TSTP Solution File: FLD012-4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD012-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n020.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 22:27:16 EDT 2023
% Result : Unsatisfiable 0.65s 0.86s
% Output : CNFRefutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 42
% Syntax : Number of formulae : 149 ( 47 unt; 14 typ; 0 def)
% Number of atoms : 308 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 342 ( 169 ~; 173 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 217 ( 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 ).
tff(decl_34,type,
u: $i ).
tff(decl_35,type,
v: $i ).
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
% 0.11/0.12 % Problem : FLD012-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 00:07:14 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.56 start to proof: theBenchmark
% 0.65/0.86 % Version : CSE_E---1.5
% 0.65/0.86 % Problem : theBenchmark.p
% 0.65/0.86 % Proof found
% 0.65/0.86 % SZS status Theorem for theBenchmark.p
% 0.65/0.86 % SZS output start Proof
% See solution above
% 0.83/0.87 % Total time : 0.297000 s
% 0.83/0.87 % SZS output end Proof
% 0.83/0.87 % Total time : 0.301000 s
%------------------------------------------------------------------------------