TSTP Solution File: BOO014-1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : BOO014-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% 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 : 600s
% DateTime : Thu Jul 14 23:48:56 EDT 2022
% Result : Unsatisfiable 7.86s 8.01s
% Output : Refutation 7.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of clauses : 42 ( 36 unt; 0 nHn; 28 RR)
% Number of literals : 62 ( 7 equ; 23 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 54 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(closure_of_addition,axiom,
sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
cnf(closure_of_multiplication,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_multiplication) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X,X),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_identity1) ).
cnf(distributivity1,axiom,
( ~ product(X,Y,Z)
| ~ product(X,U,V)
| ~ sum(Y,U,W)
| ~ product(X,W,X1)
| sum(Z,V,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity1) ).
cnf(distributivity2,axiom,
( ~ product(X,Y,Z)
| ~ product(X,U,V)
| ~ sum(Y,U,W)
| ~ sum(Z,V,X1)
| product(X,W,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity2) ).
cnf(distributivity5,axiom,
( ~ sum(X,Y,Z)
| ~ sum(X,U,V)
| ~ product(Y,U,W)
| ~ sum(X,W,X1)
| product(Z,V,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity5) ).
cnf(distributivity6,axiom,
( ~ sum(X,Y,Z)
| ~ sum(X,U,V)
| ~ product(Y,U,W)
| ~ product(Z,V,X1)
| sum(X,W,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity6) ).
cnf(additive_inverse1,axiom,
sum(inverse(X),X,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_inverse1) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X),X,additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse1) ).
cnf(addition_is_well_defined,axiom,
( ~ sum(X,Y,Z)
| ~ sum(X,Y,U)
| Z = U ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',addition_is_well_defined) ).
cnf(multiplication_is_well_defined,axiom,
( ~ product(X,Y,Z)
| ~ product(X,Y,U)
| Z = U ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplication_is_well_defined) ).
cnf(x_plus_y,negated_conjecture,
sum(x,y,x_plus_y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_plus_y) ).
cnf(x_inverse_times_y_inverse,negated_conjecture,
product(inverse(x),inverse(y),x_inverse_times_y_inverse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_inverse_times_y_inverse) ).
cnf(prove_equation,negated_conjecture,
inverse(x_plus_y) != x_inverse_times_y_inverse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
cnf(18,plain,
X = add(additive_identity,X),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,additive_identity1,closure_of_addition]) ).
cnf(20,plain,
~ sum(additive_identity,inverse(x_plus_y),x_inverse_times_y_inverse),
inference('UR-RESOLVE',[status(thm)],[addition_is_well_defined,additive_identity1,prove_equation]) ).
cnf(23,plain,
X = multiply(multiplicative_identity,X),
inference('HYPERRESOLVE',[status(thm)],[multiplication_is_well_defined,multiplicative_identity1,closure_of_multiplication]) ).
cnf(30,plain,
sum(additive_identity,multiply(X,additive_identity),additive_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,multiplicative_inverse1,closure_of_multiplication,additive_identity1,multiplicative_inverse1]) ).
cnf(56,plain,
sum(x_inverse_times_y_inverse,inverse(x),multiply(inverse(x),add(inverse(y),multiplicative_identity))),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,x_inverse_times_y_inverse,multiplicative_identity1,closure_of_addition,closure_of_multiplication]) ).
cnf(58,plain,
sum(x_inverse_times_y_inverse,inverse(y),multiply(inverse(y),add(inverse(x),multiplicative_identity))),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,x_inverse_times_y_inverse,multiplicative_identity1,closure_of_addition,closure_of_multiplication]) ).
cnf(116,plain,
product(x_plus_y,x,add(x,multiply(y,additive_identity))),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,x_plus_y,additive_identity1,closure_of_multiplication,closure_of_addition]) ).
cnf(118,plain,
product(x_plus_y,y,add(y,multiply(x,additive_identity))),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,x_plus_y,additive_identity1,closure_of_multiplication,closure_of_addition]) ).
cnf(133,plain,
product(X,add(X,Y),add(X,multiply(additive_identity,Y))),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,additive_identity1,closure_of_addition,closure_of_multiplication,closure_of_addition]) ).
cnf(238,plain,
product(X,additive_identity,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,30,additive_identity1,additive_identity1,closure_of_multiplication]) ).
cnf(239,plain,
additive_identity = multiply(X,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,30,additive_identity1]) ).
cnf(240,plain,
product(X,add(X,Y),X),
inference('REWRITE',[status(thm)],[133,18,239,theory(equality)]) ).
cnf(242,plain,
product(x_plus_y,y,y),
inference('REWRITE',[status(thm)],[118,18,239,theory(equality)]) ).
cnf(244,plain,
product(x_plus_y,x,x),
inference('REWRITE',[status(thm)],[116,18,239,theory(equality)]) ).
cnf(258,plain,
product(add(x_plus_y,inverse(y)),multiplicative_identity,multiplicative_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,242,closure_of_addition,additive_inverse1,additive_inverse1]) ).
cnf(290,plain,
product(add(x_plus_y,inverse(x)),multiplicative_identity,multiplicative_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,244,closure_of_addition,additive_inverse1,additive_inverse1]) ).
cnf(445,plain,
multiplicative_identity = add(X,multiplicative_identity),
inference('HYPERRESOLVE',[status(thm)],[multiplication_is_well_defined,240,multiplicative_identity1]) ).
cnf(448,plain,
sum(x_inverse_times_y_inverse,inverse(y),inverse(y)),
inference('REWRITE',[status(thm)],[58,23,445,theory(equality)]) ).
cnf(450,plain,
sum(x_inverse_times_y_inverse,inverse(x),inverse(x)),
inference('REWRITE',[status(thm)],[56,23,445,theory(equality)]) ).
cnf(528,plain,
sum(multiply(y,x_inverse_times_y_inverse),additive_identity,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,448,closure_of_multiplication,multiplicative_inverse1,multiplicative_inverse1]) ).
cnf(566,plain,
sum(multiply(x,x_inverse_times_y_inverse),additive_identity,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,450,closure_of_multiplication,multiplicative_inverse1,multiplicative_inverse1]) ).
cnf(701,plain,
product(y,x_inverse_times_y_inverse,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity2,528,closure_of_multiplication,238,additive_identity1]) ).
cnf(754,plain,
product(x_inverse_times_y_inverse,x_plus_y,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity2,566,closure_of_multiplication,701,x_plus_y]) ).
cnf(811,plain,
~ product(add(x_inverse_times_y_inverse,inverse(x_plus_y)),multiplicative_identity,x_inverse_times_y_inverse),
inference('UR-RESOLVE',[status(thm)],[distributivity6,754,closure_of_addition,additive_inverse1,20]) ).
cnf(2017,plain,
sum(x_plus_y,inverse(y),multiplicative_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,258,multiplicative_identity1,multiplicative_identity1,closure_of_addition]) ).
cnf(2163,plain,
sum(x_plus_y,x_inverse_times_y_inverse,multiplicative_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity6,290,closure_of_addition,2017,x_inverse_times_y_inverse]) ).
cnf(2235,plain,
$false,
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[distributivity5,2163,closure_of_addition,multiplicative_inverse1,additive_identity1]),811]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : BOO014-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.10/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n020.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 : 600
% 0.13/0.34 % DateTime : Wed Jun 1 23:09:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.45 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46 *
% 0.20/0.46 *
% 0.20/0.47 #<PACKAGE "SNARK-USER">
% 0.20/0.47 *
% 0.20/0.47 SNARK-TPTP-OPTIONS
% 0.20/0.47 *
% 0.20/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.47 (USE-FACTORING :POS)
% 0.20/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.47 *
% 0.20/0.47 "."
% 0.20/0.47 *
% 0.20/0.47 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-01T23:09:38
% 0.20/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n020.cluster.edu at 2022-06-01T23:09:38
% 0.20/0.48
% 0.20/0.48 ; Recognized relation function assertion (|sum| ?X ?Y (|add| ?X ?Y)).
% 0.20/0.48 ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.20/0.48 ; Recognized commutativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (|sum| ?Y ?X ?Z)).
% 0.20/0.48 ; Recognized commutativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (|product| ?Y ?X ?Z)).
% 0.20/0.48 ; Recognized possible left identity assertion (|sum| |additive_identity| ?X ?X).
% 0.20/0.48 ; Recognized possible right identity assertion (|sum| ?X |additive_identity| ?X).
% 0.20/0.48 ; Recognized possible left identity assertion (|product| |multiplicative_identity| ?X ?X).
% 0.20/0.48 ; Recognized possible right identity assertion (|product| ?X |multiplicative_identity| ?X).
% 0.20/0.48 ; Recognized possible left inverse assertion (|sum| (|inverse| ?X) ?X |multiplicative_identity|).
% 0.20/0.48 ; Recognized possible right inverse assertion (|sum| ?X (|inverse| ?X) |multiplicative_identity|).
% 0.20/0.48 ; Recognized possible left inverse assertion (|product| (|inverse| ?X) ?X |additive_identity|).
% 0.20/0.48 ; Recognized possible right inverse assertion (|product| ?X (|inverse| ?X) |additive_identity|).
% 0.20/0.48 ; Recognized relation functionality assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?X ?Y ?U)) (= ?Z ?U)).
% 0.20/0.48 ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.20/0.48 ; Declaring sum to be commutative.
% 0.20/0.48 ; Declaring add to be commutative.
% 0.20/0.48 ; Declaring product to be commutative.
% 7.86/8.01 ; Declaring multiply to be commutative.
% 7.86/8.01
% 7.86/8.01 #||
% 7.86/8.01 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.86/8.01 % SZS output start Refutation
% See solution above
% 7.86/8.01 ||#
% 7.86/8.01
% 7.86/8.01 ; Summary of computation:
% 7.86/8.01 ; 215056 formulas have been input or derived (from 126 formulas).
% 7.86/8.01 ; 2235 ( 1%) were retained. Of these,
% 7.86/8.01 ; 757 (34%) were simplified or subsumed later,
% 7.86/8.01 ; 1478 (66%) are still being kept.
% 7.86/8.01 ;
% 7.86/8.01 ; Run time in seconds excluding printing time:
% 7.86/8.01 ; 0.006 0% Read assertion file (1 call)
% 7.86/8.01 ; 0.001 0% Assert (25 calls)
% 7.86/8.01 ; 0.307 4% Process new row (116,020 calls)
% 7.86/8.01 ; 5.669 75% Resolution (250 calls)
% 7.86/8.01 ; 0.002 0% Paramodulation (125 calls)
% 7.86/8.01 ; 0.005 0% Condensing (10 calls)
% 7.86/8.01 ; 0.000 0% Forward subsumption (10 calls)
% 7.86/8.01 ; 0.000 0% Backward subsumption (6 calls)
% 7.86/8.01 ; 0.001 0% Clause clause subsumption (4 calls)
% 7.86/8.01 ; 1.177 16% Forward simplification (94,598 calls)
% 7.86/8.01 ; 0.050 1% Backward simplification (2,235 calls)
% 7.86/8.01 ; 0.001 0% Ordering (284 calls)
% 7.86/8.01 ; 0.001 0% Sortal reasoning (32 calls)
% 7.86/8.01 ; 0.001 0% Purity testing (1 call)
% 7.86/8.01 ; 0.323 4% Other
% 7.86/8.01 ; 7.544 Total
% 7.86/8.01 ; 7.547 Real time
% 7.86/8.01 ;
% 7.86/8.01 ; Term-hash-array has 3,549 terms in all.
% 7.86/8.01 ; Feature-vector-row-index has 6 entries (6 at peak, 6 added, 0 deleted).
% 7.86/8.01 ; Feature-vector-row-index has 15 nodes (15 at peak, 15 added, 0 deleted).
% 7.86/8.01 ; Retrieved 4 possibly forward subsuming rows in 10 calls.
% 7.86/8.01 ; Retrieved 0 possibly backward subsumed rows in 6 calls.
% 7.86/8.01 ; Path-index has 2,427 entries (2,427 at peak, 3,574 added, 1,147 deleted).
% 7.86/8.01 ; Path-index has 956 nodes (956 at peak, 1,227 added, 271 deleted).
% 7.86/8.01 ; Trie-index has 2,427 entries (2,427 at peak, 3,574 added, 1,147 deleted).
% 7.86/8.01 ; Trie-index has 10,043 nodes (10,043 at peak, 14,245 added, 4,202 deleted).
% 7.86/8.01 ; Retrieved 351,683 generalization terms in 272,336 calls.
% 7.86/8.01 ; Retrieved 3,793 instance terms in 2,228 calls.
% 7.86/8.01 ; Retrieved 7,129,393 unifiable terms in 375,929 calls.
% 7.86/8.01 ;
% 7.86/8.01 ; The agenda of rows to process has 1607 entries:
% 7.86/8.01 ; 503 with value 15 84 with value 19 4 with value 22
% 7.86/8.01 ; 452 with value 16 36 with value 20 12 with value 23
% 7.86/8.01 ; 165 with value 17 58 with value 21 12 with value 24
% 7.86/8.01 ; 281 with value 18
% 7.86/8.01 ; The agenda of rows to give has 1376 entries:
% 7.86/8.01 ; 6 with value (4 10) 132 with value (4 17) 63 with value (4 24)
% 7.86/8.01 ; 6 with value (4 11) 143 with value (4 18) 25 with value (4 25)
% 7.86/8.01 ; 58 with value (4 12) 123 with value (4 19) 8 with value (4 26)
% 7.86/8.01 ; 54 with value (4 13) 134 with value (4 20) 10 with value (4 27)
% 7.86/8.01 ; 109 with value (4 14) 97 with value (4 21) 6 with value (4 28)
% 7.86/8.01 ; 133 with value (4 15) 68 with value (4 22) 7 with value (4 29)
% 7.86/8.01 ; 143 with value (4 16) 47 with value (4 23) 4 with value (4 30)
% 7.86/8.01 Evaluation took:
% 7.86/8.01 7.547 seconds of real time
% 7.86/8.01 7.170785 seconds of user run time
% 7.86/8.01 0.376703 seconds of system run time
% 7.86/8.02 [Run times include 0.35 seconds GC run time.]
% 7.86/8.02 0 calls to %EVAL
% 7.86/8.02 0 page faults and
% 7.86/8.02 588,925,984 bytes consed.
% 7.86/8.02 :PROOF-FOUND
% 7.86/8.02 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-01T23:09:46
% 7.86/8.02 :PROOF-FOUND
% 7.86/8.02 *
%------------------------------------------------------------------------------