%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD051-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:22:51 PM UTC 2026
% Result : Unsatisfiable 37.17s 5.99s
% Output : CNFRefutation 37.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 30
% Syntax : Number of clauses : 151 ( 75 unt; 13 nHn; 151 RR)
% Number of literals : 285 ( 0 equ; 133 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 189 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(associativity_multiplication_1,axiom,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(s_is_defined,hypothesis,
defined(s),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_is_defined) ).
cnf(product_15,negated_conjecture,
product(c,multiplicative_inverse(d),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_15) ).
cnf(existence_of_inverse_multiplication,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(product_13,negated_conjecture,
product(s,multiplicative_inverse(t),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_13) ).
cnf(not_sum_12,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_12) ).
cnf(associativity_addition_1,axiom,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(distributivity_1,axiom,
( ~ product(X5,X7,X2)
| ~ product(X4,X7,X1)
| ~ product(X6,X7,X3)
| ~ sum(X4,X5,X6)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
cnf(d_is_defined,hypothesis,
defined(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_is_defined) ).
cnf(commutativity_addition,axiom,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(t_is_defined,hypothesis,
defined(t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_is_defined) ).
cnf(product_16,negated_conjecture,
product(a,d,k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_16) ).
cnf(k_is_defined,hypothesis,
defined(k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_is_defined) ).
cnf(product_14,negated_conjecture,
product(a,multiplicative_inverse(b),s),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_14) ).
cnf(associativity_addition_2,axiom,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
cnf(totality_of_multiplication,axiom,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
cnf(not_sum_10,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_10) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(associativity_multiplication_2,axiom,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(not_sum_11,negated_conjecture,
~ sum(additive_identity,c,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_11) ).
cnf(product_17,negated_conjecture,
product(b,c,l),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_17) ).
cnf(u_is_defined,hypothesis,
defined(u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_is_defined) ).
cnf(l_is_defined,hypothesis,
defined(l),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l_is_defined) ).
cnf(not_product_18,negated_conjecture,
~ product(k,multiplicative_inverse(l),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_18) ).
cnf(c_0_30,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_31,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[associativity_multiplication_1]) ).
cnf(c_0_32,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
c_0_30 ).
cnf(c_0_33,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_34,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_35,hypothesis,
defined(s),
s_is_defined ).
cnf(c_0_36,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
c_0_31 ).
cnf(c_0_37,hypothesis,
product(multiplicative_identity,c,c),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
c_0_34 ).
cnf(c_0_39,negated_conjecture,
product(c,multiplicative_inverse(d),t),
product_15 ).
cnf(c_0_40,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_multiplication]) ).
cnf(c_0_41,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_42,hypothesis,
product(multiplicative_identity,s,s),
inference(spm,[status(thm)],[c_0_32,c_0_35]) ).
cnf(c_0_43,negated_conjecture,
product(s,multiplicative_inverse(t),u),
product_13 ).
cnf(c_0_44,hypothesis,
( ~ product(X1,X3,multiplicative_identity)
| ~ product(X3,c,X2)
| product(X1,X2,c) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,negated_conjecture,
product(multiplicative_inverse(d),c,t),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
c_0_40 ).
cnf(c_0_47,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_12]) ).
cnf(c_0_48,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[associativity_addition_1]) ).
cnf(c_0_49,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
c_0_41 ).
cnf(c_0_50,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_51,hypothesis,
( ~ product(X1,X3,multiplicative_identity)
| ~ product(X3,s,X2)
| product(X1,X2,s) ),
inference(spm,[status(thm)],[c_0_36,c_0_42]) ).
cnf(c_0_52,negated_conjecture,
product(multiplicative_inverse(t),s,u),
inference(spm,[status(thm)],[c_0_38,c_0_43]) ).
cnf(c_0_53,plain,
( ~ product(X5,X7,X2)
| ~ product(X4,X7,X1)
| ~ product(X6,X7,X3)
| ~ sum(X4,X5,X6)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[distributivity_1]) ).
cnf(c_0_54,negated_conjecture,
( ~ product(X1,multiplicative_inverse(d),multiplicative_identity)
| product(X1,t,c) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_55,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(X1,multiplicative_inverse(X1),multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_38,c_0_46]) ).
cnf(c_0_56,hypothesis,
defined(d),
d_is_defined ).
cnf(c_0_57,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
c_0_47 ).
cnf(c_0_58,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
c_0_48 ).
cnf(c_0_59,hypothesis,
sum(additive_identity,a,a),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_60,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_61,negated_conjecture,
( ~ product(X1,multiplicative_inverse(t),multiplicative_identity)
| product(X1,u,s) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_62,hypothesis,
defined(t),
t_is_defined ).
cnf(c_0_63,plain,
( ~ product(X5,X7,X2)
| ~ product(X4,X7,X1)
| ~ product(X6,X7,X3)
| ~ sum(X4,X5,X6)
| sum(X1,X2,X3) ),
c_0_53 ).
cnf(c_0_64,negated_conjecture,
product(a,d,k),
product_16 ).
cnf(c_0_65,negated_conjecture,
product(d,t,c),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]),c_0_57]) ).
cnf(c_0_66,hypothesis,
( ~ sum(X1,X3,additive_identity)
| ~ sum(X3,a,X2)
| sum(X1,X2,a) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_67,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
c_0_60 ).
cnf(c_0_68,negated_conjecture,
( sum(additive_identity,t,additive_identity)
| product(t,u,s) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_55]),c_0_62])]) ).
cnf(c_0_69,negated_conjecture,
( ~ sum(X4,X3,a)
| ~ product(X4,d,X1)
| ~ product(X3,d,X2)
| sum(X1,X2,k) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_70,negated_conjecture,
product(t,d,c),
inference(spm,[status(thm)],[c_0_38,c_0_65]) ).
cnf(c_0_71,hypothesis,
( ~ sum(X1,additive_identity,additive_identity)
| sum(X1,a,a) ),
inference(spm,[status(thm)],[c_0_66,c_0_59]) ).
cnf(c_0_72,negated_conjecture,
( sum(t,additive_identity,additive_identity)
| product(t,u,s) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,hypothesis,
defined(k),
k_is_defined ).
cnf(c_0_74,negated_conjecture,
( ~ sum(X2,t,a)
| ~ product(X2,d,X1)
| sum(X1,c,k) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_75,hypothesis,
( sum(t,a,a)
| product(t,u,s) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_76,hypothesis,
product(multiplicative_identity,a,a),
inference(spm,[status(thm)],[c_0_32,c_0_50]) ).
cnf(c_0_77,negated_conjecture,
product(a,multiplicative_inverse(b),s),
product_14 ).
cnf(c_0_78,plain,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[associativity_addition_2]) ).
cnf(c_0_79,hypothesis,
sum(additive_identity,k,k),
inference(spm,[status(thm)],[c_0_49,c_0_73]) ).
cnf(c_0_80,hypothesis,
sum(additive_identity,c,c),
inference(spm,[status(thm)],[c_0_49,c_0_33]) ).
cnf(c_0_81,negated_conjecture,
( ~ sum(a,t,a)
| sum(k,c,k) ),
inference(spm,[status(thm)],[c_0_74,c_0_64]) ).
cnf(c_0_82,hypothesis,
( sum(a,t,a)
| product(t,u,s) ),
inference(spm,[status(thm)],[c_0_67,c_0_75]) ).
cnf(c_0_83,plain,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
inference(fof_simplification,[status(thm)],[totality_of_multiplication]) ).
cnf(c_0_84,hypothesis,
( ~ product(X1,X3,multiplicative_identity)
| ~ product(X3,a,X2)
| product(X1,X2,a) ),
inference(spm,[status(thm)],[c_0_36,c_0_76]) ).
cnf(c_0_85,negated_conjecture,
product(multiplicative_inverse(b),a,s),
inference(spm,[status(thm)],[c_0_38,c_0_77]) ).
cnf(c_0_86,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_10]) ).
cnf(c_0_87,plain,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
c_0_78 ).
cnf(c_0_88,hypothesis,
sum(k,additive_identity,k),
inference(spm,[status(thm)],[c_0_67,c_0_79]) ).
cnf(c_0_89,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_addition]) ).
cnf(c_0_90,hypothesis,
( ~ sum(X1,X3,additive_identity)
| ~ sum(X3,c,X2)
| sum(X1,X2,c) ),
inference(spm,[status(thm)],[c_0_58,c_0_80]) ).
cnf(c_0_91,hypothesis,
( sum(k,c,k)
| product(t,u,s) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_92,plain,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[associativity_multiplication_2]) ).
cnf(c_0_93,plain,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
c_0_83 ).
cnf(c_0_94,negated_conjecture,
( ~ product(X1,multiplicative_inverse(b),multiplicative_identity)
| product(X1,s,a) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_95,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_96,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
c_0_86 ).
cnf(c_0_97,hypothesis,
( ~ sum(X3,k,X1)
| ~ sum(X3,k,X2)
| sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_98,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
c_0_89 ).
cnf(c_0_99,hypothesis,
( ~ sum(X1,k,additive_identity)
| sum(X1,k,c)
| product(t,u,s) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_100,plain,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
c_0_92 ).
cnf(c_0_101,hypothesis,
( ~ defined(X1)
| product(t,X1,multiply(t,X1)) ),
inference(spm,[status(thm)],[c_0_93,c_0_62]) ).
cnf(c_0_102,negated_conjecture,
product(b,s,a),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_55]),c_0_95])]),c_0_96]) ).
cnf(c_0_103,hypothesis,
( ~ sum(additive_inverse(k),k,X1)
| sum(X1,additive_identity,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_73])]) ).
cnf(c_0_104,hypothesis,
( sum(additive_inverse(k),k,c)
| product(t,u,s) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_98]),c_0_73])]) ).
cnf(c_0_105,negated_conjecture,
~ sum(additive_identity,c,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_11]) ).
cnf(c_0_106,negated_conjecture,
( ~ product(X3,t,X1)
| ~ product(X3,c,X2)
| product(X1,d,X2) ),
inference(spm,[status(thm)],[c_0_100,c_0_70]) ).
cnf(c_0_107,negated_conjecture,
product(b,c,l),
product_17 ).
cnf(c_0_108,hypothesis,
product(t,b,multiply(t,b)),
inference(spm,[status(thm)],[c_0_101,c_0_95]) ).
cnf(c_0_109,negated_conjecture,
product(s,b,a),
inference(spm,[status(thm)],[c_0_38,c_0_102]) ).
cnf(c_0_110,hypothesis,
( sum(c,additive_identity,additive_identity)
| product(t,u,s) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_111,negated_conjecture,
~ sum(additive_identity,c,additive_identity),
c_0_105 ).
cnf(c_0_112,negated_conjecture,
( ~ product(b,t,X1)
| product(X1,d,l) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_113,hypothesis,
product(b,t,multiply(t,b)),
inference(spm,[status(thm)],[c_0_38,c_0_108]) ).
cnf(c_0_114,negated_conjecture,
( ~ product(X1,X3,s)
| ~ product(X3,b,X2)
| product(X1,X2,a) ),
inference(spm,[status(thm)],[c_0_36,c_0_109]) ).
cnf(c_0_115,hypothesis,
product(t,u,s),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_110]),c_0_111]) ).
cnf(c_0_116,negated_conjecture,
( ~ product(X1,X3,a)
| ~ product(X3,d,X2)
| product(X1,X2,k) ),
inference(spm,[status(thm)],[c_0_36,c_0_64]) ).
cnf(c_0_117,hypothesis,
product(multiply(t,b),d,l),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_118,hypothesis,
( ~ product(X1,t,s)
| product(X1,multiply(t,b),a) ),
inference(spm,[status(thm)],[c_0_114,c_0_108]) ).
cnf(c_0_119,hypothesis,
product(u,t,s),
inference(spm,[status(thm)],[c_0_38,c_0_115]) ).
cnf(c_0_120,hypothesis,
defined(u),
u_is_defined ).
cnf(c_0_121,negated_conjecture,
( ~ product(X1,multiply(t,b),a)
| product(X1,l,k) ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_122,hypothesis,
product(u,multiply(t,b),a),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_123,hypothesis,
product(multiplicative_identity,u,u),
inference(spm,[status(thm)],[c_0_32,c_0_120]) ).
cnf(c_0_124,negated_conjecture,
product(u,l,k),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_125,hypothesis,
( ~ product(X1,X3,multiplicative_identity)
| ~ product(X3,u,X2)
| product(X1,X2,u) ),
inference(spm,[status(thm)],[c_0_36,c_0_123]) ).
cnf(c_0_126,negated_conjecture,
product(l,u,k),
inference(spm,[status(thm)],[c_0_38,c_0_124]) ).
cnf(c_0_127,hypothesis,
( ~ product(X1,l,multiplicative_identity)
| product(X1,k,u) ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_128,hypothesis,
defined(l),
l_is_defined ).
cnf(c_0_129,negated_conjecture,
~ product(k,multiplicative_inverse(l),u),
inference(fof_simplification,[status(thm)],[not_product_18]) ).
cnf(c_0_130,negated_conjecture,
( ~ product(X1,b,multiplicative_identity)
| product(X1,l,c) ),
inference(spm,[status(thm)],[c_0_44,c_0_107]) ).
cnf(c_0_131,hypothesis,
( sum(additive_identity,l,additive_identity)
| product(multiplicative_inverse(l),k,u) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_46]),c_0_128])]) ).
cnf(c_0_132,negated_conjecture,
~ product(k,multiplicative_inverse(l),u),
c_0_129 ).
cnf(c_0_133,negated_conjecture,
product(multiplicative_inverse(b),l,c),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_46]),c_0_95])]),c_0_96]) ).
cnf(c_0_134,hypothesis,
sum(additive_identity,l,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_131]),c_0_132]) ).
cnf(c_0_135,negated_conjecture,
( ~ sum(X4,X3,a)
| ~ product(X4,multiplicative_inverse(b),X1)
| ~ product(X3,multiplicative_inverse(b),X2)
| sum(X1,X2,s) ),
inference(spm,[status(thm)],[c_0_63,c_0_77]) ).
cnf(c_0_136,negated_conjecture,
product(l,multiplicative_inverse(b),c),
inference(spm,[status(thm)],[c_0_38,c_0_133]) ).
cnf(c_0_137,hypothesis,
sum(l,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_67,c_0_134]) ).
cnf(c_0_138,negated_conjecture,
( ~ sum(X2,l,a)
| ~ product(X2,multiplicative_inverse(b),X1)
| sum(X1,c,s) ),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_139,hypothesis,
sum(l,a,a),
inference(spm,[status(thm)],[c_0_71,c_0_137]) ).
cnf(c_0_140,hypothesis,
sum(additive_identity,s,s),
inference(spm,[status(thm)],[c_0_49,c_0_35]) ).
cnf(c_0_141,negated_conjecture,
( ~ sum(a,l,a)
| sum(s,c,s) ),
inference(spm,[status(thm)],[c_0_138,c_0_77]) ).
cnf(c_0_142,hypothesis,
sum(a,l,a),
inference(spm,[status(thm)],[c_0_67,c_0_139]) ).
cnf(c_0_143,hypothesis,
sum(s,additive_identity,s),
inference(spm,[status(thm)],[c_0_67,c_0_140]) ).
cnf(c_0_144,negated_conjecture,
sum(s,c,s),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_141,c_0_142])]) ).
cnf(c_0_145,hypothesis,
( ~ sum(X3,s,X1)
| ~ sum(X3,s,X2)
| sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_87,c_0_143]) ).
cnf(c_0_146,hypothesis,
( ~ sum(X1,s,additive_identity)
| sum(X1,s,c) ),
inference(spm,[status(thm)],[c_0_90,c_0_144]) ).
cnf(c_0_147,hypothesis,
( ~ sum(additive_inverse(s),s,X1)
| sum(X1,additive_identity,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_98]),c_0_35])]) ).
cnf(c_0_148,hypothesis,
sum(additive_inverse(s),s,c),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_98]),c_0_35])]) ).
cnf(c_0_149,hypothesis,
sum(c,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_150,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_149]),c_0_111]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD051-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 15:41:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 37.17/5.99 % Version: 3.5.1
% 37.17/5.99 % Preprocessing class: FSMSSMSMSSSNFFN.
% 37.17/5.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 37.17/5.99 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 37.17/5.99 % Starting new_bool_3 with 300s (1) cores
% 37.17/5.99 % Starting new_bool_1 with 300s (1) cores
% 37.17/5.99 % Starting sh5l with 300s (1) cores
% 37.17/5.99 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 3183329 completed with status 0
% 37.17/5.99 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 37.17/5.99 % Preprocessing class: FSMSSMSMSSSNFFN.
% 37.17/5.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 37.17/5.99 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 37.17/5.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 37.17/5.99 % No SInE strategy applied
% 37.17/5.99 % Search class: FGUNF-FFMM21-SFFFFFNN
% 37.17/5.99 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 37.17/5.99 % Starting SubtermCWHack with 136s (1) cores
% 37.17/5.99 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 37.17/5.99 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 296s (1) cores
% 37.17/5.99 % Starting new_bool_3 with 269s (1) cores
% 37.17/5.99 % Starting G-E--_107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S08BN with 136s (1) cores
% 37.17/5.99 % G-E--_107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S08BN with pid 3183340 completed with status 0
% 37.17/5.99 % Result found by G-E--_107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S08BN
% 37.17/5.99 % Preprocessing class: FSMSSMSMSSSNFFN.
% 37.17/5.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 37.17/5.99 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 37.17/5.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 37.17/5.99 % No SInE strategy applied
% 37.17/5.99 % Search class: FGUNF-FFMM21-SFFFFFNN
% 37.17/5.99 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 37.17/5.99 % Starting SubtermCWHack with 136s (1) cores
% 37.17/5.99 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 37.17/5.99 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 296s (1) cores
% 37.17/5.99 % Starting new_bool_3 with 269s (1) cores
% 37.17/5.99 % Starting G-E--_107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S08BN with 136s (1) cores
% 37.17/5.99 % Preprocessing time : 0.002 s
% 37.17/5.99 % Presaturation interreduction done
% 37.17/5.99
% 37.17/5.99 % Proof found!
% 37.17/5.99 % SZS status Unsatisfiable
% 37.17/5.99 % SZS output start CNFRefutation
% See solution above
% 37.17/5.99 % Parsed axioms : 44
% 37.17/5.99 % Removed by relevancy pruning/SinE : 0
% 37.17/5.99 % Initial clauses : 44
% 37.17/5.99 % Removed in clause preprocessing : 0
% 37.17/5.99 % Initial clauses in saturation : 44
% 37.17/5.99 % Processed clauses : 13007
% 37.17/5.99 % ...of these trivial : 404
% 37.17/5.99 % ...subsumed : 2497
% 37.17/5.99 % ...remaining for further processing : 10106
% 37.17/5.99 % Other redundant clauses eliminated : 0
% 37.17/5.99 % Clauses deleted for lack of memory : 0
% 37.17/5.99 % Backward-subsumed : 204
% 37.17/5.99 % Backward-rewritten : 1272
% 37.17/5.99 % Generated clauses : 219204
% 37.17/5.99 % ...of the previous two non-redundant : 212276
% 37.17/5.99 % ...aggressively subsumed : 0
% 37.17/5.99 % Contextual simplify-reflections : 0
% 37.17/5.99 % Paramodulations : 219196
% 37.17/5.99 % Factorizations : 8
% 37.17/5.99 % NegExts : 0
% 37.17/5.99 % Equation resolutions : 0
% 37.17/5.99 % Disequality decompositions : 0
% 37.17/5.99 % Total rewrite steps : 65029
% 37.17/5.99 % ...of those cached : 63031
% 37.17/5.99 % Propositional unsat checks : 0
% 37.17/5.99 % Propositional check models : 0
% 37.17/5.99 % Propositional check unsatisfiable : 0
% 37.17/5.99 % Propositional clauses : 0
% 37.17/5.99 % Propositional clauses after purity: 0
% 37.17/5.99 % Propositional unsat core size : 0
% 37.17/5.99 % Propositional preprocessing time : 0.000
% 37.17/5.99 % Propositional encoding time : 0.000
% 37.17/5.99 % Propositional solver time : 0.000
% 37.17/5.99 % Success case prop preproc time : 0.000
% 37.17/5.99 % Success case prop encoding time : 0.000
% 37.17/5.99 % Success case prop solver time : 0.000
% 37.17/5.99 % Current number of processed clauses : 8586
% 37.17/5.99 % Positive orientable unit clauses : 3242
% 37.17/5.99 % Positive unorientable unit clauses: 0
% 37.17/5.99 % Negative unit clauses : 5
% 37.17/5.99 % Non-unit-clauses : 5339
% 37.17/5.99 % Current number of unprocessed clauses: 199336
% 37.17/5.99 % ...number of literals in the above : 717372
% 37.17/5.99 % Current number of archived formulas : 0
% 37.17/5.99 % Current number of archived clauses : 1520
% 37.17/5.99 % Clause-clause subsumption calls (NU) : 2584536
% 37.17/5.99 % Rec. Clause-clause subsumption calls : 2118261
% 37.17/5.99 % Non-unit clause-clause subsumptions : 2532
% 37.17/5.99 % Unit Clause-clause subsumption calls : 599676
% 37.17/5.99 % Rewrite failures with RHS unbound : 0
% 37.17/5.99 % BW rewrite match attempts : 2457
% 37.17/5.99 % BW rewrite match successes : 49
% 37.17/5.99 % Condensation attempts : 0
% 37.17/5.99 % Condensation successes : 0
% 37.17/5.99 % Termbank termtop insertions : 3715132
% 37.17/5.99 % Search garbage collected termcells : 122
% 37.17/5.99
% 37.17/5.99 % -------------------------------------------------
% 37.17/5.99 % User time : 5.147 s
% 37.17/5.99 % System time : 0.194 s
% 37.17/5.99 % Total time : 5.341 s
% 37.17/5.99 % Maximum resident set size: 3668 pages
% 37.17/5.99
% 37.17/5.99 % -------------------------------------------------
% 37.17/5.99 % User time : 25.263 s
% 37.17/5.99 % System time : 1.051 s
% 37.17/5.99 % Total time : 26.314 s
% 37.17/5.99 % Maximum resident set size: 4864 pages
% 37.17/5.99 % E exiting
%------------------------------------------------------------------------------