%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD047-4 : TPTP v9.2.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n013.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 04:18:22 PM UTC 2026
% Result : Unsatisfiable 9.50s 6.12s
% Output : CNFRefutation 9.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 28
% Syntax : Number of clauses : 117 ( 47 unt; 6 nHn; 117 RR)
% Number of literals : 260 ( 0 equ; 143 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 : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 193 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_multiplication,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(product_11,negated_conjecture,
product(b,c,t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_11) ).
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(product_10,negated_conjecture,
product(a,c,s),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_10) ).
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(totality_of_multiplication,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
cnf(t_is_defined,hypothesis,
defined(t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_is_defined) ).
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(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(product_9,negated_conjecture,
product(a,multiplicative_inverse(b),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_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/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(not_sum_7,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_7) ).
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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_order_relation) ).
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(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_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(antisymmetry_of_order_relation,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
cnf(not_product_12,negated_conjecture,
~ product(s,multiplicative_inverse(t),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_12) ).
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(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(well_definedness_of_additive_inverse,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
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(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
cnf(u_is_defined,hypothesis,
defined(u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_is_defined) ).
cnf(not_sum_8,negated_conjecture,
~ sum(additive_identity,c,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_8) ).
cnf(c_0_28,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_29,negated_conjecture,
product(b,c,t),
product_11 ).
cnf(c_0_30,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1 ).
cnf(c_0_31,negated_conjecture,
product(a,c,s),
product_10 ).
cnf(c_0_32,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
associativity_multiplication_2 ).
cnf(c_0_33,negated_conjecture,
product(c,b,t),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( product(X1,X2,s)
| ~ product(X3,c,X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( product(X1,b,X2)
| ~ product(X3,t,X2)
| ~ product(X3,c,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_multiplication ).
cnf(c_0_37,hypothesis,
defined(t),
t_is_defined ).
cnf(c_0_38,negated_conjecture,
( product(X1,s,s)
| ~ product(X1,a,a) ),
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
cnf(c_0_39,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_40,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_41,negated_conjecture,
( product(X1,b,multiply(X2,t))
| ~ product(X2,c,X1)
| ~ defined(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_42,negated_conjecture,
product(multiplicative_identity,s,s),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_43,negated_conjecture,
product(s,b,multiply(a,t)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_31]),c_0_40])]) ).
cnf(c_0_44,negated_conjecture,
( product(X1,X2,s)
| ~ product(X3,s,X2)
| ~ product(X1,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_30,c_0_42]) ).
cnf(c_0_45,negated_conjecture,
product(b,s,multiply(a,t)),
inference(spm,[status(thm)],[c_0_28,c_0_43]) ).
cnf(c_0_46,negated_conjecture,
product(a,multiplicative_inverse(b),u),
product_9 ).
cnf(c_0_47,negated_conjecture,
( product(X1,multiply(a,t),s)
| ~ product(X1,b,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_49,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_50,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
not_sum_7 ).
cnf(c_0_51,negated_conjecture,
( product(X1,X2,u)
| ~ product(X3,multiplicative_inverse(b),X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_30,c_0_46]) ).
cnf(c_0_52,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_32,c_0_36]) ).
cnf(c_0_53,negated_conjecture,
product(multiplicative_inverse(b),multiply(a,t),s),
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,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_55,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_56,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_57,negated_conjecture,
( product(multiplicative_identity,X1,u)
| ~ product(a,multiplicative_inverse(b),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_39]),c_0_40])]) ).
cnf(c_0_58,negated_conjecture,
( product(X1,t,s)
| ~ product(multiplicative_inverse(b),a,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_37]),c_0_40])]) ).
cnf(c_0_59,negated_conjecture,
product(multiplicative_inverse(b),a,u),
inference(spm,[status(thm)],[c_0_28,c_0_46]) ).
cnf(c_0_60,plain,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,additive_identity)
| ~ defined(X2)
| ~ sum(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_61,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_56]) ).
cnf(c_0_62,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_63,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_64,negated_conjecture,
product(multiplicative_identity,u,u),
inference(spm,[status(thm)],[c_0_57,c_0_46]) ).
cnf(c_0_65,negated_conjecture,
product(u,t,s),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_66,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_60,c_0_61]),c_0_62])]) ).
cnf(c_0_67,plain,
( sum(X1,additive_identity,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_55]) ).
cnf(c_0_68,negated_conjecture,
( product(X1,X2,u)
| ~ product(X3,u,X2)
| ~ product(X1,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_30,c_0_64]) ).
cnf(c_0_69,negated_conjecture,
product(t,u,s),
inference(spm,[status(thm)],[c_0_28,c_0_65]) ).
cnf(c_0_70,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1 ).
cnf(c_0_71,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_72,plain,
less_or_equal(additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_62])]) ).
cnf(c_0_73,negated_conjecture,
( product(X1,s,u)
| ~ product(X1,t,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_74,plain,
( sum(X1,X2,X3)
| ~ defined(X3)
| ~ sum(X1,X4,additive_identity)
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_70,c_0_55]) ).
cnf(c_0_75,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_72])]) ).
cnf(c_0_76,negated_conjecture,
( product(multiplicative_inverse(t),s,u)
| sum(additive_identity,t,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_48]),c_0_37])]) ).
cnf(c_0_77,negated_conjecture,
~ product(s,multiplicative_inverse(t),u),
not_product_12 ).
cnf(c_0_78,negated_conjecture,
( product(X1,X2,t)
| ~ product(X3,c,X2)
| ~ product(X1,X3,b) ),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_79,plain,
( sum(additive_identity,X1,X2)
| ~ defined(X2)
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_80,negated_conjecture,
sum(additive_identity,t,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_76]),c_0_77]) ).
cnf(c_0_81,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_82,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_83,negated_conjecture,
( product(X1,t,t)
| ~ product(X1,b,b) ),
inference(spm,[status(thm)],[c_0_78,c_0_29]) ).
cnf(c_0_84,negated_conjecture,
sum(additive_identity,additive_identity,t),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_37])]) ).
cnf(c_0_85,plain,
( product(X1,X2,additive_identity)
| ~ product(X3,X2,additive_inverse(X4))
| ~ product(X5,X2,X4)
| ~ defined(X4)
| ~ sum(X3,X5,X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_86,plain,
( product(X1,multiplicative_identity,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_39]) ).
cnf(c_0_87,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_88,negated_conjecture,
product(multiplicative_identity,t,t),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_39]),c_0_49])]) ).
cnf(c_0_89,negated_conjecture,
( sum(X1,X2,t)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_70,c_0_84]) ).
cnf(c_0_90,plain,
( product(X1,multiplicative_identity,additive_identity)
| ~ product(X2,multiplicative_identity,X3)
| ~ defined(X3)
| ~ sum(additive_inverse(X3),X2,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]) ).
cnf(c_0_91,negated_conjecture,
product(t,multiplicative_identity,t),
inference(spm,[status(thm)],[c_0_28,c_0_88]) ).
cnf(c_0_92,negated_conjecture,
( sum(X1,X2,t)
| ~ defined(X2)
| ~ sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_89,c_0_67]) ).
cnf(c_0_93,negated_conjecture,
( product(X1,multiplicative_identity,additive_identity)
| ~ sum(additive_inverse(t),t,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_37])]) ).
cnf(c_0_94,negated_conjecture,
( sum(additive_inverse(X1),X1,t)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_92,c_0_82]) ).
cnf(c_0_95,negated_conjecture,
product(t,multiplicative_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_37])]) ).
cnf(c_0_96,negated_conjecture,
( product(X1,c,X2)
| ~ product(X3,t,X2)
| ~ product(X3,b,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_29]) ).
cnf(c_0_97,negated_conjecture,
product(multiplicative_identity,t,additive_identity),
inference(spm,[status(thm)],[c_0_28,c_0_95]) ).
cnf(c_0_98,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_99,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,multiplicative_identity)
| ~ product(X4,X3,X2)
| ~ defined(X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_39]) ).
cnf(c_0_100,negated_conjecture,
( product(X1,c,additive_identity)
| ~ product(multiplicative_identity,b,X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_101,negated_conjecture,
( sum(X1,X2,u)
| ~ product(X3,multiplicative_inverse(b),X2)
| ~ product(X4,multiplicative_inverse(b),X1)
| ~ sum(X4,X3,a) ),
inference(spm,[status(thm)],[c_0_98,c_0_46]) ).
cnf(c_0_102,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_99,c_0_48]) ).
cnf(c_0_103,negated_conjecture,
product(b,c,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_39]),c_0_49])]) ).
cnf(c_0_104,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_105,plain,
( sum(X1,additive_inverse(X1),additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_82]) ).
cnf(c_0_106,negated_conjecture,
( sum(X1,X2,u)
| ~ 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_101,c_0_55]),c_0_40])]) ).
cnf(c_0_107,negated_conjecture,
product(multiplicative_inverse(b),additive_identity,c),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]),c_0_49])]),c_0_50]) ).
cnf(c_0_108,plain,
( sum(X1,X2,additive_identity)
| ~ defined(X3)
| ~ sum(X4,additive_inverse(X3),X2)
| ~ sum(X1,X4,X3) ),
inference(spm,[status(thm)],[c_0_70,c_0_105]) ).
cnf(c_0_109,negated_conjecture,
( sum(X1,u,u)
| ~ product(additive_identity,multiplicative_inverse(b),X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_46]) ).
cnf(c_0_110,negated_conjecture,
product(additive_identity,multiplicative_inverse(b),c),
inference(spm,[status(thm)],[c_0_28,c_0_107]) ).
cnf(c_0_111,plain,
( sum(X1,additive_identity,additive_identity)
| ~ defined(X2)
| ~ sum(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_108,c_0_105]) ).
cnf(c_0_112,negated_conjecture,
sum(c,u,u),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_113,hypothesis,
defined(u),
u_is_defined ).
cnf(c_0_114,negated_conjecture,
sum(c,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113])]) ).
cnf(c_0_115,negated_conjecture,
~ sum(additive_identity,c,additive_identity),
not_sum_8 ).
cnf(c_0_116,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_114]),c_0_115]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD047-4 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n013.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 17:27:56 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 9.50/6.12 % Version : CSE_E---1.7
% 9.50/6.12 % Problem : theBenchmark.p
% 9.50/6.12 % SZS status Unsatisfiable for theBenchmark.p
% 9.50/6.12 % SZS output start CNFRefutation
% See solution above
% 9.50/6.16 % Total time : 4.374s
%------------------------------------------------------------------------------