%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD048-4 : 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 : n024.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 04:18:23 PM UTC 2026
% Result : Unsatisfiable 7.46s 5.44s
% Output : CNFRefutation 7.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 35
% Syntax : Number of clauses : 138 ( 63 unt; 8 nHn; 138 RR)
% Number of literals : 292 ( 0 equ; 152 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 : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 201 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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_14,negated_conjecture,
product(c,multiplicative_inverse(d),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_14) ).
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(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(totality_of_multiplication,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
cnf(t_is_defined,hypothesis,
defined(t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_is_defined) ).
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(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(d_is_defined,hypothesis,
defined(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_is_defined) ).
cnf(not_sum_11,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_11) ).
cnf(product_12,negated_conjecture,
product(s,t,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_12) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).
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(u_is_defined,hypothesis,
defined(u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_is_defined) ).
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(product_15,negated_conjecture,
product(a,c,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_15) ).
cnf(product_13,negated_conjecture,
product(a,multiplicative_inverse(b),s),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_13) ).
cnf(associativity_addition_2,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_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_10,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_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(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(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(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(product_16,negated_conjecture,
product(b,d,l),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_16) ).
cnf(l_is_defined,hypothesis,
defined(l),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_is_defined) ).
cnf(not_product_17,negated_conjecture,
~ product(k,multiplicative_inverse(l),u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_17) ).
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(s_is_defined,hypothesis,
defined(s),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_is_defined) ).
cnf(c_0_35,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_36,negated_conjecture,
product(c,multiplicative_inverse(d),t),
product_14 ).
cnf(c_0_37,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
associativity_multiplication_2 ).
cnf(c_0_38,negated_conjecture,
product(multiplicative_inverse(d),c,t),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1 ).
cnf(c_0_40,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_41,negated_conjecture,
( product(X1,c,X2)
| ~ product(X3,multiplicative_inverse(d),X1)
| ~ product(X3,t,X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_multiplication ).
cnf(c_0_43,hypothesis,
defined(t),
t_is_defined ).
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,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,multiplicative_identity)
| ~ product(X4,X3,X2)
| ~ defined(X3) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_47,negated_conjecture,
( product(X1,c,multiply(X2,t))
| ~ product(X2,multiplicative_inverse(d),X1)
| ~ defined(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
cnf(c_0_48,plain,
( product(X1,multiplicative_inverse(X1),multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_44]) ).
cnf(c_0_49,hypothesis,
defined(d),
d_is_defined ).
cnf(c_0_50,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
not_sum_11 ).
cnf(c_0_51,negated_conjecture,
product(s,t,u),
product_12 ).
cnf(c_0_52,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_45,c_0_40]),c_0_46])]) ).
cnf(c_0_53,negated_conjecture,
product(multiplicative_identity,c,multiply(d,t)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_54,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_55,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_56,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_57,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_58,negated_conjecture,
product(t,s,u),
inference(spm,[status(thm)],[c_0_35,c_0_51]) ).
cnf(c_0_59,plain,
( product(X1,X2,X3)
| ~ product(X4,multiply(X5,X2),X3)
| ~ product(X4,X5,X1)
| ~ defined(X2)
| ~ defined(X5) ),
inference(spm,[status(thm)],[c_0_37,c_0_42]) ).
cnf(c_0_60,negated_conjecture,
product(multiplicative_identity,multiply(d,t),c),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54])]) ).
cnf(c_0_61,plain,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,additive_identity)
| ~ defined(X2)
| ~ sum(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_57]) ).
cnf(c_0_63,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_64,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_65,negated_conjecture,
( product(X1,s,X2)
| ~ product(X3,u,X2)
| ~ product(X3,t,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_58]) ).
cnf(c_0_66,hypothesis,
defined(u),
u_is_defined ).
cnf(c_0_67,negated_conjecture,
( product(X1,t,c)
| ~ product(multiplicative_identity,d,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_43]),c_0_49])]) ).
cnf(c_0_68,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_61,c_0_62]),c_0_63])]) ).
cnf(c_0_69,plain,
( sum(X1,additive_identity,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_56]) ).
cnf(c_0_70,negated_conjecture,
( product(X1,s,multiply(X2,u))
| ~ product(X2,t,X1)
| ~ defined(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_42]),c_0_66])]) ).
cnf(c_0_71,negated_conjecture,
product(d,t,c),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_40]),c_0_49])]) ).
cnf(c_0_72,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_73,plain,
less_or_equal(additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_63])]) ).
cnf(c_0_74,negated_conjecture,
product(a,c,k),
product_15 ).
cnf(c_0_75,negated_conjecture,
product(c,s,multiply(d,u)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_49])]) ).
cnf(c_0_76,negated_conjecture,
product(a,multiplicative_inverse(b),s),
product_13 ).
cnf(c_0_77,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
associativity_addition_2 ).
cnf(c_0_78,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_73])]) ).
cnf(c_0_79,negated_conjecture,
( product(X1,X2,k)
| ~ product(X3,c,X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_39,c_0_74]) ).
cnf(c_0_80,negated_conjecture,
product(s,c,multiply(d,u)),
inference(spm,[status(thm)],[c_0_35,c_0_75]) ).
cnf(c_0_81,plain,
( product(X1,X2,X3)
| sum(additive_identity,X1,additive_identity)
| ~ product(multiplicative_inverse(X1),X3,X2)
| ~ defined(X3)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_48]) ).
cnf(c_0_82,negated_conjecture,
product(multiplicative_inverse(b),a,s),
inference(spm,[status(thm)],[c_0_35,c_0_76]) ).
cnf(c_0_83,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_84,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_85,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
not_sum_10 ).
cnf(c_0_86,plain,
( sum(X1,additive_identity,X2)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_87,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_88,negated_conjecture,
( product(X1,multiply(d,u),k)
| ~ product(X1,s,a) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_89,negated_conjecture,
product(b,s,a),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]),c_0_84])]),c_0_85]) ).
cnf(c_0_90,plain,
( sum(X1,additive_identity,additive_identity)
| ~ sum(additive_inverse(additive_identity),additive_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_63])]) ).
cnf(c_0_91,negated_conjecture,
product(b,multiply(d,u),k),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_92,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1 ).
cnf(c_0_93,plain,
( sum(additive_inverse(additive_identity),additive_identity,additive_identity)
| ~ defined(additive_inverse(additive_identity)) ),
inference(spm,[status(thm)],[c_0_90,c_0_69]) ).
cnf(c_0_94,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_95,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_96,plain,
( sum(X1,additive_identity,X2)
| ~ defined(X2)
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_69]) ).
cnf(c_0_97,negated_conjecture,
( product(X1,u,k)
| ~ product(b,d,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_91]),c_0_66]),c_0_49])]) ).
cnf(c_0_98,negated_conjecture,
product(b,d,l),
product_16 ).
cnf(c_0_99,plain,
( sum(X1,X2,X3)
| ~ defined(X3)
| ~ sum(X1,X4,additive_identity)
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_92,c_0_56]) ).
cnf(c_0_100,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_63])]) ).
cnf(c_0_101,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_95,c_0_78]) ).
cnf(c_0_102,plain,
( product(X1,multiplicative_identity,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_40]) ).
cnf(c_0_103,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_96,c_0_87]),c_0_63])]) ).
cnf(c_0_104,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_45,c_0_44]) ).
cnf(c_0_105,negated_conjecture,
product(l,u,k),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_106,hypothesis,
defined(l),
l_is_defined ).
cnf(c_0_107,plain,
( sum(additive_inverse(additive_identity),X1,X2)
| ~ defined(X2)
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_108,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_101,c_0_102]),c_0_63])]) ).
cnf(c_0_109,plain,
sum(additive_identity,additive_identity,additive_inverse(additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_94]),c_0_63])]) ).
cnf(c_0_110,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_104,c_0_105]),c_0_66]),c_0_106])]) ).
cnf(c_0_111,negated_conjecture,
~ product(k,multiplicative_inverse(l),u),
not_product_17 ).
cnf(c_0_112,plain,
( sum(additive_inverse(additive_identity),X1,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_107,c_0_56]) ).
cnf(c_0_113,plain,
( product(additive_inverse(additive_identity),multiplicative_identity,additive_identity)
| ~ product(additive_identity,multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_114,plain,
( sum(additive_identity,X1,X2)
| ~ defined(X2)
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_99,c_0_78]) ).
cnf(c_0_115,negated_conjecture,
sum(additive_identity,l,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_110]),c_0_111]) ).
cnf(c_0_116,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_108,c_0_112]),c_0_63])]) ).
cnf(c_0_117,plain,
product(additive_inverse(additive_identity),multiplicative_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_102]),c_0_63])]) ).
cnf(c_0_118,negated_conjecture,
sum(additive_identity,additive_identity,l),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_106])]) ).
cnf(c_0_119,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_117])]) ).
cnf(c_0_120,negated_conjecture,
product(l,multiplicative_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_118]),c_0_119])]) ).
cnf(c_0_121,negated_conjecture,
( product(X1,d,X2)
| ~ product(X3,l,X2)
| ~ product(X3,b,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_98]) ).
cnf(c_0_122,negated_conjecture,
product(multiplicative_identity,l,additive_identity),
inference(spm,[status(thm)],[c_0_35,c_0_120]) ).
cnf(c_0_123,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_124,negated_conjecture,
( product(X1,d,additive_identity)
| ~ product(multiplicative_identity,b,X1) ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_125,negated_conjecture,
( sum(X1,X2,s)
| ~ product(X3,multiplicative_inverse(b),X2)
| ~ product(X4,multiplicative_inverse(b),X1)
| ~ sum(X4,X3,a) ),
inference(spm,[status(thm)],[c_0_123,c_0_76]) ).
cnf(c_0_126,negated_conjecture,
product(b,d,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_40]),c_0_84])]) ).
cnf(c_0_127,plain,
( sum(X1,additive_inverse(X1),additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_87]) ).
cnf(c_0_128,negated_conjecture,
( sum(X1,X2,s)
| ~ product(a,multiplicative_inverse(b),X2)
| ~ product(additive_identity,multiplicative_inverse(b),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_56]),c_0_83])]) ).
cnf(c_0_129,negated_conjecture,
product(multiplicative_inverse(b),additive_identity,d),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_126]),c_0_49]),c_0_84])]),c_0_85]) ).
cnf(c_0_130,plain,
( sum(X1,X2,additive_identity)
| ~ defined(X3)
| ~ sum(X4,additive_inverse(X3),X2)
| ~ sum(X1,X4,X3) ),
inference(spm,[status(thm)],[c_0_92,c_0_127]) ).
cnf(c_0_131,negated_conjecture,
( sum(X1,s,s)
| ~ product(additive_identity,multiplicative_inverse(b),X1) ),
inference(spm,[status(thm)],[c_0_128,c_0_76]) ).
cnf(c_0_132,negated_conjecture,
product(additive_identity,multiplicative_inverse(b),d),
inference(spm,[status(thm)],[c_0_35,c_0_129]) ).
cnf(c_0_133,plain,
( sum(X1,additive_identity,additive_identity)
| ~ defined(X2)
| ~ sum(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_130,c_0_127]) ).
cnf(c_0_134,negated_conjecture,
sum(d,s,s),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_135,hypothesis,
defined(s),
s_is_defined ).
cnf(c_0_136,negated_conjecture,
sum(d,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135])]) ).
cnf(c_0_137,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_136]),c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : FLD048-4 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 12:27:56 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.24 % start to proof: theBenchmark
% 7.46/5.44 % Version : CSE_E---1.7
% 7.46/5.44 % Problem : theBenchmark.p
% 7.46/5.44 % SZS status Unsatisfiable for theBenchmark.p
% 7.46/5.44 % SZS output start CNFRefutation
% See solution above
% 7.46/5.47 % Total time : 4.361s
%------------------------------------------------------------------------------