TSTP Solution File: FLD001-3 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD001-3 : 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 : n002.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 22:27:11 EDT 2023
% Result : Unsatisfiable 1.72s 1.79s
% Output : CNFRefutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 32
% Syntax : Number of formulae : 108 ( 39 unt; 12 typ; 0 def)
% Number of atoms : 196 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 201 ( 101 ~; 100 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 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 : 138 ( 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(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(sum_3,hypothesis,
sum(additive_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_3) ).
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(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
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(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(associativity_multiplication_1,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(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(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(commutativity_multiplication,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
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_additive_inverse,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
cnf(associativity_multiplication_2,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
cnf(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(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(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_4,negated_conjecture,
~ product(multiplicative_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_4) ).
cnf(c_0_20,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_21,hypothesis,
sum(additive_identity,a,b),
sum_3 ).
cnf(c_0_22,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_23,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_24,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_25,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_26,hypothesis,
sum(a,additive_identity,b),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,hypothesis,
sum(additive_identity,a,a),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_24]) ).
cnf(c_0_29,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_30,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_31,hypothesis,
( less_or_equal(X1,b)
| ~ less_or_equal(X2,a)
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,hypothesis,
sum(a,additive_identity,a),
inference(spm,[status(thm)],[c_0_20,c_0_27]) ).
cnf(c_0_33,hypothesis,
less_or_equal(a,a),
inference(spm,[status(thm)],[c_0_28,c_0_23]) ).
cnf(c_0_34,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_35,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1 ).
cnf(c_0_36,hypothesis,
product(multiplicative_identity,b,b),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_multiplication ).
cnf(c_0_38,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_39,hypothesis,
less_or_equal(a,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_40,hypothesis,
( less_or_equal(X1,a)
| ~ less_or_equal(X2,additive_identity)
| ~ sum(X2,a,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_27]) ).
cnf(c_0_41,plain,
less_or_equal(additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_28,c_0_34]) ).
cnf(c_0_42,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_43,hypothesis,
product(multiplicative_identity,a,a),
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_44,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_45,hypothesis,
( product(X1,X2,b)
| ~ product(X3,b,X2)
| ~ product(X1,X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_46,hypothesis,
( product(X1,a,multiply(X1,a))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_23]) ).
cnf(c_0_47,hypothesis,
( sum(additive_identity,b,a)
| ~ less_or_equal(b,a) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,hypothesis,
less_or_equal(b,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_21]),c_0_41])]) ).
cnf(c_0_49,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_50,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
associativity_multiplication_2 ).
cnf(c_0_51,hypothesis,
product(a,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_52,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_29,c_0_44]) ).
cnf(c_0_53,hypothesis,
( product(X1,b,b)
| ~ product(X1,multiplicative_identity,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_45,c_0_36]) ).
cnf(c_0_54,hypothesis,
product(multiplicative_identity,a,multiply(multiplicative_identity,a)),
inference(spm,[status(thm)],[c_0_46,c_0_44]) ).
cnf(c_0_55,hypothesis,
sum(additive_identity,b,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
cnf(c_0_56,plain,
( sum(additive_identity,additive_inverse(X1),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_49]) ).
cnf(c_0_57,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1 ).
cnf(c_0_58,hypothesis,
sum(additive_identity,b,b),
inference(spm,[status(thm)],[c_0_22,c_0_30]) ).
cnf(c_0_59,plain,
( product(multiplicative_identity,additive_inverse(X1),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_49]) ).
cnf(c_0_60,hypothesis,
( product(X1,multiplicative_identity,X2)
| ~ product(X3,a,X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_61,plain,
( product(X1,multiplicative_identity,X2)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X3,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_52]) ).
cnf(c_0_62,hypothesis,
( product(b,X1,b)
| ~ product(X1,multiplicative_identity,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_42,c_0_53]) ).
cnf(c_0_63,hypothesis,
product(a,multiplicative_identity,multiply(multiplicative_identity,a)),
inference(spm,[status(thm)],[c_0_42,c_0_54]) ).
cnf(c_0_64,hypothesis,
sum(b,additive_identity,a),
inference(spm,[status(thm)],[c_0_20,c_0_55]) ).
cnf(c_0_65,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_56,c_0_34]) ).
cnf(c_0_66,hypothesis,
( sum(X1,X2,b)
| ~ sum(X3,b,X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_67,plain,
product(multiplicative_identity,additive_inverse(additive_identity),additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_59,c_0_34]) ).
cnf(c_0_68,hypothesis,
( sum(X1,X2,b)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_57,c_0_26]) ).
cnf(c_0_69,hypothesis,
product(b,multiplicative_identity,b),
inference(spm,[status(thm)],[c_0_42,c_0_36]) ).
cnf(c_0_70,hypothesis,
( product(X1,multiplicative_identity,a)
| ~ product(multiplicative_identity,a,X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_43]) ).
cnf(c_0_71,hypothesis,
( product(X1,multiplicative_identity,b)
| ~ product(b,multiplicative_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_52])]) ).
cnf(c_0_72,hypothesis,
( product(X1,multiplicative_identity,multiply(multiplicative_identity,a))
| ~ product(a,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_63]) ).
cnf(c_0_73,hypothesis,
( sum(X1,X2,a)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X1,X3,b) ),
inference(spm,[status(thm)],[c_0_57,c_0_64]) ).
cnf(c_0_74,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_20,c_0_65]) ).
cnf(c_0_75,hypothesis,
( sum(X1,a,b)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_66,c_0_55]) ).
cnf(c_0_76,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_77,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_78,plain,
product(additive_inverse(additive_identity),multiplicative_identity,additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_42,c_0_67]) ).
cnf(c_0_79,hypothesis,
( sum(X1,a,b)
| ~ sum(X1,a,a) ),
inference(spm,[status(thm)],[c_0_68,c_0_32]) ).
cnf(c_0_80,hypothesis,
( product(X1,X2,b)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X1,X3,b) ),
inference(spm,[status(thm)],[c_0_35,c_0_69]) ).
cnf(c_0_81,hypothesis,
product(multiply(multiplicative_identity,a),multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_70,c_0_54]) ).
cnf(c_0_82,hypothesis,
( product(multiply(multiplicative_identity,a),multiplicative_identity,b)
| ~ product(a,multiplicative_identity,b) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_83,hypothesis,
( sum(X1,additive_inverse(additive_identity),a)
| ~ sum(X1,additive_inverse(additive_identity),b) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_84,hypothesis,
( sum(a,X1,b)
| ~ sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_20,c_0_75]) ).
cnf(c_0_85,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_76,c_0_34]) ).
cnf(c_0_86,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_77,c_0_78]) ).
cnf(c_0_87,hypothesis,
( sum(a,X1,b)
| ~ sum(X1,a,a) ),
inference(spm,[status(thm)],[c_0_20,c_0_79]) ).
cnf(c_0_88,hypothesis,
( product(X1,a,b)
| ~ product(X1,multiply(multiplicative_identity,a),b) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_89,hypothesis,
( product(multiplicative_identity,multiply(multiplicative_identity,a),b)
| ~ product(a,multiplicative_identity,b) ),
inference(spm,[status(thm)],[c_0_42,c_0_82]) ).
cnf(c_0_90,negated_conjecture,
~ product(multiplicative_identity,a,b),
not_product_4 ).
cnf(c_0_91,hypothesis,
sum(a,additive_inverse(additive_identity),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85])]) ).
cnf(c_0_92,hypothesis,
( product(X1,multiplicative_identity,b)
| ~ product(X2,multiplicative_identity,a)
| ~ sum(X2,additive_inverse(additive_identity),X1)
| ~ sum(additive_inverse(additive_identity),a,a) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_93,hypothesis,
~ product(a,multiplicative_identity,b),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]) ).
cnf(c_0_94,hypothesis,
sum(additive_inverse(additive_identity),a,a),
inference(spm,[status(thm)],[c_0_20,c_0_91]) ).
cnf(c_0_95,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_92,c_0_93,c_0_94,c_0_91,c_0_51]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : FLD001-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n002.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 : Sun Aug 27 23:46:34 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 1.72/1.79 % Version : CSE_E---1.5
% 1.72/1.79 % Problem : theBenchmark.p
% 1.72/1.79 % Proof found
% 1.72/1.79 % SZS status Theorem for theBenchmark.p
% 1.72/1.79 % SZS output start Proof
% See solution above
% 1.72/1.80 % Total time : 1.214000 s
% 1.72/1.80 % SZS output end Proof
% 1.72/1.80 % Total time : 1.218000 s
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