TSTP Solution File: NUM017-2 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM017-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n018.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 : Thu Aug 31 10:26:10 EDT 2023
% Result : Unsatisfiable 7.31s 7.43s
% Output : CNFRefutation 7.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 23
% Syntax : Number of formulae : 100 ( 23 unt; 10 typ; 0 def)
% Number of atoms : 192 ( 22 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 218 ( 116 ~; 102 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 5 >; 5 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 179 ( 13 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
multiply: ( $i * $i ) > $i ).
tff(decl_23,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_24,type,
divides: ( $i * $i ) > $o ).
tff(decl_25,type,
second_divided_by_1st: ( $i * $i ) > $i ).
tff(decl_26,type,
prime: $i > $o ).
tff(decl_27,type,
a: $i ).
tff(decl_28,type,
b: $i ).
tff(decl_29,type,
d: $i ).
tff(decl_30,type,
c: $i ).
tff(decl_31,type,
e: $i ).
cnf(product_associativity2,axiom,
( product(X6,X5,X3)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ product(X6,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_associativity2) ).
cnf(c_squared,hypothesis,
product(c,c,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_squared) ).
cnf(product_commutativity,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_commutativity) ).
cnf(divides_implies_product,axiom,
( product(X1,second_divided_by_1st(X1,X2),X2)
| ~ divides(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divides_implies_product) ).
cnf(product_left_cancellation,axiom,
( X2 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(closure_of_product,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_product) ).
cnf(product_divisible_by_operand,axiom,
( divides(X1,X3)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_divisible_by_operand) ).
cnf(transitivity_of_divides,axiom,
( divides(X3,X2)
| ~ divides(X1,X2)
| ~ divides(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_divides) ).
cnf(well_defined_product,axiom,
( X4 = X3
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_defined_product) ).
cnf(prove_there_is_no_common_divisor,negated_conjecture,
( ~ divides(X1,c)
| ~ divides(X1,b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_no_common_divisor) ).
cnf(product_associativity1,axiom,
( product(X6,X5,X3)
| ~ product(X1,X2,X3)
| ~ product(X4,X5,X2)
| ~ product(X1,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_associativity1) ).
cnf(primes_lemma1,axiom,
( divides(X1,X3)
| ~ divides(X1,X2)
| ~ product(X3,X3,X2)
| ~ prime(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',primes_lemma1) ).
cnf(a_is_prime,hypothesis,
prime(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_prime) ).
cnf(c_0_13,axiom,
( product(X6,X5,X3)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ product(X6,X4,X1) ),
product_associativity2 ).
cnf(c_0_14,hypothesis,
product(c,c,e),
c_squared ).
cnf(c_0_15,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
product_commutativity ).
cnf(c_0_16,axiom,
( product(X1,second_divided_by_1st(X1,X2),X2)
| ~ divides(X1,X2) ),
divides_implies_product ).
cnf(c_0_17,axiom,
( X2 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_left_cancellation ).
cnf(c_0_18,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_product ).
cnf(c_0_19,axiom,
( divides(X1,X3)
| ~ product(X1,X2,X3) ),
product_divisible_by_operand ).
cnf(c_0_20,hypothesis,
( product(c,X1,X2)
| ~ product(c,X3,X1)
| ~ product(e,X3,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,plain,
( product(second_divided_by_1st(X1,X2),X1,X2)
| ~ divides(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( X1 = X2
| ~ product(X3,X1,multiply(X3,X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
divides(X1,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_24,hypothesis,
( X1 = c
| ~ product(c,X1,e) ),
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_25,hypothesis,
( product(c,multiply(c,X1),X2)
| ~ product(e,X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_26,axiom,
( divides(X3,X2)
| ~ divides(X1,X2)
| ~ divides(X3,X1) ),
transitivity_of_divides ).
cnf(c_0_27,plain,
( divides(second_divided_by_1st(X1,X2),X2)
| ~ divides(X1,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_21]) ).
cnf(c_0_28,axiom,
( X4 = X3
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
well_defined_product ).
cnf(c_0_29,plain,
second_divided_by_1st(X1,multiply(X1,X2)) = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_16]),c_0_23])]) ).
cnf(c_0_30,hypothesis,
( multiply(c,X1) = c
| ~ product(e,X1,e) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
( ~ divides(X1,c)
| ~ divides(X1,b) ),
prove_there_is_no_common_divisor ).
cnf(c_0_32,plain,
( divides(second_divided_by_1st(X1,X2),X3)
| ~ divides(X2,X3)
| ~ divides(X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
product(X1,X2,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_34,plain,
( X1 = second_divided_by_1st(X2,X3)
| ~ product(X2,X1,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_16]),c_0_19]) ).
cnf(c_0_35,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_18]) ).
cnf(c_0_36,hypothesis,
( second_divided_by_1st(c,c) = X1
| ~ product(e,X1,e) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,negated_conjecture,
( ~ divides(second_divided_by_1st(X1,X2),b)
| ~ divides(X2,c)
| ~ divides(X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,plain,
divides(X1,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_33]) ).
cnf(c_0_39,axiom,
( product(X6,X5,X3)
| ~ product(X1,X2,X3)
| ~ product(X4,X5,X2)
| ~ product(X1,X4,X6) ),
product_associativity1 ).
cnf(c_0_40,hypothesis,
( multiply(c,X1) = second_divided_by_1st(c,X2)
| ~ product(e,X1,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_25]) ).
cnf(c_0_41,plain,
( multiply(X1,second_divided_by_1st(X1,X2)) = X2
| ~ divides(X1,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_16]) ).
cnf(c_0_42,hypothesis,
( second_divided_by_1st(e,e) = second_divided_by_1st(c,c)
| ~ divides(e,e) ),
inference(spm,[status(thm)],[c_0_36,c_0_16]) ).
cnf(c_0_43,hypothesis,
divides(c,e),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_44,negated_conjecture,
( ~ divides(multiply(X1,X2),c)
| ~ divides(X2,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_29]),c_0_23])]) ).
cnf(c_0_45,hypothesis,
( divides(X1,c)
| ~ product(e,X1,e) ),
inference(spm,[status(thm)],[c_0_38,c_0_30]) ).
cnf(c_0_46,plain,
( product(X1,X2,X3)
| ~ divides(X1,X4)
| ~ product(second_divided_by_1st(X1,X4),X5,X2)
| ~ product(X4,X5,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_47,plain,
( product(X1,X2,X3)
| ~ product(X4,multiply(X5,X2),X3)
| ~ product(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_18]) ).
cnf(c_0_48,hypothesis,
second_divided_by_1st(c,multiply(e,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_40,c_0_18]) ).
cnf(c_0_49,hypothesis,
( multiply(e,second_divided_by_1st(c,c)) = e
| ~ divides(e,e) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_50,hypothesis,
second_divided_by_1st(c,e) = c,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_16]),c_0_43])]) ).
cnf(c_0_51,plain,
( product(X1,second_divided_by_1st(X2,X3),X4)
| ~ divides(X2,X3)
| ~ product(X5,X2,X1)
| ~ product(X5,X3,X4) ),
inference(spm,[status(thm)],[c_0_39,c_0_16]) ).
cnf(c_0_52,hypothesis,
( ~ divides(X1,b)
| ~ product(e,multiply(X2,X1),e) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_53,plain,
( product(X1,multiply(second_divided_by_1st(X1,X2),X3),X4)
| ~ divides(X1,X2)
| ~ product(X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_46,c_0_18]) ).
cnf(c_0_54,plain,
( product(X1,X2,multiply(X3,multiply(X4,X2)))
| ~ product(X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_18]) ).
cnf(c_0_55,hypothesis,
( multiply(c,second_divided_by_1st(c,c)) = c
| ~ divides(e,e) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_56,hypothesis,
( divides(c,c)
| ~ product(e,X1,e) ),
inference(spm,[status(thm)],[c_0_23,c_0_30]) ).
cnf(c_0_57,hypothesis,
( product(e,second_divided_by_1st(c,X1),X2)
| ~ divides(c,X1)
| ~ product(c,X1,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_14]) ).
cnf(c_0_58,hypothesis,
( ~ divides(X1,b)
| ~ divides(e,X2)
| ~ product(X2,X1,e) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,plain,
( multiply(X1,X2) = X2
| ~ product(X3,X1,X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_54]) ).
cnf(c_0_60,hypothesis,
( product(c,second_divided_by_1st(c,c),c)
| ~ divides(e,e) ),
inference(spm,[status(thm)],[c_0_18,c_0_55]) ).
cnf(c_0_61,hypothesis,
( divides(c,c)
| ~ divides(c,X1)
| ~ product(c,X1,e) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_62,hypothesis,
( ~ divides(second_divided_by_1st(X1,e),b)
| ~ divides(e,X1)
| ~ divides(X1,e) ),
inference(spm,[status(thm)],[c_0_58,c_0_16]) ).
cnf(c_0_63,hypothesis,
( multiply(second_divided_by_1st(c,c),X1) = X1
| ~ divides(e,e) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,hypothesis,
( divides(c,c)
| ~ product(c,multiply(c,X1),e) ),
inference(spm,[status(thm)],[c_0_61,c_0_23]) ).
cnf(c_0_65,plain,
( product(X1,multiply(X2,second_divided_by_1st(X1,X3)),X4)
| ~ divides(X1,X3)
| ~ product(X3,X2,X4) ),
inference(spm,[status(thm)],[c_0_46,c_0_33]) ).
cnf(c_0_66,hypothesis,
( ~ divides(second_divided_by_1st(c,c),b)
| ~ divides(e,e) ),
inference(spm,[status(thm)],[c_0_62,c_0_42]) ).
cnf(c_0_67,hypothesis,
( divides(second_divided_by_1st(c,c),X1)
| ~ divides(e,e) ),
inference(spm,[status(thm)],[c_0_23,c_0_63]) ).
cnf(c_0_68,hypothesis,
( divides(c,c)
| ~ divides(c,X1)
| ~ product(X1,c,e) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_69,hypothesis,
( product(c,multiply(X1,c),X2)
| ~ product(e,X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_33]) ).
cnf(c_0_70,hypothesis,
( divides(e,X1)
| ~ divides(c,X2)
| ~ product(c,X2,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_57]) ).
cnf(c_0_71,hypothesis,
~ divides(e,e),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_72,hypothesis,
( divides(c,c)
| ~ product(multiply(X1,c),c,e) ),
inference(spm,[status(thm)],[c_0_68,c_0_38]) ).
cnf(c_0_73,hypothesis,
( product(multiply(X1,c),c,X2)
| ~ product(e,X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_69]) ).
cnf(c_0_74,hypothesis,
~ divides(c,c),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_14]),c_0_71]) ).
cnf(c_0_75,axiom,
( divides(X1,X3)
| ~ divides(X1,X2)
| ~ product(X3,X3,X2)
| ~ prime(X1) ),
primes_lemma1 ).
cnf(c_0_76,hypothesis,
( divides(c,X1)
| ~ divides(e,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_43]) ).
cnf(c_0_77,hypothesis,
~ product(e,X1,e),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_78,plain,
( divides(X1,X2)
| ~ prime(X1)
| ~ divides(X1,multiply(X2,X2)) ),
inference(spm,[status(thm)],[c_0_75,c_0_18]) ).
cnf(c_0_79,hypothesis,
second_divided_by_1st(c,multiply(X1,e)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_40,c_0_33]) ).
cnf(c_0_80,hypothesis,
divides(c,multiply(X1,e)),
inference(spm,[status(thm)],[c_0_76,c_0_38]) ).
cnf(c_0_81,hypothesis,
( ~ divides(c,X1)
| ~ product(c,X1,e) ),
inference(spm,[status(thm)],[c_0_77,c_0_57]) ).
cnf(c_0_82,plain,
( divides(X1,X1)
| ~ prime(X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_23]) ).
cnf(c_0_83,hypothesis,
prime(a),
a_is_prime ).
cnf(c_0_84,hypothesis,
product(c,multiply(c,X1),multiply(X1,e)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_79]),c_0_80])]) ).
cnf(c_0_85,plain,
( multiply(second_divided_by_1st(X1,X1),X2) = X2
| ~ divides(X1,X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_16]) ).
cnf(c_0_86,hypothesis,
~ product(c,multiply(c,X1),e),
inference(spm,[status(thm)],[c_0_81,c_0_23]) ).
cnf(c_0_87,hypothesis,
divides(a,a),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_88,hypothesis,
~ divides(X1,X1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]) ).
cnf(c_0_89,hypothesis,
$false,
inference(sr,[status(thm)],[c_0_87,c_0_88]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM017-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.33 % Computer : n018.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Aug 25 08:53:43 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.18/0.56 start to proof: theBenchmark
% 7.31/7.43 % Version : CSE_E---1.5
% 7.31/7.43 % Problem : theBenchmark.p
% 7.31/7.43 % Proof found
% 7.31/7.43 % SZS status Theorem for theBenchmark.p
% 7.31/7.43 % SZS output start Proof
% See solution above
% 7.31/7.44 % Total time : 6.862000 s
% 7.31/7.44 % SZS output end Proof
% 7.31/7.44 % Total time : 6.865000 s
%------------------------------------------------------------------------------