%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD026-3 : 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 : n017.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 04:18:16 PM UTC 2026
% Result : Unsatisfiable 41.25s 23.84s
% Output : CNFRefutation 41.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 24
% Syntax : Number of clauses : 196 ( 68 unt; 12 nHn; 196 RR)
% Number of literals : 398 ( 0 equ; 198 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 252 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(not_sum_3,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(associativity_multiplication_2,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
cnf(existence_of_identity_multiplication,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
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(commutativity_multiplication,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(existence_of_identity_addition,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(product_4,negated_conjecture,
product(multiplicative_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_4) ).
cnf(totality_of_addition,axiom,
( sum(X1,X2,add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_addition) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_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/sandbox2/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_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(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(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(associativity_multiplication_1,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
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(associativity_addition_2,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
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(not_product_5,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_5) ).
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_0_24,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_25,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_26,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
not_sum_3 ).
cnf(c_0_27,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_28,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
associativity_multiplication_2 ).
cnf(c_0_29,hypothesis,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_30,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_31,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_25]),c_0_26]) ).
cnf(c_0_32,hypothesis,
( product(X1,a,X2)
| ~ product(X3,multiplicative_inverse(a),X1)
| ~ product(X3,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,hypothesis,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_35,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_36,hypothesis,
( product(multiplicative_inverse(a),a,X1)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_38,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_39,hypothesis,
sum(additive_inverse(multiplicative_inverse(a)),multiplicative_inverse(a),additive_identity),
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
cnf(c_0_40,hypothesis,
( product(a,multiplicative_inverse(a),X1)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
product(multiplicative_identity,a,b),
product_4 ).
cnf(c_0_42,hypothesis,
sum(additive_identity,multiplicative_inverse(a),multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_37,c_0_31]) ).
cnf(c_0_43,axiom,
( sum(X1,X2,add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_addition ).
cnf(c_0_44,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_45,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_46,hypothesis,
sum(multiplicative_inverse(a),additive_inverse(multiplicative_inverse(a)),additive_identity),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_47,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_48,hypothesis,
product(multiplicative_identity,a,a),
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
cnf(c_0_49,hypothesis,
( product(X1,a,X2)
| ~ product(a,multiplicative_identity,X2)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_40]) ).
cnf(c_0_50,negated_conjecture,
product(a,multiplicative_identity,b),
inference(spm,[status(thm)],[c_0_35,c_0_41]) ).
cnf(c_0_51,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1 ).
cnf(c_0_52,hypothesis,
sum(multiplicative_inverse(a),additive_identity,multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_38,c_0_42]) ).
cnf(c_0_53,hypothesis,
( sum(X1,b,add(X1,b))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_54,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_55,hypothesis,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X2,multiplicative_inverse(a))
| ~ sum(X2,additive_inverse(multiplicative_inverse(a)),X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_56,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_47]) ).
cnf(c_0_57,hypothesis,
sum(additive_identity,b,b),
inference(spm,[status(thm)],[c_0_37,c_0_44]) ).
cnf(c_0_58,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1 ).
cnf(c_0_59,hypothesis,
product(a,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_35,c_0_48]) ).
cnf(c_0_60,negated_conjecture,
( product(X1,a,b)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_61,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_62,hypothesis,
( sum(X1,X2,multiplicative_inverse(a))
| ~ sum(X1,X3,multiplicative_inverse(a))
| ~ sum(X3,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_63,hypothesis,
sum(additive_identity,b,add(additive_identity,b)),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_64,hypothesis,
( less_or_equal(additive_identity,additive_identity)
| ~ less_or_equal(multiplicative_inverse(a),multiplicative_inverse(a)) ),
inference(spm,[status(thm)],[c_0_55,c_0_46]) ).
cnf(c_0_65,hypothesis,
less_or_equal(multiplicative_inverse(a),multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_56,c_0_31]) ).
cnf(c_0_66,hypothesis,
sum(b,additive_identity,b),
inference(spm,[status(thm)],[c_0_38,c_0_57]) ).
cnf(c_0_67,hypothesis,
( product(X1,X2,a)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_68,negated_conjecture,
( product(a,X1,b)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_60]) ).
cnf(c_0_69,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_30,c_0_61]) ).
cnf(c_0_70,hypothesis,
( sum(X1,X2,additive_identity)
| ~ sum(X3,additive_inverse(multiplicative_inverse(a)),X2)
| ~ sum(X1,X3,multiplicative_inverse(a)) ),
inference(spm,[status(thm)],[c_0_51,c_0_46]) ).
cnf(c_0_71,hypothesis,
( sum(multiplicative_inverse(a),X1,multiplicative_inverse(a))
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_52]) ).
cnf(c_0_72,hypothesis,
( less_or_equal(X1,add(additive_identity,b))
| ~ less_or_equal(X2,additive_identity)
| ~ sum(X2,b,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_63]) ).
cnf(c_0_73,hypothesis,
less_or_equal(additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]) ).
cnf(c_0_74,hypothesis,
( less_or_equal(X1,b)
| ~ less_or_equal(X2,b)
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_66]) ).
cnf(c_0_75,hypothesis,
sum(b,additive_identity,add(additive_identity,b)),
inference(spm,[status(thm)],[c_0_38,c_0_63]) ).
cnf(c_0_76,hypothesis,
less_or_equal(b,b),
inference(spm,[status(thm)],[c_0_56,c_0_44]) ).
cnf(c_0_77,hypothesis,
( defined(multiplicative_inverse(b))
| sum(additive_identity,b,additive_identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_44]) ).
cnf(c_0_78,negated_conjecture,
( product(X1,b,a)
| ~ product(X1,a,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69])]) ).
cnf(c_0_79,plain,
( sum(X1,additive_identity,add(X1,additive_identity))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_54]) ).
cnf(c_0_80,hypothesis,
( sum(X1,X2,b)
| ~ sum(X3,b,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_51,c_0_57]) ).
cnf(c_0_81,hypothesis,
( sum(X1,additive_identity,additive_identity)
| ~ sum(X1,multiplicative_inverse(a),multiplicative_inverse(a)) ),
inference(spm,[status(thm)],[c_0_70,c_0_46]) ).
cnf(c_0_82,hypothesis,
( sum(X1,multiplicative_inverse(a),multiplicative_inverse(a))
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_71]) ).
cnf(c_0_83,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_84,hypothesis,
less_or_equal(b,add(additive_identity,b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_57]),c_0_73])]) ).
cnf(c_0_85,hypothesis,
less_or_equal(add(additive_identity,b),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76])]) ).
cnf(c_0_86,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
associativity_addition_2 ).
cnf(c_0_87,hypothesis,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(spm,[status(thm)],[c_0_35,c_0_29]) ).
cnf(c_0_88,hypothesis,
( product(multiplicative_identity,multiplicative_inverse(b),multiplicative_inverse(b))
| sum(additive_identity,b,additive_identity) ),
inference(spm,[status(thm)],[c_0_30,c_0_77]) ).
cnf(c_0_89,plain,
( product(X1,X2,multiplicative_identity)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X1,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_58,c_0_69]) ).
cnf(c_0_90,negated_conjecture,
( product(b,X1,a)
| ~ product(X1,a,a) ),
inference(spm,[status(thm)],[c_0_35,c_0_78]) ).
cnf(c_0_91,plain,
sum(additive_identity,additive_identity,add(additive_identity,additive_identity)),
inference(spm,[status(thm)],[c_0_79,c_0_54]) ).
cnf(c_0_92,hypothesis,
( sum(X1,b,b)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_80,c_0_57]) ).
cnf(c_0_93,hypothesis,
( sum(X1,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_94,hypothesis,
sum(additive_identity,add(additive_identity,b),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85])]) ).
cnf(c_0_95,hypothesis,
( sum(X1,b,X2)
| ~ sum(X3,b,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_57]) ).
cnf(c_0_96,hypothesis,
( product(X1,multiplicative_inverse(a),X2)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_87]) ).
cnf(c_0_97,hypothesis,
( product(multiplicative_inverse(b),multiplicative_identity,multiplicative_inverse(b))
| sum(additive_identity,b,additive_identity) ),
inference(spm,[status(thm)],[c_0_35,c_0_88]) ).
cnf(c_0_98,negated_conjecture,
( product(X1,a,multiplicative_identity)
| ~ product(X1,b,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_48])]) ).
cnf(c_0_99,hypothesis,
( product(multiplicative_inverse(b),b,multiplicative_identity)
| sum(additive_identity,b,additive_identity) ),
inference(spm,[status(thm)],[c_0_24,c_0_44]) ).
cnf(c_0_100,plain,
( sum(X1,additive_identity,X2)
| ~ sum(X3,add(additive_identity,additive_identity),X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_91]) ).
cnf(c_0_101,hypothesis,
( sum(b,X1,b)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_38,c_0_92]) ).
cnf(c_0_102,hypothesis,
sum(add(additive_identity,additive_identity),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_93,c_0_91]) ).
cnf(c_0_103,hypothesis,
( sum(X1,additive_identity,X2)
| ~ sum(X3,b,X2)
| ~ sum(X3,b,X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_66]) ).
cnf(c_0_104,hypothesis,
sum(b,b,add(b,b)),
inference(spm,[status(thm)],[c_0_53,c_0_44]) ).
cnf(c_0_105,hypothesis,
( sum(X1,X2,b)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X1,X3,b) ),
inference(spm,[status(thm)],[c_0_51,c_0_66]) ).
cnf(c_0_106,hypothesis,
sum(add(additive_identity,b),additive_identity,b),
inference(spm,[status(thm)],[c_0_38,c_0_94]) ).
cnf(c_0_107,hypothesis,
( sum(X1,b,b)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_57]) ).
cnf(c_0_108,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_109,hypothesis,
( product(X1,multiplicative_inverse(a),multiplicative_inverse(b))
| sum(additive_identity,b,additive_identity)
| ~ product(multiplicative_inverse(b),a,X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_110,hypothesis,
( product(multiplicative_inverse(b),a,multiplicative_identity)
| sum(additive_identity,b,additive_identity) ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_111,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
not_product_5 ).
cnf(c_0_112,hypothesis,
sum(additive_inverse(a),a,additive_identity),
inference(spm,[status(thm)],[c_0_34,c_0_25]) ).
cnf(c_0_113,hypothesis,
( sum(X1,additive_identity,b)
| ~ sum(b,additive_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102])]) ).
cnf(c_0_114,hypothesis,
( sum(X1,additive_identity,add(b,b))
| ~ sum(b,b,X1) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_115,hypothesis,
( sum(X1,b,b)
| ~ sum(X1,add(additive_identity,b),b) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_116,hypothesis,
( sum(b,X1,b)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_107]) ).
cnf(c_0_117,plain,
( sum(additive_identity,additive_inverse(X1),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_108]) ).
cnf(c_0_118,hypothesis,
sum(additive_identity,b,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_111]) ).
cnf(c_0_119,hypothesis,
sum(additive_inverse(b),b,additive_identity),
inference(spm,[status(thm)],[c_0_34,c_0_44]) ).
cnf(c_0_120,hypothesis,
( sum(X1,additive_identity,X2)
| ~ sum(X3,add(additive_identity,b),X2)
| ~ sum(X3,b,X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_75]) ).
cnf(c_0_121,hypothesis,
sum(a,additive_inverse(a),additive_identity),
inference(spm,[status(thm)],[c_0_38,c_0_112]) ).
cnf(c_0_122,hypothesis,
sum(additive_identity,a,a),
inference(spm,[status(thm)],[c_0_37,c_0_25]) ).
cnf(c_0_123,hypothesis,
( sum(X1,a,add(X1,a))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_25]) ).
cnf(c_0_124,hypothesis,
( sum(add(b,b),additive_identity,b)
| ~ sum(b,b,b) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_125,hypothesis,
( sum(b,b,b)
| ~ sum(additive_identity,additive_identity,add(additive_identity,b)) ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_126,hypothesis,
( sum(X1,additive_identity,add(additive_identity,b))
| ~ sum(additive_identity,b,X1) ),
inference(spm,[status(thm)],[c_0_103,c_0_63]) ).
cnf(c_0_127,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_37,c_0_54]) ).
cnf(c_0_128,hypothesis,
sum(additive_identity,additive_inverse(b),additive_inverse(b)),
inference(spm,[status(thm)],[c_0_117,c_0_44]) ).
cnf(c_0_129,hypothesis,
sum(b,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_38,c_0_118]) ).
cnf(c_0_130,hypothesis,
( sum(X1,b,X2)
| ~ sum(X3,additive_inverse(b),X1)
| ~ sum(X3,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_86,c_0_119]) ).
cnf(c_0_131,hypothesis,
( sum(X1,additive_identity,b)
| ~ sum(additive_identity,b,X1) ),
inference(spm,[status(thm)],[c_0_120,c_0_94]) ).
cnf(c_0_132,hypothesis,
( sum(X1,additive_inverse(a),X2)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_121]) ).
cnf(c_0_133,hypothesis,
( sum(X1,a,X2)
| ~ sum(X3,a,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_122]) ).
cnf(c_0_134,hypothesis,
sum(additive_identity,a,add(additive_identity,a)),
inference(spm,[status(thm)],[c_0_123,c_0_54]) ).
cnf(c_0_135,hypothesis,
product(multiplicative_identity,b,b),
inference(spm,[status(thm)],[c_0_30,c_0_44]) ).
cnf(c_0_136,hypothesis,
( product(X1,X2,multiplicative_identity)
| ~ product(X3,multiplicative_inverse(a),X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_58,c_0_87]) ).
cnf(c_0_137,hypothesis,
( sum(X1,b,X2)
| ~ sum(X3,add(b,b),X2)
| ~ sum(X3,b,X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_104]) ).
cnf(c_0_138,hypothesis,
( sum(additive_identity,add(b,b),b)
| ~ sum(b,b,b) ),
inference(spm,[status(thm)],[c_0_38,c_0_124]) ).
cnf(c_0_139,hypothesis,
( sum(b,b,b)
| ~ sum(additive_identity,b,additive_identity) ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_140,plain,
( sum(X1,additive_identity,X2)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_127]) ).
cnf(c_0_141,hypothesis,
sum(additive_inverse(b),additive_identity,additive_inverse(b)),
inference(spm,[status(thm)],[c_0_38,c_0_128]) ).
cnf(c_0_142,hypothesis,
( sum(X1,additive_identity,b)
| ~ sum(X1,b,b) ),
inference(spm,[status(thm)],[c_0_105,c_0_129]) ).
cnf(c_0_143,hypothesis,
( sum(additive_inverse(b),b,X1)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_130,c_0_128]) ).
cnf(c_0_144,hypothesis,
sum(additive_identity,additive_identity,b),
inference(spm,[status(thm)],[c_0_131,c_0_118]) ).
cnf(c_0_145,hypothesis,
( sum(X1,additive_inverse(a),additive_identity)
| ~ sum(add(additive_identity,additive_identity),a,X1) ),
inference(spm,[status(thm)],[c_0_132,c_0_102]) ).
cnf(c_0_146,hypothesis,
( sum(X1,a,add(additive_identity,a))
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_147,hypothesis,
( sum(X1,X2,a)
| ~ sum(X3,a,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_51,c_0_122]) ).
cnf(c_0_148,hypothesis,
( sum(X1,X2,additive_identity)
| ~ sum(X1,X3,additive_inverse(b))
| ~ sum(X3,b,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_119]) ).
cnf(c_0_149,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_150,hypothesis,
product(b,multiplicative_identity,b),
inference(spm,[status(thm)],[c_0_35,c_0_135]) ).
cnf(c_0_151,hypothesis,
( product(X1,X2,multiplicative_identity)
| ~ product(X1,X3,multiplicative_inverse(a))
| ~ product(X3,a,X2) ),
inference(spm,[status(thm)],[c_0_58,c_0_29]) ).
cnf(c_0_152,hypothesis,
product(multiplicative_inverse(a),multiplicative_identity,multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_35,c_0_33]) ).
cnf(c_0_153,hypothesis,
( product(X1,multiplicative_inverse(a),multiplicative_identity)
| ~ product(X1,multiplicative_identity,a) ),
inference(spm,[status(thm)],[c_0_136,c_0_33]) ).
cnf(c_0_154,hypothesis,
( sum(X1,b,b)
| ~ sum(b,b,b)
| ~ sum(additive_identity,b,X1) ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_155,hypothesis,
sum(b,b,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_118])]) ).
cnf(c_0_156,hypothesis,
( sum(X1,additive_identity,additive_inverse(b))
| ~ sum(additive_inverse(b),additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_157,hypothesis,
sum(additive_inverse(b),additive_identity,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_144])]) ).
cnf(c_0_158,hypothesis,
( sum(X1,X2,additive_identity)
| ~ sum(X3,additive_inverse(a),X2)
| ~ sum(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_51,c_0_121]) ).
cnf(c_0_159,hypothesis,
sum(add(additive_identity,a),additive_inverse(a),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_91])]) ).
cnf(c_0_160,hypothesis,
( sum(X1,a,a)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_147,c_0_122]) ).
cnf(c_0_161,hypothesis,
( sum(additive_identity,X1,additive_identity)
| ~ sum(additive_inverse(b),b,X1) ),
inference(spm,[status(thm)],[c_0_148,c_0_128]) ).
cnf(c_0_162,hypothesis,
( sum(X1,b,a)
| ~ sum(a,additive_identity,additive_identity)
| ~ sum(X1,b,additive_identity) ),
inference(spm,[status(thm)],[c_0_147,c_0_101]) ).
cnf(c_0_163,hypothesis,
( sum(X1,X2,b)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X4,multiplicative_identity,X1)
| ~ sum(X4,X3,b) ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_164,hypothesis,
( product(X1,X2,b)
| ~ product(X3,b,X2)
| ~ product(X1,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_58,c_0_135]) ).
cnf(c_0_165,hypothesis,
( product(multiplicative_inverse(a),X1,multiplicative_identity)
| ~ product(multiplicative_identity,a,X1) ),
inference(spm,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_166,hypothesis,
( product(X1,X2,a)
| ~ product(X3,a,X2)
| ~ product(X1,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_58,c_0_48]) ).
cnf(c_0_167,hypothesis,
( product(multiplicative_inverse(a),X1,multiplicative_identity)
| ~ product(X1,multiplicative_identity,a) ),
inference(spm,[status(thm)],[c_0_35,c_0_153]) ).
cnf(c_0_168,negated_conjecture,
( product(X1,b,multiplicative_identity)
| ~ product(X1,a,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_68]),c_0_69])]) ).
cnf(c_0_169,hypothesis,
( sum(X1,b,b)
| ~ sum(additive_identity,b,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_154,c_0_155])]) ).
cnf(c_0_170,hypothesis,
sum(b,additive_identity,additive_inverse(b)),
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_171,hypothesis,
sum(b,additive_inverse(b),additive_identity),
inference(spm,[status(thm)],[c_0_38,c_0_119]) ).
cnf(c_0_172,hypothesis,
sum(a,additive_identity,add(additive_identity,a)),
inference(spm,[status(thm)],[c_0_38,c_0_134]) ).
cnf(c_0_173,hypothesis,
( sum(X1,additive_identity,additive_identity)
| ~ sum(X1,add(additive_identity,a),a) ),
inference(spm,[status(thm)],[c_0_158,c_0_159]) ).
cnf(c_0_174,hypothesis,
( sum(a,X1,a)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_38,c_0_160]) ).
cnf(c_0_175,hypothesis,
~ sum(a,additive_identity,additive_identity),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_119])]),c_0_26]) ).
cnf(c_0_176,negated_conjecture,
( sum(X1,a,b)
| ~ product(X2,multiplicative_identity,X1)
| ~ sum(X2,b,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_90]),c_0_48])]) ).
cnf(c_0_177,hypothesis,
( product(X1,multiplicative_identity,b)
| ~ product(X1,multiplicative_inverse(a),multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_41])]) ).
cnf(c_0_178,hypothesis,
( product(X1,multiplicative_identity,a)
| ~ product(X1,multiplicative_inverse(a),multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_59])]) ).
cnf(c_0_179,negated_conjecture,
( product(b,X1,multiplicative_identity)
| ~ product(X1,a,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_35,c_0_168]) ).
cnf(c_0_180,hypothesis,
( sum(X1,additive_identity,X2)
| ~ sum(X3,additive_inverse(b),X2)
| ~ sum(X3,additive_inverse(b),X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_141]) ).
cnf(c_0_181,hypothesis,
( sum(b,X1,b)
| ~ sum(additive_identity,b,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_169]) ).
cnf(c_0_182,hypothesis,
sum(additive_identity,b,additive_inverse(b)),
inference(spm,[status(thm)],[c_0_38,c_0_170]) ).
cnf(c_0_183,hypothesis,
( sum(X1,additive_inverse(b),X2)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X3,b,X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_171]) ).
cnf(c_0_184,hypothesis,
( sum(X1,additive_identity,additive_identity)
| ~ sum(b,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_140,c_0_129]) ).
cnf(c_0_185,hypothesis,
( sum(X1,additive_identity,add(additive_identity,a))
| ~ sum(a,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_140,c_0_172]) ).
cnf(c_0_186,hypothesis,
~ sum(add(additive_identity,a),additive_identity,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_175]) ).
cnf(c_0_187,hypothesis,
( sum(X1,a,b)
| ~ product(b,multiplicative_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_101]),c_0_129])]) ).
cnf(c_0_188,hypothesis,
( product(X1,multiplicative_identity,b)
| ~ product(X1,multiplicative_identity,a) ),
inference(spm,[status(thm)],[c_0_177,c_0_153]) ).
cnf(c_0_189,hypothesis,
product(b,multiplicative_identity,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_179]),c_0_29])]) ).
cnf(c_0_190,hypothesis,
( sum(X1,additive_identity,b)
| ~ sum(b,additive_inverse(b),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_182])]) ).
cnf(c_0_191,hypothesis,
( sum(X1,additive_inverse(b),a)
| ~ sum(a,b,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_174]),c_0_127])]) ).
cnf(c_0_192,hypothesis,
~ sum(a,additive_identity,b),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_186]) ).
cnf(c_0_193,hypothesis,
sum(b,a,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_188]),c_0_189])]) ).
cnf(c_0_194,hypothesis,
~ sum(a,b,b),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_191]),c_0_192]) ).
cnf(c_0_195,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_193]),c_0_194]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD026-3 : 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 : n017.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 17:25:58 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 41.25/23.84 % Version : CSE_E---1.7
% 41.25/23.84 % Problem : theBenchmark.p
% 41.25/23.84 % SZS status Unsatisfiable for theBenchmark.p
% 41.25/23.84 % SZS output start CNFRefutation
% See solution above
% 41.36/23.98 % Total time : 18.403s
%------------------------------------------------------------------------------