%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD012-4 : 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 : n006.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 04:18:11 PM UTC 2026
% Result : Unsatisfiable 3.97s 3.28s
% Output : CNFRefutation 4.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 28
% Syntax : Number of clauses : 135 ( 47 unt; 10 nHn; 135 RR)
% Number of literals : 308 ( 0 equ; 169 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 217 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(product_7,negated_conjecture,
product(a,b,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_7) ).
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(u_is_defined,hypothesis,
defined(u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_is_defined) ).
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(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_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_5,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_5) ).
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(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(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(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(commutativity_multiplication,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(product_8,negated_conjecture,
product(multiplicative_inverse(a),multiplicative_inverse(b),v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_8) ).
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(not_sum_6,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_6) ).
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(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_inverse,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_2) ).
cnf(not_product_9,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(u),v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_9) ).
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_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,negated_conjecture,
product(a,b,u),
product_7 ).
cnf(c_0_30,negated_conjecture,
( product(X1,b,X2)
| ~ product(X3,u,X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_31,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_multiplication ).
cnf(c_0_32,hypothesis,
defined(u),
u_is_defined ).
cnf(c_0_33,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1 ).
cnf(c_0_34,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_35,negated_conjecture,
( product(X1,b,multiply(X2,u))
| ~ product(X2,a,X1)
| ~ defined(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_36,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_37,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_38,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
not_sum_5 ).
cnf(c_0_39,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,multiplicative_identity)
| ~ product(X4,X3,X2)
| ~ defined(X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_41,negated_conjecture,
( product(multiplicative_identity,b,multiply(multiplicative_inverse(a),u))
| ~ defined(multiplicative_inverse(a)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]),c_0_38]) ).
cnf(c_0_42,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_43,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_39,c_0_34]),c_0_40])]) ).
cnf(c_0_44,negated_conjecture,
product(multiplicative_identity,b,multiply(multiplicative_inverse(a),u)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_37])]),c_0_38]) ).
cnf(c_0_45,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_46,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_47,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_48,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_49,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_28,c_0_31]) ).
cnf(c_0_50,negated_conjecture,
product(multiplicative_identity,multiply(multiplicative_inverse(a),u),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_51,plain,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,additive_identity)
| ~ defined(X2)
| ~ sum(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_48]) ).
cnf(c_0_53,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_54,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_55,negated_conjecture,
( product(X1,u,b)
| ~ product(multiplicative_identity,multiplicative_inverse(a),X1)
| ~ defined(multiplicative_inverse(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_32])]) ).
cnf(c_0_56,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_51,c_0_52]),c_0_53])]) ).
cnf(c_0_57,plain,
( sum(X1,additive_identity,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_47]) ).
cnf(c_0_58,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_59,negated_conjecture,
( product(X1,u,b)
| ~ product(multiplicative_identity,multiplicative_inverse(a),X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_42]),c_0_37])]),c_0_38]) ).
cnf(c_0_60,negated_conjecture,
product(multiplicative_inverse(a),multiplicative_inverse(b),v),
product_8 ).
cnf(c_0_61,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_62,plain,
less_or_equal(additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_53])]) ).
cnf(c_0_63,plain,
( product(X1,multiplicative_inverse(X1),multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_36]) ).
cnf(c_0_64,negated_conjecture,
( product(multiplicative_inverse(a),u,b)
| ~ defined(multiplicative_inverse(a)) ),
inference(spm,[status(thm)],[c_0_59,c_0_34]) ).
cnf(c_0_65,negated_conjecture,
( product(X1,X2,v)
| ~ product(X3,multiplicative_inverse(b),X2)
| ~ product(X1,X3,multiplicative_inverse(a)) ),
inference(spm,[status(thm)],[c_0_33,c_0_60]) ).
cnf(c_0_66,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
associativity_addition_2 ).
cnf(c_0_67,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_62])]) ).
cnf(c_0_68,plain,
( product(X1,X2,multiplicative_identity)
| sum(additive_identity,X3,additive_identity)
| ~ product(X4,multiplicative_inverse(X3),X2)
| ~ product(X1,X4,X3)
| ~ defined(X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_63]) ).
cnf(c_0_69,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
not_sum_6 ).
cnf(c_0_70,negated_conjecture,
product(multiplicative_inverse(a),u,b),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_42]),c_0_37])]),c_0_38]) ).
cnf(c_0_71,negated_conjecture,
( product(X1,v,v)
| ~ product(X1,multiplicative_inverse(a),multiplicative_inverse(a)) ),
inference(spm,[status(thm)],[c_0_65,c_0_60]) ).
cnf(c_0_72,plain,
( sum(X1,additive_identity,X2)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_73,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_74,negated_conjecture,
( product(X1,v,multiplicative_identity)
| ~ product(X1,multiplicative_inverse(a),b) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_60]),c_0_45])]),c_0_69]) ).
cnf(c_0_75,negated_conjecture,
product(u,multiplicative_inverse(a),b),
inference(spm,[status(thm)],[c_0_58,c_0_70]) ).
cnf(c_0_76,negated_conjecture,
( product(multiplicative_identity,v,v)
| ~ defined(multiplicative_inverse(a)) ),
inference(spm,[status(thm)],[c_0_71,c_0_34]) ).
cnf(c_0_77,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_72,c_0_73]),c_0_53])]) ).
cnf(c_0_78,negated_conjecture,
product(u,v,multiplicative_identity),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_79,negated_conjecture,
product(multiplicative_identity,v,v),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_42]),c_0_37])]),c_0_38]) ).
cnf(c_0_80,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1 ).
cnf(c_0_81,plain,
( sum(additive_inverse(additive_identity),additive_identity,additive_identity)
| ~ defined(additive_inverse(additive_identity)) ),
inference(spm,[status(thm)],[c_0_77,c_0_57]) ).
cnf(c_0_82,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_83,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_84,plain,
( sum(X1,additive_identity,X2)
| ~ defined(X2)
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_57]) ).
cnf(c_0_85,negated_conjecture,
product(v,u,multiplicative_identity),
inference(spm,[status(thm)],[c_0_58,c_0_78]) ).
cnf(c_0_86,plain,
( product(X1,multiplicative_identity,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_34]) ).
cnf(c_0_87,negated_conjecture,
( product(X1,X2,v)
| ~ product(X3,v,X2)
| ~ product(X1,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_33,c_0_79]) ).
cnf(c_0_88,plain,
( sum(X1,X2,X3)
| ~ defined(X3)
| ~ sum(X1,X4,additive_identity)
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_80,c_0_47]) ).
cnf(c_0_89,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_53])]) ).
cnf(c_0_90,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_83,c_0_67]) ).
cnf(c_0_91,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_84,c_0_73]),c_0_53])]) ).
cnf(c_0_92,negated_conjecture,
product(b,a,u),
inference(spm,[status(thm)],[c_0_58,c_0_29]) ).
cnf(c_0_93,negated_conjecture,
( product(v,X1,X2)
| ~ product(u,X2,X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_85]) ).
cnf(c_0_94,plain,
( product(X1,multiplicative_identity,X2)
| ~ product(X3,X4,X2)
| ~ product(X3,X4,X1)
| ~ defined(X4) ),
inference(spm,[status(thm)],[c_0_28,c_0_86]) ).
cnf(c_0_95,negated_conjecture,
( product(X1,multiplicative_identity,v)
| ~ product(X1,u,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_87,c_0_78]) ).
cnf(c_0_96,plain,
( sum(additive_inverse(additive_identity),X1,X2)
| ~ defined(X2)
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_97,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_90,c_0_86]),c_0_53])]) ).
cnf(c_0_98,plain,
sum(additive_identity,additive_identity,additive_inverse(additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_82]),c_0_53])]) ).
cnf(c_0_99,negated_conjecture,
( product(X1,a,X2)
| ~ product(X3,u,X2)
| ~ product(X3,b,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_92]) ).
cnf(c_0_100,negated_conjecture,
( product(v,b,multiplicative_inverse(a))
| ~ defined(multiplicative_inverse(a)) ),
inference(spm,[status(thm)],[c_0_93,c_0_75]) ).
cnf(c_0_101,negated_conjecture,
( product(X1,multiplicative_identity,b)
| ~ product(multiplicative_inverse(a),u,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_70]),c_0_32])]) ).
cnf(c_0_102,negated_conjecture,
( product(multiplicative_inverse(u),multiplicative_identity,v)
| sum(additive_identity,u,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_36]),c_0_32])]) ).
cnf(c_0_103,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(u),v),
not_product_9 ).
cnf(c_0_104,plain,
( sum(additive_inverse(additive_identity),X1,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_47]) ).
cnf(c_0_105,plain,
( product(additive_inverse(additive_identity),multiplicative_identity,additive_identity)
| ~ product(additive_identity,multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_106,negated_conjecture,
( product(X1,a,multiplicative_identity)
| ~ product(v,b,X1) ),
inference(spm,[status(thm)],[c_0_99,c_0_85]) ).
cnf(c_0_107,negated_conjecture,
product(v,b,multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_42]),c_0_37])]),c_0_38]) ).
cnf(c_0_108,negated_conjecture,
product(b,multiplicative_identity,b),
inference(spm,[status(thm)],[c_0_101,c_0_70]) ).
cnf(c_0_109,plain,
( sum(additive_identity,X1,X2)
| ~ defined(X2)
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_67]) ).
cnf(c_0_110,negated_conjecture,
sum(additive_identity,u,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_102]),c_0_103]) ).
cnf(c_0_111,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_97,c_0_104]),c_0_53])]) ).
cnf(c_0_112,plain,
product(additive_inverse(additive_identity),multiplicative_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_86]),c_0_53])]) ).
cnf(c_0_113,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_114,negated_conjecture,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_115,negated_conjecture,
product(multiplicative_identity,b,b),
inference(spm,[status(thm)],[c_0_58,c_0_108]) ).
cnf(c_0_116,negated_conjecture,
( product(X1,v,X2)
| ~ product(X3,v,X2)
| ~ product(X3,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_79]) ).
cnf(c_0_117,negated_conjecture,
sum(additive_identity,additive_identity,u),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_32])]) ).
cnf(c_0_118,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_112])]) ).
cnf(c_0_119,plain,
( sum(additive_identity,X1,additive_identity)
| sum(X2,X3,multiplicative_identity)
| ~ product(X4,multiplicative_inverse(X1),X3)
| ~ product(X5,multiplicative_inverse(X1),X2)
| ~ defined(X1)
| ~ sum(X5,X4,X1) ),
inference(spm,[status(thm)],[c_0_113,c_0_63]) ).
cnf(c_0_120,negated_conjecture,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(spm,[status(thm)],[c_0_58,c_0_114]) ).
cnf(c_0_121,negated_conjecture,
( product(X1,X2,b)
| ~ product(X3,b,X2)
| ~ product(X1,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_33,c_0_115]) ).
cnf(c_0_122,negated_conjecture,
( product(X1,v,multiplicative_identity)
| ~ product(u,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_116,c_0_78]) ).
cnf(c_0_123,negated_conjecture,
product(u,multiplicative_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_117]),c_0_118])]) ).
cnf(c_0_124,plain,
( sum(X1,additive_inverse(X1),additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_73]) ).
cnf(c_0_125,negated_conjecture,
( sum(X1,multiplicative_identity,multiplicative_identity)
| ~ product(X2,multiplicative_inverse(a),X1)
| ~ sum(X2,a,a) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_37])]),c_0_38]) ).
cnf(c_0_126,negated_conjecture,
( product(X1,multiplicative_inverse(a),b)
| ~ product(X1,v,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_121,c_0_107]) ).
cnf(c_0_127,negated_conjecture,
product(additive_identity,v,multiplicative_identity),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_128,plain,
( sum(X1,X2,additive_identity)
| ~ defined(X3)
| ~ sum(X4,additive_inverse(X3),X2)
| ~ sum(X1,X4,X3) ),
inference(spm,[status(thm)],[c_0_80,c_0_124]) ).
cnf(c_0_129,negated_conjecture,
( sum(X1,multiplicative_identity,multiplicative_identity)
| ~ product(additive_identity,multiplicative_inverse(a),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_47]),c_0_37])]) ).
cnf(c_0_130,negated_conjecture,
product(additive_identity,multiplicative_inverse(a),b),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_131,plain,
( sum(X1,additive_identity,additive_identity)
| ~ defined(X2)
| ~ sum(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_128,c_0_124]) ).
cnf(c_0_132,negated_conjecture,
sum(b,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_133,negated_conjecture,
sum(b,additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_40])]) ).
cnf(c_0_134,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_133]),c_0_69]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD012-4 : 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
% 0.14/0.33 % Computer : n006.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 17:26:16 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 3.97/3.28 % Version : CSE_E---1.7
% 3.97/3.28 % Problem : theBenchmark.p
% 3.97/3.28 % SZS status Unsatisfiable for theBenchmark.p
% 3.97/3.28 % SZS output start CNFRefutation
% See solution above
% 4.07/3.30 % Total time : 2.374s
%------------------------------------------------------------------------------