TSTP Solution File: FLD043-5 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD043-5 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n027.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 : Wed Aug 30 22:27:33 EDT 2023
% Result : Unsatisfiable 7.32s 7.46s
% Output : CNFRefutation 7.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 36
% Syntax : Number of formulae : 193 ( 58 unt; 11 typ; 0 def)
% Number of atoms : 400 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 432 ( 214 ~; 218 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 8 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 265 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
sum: ( $i * $i * $i ) > $o ).
tff(decl_23,type,
additive_identity: $i ).
tff(decl_24,type,
defined: $i > $o ).
tff(decl_25,type,
additive_inverse: $i > $i ).
tff(decl_26,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
multiplicative_identity: $i ).
tff(decl_28,type,
multiplicative_inverse: $i > $i ).
tff(decl_29,type,
add: ( $i * $i ) > $i ).
tff(decl_30,type,
multiply: ( $i * $i ) > $i ).
tff(decl_31,type,
less_or_equal: ( $i * $i ) > $o ).
tff(decl_32,type,
a: $i ).
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(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(associativity_multiplication_2,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
cnf(distributivity_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(commutativity_multiplication,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
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(distributivity_1,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X6)
| ~ product(X6,X7,X3)
| ~ product(X4,X7,X1)
| ~ product(X5,X7,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
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(different_identities,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',different_identities) ).
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(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(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(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(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(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
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(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(well_definedness_of_multiplication,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplication) ).
cnf(compatibility_of_order_relation_and_multiplication,axiom,
( less_or_equal(additive_identity,X1)
| ~ less_or_equal(additive_identity,X2)
| ~ less_or_equal(additive_identity,X3)
| ~ product(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_multiplication) ).
cnf(transitivity_of_order_relation,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',transitivity_of_order_relation) ).
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(not_product_2,negated_conjecture,
~ product(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_2) ).
cnf(c_0_25,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_26,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_27,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
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,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,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_31,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_32,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_25,c_0_27]) ).
cnf(c_0_33,plain,
( product(X1,multiplicative_identity,X2)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X3,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( product(X1,multiplicative_identity,X2)
| ~ product(X3,multiplicative_identity,X4)
| ~ sum(X4,multiplicative_identity,X2)
| ~ sum(X3,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_35,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_37,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_38,plain,
( product(X1,multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_29]) ).
cnf(c_0_39,plain,
( product(X1,multiplicative_identity,X2)
| ~ sum(additive_identity,multiplicative_identity,X2)
| ~ sum(additive_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_36,c_0_26]) ).
cnf(c_0_41,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_42,plain,
( sum(X1,X2,multiplicative_identity)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X4,multiplicative_identity,X1)
| ~ sum(X4,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_37,c_0_29]) ).
cnf(c_0_43,plain,
( product(X1,multiplicative_identity,additive_identity)
| ~ product(additive_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_35]) ).
cnf(c_0_44,plain,
( product(X1,multiplicative_identity,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_45,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_46,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_47,plain,
( defined(multiplicative_inverse(multiplicative_identity))
| sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_41,c_0_26]) ).
cnf(c_0_48,plain,
( sum(X1,additive_identity,multiplicative_identity)
| ~ product(X2,multiplicative_identity,X1)
| ~ sum(X2,additive_identity,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_42,c_0_35]) ).
cnf(c_0_49,plain,
( product(multiplicative_identity,multiplicative_identity,additive_identity)
| ~ sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,plain,
sum(multiplicative_identity,additive_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_45,c_0_40]) ).
cnf(c_0_51,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
different_identities ).
cnf(c_0_52,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1 ).
cnf(c_0_53,plain,
( product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_46,c_0_26]) ).
cnf(c_0_54,plain,
( product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity))
| sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_25,c_0_47]) ).
cnf(c_0_55,plain,
~ sum(additive_identity,multiplicative_identity,additive_identity),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50])]),c_0_51]) ).
cnf(c_0_56,plain,
( product(X1,X2,multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ product(X1,X3,multiplicative_inverse(multiplicative_identity))
| ~ product(X3,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,plain,
product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)),
inference(sr,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_58,plain,
( product(X1,multiplicative_identity,X2)
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ product(X3,multiplicative_inverse(multiplicative_identity),X1)
| ~ product(X3,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_53]) ).
cnf(c_0_59,plain,
( product(multiplicative_identity,X1,multiplicative_identity)
| ~ product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_55]) ).
cnf(c_0_60,plain,
( product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,X1)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_57]),c_0_55]) ).
cnf(c_0_61,plain,
( product(multiplicative_identity,X1,multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_62,plain,
( product(X1,additive_identity,X2)
| ~ product(X3,additive_identity,X2)
| ~ product(X3,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_32]) ).
cnf(c_0_63,plain,
( product(X1,multiplicative_identity,X2)
| ~ product(X3,multiplicative_identity,X4)
| ~ sum(X4,additive_identity,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_35]) ).
cnf(c_0_64,plain,
( product(multiplicative_identity,X1,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_39]),c_0_40])]) ).
cnf(c_0_65,plain,
( product(X1,additive_identity,additive_identity)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_32]) ).
cnf(c_0_66,plain,
( product(X1,multiplicative_identity,X2)
| ~ sum(multiplicative_identity,additive_identity,X2)
| ~ sum(multiplicative_identity,additive_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_40])]) ).
cnf(c_0_67,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1 ).
cnf(c_0_68,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_36,c_0_27]) ).
cnf(c_0_69,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_70,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_71,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_multiplication ).
cnf(c_0_72,plain,
( product(X1,additive_identity,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_50])]) ).
cnf(c_0_73,plain,
( sum(X1,X2,additive_identity)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_69,c_0_27]) ).
cnf(c_0_75,plain,
( sum(additive_inverse(additive_inverse(X1)),additive_inverse(X1),additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_76,plain,
( product(X1,multiplicative_identity,multiply(X1,multiplicative_identity))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_26]) ).
cnf(c_0_77,plain,
( product(additive_identity,X1,additive_identity)
| ~ sum(multiplicative_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_72]) ).
cnf(c_0_78,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_79,plain,
( sum(X1,additive_identity,additive_identity)
| ~ sum(X1,additive_inverse(additive_identity),additive_identity) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_80,plain,
sum(additive_inverse(additive_inverse(additive_identity)),additive_inverse(additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_75,c_0_27]) ).
cnf(c_0_81,plain,
product(multiplicative_identity,multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity)),
inference(spm,[status(thm)],[c_0_76,c_0_26]) ).
cnf(c_0_82,plain,
( product(X1,additive_identity,multiply(X1,additive_identity))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_27]) ).
cnf(c_0_83,plain,
( product(X1,multiplicative_identity,X2)
| ~ sum(additive_identity,additive_identity,X2)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_77]),c_0_50])]) ).
cnf(c_0_84,hypothesis,
product(multiplicative_identity,a,a),
inference(spm,[status(thm)],[c_0_25,c_0_78]) ).
cnf(c_0_85,hypothesis,
( product(X1,a,multiply(X1,a))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_78]) ).
cnf(c_0_86,plain,
sum(additive_inverse(additive_inverse(additive_identity)),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_87,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_88,plain,
( sum(X1,X2,additive_identity)
| ~ product(X3,additive_identity,X2)
| ~ product(X4,additive_identity,X1)
| ~ sum(X4,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_37,c_0_32]) ).
cnf(c_0_89,plain,
product(multiply(multiplicative_identity,multiplicative_identity),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_65,c_0_81]) ).
cnf(c_0_90,plain,
sum(multiply(multiplicative_identity,multiplicative_identity),additive_identity,multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_81]),c_0_50])]) ).
cnf(c_0_91,plain,
product(additive_identity,additive_identity,multiply(additive_identity,additive_identity)),
inference(spm,[status(thm)],[c_0_82,c_0_27]) ).
cnf(c_0_92,plain,
( product(X1,multiplicative_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_83]),c_0_68])]) ).
cnf(c_0_93,hypothesis,
( product(X1,a,X2)
| ~ product(X3,a,X2)
| ~ product(X3,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_84]) ).
cnf(c_0_94,hypothesis,
product(additive_identity,a,multiply(additive_identity,a)),
inference(spm,[status(thm)],[c_0_85,c_0_27]) ).
cnf(c_0_95,plain,
( sum(additive_identity,additive_inverse(X1),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_70]) ).
cnf(c_0_96,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_97,plain,
sum(additive_identity,additive_inverse(additive_inverse(additive_identity)),additive_identity),
inference(spm,[status(thm)],[c_0_45,c_0_86]) ).
cnf(c_0_98,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_87]) ).
cnf(c_0_99,plain,
( sum(X1,additive_identity,additive_identity)
| ~ product(X2,additive_identity,X1)
| ~ sum(X2,multiply(multiplicative_identity,multiplicative_identity),multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_100,plain,
sum(additive_identity,multiply(multiplicative_identity,multiplicative_identity),multiplicative_identity),
inference(spm,[status(thm)],[c_0_45,c_0_90]) ).
cnf(c_0_101,plain,
( product(X1,X2,multiply(additive_identity,additive_identity))
| ~ product(X3,additive_identity,X2)
| ~ product(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_52,c_0_91]) ).
cnf(c_0_102,plain,
( product(multiplicative_identity,X1,additive_identity)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_92]) ).
cnf(c_0_103,hypothesis,
( product(X1,a,multiply(additive_identity,a))
| ~ product(additive_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_104,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_95,c_0_27]) ).
cnf(c_0_105,plain,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X2,additive_identity)
| ~ sum(X2,additive_inverse(additive_inverse(additive_identity)),X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_106,plain,
( sum(additive_identity,additive_inverse(additive_inverse(X1)),additive_inverse(additive_inverse(X1)))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_70]) ).
cnf(c_0_107,plain,
less_or_equal(additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_98,c_0_27]) ).
cnf(c_0_108,plain,
( sum(X1,additive_identity,additive_identity)
| ~ product(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_109,plain,
( product(X1,additive_identity,multiply(additive_identity,additive_identity))
| ~ product(X1,multiplicative_identity,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_68])]) ).
cnf(c_0_110,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_multiplication ).
cnf(c_0_111,hypothesis,
sum(additive_inverse(a),a,additive_identity),
inference(spm,[status(thm)],[c_0_69,c_0_78]) ).
cnf(c_0_112,plain,
( product(X1,multiplicative_identity,X2)
| ~ product(X3,additive_identity,X2)
| ~ product(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_35]) ).
cnf(c_0_113,hypothesis,
( product(a,X1,multiply(additive_identity,a))
| ~ product(additive_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_103]) ).
cnf(c_0_114,plain,
( product(multiplicative_identity,additive_inverse(X1),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_70]) ).
cnf(c_0_115,plain,
( less_or_equal(X1,additive_inverse(additive_identity))
| ~ less_or_equal(X2,additive_identity)
| ~ sum(X2,additive_inverse(additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_104]) ).
cnf(c_0_116,plain,
less_or_equal(additive_inverse(additive_inverse(additive_identity)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]),c_0_27])]) ).
cnf(c_0_117,axiom,
( less_or_equal(additive_identity,X1)
| ~ less_or_equal(additive_identity,X2)
| ~ less_or_equal(additive_identity,X3)
| ~ product(X2,X3,X1) ),
compatibility_of_order_relation_and_multiplication ).
cnf(c_0_118,plain,
sum(multiply(additive_identity,additive_identity),additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_35])]) ).
cnf(c_0_119,plain,
( sum(additive_identity,multiply(X1,X2),multiply(X1,X2))
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_110]) ).
cnf(c_0_120,hypothesis,
sum(a,additive_inverse(a),additive_identity),
inference(spm,[status(thm)],[c_0_45,c_0_111]) ).
cnf(c_0_121,hypothesis,
( sum(X1,X2,a)
| ~ product(X3,a,X2)
| ~ product(X4,a,X1)
| ~ sum(X4,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_37,c_0_84]) ).
cnf(c_0_122,hypothesis,
product(a,additive_identity,multiply(a,additive_identity)),
inference(spm,[status(thm)],[c_0_82,c_0_78]) ).
cnf(c_0_123,hypothesis,
( product(X1,multiplicative_identity,multiply(additive_identity,a))
| ~ product(a,additive_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_35])]) ).
cnf(c_0_124,plain,
product(multiplicative_identity,additive_inverse(additive_identity),additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_114,c_0_27]) ).
cnf(c_0_125,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
transitivity_of_order_relation ).
cnf(c_0_126,plain,
less_or_equal(additive_identity,additive_inverse(additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_80]),c_0_116])]) ).
cnf(c_0_127,plain,
( less_or_equal(additive_identity,X1)
| ~ less_or_equal(additive_identity,X2)
| ~ product(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_117,c_0_107]) ).
cnf(c_0_128,plain,
sum(additive_identity,multiply(additive_identity,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_45,c_0_118]) ).
cnf(c_0_129,plain,
( sum(additive_identity,multiply(X1,additive_identity),multiply(X1,additive_identity))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_119,c_0_27]) ).
cnf(c_0_130,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_45,c_0_74]) ).
cnf(c_0_131,hypothesis,
( sum(X1,X2,additive_identity)
| ~ sum(X3,additive_inverse(a),X2)
| ~ sum(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_67,c_0_120]) ).
cnf(c_0_132,hypothesis,
( sum(X1,a,a)
| ~ product(X2,a,X1)
| ~ sum(X2,multiplicative_identity,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_121,c_0_84]) ).
cnf(c_0_133,hypothesis,
( product(X1,X2,multiply(a,additive_identity))
| ~ product(X3,additive_identity,X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_52,c_0_122]) ).
cnf(c_0_134,hypothesis,
product(a,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_31,c_0_84]) ).
cnf(c_0_135,hypothesis,
product(a,additive_identity,multiply(additive_identity,a)),
inference(spm,[status(thm)],[c_0_31,c_0_94]) ).
cnf(c_0_136,hypothesis,
( product(multiply(additive_identity,a),multiplicative_identity,additive_identity)
| ~ product(a,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_43,c_0_123]) ).
cnf(c_0_137,plain,
product(additive_inverse(additive_identity),multiplicative_identity,additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_31,c_0_124]) ).
cnf(c_0_138,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_139,plain,
( less_or_equal(X1,additive_inverse(additive_identity))
| ~ less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_140,plain,
less_or_equal(additive_identity,multiply(additive_identity,additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_91]),c_0_107])]) ).
cnf(c_0_141,plain,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X2,additive_identity)
| ~ sum(X2,multiply(additive_identity,additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_128]) ).
cnf(c_0_142,plain,
sum(additive_identity,multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity)),
inference(spm,[status(thm)],[c_0_129,c_0_27]) ).
cnf(c_0_143,plain,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X2,additive_identity)
| ~ sum(X2,additive_inverse(additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_130]) ).
cnf(c_0_144,hypothesis,
( sum(X1,additive_identity,additive_identity)
| ~ sum(X1,a,a) ),
inference(spm,[status(thm)],[c_0_131,c_0_120]) ).
cnf(c_0_145,hypothesis,
( sum(X1,a,a)
| ~ product(additive_identity,a,X1) ),
inference(spm,[status(thm)],[c_0_132,c_0_40]) ).
cnf(c_0_146,hypothesis,
( product(X1,additive_identity,multiply(a,additive_identity))
| ~ product(X1,multiplicative_identity,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_102]),c_0_68])]) ).
cnf(c_0_147,hypothesis,
( product(X1,multiplicative_identity,X2)
| ~ product(X3,a,X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_134]) ).
cnf(c_0_148,hypothesis,
( product(X1,additive_identity,X2)
| ~ product(X3,multiply(additive_identity,a),X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_135]) ).
cnf(c_0_149,hypothesis,
( product(multiplicative_identity,multiply(additive_identity,a),additive_identity)
| ~ product(a,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_31,c_0_136]) ).
cnf(c_0_150,hypothesis,
product(multiplicative_identity,a,multiply(multiplicative_identity,a)),
inference(spm,[status(thm)],[c_0_85,c_0_26]) ).
cnf(c_0_151,plain,
( product(X1,multiplicative_identity,X2)
| ~ product(X3,multiplicative_identity,X4)
| ~ sum(X4,additive_inverse(additive_identity),X2)
| ~ sum(X3,additive_inverse(additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_137]) ).
cnf(c_0_152,plain,
( sum(additive_identity,additive_inverse(additive_identity),X1)
| ~ less_or_equal(additive_inverse(additive_identity),X1)
| ~ less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_153,plain,
( less_or_equal(X1,multiply(additive_identity,additive_identity))
| ~ less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_125,c_0_140]) ).
cnf(c_0_154,plain,
less_or_equal(multiply(additive_identity,additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_107])]) ).
cnf(c_0_155,plain,
less_or_equal(additive_inverse(additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_104]),c_0_107])]) ).
cnf(c_0_156,hypothesis,
( sum(X1,additive_identity,additive_identity)
| ~ product(additive_identity,a,X1) ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_157,hypothesis,
( product(additive_identity,X1,multiply(a,additive_identity))
| ~ product(X1,multiplicative_identity,a) ),
inference(spm,[status(thm)],[c_0_31,c_0_146]) ).
cnf(c_0_158,hypothesis,
( product(X1,multiplicative_identity,a)
| ~ product(multiplicative_identity,a,X1) ),
inference(spm,[status(thm)],[c_0_147,c_0_84]) ).
cnf(c_0_159,hypothesis,
( product(X1,additive_identity,additive_identity)
| ~ product(a,additive_identity,additive_identity)
| ~ product(multiplicative_identity,a,X1) ),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_160,hypothesis,
( product(X1,a,multiply(multiplicative_identity,a))
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_150]) ).
cnf(c_0_161,plain,
( product(X1,multiplicative_identity,additive_identity)
| ~ product(X2,multiplicative_identity,additive_identity)
| ~ sum(X2,additive_inverse(additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_151,c_0_130]) ).
cnf(c_0_162,plain,
sum(additive_identity,additive_inverse(additive_identity),multiply(additive_identity,additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_154]),c_0_155])]) ).
cnf(c_0_163,hypothesis,
sum(multiply(a,additive_identity),additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_134])]) ).
cnf(c_0_164,plain,
( product(X1,X2,additive_identity)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_52,c_0_35]) ).
cnf(c_0_165,hypothesis,
product(multiply(multiplicative_identity,a),multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_158,c_0_150]) ).
cnf(c_0_166,hypothesis,
( product(multiply(multiplicative_identity,a),additive_identity,additive_identity)
| ~ product(a,additive_identity,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_29])]) ).
cnf(c_0_167,plain,
product(multiply(additive_identity,additive_identity),multiplicative_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_35])]) ).
cnf(c_0_168,hypothesis,
( product(X1,additive_identity,X2)
| ~ product(X3,additive_identity,X4)
| ~ sum(X4,multiply(a,additive_identity),X2)
| ~ sum(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_122]) ).
cnf(c_0_169,hypothesis,
sum(additive_identity,multiply(a,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_45,c_0_163]) ).
cnf(c_0_170,hypothesis,
( product(X1,a,additive_identity)
| ~ product(X1,multiply(multiplicative_identity,a),additive_identity) ),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_171,hypothesis,
( product(additive_identity,multiply(multiplicative_identity,a),additive_identity)
| ~ product(a,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_31,c_0_166]) ).
cnf(c_0_172,negated_conjecture,
~ product(additive_identity,a,additive_identity),
not_product_2 ).
cnf(c_0_173,plain,
( product(X1,additive_identity,X2)
| ~ product(X3,multiply(additive_identity,additive_identity),X2)
| ~ product(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_91]) ).
cnf(c_0_174,plain,
product(multiplicative_identity,multiply(additive_identity,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_31,c_0_167]) ).
cnf(c_0_175,hypothesis,
( product(X1,additive_identity,additive_identity)
| ~ product(X2,additive_identity,additive_identity)
| ~ sum(X2,a,X1) ),
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_176,hypothesis,
sum(additive_identity,a,a),
inference(spm,[status(thm)],[c_0_36,c_0_78]) ).
cnf(c_0_177,hypothesis,
~ product(a,additive_identity,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_172]) ).
cnf(c_0_178,plain,
( product(X1,additive_identity,additive_identity)
| ~ product(multiplicative_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_173,c_0_174]) ).
cnf(c_0_179,plain,
( product(X1,additive_identity,additive_identity)
| ~ sum(additive_identity,multiplicative_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_39]),c_0_40])]) ).
cnf(c_0_180,hypothesis,
~ product(additive_identity,additive_identity,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_176]),c_0_177]) ).
cnf(c_0_181,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_179]),c_0_40])]),c_0_180]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : FLD043-5 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32 % Computer : n027.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun Aug 27 23:58:51 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.56 start to proof: theBenchmark
% 7.32/7.46 % Version : CSE_E---1.5
% 7.32/7.46 % Problem : theBenchmark.p
% 7.32/7.46 % Proof found
% 7.32/7.46 % SZS status Theorem for theBenchmark.p
% 7.32/7.46 % SZS output start Proof
% See solution above
% 7.32/7.47 % Total time : 6.852000 s
% 7.32/7.47 % SZS output end Proof
% 7.32/7.48 % Total time : 6.854000 s
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