/0.87 # Equation resolutions : 0
% 3.08/0.87 # Disequality decompositions : 0
% 3.08/0.87 # Total rewrite steps : 18507
% 3.08/0.87 # ...of those cached : 18134
% 3.08/0.87 # Propositional unsat checks : 0
% 3.08/0.87 # Propositional check models : 0
% 3.08/0.87 # Propositional check unsatisfiable : 0
% 3.08/0.87 # Propositional clauses : 0
% 3.08/0.87 # Propositional clauses after purity: 0
% 3.08/0.87 # Propositional unsat core size : 0
% 3.08/0.87 # Propositional preprocessing time : 0.000
% 3.08/0.87 # Propositional encoding time : 0.000
% 3.08/0.87 # Propositional solver time : 0.000
% 3.08/0.87 # Success case prop preproc time : 0.000
% 3.08/0.87 # Success case prop encoding time : 0.000
% 3.08/0.87 # Success case prop solver time : 0.000
% 3.08/0.87 # Current number of processed clauses : 3289
% 3.08/0.87 # Positive orientable unit clauses : 382
% 3.08/0.87 # Positive unorientable unit clauses: 0
% 3.08/0.87 # Negative unit clauses : 4
% 3.08/0.87 # Non-unit-clauses : 2903
% 3.08/0.87 # Current number of unprocessed clauses: 8942
% 3.08/0.87 # ...number of literals in the above : 28732
% 3.08/0.87 # Current number of archived formulas : 0
% 3.08/0.87 # Current number of archived clauses : 112
% 3.08/0.87 # Clause-clause subsumption calls (NU) : 547508
% 3.08/0.87 # Rec. Clause-clause subsumption calls : 402805
% 3.08/0.87 # Non-unit clause-clause subsumptions : 1164
% 3.08/0.87 # Unit Clause-clause subsumption calls : 65228
% 3.08/0.87 # Rewrite failures with RHS unbound : 0
% 3.08/0.87 # BW rewrite match attempts : 641
% 3.08/0.87 # BW rewrite match successes : 44
% 3.08/0.87 # Condensation attempts : 0
% 3.08/0.87 # Condensation successes : 0
% 3.08/0.87 # Termbank termtop insertions : 303856
% 3.08/0.87 # Search garbage collected termcells : 130
% 3.08/0.87
% 3.08/0.87 # -------------------------------------------------
% 3.08/0.87 # User time : 0.369 s
% 3.08/0.87 # System time : 0.008 s
% 3.08/0.87 # Total time : 0.377 s
% 3.08/0.87 # Maximum resident set size: 1756 pages
% 3.08/0.87
% 3.08/0.87 # -------------------------------------------------
% 3.08/0.87 # User time : 0.370 s
% 3.08/0.87 # System time : 0.009 s
% 3.08/0.87 # Total time : 0.379 s
% 3.08/0.87 # Maximum resident set size: 1764 pages
% 3.08/0.87 % E---3.1 exiting
% 3.08/0.87 % E exiting
%------------------------------------------------------------------------------