TSTP Solution File: BOO015-1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : BOO015-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n022.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 23:48:57 EDT 2022
% Result : Unsatisfiable 76.18s 76.41s
% Output : Refutation 76.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of clauses : 43 ( 37 unt; 0 nHn; 27 RR)
% Number of literals : 63 ( 6 equ; 24 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 : 57 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(closure_of_addition,axiom,
sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
cnf(closure_of_multiplication,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',closure_of_multiplication) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X,X),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X,X),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity6) ).
cnf(additive_inverse1,axiom,
sum(inverse(X),X,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_inverse1) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X),X,additive_identity),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplication_is_well_defined) ).
cnf(x_times_y,negated_conjecture,
product(x,y,x_times_y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_times_y) ).
cnf(x_inverse_plus_y_inverse,negated_conjecture,
sum(inverse(x),inverse(y),x_inverse_plus_y_inverse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_inverse_plus_y_inverse) ).
cnf(prove_equation,negated_conjecture,
inverse(x_times_y) != x_inverse_plus_y_inverse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
cnf(17,plain,
X = add(additive_identity,X),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,additive_identity1,closure_of_addition]) ).
cnf(27,plain,
~ product(multiplicative_identity,inverse(x_times_y),x_inverse_plus_y_inverse),
inference('UR-RESOLVE',[status(thm)],[multiplication_is_well_defined,multiplicative_identity1,prove_equation]) ).
cnf(31,plain,
sum(additive_identity,multiply(X,X),X),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,multiplicative_inverse1,closure_of_multiplication,additive_inverse1,multiplicative_identity1]) ).
cnf(32,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(45,plain,
sum(multiply(X,inverse(Y)),multiply(X,Y),X),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,closure_of_multiplication,closure_of_multiplication,additive_inverse1,multiplicative_identity1]) ).
cnf(109,plain,
product(x_inverse_plus_y_inverse,add(y,inverse(x)),inverse(x)),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,x_inverse_plus_y_inverse,closure_of_addition,multiplicative_inverse1,additive_identity1]) ).
cnf(122,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(131,plain,
product(x_inverse_plus_y_inverse,inverse(x),add(inverse(x),multiply(inverse(y),additive_identity))),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,x_inverse_plus_y_inverse,additive_identity1,closure_of_multiplication,closure_of_addition]) ).
cnf(133,plain,
product(x_inverse_plus_y_inverse,inverse(y),add(inverse(y),multiply(inverse(x),additive_identity))),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,x_inverse_plus_y_inverse,additive_identity1,closure_of_multiplication,closure_of_addition]) ).
cnf(154,plain,
sum(inverse(x),x_times_y,add(y,inverse(x))),
inference('HYPERRESOLVE',[status(thm)],[distributivity6,additive_inverse1,closure_of_addition,x_times_y,multiplicative_identity1]) ).
cnf(279,plain,
product(X,X,X),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,31,additive_identity1,additive_identity1,closure_of_multiplication]) ).
cnf(311,plain,
product(X,additive_identity,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,32,additive_identity1,additive_identity1,closure_of_multiplication]) ).
cnf(312,plain,
additive_identity = multiply(X,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,32,additive_identity1]) ).
cnf(313,plain,
product(x_inverse_plus_y_inverse,inverse(y),inverse(y)),
inference('REWRITE',[status(thm)],[133,17,312,theory(equality)]) ).
cnf(315,plain,
product(x_inverse_plus_y_inverse,inverse(x),inverse(x)),
inference('REWRITE',[status(thm)],[131,17,312,theory(equality)]) ).
cnf(317,plain,
product(X,add(X,Y),X),
inference('REWRITE',[status(thm)],[122,17,312,theory(equality)]) ).
cnf(327,plain,
product(add(y,x_inverse_plus_y_inverse),multiplicative_identity,multiplicative_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,313,closure_of_addition,additive_inverse1,additive_inverse1]) ).
cnf(364,plain,
product(add(x,x_inverse_plus_y_inverse),multiplicative_identity,multiplicative_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,315,closure_of_addition,additive_inverse1,additive_inverse1]) ).
cnf(399,plain,
sum(x_times_y,x,x),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,317,x_times_y,279,closure_of_addition]) ).
cnf(485,plain,
sum(x,multiply(X,x_times_y),x),
inference('HYPERRESOLVE',[status(thm)],[distributivity6,399,closure_of_addition,closure_of_multiplication,317]) ).
cnf(683,plain,
sum(y,x_inverse_plus_y_inverse,multiplicative_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,327,multiplicative_identity1,multiplicative_identity1,closure_of_addition]) ).
cnf(720,plain,
sum(x_inverse_plus_y_inverse,x_times_y,multiplicative_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity6,364,closure_of_addition,683,x_times_y]) ).
cnf(758,plain,
~ product(inverse(x_times_y),x_inverse_plus_y_inverse,x_inverse_plus_y_inverse),
inference('UR-RESOLVE',[status(thm)],[distributivity2,720,multiplicative_inverse1,additive_identity1,27]) ).
cnf(1577,plain,
sum(inverse(x),multiply(x_inverse_plus_y_inverse,x_times_y),inverse(x)),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,154,315,closure_of_multiplication,109]) ).
cnf(2292,plain,
sum(multiply(x_inverse_plus_y_inverse,x_times_y),additive_identity,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity6,1577,485,multiplicative_inverse1,multiplicative_inverse1]) ).
cnf(2596,plain,
~ product(x_inverse_plus_y_inverse,additive_identity,multiply(x_inverse_plus_y_inverse,x_times_y)),
inference('UR-RESOLVE',[status(thm)],[distributivity2,45,closure_of_multiplication,additive_identity1,758]) ).
cnf(9077,plain,
additive_identity = multiply(x_inverse_plus_y_inverse,x_times_y),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,2292,additive_identity1]) ).
cnf(9100,plain,
$false,
inference('REWRITE',[status(thm)],[2596,311,9077,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : BOO015-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.09/0.15 % Command : run-snark %s %d
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Wed Jun 1 18:56:52 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.21/0.48 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.49 *
% 0.21/0.49 *
% 0.21/0.50 #<PACKAGE "SNARK-USER">
% 0.21/0.50 *
% 0.21/0.50 SNARK-TPTP-OPTIONS
% 0.21/0.50 *
% 0.21/0.50 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.50 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.50 (USE-FACTORING :POS)
% 0.21/0.50 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.50 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.50 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.50 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.50 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.50 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.50 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.50 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.50 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.50 (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.50 *
% 0.21/0.50 "."
% 0.21/0.50 *
% 0.21/0.50 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-01T18:56:52
% 0.21/0.50 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n022.cluster.edu at 2022-06-01T18:56:52
% 0.21/0.52
% 0.21/0.52 ; Recognized relation function assertion (|sum| ?X ?Y (|add| ?X ?Y)).
% 0.21/0.52 ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.21/0.52 ; Recognized commutativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (|sum| ?Y ?X ?Z)).
% 0.21/0.52 ; Recognized commutativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (|product| ?Y ?X ?Z)).
% 0.21/0.52 ; Recognized possible left identity assertion (|sum| |additive_identity| ?X ?X).
% 0.21/0.52 ; Recognized possible right identity assertion (|sum| ?X |additive_identity| ?X).
% 0.21/0.52 ; Recognized possible left identity assertion (|product| |multiplicative_identity| ?X ?X).
% 0.21/0.52 ; Recognized possible right identity assertion (|product| ?X |multiplicative_identity| ?X).
% 0.21/0.52 ; Recognized possible left inverse assertion (|sum| (|inverse| ?X) ?X |multiplicative_identity|).
% 0.21/0.52 ; Recognized possible right inverse assertion (|sum| ?X (|inverse| ?X) |multiplicative_identity|).
% 0.21/0.52 ; Recognized possible left inverse assertion (|product| (|inverse| ?X) ?X |additive_identity|).
% 0.21/0.52 ; Recognized possible right inverse assertion (|product| ?X (|inverse| ?X) |additive_identity|).
% 0.21/0.52 ; Recognized relation functionality assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?X ?Y ?U)) (= ?Z ?U)).
% 0.21/0.52 ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.21/0.52 ; Declaring sum to be commutative.
% 0.21/0.52 ; Declaring add to be commutative.
% 0.21/0.52 ; Declaring product to be commutative.
% 76.18/76.41 ; Declaring multiply to be commutative.
% 76.18/76.41
% 76.18/76.41 #||
% 76.18/76.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 76.18/76.41 % SZS output start Refutation
% See solution above
% 76.18/76.41 ||#
% 76.18/76.41
% 76.18/76.41 ; Summary of computation:
% 76.18/76.41 ; 1000859 formulas have been input or derived (from 253 formulas).
% 76.18/76.41 ; 9100 ( 1%) were retained. Of these,
% 76.18/76.41 ; 2693 (30%) were simplified or subsumed later,
% 76.18/76.41 ; 6407 (70%) are still being kept.
% 76.18/76.41 ;
% 76.18/76.41 ; Run time in seconds excluding printing time:
% 76.18/76.41 ; 0.006 0% Read assertion file (1 call)
% 76.18/76.41 ; 0.001 0% Assert (25 calls)
% 76.18/76.41 ; 2.211 3% Process new row (691,281 calls)
% 76.18/76.41 ; 55.394 73% Resolution (504 calls)
% 76.18/76.41 ; 0.023 0% Paramodulation (252 calls)
% 76.18/76.41 ; 0.005 0% Condensing (10 calls)
% 76.18/76.41 ; 0.000 0% Forward subsumption (10 calls)
% 76.18/76.41 ; 0.000 0% Backward subsumption (6 calls)
% 76.18/76.41 ; 0.001 0% Clause clause subsumption (4 calls)
% 76.18/76.41 ; 15.897 21% Forward simplification (633,916 calls)
% 76.18/76.41 ; 0.431 1% Backward simplification (9,100 calls)
% 76.18/76.41 ; 0.002 0% Ordering (801 calls)
% 76.18/76.41 ; 0.000 0% Sortal reasoning (32 calls)
% 76.18/76.41 ; 0.000 0% Purity testing (1 call)
% 76.18/76.41 ; 1.923 3% Other
% 76.18/76.41 ; 75.894 Total
% 76.18/76.41 ; 75.909 Real time
% 76.18/76.41 ;
% 76.18/76.41 ; Term-hash-array has 15,167 terms in all.
% 76.18/76.41 ; Feature-vector-row-index has 6 entries (6 at peak, 6 added, 0 deleted).
% 76.18/76.41 ; Feature-vector-row-index has 15 nodes (15 at peak, 15 added, 0 deleted).
% 76.18/76.41 ; Retrieved 4 possibly forward subsuming rows in 10 calls.
% 76.18/76.41 ; Retrieved 0 possibly backward subsumed rows in 6 calls.
% 76.18/76.41 ; Path-index has 11,298 entries (11,996 at peak, 15,279 added, 3,981 deleted).
% 76.18/76.41 ; Path-index has 2,679 nodes (2,727 at peak, 3,210 added, 531 deleted).
% 76.18/76.41 ; Trie-index has 11,298 entries (11,996 at peak, 15,279 added, 3,981 deleted).
% 76.18/76.41 ; Trie-index has 62,913 nodes (66,410 at peak, 79,832 added, 16,919 deleted).
% 76.18/76.41 ; Retrieved 3,490,697 generalization terms in 2,527,074 calls.
% 76.18/76.41 ; Retrieved 23,696 instance terms in 9,093 calls.
% 76.18/76.41 ; Retrieved 77,893,679 unifiable terms in 1,274,356 calls.
% 76.18/76.41 ;
% 76.18/76.41 ; The agenda of backward simplifiable rows to process has 342 entries:
% 76.18/76.41 ; 342 with value 0
% 76.18/76.41 ; The agenda of rows to process has 12009 entries:
% 76.18/76.41 ; 535 with value 13 976 with value 21 161 with value 28
% 76.18/76.41 ; 710 with value 14 634 with value 22 52 with value 29
% 76.18/76.41 ; 1055 with value 15 428 with value 23 38 with value 30
% 76.18/76.41 ; 1873 with value 16 471 with value 24 14 with value 31
% 76.18/76.41 ; 1221 with value 17 312 with value 25 16 with value 32
% 76.18/76.41 ; 1121 with value 18 196 with value 26 36 with value 33
% 76.18/76.41 ; 1419 with value 19 177 with value 27 12 with value 34
% 76.18/76.41 ; 552 with value 20
% 76.18/76.41 ; The agenda of rows to give has 6209 entries:
% 76.18/76.41 ; 2 with value (4 10) 483 with value (4 21) 138 with value (4 32)
% 76.18/76.41 ; 6 with value (4 11) 481 with value (4 22) 115 with value (4 33)
% 76.18/76.41 ; 3 with value (4 12) 387 with value (4 23) 70 with value (4 34)
% 76.18/76.41 ; 38 with value (4 13) 435 with value (4 24) 65 with value (4 35)
% 76.18/76.41 ; 155 with value (4 14) 450 with value (4 25) 35 with value (4 36)
% 76.18/76.41 ; 184 with value (4 15) 303 with value (4 26) 50 with value (4 37)
% 76.18/76.41 ; 197 with value (4 16) 310 with value (4 27) 15 with value (4 38)
% 76.18/76.41 ; 267 with value (4 17) 263 with value (4 28) 6 with value (4 39)
% 76.18/76.41 ; 308 with value (4 18) 239 with value (4 29) 1 with value (4 40)
% 76.18/76.41 ; 378 with value (4 19) 212 with value (4 30) 2 with value (4 42)
% 76.18/76.41 ; 435 with value (4 20) 174 with value (4 31) 2 with value (4 43)
% 76.18/76.41 Evaluation took:
% 76.18/76.41 75.91 seconds of real time
% 76.18/76.41 73.089554 seconds of user run time
% 76.18/76.41 2.808898 seconds of system run time
% 76.18/76.41 [Run times include 5.871 seconds GC run time.]
% 76.18/76.41 0 calls to %EVAL
% 76.18/76.41 0 page faults and
% 76.18/76.41 4,444,147,000 bytes consed.
% 76.18/76.41 :PROOF-FOUND
% 76.18/76.41 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-01T18:58:08
% 76.18/76.41 :PROOF-FOUND
% 76.18/76.41 *
%------------------------------------------------------------------------------