TSTP Solution File: FLD026-3 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD026-3 : 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 : n021.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 22:27:24 EDT 2023
% Result : Unsatisfiable 7.67s 7.73s
% Output : CNFRefutation 7.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 36
% Syntax : Number of formulae : 196 ( 61 unt; 12 typ; 0 def)
% Number of atoms : 378 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 384 ( 190 ~; 194 |; 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 239 ( 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 ).
tff(decl_33,type,
b: $i ).
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(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(not_sum_3,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
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(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(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
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(totality_of_addition,axiom,
( sum(X1,X2,add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_addition) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_order_relation) ).
cnf(product_4,negated_conjecture,
product(multiplicative_identity,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_4) ).
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_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(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(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
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(not_product_5,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
file('/export/starexec/sandbox/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/sandbox/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,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_33,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_34,hypothesis,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_36,hypothesis,
sum(additive_inverse(multiplicative_inverse(a)),multiplicative_inverse(a),additive_identity),
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
cnf(c_0_37,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_38,hypothesis,
( product(multiplicative_inverse(a),a,X1)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_40,axiom,
( sum(X1,X2,add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_addition ).
cnf(c_0_41,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_42,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_43,hypothesis,
sum(multiplicative_inverse(a),additive_inverse(multiplicative_inverse(a)),additive_identity),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_45,hypothesis,
( product(a,multiplicative_inverse(a),X1)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,negated_conjecture,
product(multiplicative_identity,a,b),
product_4 ).
cnf(c_0_47,hypothesis,
sum(additive_identity,multiplicative_inverse(a),multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_39,c_0_31]) ).
cnf(c_0_48,hypothesis,
( sum(X1,b,add(X1,b))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_50,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_42,c_0_43]) ).
cnf(c_0_51,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_44]) ).
cnf(c_0_52,hypothesis,
sum(additive_identity,b,b),
inference(spm,[status(thm)],[c_0_39,c_0_41]) ).
cnf(c_0_53,hypothesis,
product(multiplicative_identity,a,a),
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
cnf(c_0_54,hypothesis,
( product(X1,a,X2)
| ~ product(a,multiplicative_identity,X2)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_45]) ).
cnf(c_0_55,negated_conjecture,
product(a,multiplicative_identity,b),
inference(spm,[status(thm)],[c_0_37,c_0_46]) ).
cnf(c_0_56,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1 ).
cnf(c_0_57,hypothesis,
sum(multiplicative_inverse(a),additive_identity,multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_35,c_0_47]) ).
cnf(c_0_58,hypothesis,
sum(additive_identity,b,add(additive_identity,b)),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_59,hypothesis,
( less_or_equal(additive_identity,additive_identity)
| ~ less_or_equal(multiplicative_inverse(a),multiplicative_inverse(a)) ),
inference(spm,[status(thm)],[c_0_50,c_0_43]) ).
cnf(c_0_60,hypothesis,
less_or_equal(multiplicative_inverse(a),multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_51,c_0_31]) ).
cnf(c_0_61,hypothesis,
sum(b,additive_identity,b),
inference(spm,[status(thm)],[c_0_35,c_0_52]) ).
cnf(c_0_62,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1 ).
cnf(c_0_63,hypothesis,
product(a,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_37,c_0_53]) ).
cnf(c_0_64,negated_conjecture,
( product(X1,a,b)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_65,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_66,hypothesis,
( sum(X1,X2,multiplicative_inverse(a))
| ~ sum(X1,X3,multiplicative_inverse(a))
| ~ sum(X3,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_67,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_42,c_0_58]) ).
cnf(c_0_68,hypothesis,
less_or_equal(additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60])]) ).
cnf(c_0_69,hypothesis,
( less_or_equal(X1,b)
| ~ less_or_equal(X2,b)
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_61]) ).
cnf(c_0_70,hypothesis,
sum(b,additive_identity,add(additive_identity,b)),
inference(spm,[status(thm)],[c_0_35,c_0_58]) ).
cnf(c_0_71,hypothesis,
less_or_equal(b,b),
inference(spm,[status(thm)],[c_0_51,c_0_41]) ).
cnf(c_0_72,hypothesis,
( product(X1,X2,a)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_73,negated_conjecture,
( product(a,X1,b)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_64]) ).
cnf(c_0_74,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_30,c_0_65]) ).
cnf(c_0_75,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_56,c_0_43]) ).
cnf(c_0_76,hypothesis,
( sum(multiplicative_inverse(a),X1,multiplicative_inverse(a))
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_57]) ).
cnf(c_0_77,hypothesis,
product(multiplicative_identity,b,b),
inference(spm,[status(thm)],[c_0_30,c_0_41]) ).
cnf(c_0_78,hypothesis,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(spm,[status(thm)],[c_0_37,c_0_29]) ).
cnf(c_0_79,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_80,hypothesis,
less_or_equal(b,add(additive_identity,b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_52]),c_0_68])]) ).
cnf(c_0_81,hypothesis,
less_or_equal(add(additive_identity,b),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71])]) ).
cnf(c_0_82,axiom,
( sum(X1,X2,X3)
| ~ sum(X4,X5,X1)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X6,X3) ),
associativity_addition_2 ).
cnf(c_0_83,hypothesis,
( defined(multiplicative_inverse(b))
| sum(additive_identity,b,additive_identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_41]) ).
cnf(c_0_84,negated_conjecture,
( product(X1,b,a)
| ~ product(X1,a,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74])]) ).
cnf(c_0_85,hypothesis,
sum(additive_inverse(a),a,additive_identity),
inference(spm,[status(thm)],[c_0_32,c_0_25]) ).
cnf(c_0_86,hypothesis,
( sum(X1,additive_identity,additive_identity)
| ~ sum(X1,multiplicative_inverse(a),multiplicative_inverse(a)) ),
inference(spm,[status(thm)],[c_0_75,c_0_43]) ).
cnf(c_0_87,hypothesis,
( sum(X1,multiplicative_inverse(a),multiplicative_inverse(a))
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_76]) ).
cnf(c_0_88,plain,
( sum(X1,additive_identity,add(X1,additive_identity))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_49]) ).
cnf(c_0_89,hypothesis,
sum(additive_identity,a,a),
inference(spm,[status(thm)],[c_0_39,c_0_25]) ).
cnf(c_0_90,hypothesis,
product(b,multiplicative_identity,b),
inference(spm,[status(thm)],[c_0_37,c_0_77]) ).
cnf(c_0_91,hypothesis,
( product(X1,X2,multiplicative_identity)
| ~ product(X3,multiplicative_inverse(a),X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_62,c_0_78]) ).
cnf(c_0_92,hypothesis,
sum(additive_identity,add(additive_identity,b),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81])]) ).
cnf(c_0_93,hypothesis,
( sum(X1,b,X2)
| ~ sum(X3,b,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_52]) ).
cnf(c_0_94,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_83]) ).
cnf(c_0_95,plain,
( product(X1,X2,multiplicative_identity)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X1,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_62,c_0_74]) ).
cnf(c_0_96,negated_conjecture,
( product(b,X1,a)
| ~ product(X1,a,a) ),
inference(spm,[status(thm)],[c_0_37,c_0_84]) ).
cnf(c_0_97,hypothesis,
sum(a,additive_inverse(a),additive_identity),
inference(spm,[status(thm)],[c_0_35,c_0_85]) ).
cnf(c_0_98,hypothesis,
( sum(X1,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_99,plain,
sum(additive_identity,additive_identity,add(additive_identity,additive_identity)),
inference(spm,[status(thm)],[c_0_88,c_0_49]) ).
cnf(c_0_100,hypothesis,
( sum(X1,a,add(X1,a))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_25]) ).
cnf(c_0_101,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_102,hypothesis,
( sum(X1,X2,b)
| ~ sum(X3,b,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_56,c_0_52]) ).
cnf(c_0_103,hypothesis,
sum(a,additive_identity,a),
inference(spm,[status(thm)],[c_0_35,c_0_89]) ).
cnf(c_0_104,hypothesis,
( sum(X1,a,X2)
| ~ sum(X3,a,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_89]) ).
cnf(c_0_105,hypothesis,
( product(X1,X2,b)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X1,X3,b) ),
inference(spm,[status(thm)],[c_0_62,c_0_90]) ).
cnf(c_0_106,hypothesis,
( product(X1,multiplicative_inverse(a),multiplicative_identity)
| ~ product(X1,multiplicative_identity,a) ),
inference(spm,[status(thm)],[c_0_91,c_0_34]) ).
cnf(c_0_107,hypothesis,
( sum(X1,X2,b)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X1,X3,b) ),
inference(spm,[status(thm)],[c_0_56,c_0_61]) ).
cnf(c_0_108,hypothesis,
sum(add(additive_identity,b),additive_identity,b),
inference(spm,[status(thm)],[c_0_35,c_0_92]) ).
cnf(c_0_109,hypothesis,
( sum(X1,b,b)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_52]) ).
cnf(c_0_110,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_78]) ).
cnf(c_0_111,hypothesis,
( product(multiplicative_inverse(b),multiplicative_identity,multiplicative_inverse(b))
| sum(additive_identity,b,additive_identity) ),
inference(spm,[status(thm)],[c_0_37,c_0_94]) ).
cnf(c_0_112,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_95,c_0_96]),c_0_53])]) ).
cnf(c_0_113,hypothesis,
( product(multiplicative_inverse(b),b,multiplicative_identity)
| sum(additive_identity,b,additive_identity) ),
inference(spm,[status(thm)],[c_0_24,c_0_41]) ).
cnf(c_0_114,hypothesis,
( sum(X1,additive_inverse(a),X2)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_97]) ).
cnf(c_0_115,hypothesis,
sum(add(additive_identity,additive_identity),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_116,hypothesis,
sum(additive_identity,a,add(additive_identity,a)),
inference(spm,[status(thm)],[c_0_100,c_0_49]) ).
cnf(c_0_117,hypothesis,
sum(additive_inverse(b),b,additive_identity),
inference(spm,[status(thm)],[c_0_32,c_0_41]) ).
cnf(c_0_118,plain,
( sum(additive_identity,additive_inverse(X1),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_101]) ).
cnf(c_0_119,hypothesis,
( sum(X1,b,b)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_102,c_0_52]) ).
cnf(c_0_120,hypothesis,
( sum(X1,X2,a)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_56,c_0_103]) ).
cnf(c_0_121,hypothesis,
( sum(X1,a,a)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_104,c_0_89]) ).
cnf(c_0_122,negated_conjecture,
( product(X1,b,b)
| ~ product(X1,a,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_73]),c_0_74])]) ).
cnf(c_0_123,hypothesis,
( product(X1,X2,a)
| ~ product(X3,a,X2)
| ~ product(X1,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_62,c_0_53]) ).
cnf(c_0_124,hypothesis,
( product(multiplicative_inverse(a),X1,multiplicative_identity)
| ~ product(X1,multiplicative_identity,a) ),
inference(spm,[status(thm)],[c_0_37,c_0_106]) ).
cnf(c_0_125,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_95,c_0_73]),c_0_74])]) ).
cnf(c_0_126,hypothesis,
( sum(X1,b,b)
| ~ sum(X1,add(additive_identity,b),b) ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_127,hypothesis,
( sum(b,X1,b)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_109]) ).
cnf(c_0_128,hypothesis,
( sum(X1,additive_identity,X2)
| ~ sum(X3,b,X2)
| ~ sum(X3,b,X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_61]) ).
cnf(c_0_129,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_110,c_0_111]) ).
cnf(c_0_130,hypothesis,
( product(multiplicative_inverse(b),a,multiplicative_identity)
| sum(additive_identity,b,additive_identity) ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_131,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
not_product_5 ).
cnf(c_0_132,hypothesis,
( sum(X1,additive_inverse(a),additive_identity)
| ~ sum(add(additive_identity,additive_identity),a,X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_133,hypothesis,
( sum(X1,a,add(additive_identity,a))
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_104,c_0_116]) ).
cnf(c_0_134,hypothesis,
( sum(X1,X2,a)
| ~ sum(X3,a,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_56,c_0_89]) ).
cnf(c_0_135,hypothesis,
( sum(X1,X2,additive_identity)
| ~ sum(X1,X3,additive_inverse(b))
| ~ sum(X3,b,X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_117]) ).
cnf(c_0_136,hypothesis,
sum(additive_identity,additive_inverse(b),additive_inverse(b)),
inference(spm,[status(thm)],[c_0_118,c_0_41]) ).
cnf(c_0_137,hypothesis,
( sum(b,X1,b)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_35,c_0_119]) ).
cnf(c_0_138,hypothesis,
( sum(X1,b,a)
| ~ sum(X1,add(additive_identity,b),a) ),
inference(spm,[status(thm)],[c_0_120,c_0_108]) ).
cnf(c_0_139,hypothesis,
( sum(a,X1,a)
| ~ sum(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_121]) ).
cnf(c_0_140,negated_conjecture,
( product(X1,X2,b)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_62,c_0_55]) ).
cnf(c_0_141,negated_conjecture,
( product(b,X1,b)
| ~ product(X1,a,b) ),
inference(spm,[status(thm)],[c_0_37,c_0_122]) ).
cnf(c_0_142,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_123,c_0_124]),c_0_63])]) ).
cnf(c_0_143,negated_conjecture,
( product(b,X1,multiplicative_identity)
| ~ product(X1,a,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_37,c_0_125]) ).
cnf(c_0_144,hypothesis,
( sum(b,b,b)
| ~ sum(additive_identity,additive_identity,add(additive_identity,b)) ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_145,hypothesis,
( sum(X1,additive_identity,add(additive_identity,b))
| ~ sum(additive_identity,b,X1) ),
inference(spm,[status(thm)],[c_0_128,c_0_58]) ).
cnf(c_0_146,hypothesis,
( sum(X1,additive_identity,X2)
| ~ sum(X3,add(additive_identity,b),X2)
| ~ sum(X3,b,X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_70]) ).
cnf(c_0_147,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_39,c_0_49]) ).
cnf(c_0_148,hypothesis,
sum(additive_identity,b,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_131]) ).
cnf(c_0_149,hypothesis,
( sum(X1,X2,additive_identity)
| ~ sum(X3,additive_inverse(a),X2)
| ~ sum(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_56,c_0_97]) ).
cnf(c_0_150,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_132,c_0_133]),c_0_99])]) ).
cnf(c_0_151,hypothesis,
( sum(X1,a,a)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_134,c_0_89]) ).
cnf(c_0_152,hypothesis,
( sum(additive_identity,X1,additive_identity)
| ~ sum(additive_inverse(b),b,X1) ),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_153,hypothesis,
( sum(X1,b,a)
| ~ sum(a,additive_identity,additive_identity)
| ~ sum(X1,b,additive_identity) ),
inference(spm,[status(thm)],[c_0_134,c_0_137]) ).
cnf(c_0_154,hypothesis,
( sum(a,b,a)
| ~ sum(additive_identity,additive_identity,add(additive_identity,b)) ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_155,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_156,negated_conjecture,
( product(X1,b,b)
| ~ product(X1,b,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_46])]) ).
cnf(c_0_157,hypothesis,
product(b,multiplicative_identity,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_29])]) ).
cnf(c_0_158,hypothesis,
( sum(b,b,b)
| ~ sum(additive_identity,b,additive_identity) ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_159,hypothesis,
( sum(X1,additive_identity,b)
| ~ sum(additive_identity,b,X1) ),
inference(spm,[status(thm)],[c_0_146,c_0_92]) ).
cnf(c_0_160,plain,
( sum(X1,additive_identity,X2)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_147]) ).
cnf(c_0_161,hypothesis,
sum(b,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_35,c_0_148]) ).
cnf(c_0_162,hypothesis,
sum(a,additive_identity,add(additive_identity,a)),
inference(spm,[status(thm)],[c_0_35,c_0_116]) ).
cnf(c_0_163,hypothesis,
( sum(X1,additive_identity,additive_identity)
| ~ sum(X1,add(additive_identity,a),a) ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_164,hypothesis,
( sum(a,X1,a)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_35,c_0_151]) ).
cnf(c_0_165,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_152,c_0_153]),c_0_117])]),c_0_26]) ).
cnf(c_0_166,hypothesis,
( sum(a,b,a)
| ~ sum(additive_identity,b,additive_identity) ),
inference(spm,[status(thm)],[c_0_154,c_0_145]) ).
cnf(c_0_167,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_155,c_0_90]) ).
cnf(c_0_168,negated_conjecture,
( product(b,X1,b)
| ~ product(X1,b,a) ),
inference(spm,[status(thm)],[c_0_37,c_0_156]) ).
cnf(c_0_169,hypothesis,
product(multiplicative_identity,b,a),
inference(spm,[status(thm)],[c_0_37,c_0_157]) ).
cnf(c_0_170,hypothesis,
( sum(X1,additive_identity,b)
| ~ sum(additive_identity,b,additive_identity)
| ~ sum(b,b,X1) ),
inference(spm,[status(thm)],[c_0_128,c_0_158]) ).
cnf(c_0_171,hypothesis,
sum(additive_identity,additive_identity,b),
inference(spm,[status(thm)],[c_0_159,c_0_148]) ).
cnf(c_0_172,hypothesis,
( sum(X1,additive_identity,additive_identity)
| ~ sum(b,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_173,hypothesis,
( sum(X1,additive_identity,add(additive_identity,a))
| ~ sum(a,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_160,c_0_162]) ).
cnf(c_0_174,hypothesis,
~ sum(add(additive_identity,a),additive_identity,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_165]) ).
cnf(c_0_175,hypothesis,
( sum(X1,additive_identity,a)
| ~ sum(additive_identity,b,additive_identity)
| ~ sum(a,b,X1) ),
inference(spm,[status(thm)],[c_0_128,c_0_166]) ).
cnf(c_0_176,negated_conjecture,
( sum(X1,b,b)
| ~ product(X2,multiplicative_identity,X1)
| ~ sum(X2,b,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_169])]) ).
cnf(c_0_177,hypothesis,
( sum(X1,additive_identity,b)
| ~ sum(b,b,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_148])]) ).
cnf(c_0_178,hypothesis,
( sum(X1,b,a)
| ~ sum(X1,additive_identity,a) ),
inference(spm,[status(thm)],[c_0_120,c_0_171]) ).
cnf(c_0_179,hypothesis,
~ sum(a,additive_identity,b),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_174]) ).
cnf(c_0_180,hypothesis,
( sum(X1,additive_identity,a)
| ~ sum(a,b,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_175,c_0_148])]) ).
cnf(c_0_181,hypothesis,
( sum(X1,b,b)
| ~ product(b,multiplicative_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_137]),c_0_161])]) ).
cnf(c_0_182,hypothesis,
~ sum(b,additive_identity,a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_179]) ).
cnf(c_0_183,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_157])]),c_0_182]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD026-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 00:48:58 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 7.67/7.73 % Version : CSE_E---1.5
% 7.67/7.73 % Problem : theBenchmark.p
% 7.67/7.73 % Proof found
% 7.67/7.73 % SZS status Theorem for theBenchmark.p
% 7.67/7.73 % SZS output start Proof
% See solution above
% 7.67/7.75 % Total time : 7.160000 s
% 7.67/7.75 % SZS output end Proof
% 7.67/7.75 % Total time : 7.164000 s
%------------------------------------------------------------------------------