%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD054-4 : TPTP v9.2.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:18:25 PM UTC 2026
% Result : Unsatisfiable 15.99s 10.11s
% Output : CNFRefutation 16.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 28
% Syntax : Number of clauses : 113 ( 50 unt; 8 nHn; 113 RR)
% Number of literals : 243 ( 0 equ; 128 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-1 aty)
% Number of variables : 168 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(compatibility_of_order_relation_and_addition,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X4,X5,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(existence_of_identity_addition,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(totality_of_order_relation,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_order_relation) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(associativity_multiplication_1,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(existence_of_identity_multiplication,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(associativity_addition_1,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(antisymmetry_of_order_relation,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
cnf(sum_9,negated_conjecture,
sum(a,b,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_9) ).
cnf(existence_of_inverse_multiplication,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(commutativity_multiplication,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(product_10,negated_conjecture,
product(a,b,l),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_10) ).
cnf(existence_of_inverse_addition,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(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/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_2) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(not_sum_7,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_7) ).
cnf(not_sum_6,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_6) ).
cnf(well_definedness_of_additive_inverse,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
cnf(sum_8,negated_conjecture,
sum(multiplicative_inverse(a),multiplicative_inverse(b),u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_8) ).
cnf(u_is_defined,hypothesis,
defined(u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_is_defined) ).
cnf(l_is_defined,hypothesis,
defined(l),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_is_defined) ).
cnf(not_product_11,negated_conjecture,
~ product(k,multiplicative_inverse(l),u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_11) ).
cnf(associativity_multiplication_2,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
cnf(distributivity_1,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X6)
| ~ product(X6,X7,X3)
| ~ product(X4,X7,X1)
| ~ product(X5,X7,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(c_0_28,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X4,X5,X2) ),
compatibility_of_order_relation_and_addition ).
cnf(c_0_29,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_30,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_31,plain,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,additive_identity)
| ~ defined(X2)
| ~ sum(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_30]) ).
cnf(c_0_33,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_34,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_35,plain,
( less_or_equal(X1,X2)
| ~ defined(X2)
| ~ sum(additive_identity,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_36,plain,
( sum(X1,additive_identity,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_29]) ).
cnf(c_0_37,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1 ).
cnf(c_0_38,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_39,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1 ).
cnf(c_0_40,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_41,plain,
less_or_equal(additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_33])]) ).
cnf(c_0_42,negated_conjecture,
sum(a,b,k),
sum_9 ).
cnf(c_0_43,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,multiplicative_identity)
| ~ product(X4,X3,X2)
| ~ defined(X3) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_45,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_46,negated_conjecture,
product(a,b,l),
product_10 ).
cnf(c_0_47,plain,
( sum(X1,X2,X3)
| ~ defined(X3)
| ~ sum(X1,X4,additive_identity)
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_29]) ).
cnf(c_0_48,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_41])]) ).
cnf(c_0_49,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_50,axiom,
( product(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ product(X4,X2,X6)
| ~ product(X5,X2,X7)
| ~ sum(X6,X7,X3) ),
distributivity_2 ).
cnf(c_0_51,negated_conjecture,
sum(b,a,k),
inference(spm,[status(thm)],[c_0_34,c_0_42]) ).
cnf(c_0_52,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_43,c_0_44]) ).
cnf(c_0_53,negated_conjecture,
product(b,a,l),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_54,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_55,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_56,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
not_sum_7 ).
cnf(c_0_57,plain,
( sum(additive_identity,X1,X2)
| ~ defined(X2)
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_58,plain,
( sum(X1,additive_inverse(X1),additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_49]) ).
cnf(c_0_59,negated_conjecture,
( product(X1,X2,k)
| ~ product(X3,X2,a)
| ~ product(X4,X2,b)
| ~ sum(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_60,negated_conjecture,
product(multiplicative_inverse(b),l,a),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_55])]),c_0_56]) ).
cnf(c_0_61,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
not_sum_6 ).
cnf(c_0_62,plain,
( sum(additive_identity,additive_identity,additive_inverse(additive_identity))
| ~ defined(additive_inverse(additive_identity)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_33])]) ).
cnf(c_0_63,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_64,negated_conjecture,
( product(X1,l,k)
| ~ product(X2,l,b)
| ~ sum(X2,multiplicative_inverse(b),X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_65,negated_conjecture,
product(multiplicative_inverse(a),l,b),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_46]),c_0_55]),c_0_54])]),c_0_61]) ).
cnf(c_0_66,plain,
sum(additive_identity,additive_identity,additive_inverse(additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_33])]) ).
cnf(c_0_67,negated_conjecture,
( product(X1,l,k)
| ~ sum(multiplicative_inverse(a),multiplicative_inverse(b),X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_68,negated_conjecture,
sum(multiplicative_inverse(a),multiplicative_inverse(b),u),
sum_8 ).
cnf(c_0_69,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_66]),c_0_33])]) ).
cnf(c_0_70,negated_conjecture,
product(u,l,k),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_71,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_34,c_0_69]) ).
cnf(c_0_72,plain,
( product(X1,X2,additive_identity)
| ~ product(X3,X2,additive_identity)
| ~ product(X4,X2,additive_identity)
| ~ sum(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_48]) ).
cnf(c_0_73,plain,
( product(X1,multiplicative_identity,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_38]) ).
cnf(c_0_74,negated_conjecture,
product(l,u,k),
inference(spm,[status(thm)],[c_0_45,c_0_70]) ).
cnf(c_0_75,hypothesis,
defined(u),
u_is_defined ).
cnf(c_0_76,hypothesis,
defined(l),
l_is_defined ).
cnf(c_0_77,plain,
( sum(additive_inverse(additive_identity),X1,X2)
| ~ defined(X2)
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_71]) ).
cnf(c_0_78,plain,
( product(X1,multiplicative_identity,additive_identity)
| ~ product(X2,multiplicative_identity,additive_identity)
| ~ sum(X2,additive_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_33])]) ).
cnf(c_0_79,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_52,c_0_74]),c_0_75]),c_0_76])]) ).
cnf(c_0_80,negated_conjecture,
~ product(k,multiplicative_inverse(l),u),
not_product_11 ).
cnf(c_0_81,plain,
( sum(additive_inverse(additive_identity),X1,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_29]) ).
cnf(c_0_82,plain,
( product(additive_inverse(additive_identity),multiplicative_identity,additive_identity)
| ~ product(additive_identity,multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_78,c_0_66]) ).
cnf(c_0_83,negated_conjecture,
sum(additive_identity,l,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_79]),c_0_80]) ).
cnf(c_0_84,plain,
( product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(additive_inverse(additive_identity),multiplicative_identity,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_81]),c_0_33])]) ).
cnf(c_0_85,plain,
product(additive_inverse(additive_identity),multiplicative_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_73]),c_0_33])]) ).
cnf(c_0_86,negated_conjecture,
sum(additive_identity,additive_identity,l),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_83]),c_0_76])]) ).
cnf(c_0_87,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85])]) ).
cnf(c_0_88,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
associativity_multiplication_2 ).
cnf(c_0_89,negated_conjecture,
product(l,multiplicative_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_86]),c_0_87])]) ).
cnf(c_0_90,negated_conjecture,
( product(X1,b,X2)
| ~ product(X3,l,X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_46]) ).
cnf(c_0_91,negated_conjecture,
product(multiplicative_identity,l,additive_identity),
inference(spm,[status(thm)],[c_0_45,c_0_89]) ).
cnf(c_0_92,negated_conjecture,
( product(X1,b,additive_identity)
| ~ product(multiplicative_identity,a,X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_93,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X6)
| ~ product(X6,X7,X3)
| ~ product(X4,X7,X1)
| ~ product(X5,X7,X2) ),
distributivity_1 ).
cnf(c_0_94,negated_conjecture,
product(a,b,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_38]),c_0_54])]) ).
cnf(c_0_95,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_93,c_0_38]) ).
cnf(c_0_96,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_97,negated_conjecture,
product(b,a,additive_identity),
inference(spm,[status(thm)],[c_0_45,c_0_94]) ).
cnf(c_0_98,plain,
( sum(X1,X2,X3)
| ~ product(multiplicative_identity,X3,X2)
| ~ product(additive_identity,X3,X1)
| ~ defined(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_29]),c_0_96])]) ).
cnf(c_0_99,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_52,c_0_97]),c_0_54]),c_0_55])]),c_0_56]) ).
cnf(c_0_100,negated_conjecture,
sum(multiplicative_inverse(b),multiplicative_inverse(a),u),
inference(spm,[status(thm)],[c_0_34,c_0_68]) ).
cnf(c_0_101,plain,
( sum(X1,X2,X2)
| ~ product(additive_identity,X2,X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_98,c_0_38]) ).
cnf(c_0_102,negated_conjecture,
product(additive_identity,multiplicative_inverse(b),a),
inference(spm,[status(thm)],[c_0_45,c_0_99]) ).
cnf(c_0_103,negated_conjecture,
( sum(X1,X2,u)
| ~ sum(X3,multiplicative_inverse(a),X2)
| ~ sum(X1,X3,multiplicative_inverse(b)) ),
inference(spm,[status(thm)],[c_0_39,c_0_100]) ).
cnf(c_0_104,negated_conjecture,
( sum(a,multiplicative_inverse(b),multiplicative_inverse(b))
| ~ defined(multiplicative_inverse(b)) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_105,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_106,plain,
( sum(X1,X2,additive_identity)
| ~ defined(X3)
| ~ sum(X4,additive_inverse(X3),X2)
| ~ sum(X1,X4,X3) ),
inference(spm,[status(thm)],[c_0_39,c_0_58]) ).
cnf(c_0_107,negated_conjecture,
( sum(X1,u,u)
| ~ sum(X1,multiplicative_inverse(b),multiplicative_inverse(b)) ),
inference(spm,[status(thm)],[c_0_103,c_0_100]) ).
cnf(c_0_108,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_104,c_0_105]),c_0_55])]),c_0_56]) ).
cnf(c_0_109,plain,
( sum(X1,additive_identity,additive_identity)
| ~ defined(X2)
| ~ sum(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_106,c_0_58]) ).
cnf(c_0_110,negated_conjecture,
sum(a,u,u),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_111,negated_conjecture,
sum(a,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_75])]) ).
cnf(c_0_112,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_111]),c_0_61]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD054-4 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n010.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 17:30:36 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 15.99/10.11 % Version : CSE_E---1.7
% 15.99/10.11 % Problem : theBenchmark.p
% 15.99/10.11 % SZS status Unsatisfiable for theBenchmark.p
% 15.99/10.11 % SZS output start CNFRefutation
% See solution above
% 16.09/10.18 % Total time : 7.379s
%------------------------------------------------------------------------------