TSTP Solution File: BOO014-3 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : BOO014-3 : TPTP v8.1.0. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n017.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 6.53s 6.77s
% Output : Refutation 6.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of clauses : 42 ( 35 unt; 0 nHn; 28 RR)
% Number of literals : 66 ( 9 equ; 27 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/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(inverse_is_unique,axiom,
( ~ sum(X,Y,multiplicative_identity)
| ~ sum(X,Z,multiplicative_identity)
| ~ product(X,Y,additive_identity)
| ~ product(X,Z,additive_identity)
| Y = Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_is_unique) ).
cnf(x_plus_y,hypothesis,
sum(x,y,x_plus_y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_plus_y) ).
cnf(x_inverse_times_y_inverse,hypothesis,
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(20,plain,
X = add(additive_identity,X),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,additive_identity1,closure_of_addition]) ).
cnf(25,plain,
X = multiply(multiplicative_identity,X),
inference('HYPERRESOLVE',[status(thm)],[multiplication_is_well_defined,multiplicative_identity1,closure_of_multiplication]) ).
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(54,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(56,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(104,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(106,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(120,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(204,plain,
product(X,additive_identity,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,32,additive_identity1,additive_identity1,closure_of_multiplication]) ).
cnf(205,plain,
additive_identity = multiply(X,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,32,additive_identity1]) ).
cnf(206,plain,
product(X,add(X,Y),X),
inference('REWRITE',[status(thm)],[120,20,205,theory(equality)]) ).
cnf(208,plain,
product(x_plus_y,y,y),
inference('REWRITE',[status(thm)],[106,20,205,theory(equality)]) ).
cnf(210,plain,
product(x_plus_y,x,x),
inference('REWRITE',[status(thm)],[104,20,205,theory(equality)]) ).
cnf(224,plain,
product(add(x_plus_y,inverse(y)),multiplicative_identity,multiplicative_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,208,closure_of_addition,additive_inverse1,additive_inverse1]) ).
cnf(256,plain,
product(add(x_plus_y,inverse(x)),multiplicative_identity,multiplicative_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,210,closure_of_addition,additive_inverse1,additive_inverse1]) ).
cnf(411,plain,
multiplicative_identity = add(X,multiplicative_identity),
inference('HYPERRESOLVE',[status(thm)],[multiplication_is_well_defined,206,multiplicative_identity1]) ).
cnf(414,plain,
sum(x_inverse_times_y_inverse,inverse(y),inverse(y)),
inference('REWRITE',[status(thm)],[56,25,411,theory(equality)]) ).
cnf(416,plain,
sum(x_inverse_times_y_inverse,inverse(x),inverse(x)),
inference('REWRITE',[status(thm)],[54,25,411,theory(equality)]) ).
cnf(492,plain,
sum(multiply(y,x_inverse_times_y_inverse),additive_identity,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,414,closure_of_multiplication,multiplicative_inverse1,multiplicative_inverse1]) ).
cnf(524,plain,
sum(multiply(x,x_inverse_times_y_inverse),additive_identity,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,416,closure_of_multiplication,multiplicative_inverse1,multiplicative_inverse1]) ).
cnf(651,plain,
product(y,x_inverse_times_y_inverse,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity2,492,closure_of_multiplication,204,additive_identity1]) ).
cnf(704,plain,
product(x_inverse_times_y_inverse,x_plus_y,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity2,524,closure_of_multiplication,651,x_plus_y]) ).
cnf(742,plain,
~ sum(x_plus_y,x_inverse_times_y_inverse,multiplicative_identity),
inference('UR-RESOLVE',[status(thm)],[inverse_is_unique,704,additive_inverse1,multiplicative_inverse1,prove_equation]) ).
cnf(919,plain,
~ product(add(x_plus_y,inverse(x)),add(x_plus_y,inverse(y)),multiplicative_identity),
inference('UR-RESOLVE',[status(thm)],[distributivity6,742,closure_of_addition,closure_of_addition,x_inverse_times_y_inverse]) ).
cnf(1936,plain,
multiplicative_identity = add(x_plus_y,inverse(y)),
inference('HYPERRESOLVE',[status(thm)],[multiplication_is_well_defined,224,multiplicative_identity1]) ).
cnf(1938,plain,
$false,
inference('REWRITE',[status(thm)],[919,256,1936,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : BOO014-3 : TPTP v8.1.0. Bugfixed v2.2.0.
% 0.10/0.13 % Command : run-snark %s %d
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jun 1 22:03:42 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.46 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 *
% 0.20/0.47 *
% 0.20/0.48 #<PACKAGE "SNARK-USER">
% 0.20/0.48 *
% 0.20/0.48 SNARK-TPTP-OPTIONS
% 0.20/0.48 *
% 0.20/0.48 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.48 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.48 (USE-FACTORING :POS)
% 0.20/0.48 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.48 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.48 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.48 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.48 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.48 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.48 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.48 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.48 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.48 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.48 *
% 0.20/0.48 "."
% 0.20/0.48 *
% 0.20/0.48 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-01T22:03:42
% 0.20/0.48 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n017.cluster.edu at 2022-06-01T22:03:42
% 0.20/0.50
% 0.20/0.50 ; Recognized relation function assertion (|sum| ?X ?Y (|add| ?X ?Y)).
% 0.20/0.50 ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.20/0.50 ; Recognized commutativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (|sum| ?Y ?X ?Z)).
% 0.20/0.50 ; Recognized commutativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (|product| ?Y ?X ?Z)).
% 0.20/0.50 ; Recognized possible left identity assertion (|sum| |additive_identity| ?X ?X).
% 0.20/0.50 ; Recognized possible right identity assertion (|sum| ?X |additive_identity| ?X).
% 0.20/0.50 ; Recognized possible left identity assertion (|product| |multiplicative_identity| ?X ?X).
% 0.20/0.50 ; Recognized possible right identity assertion (|product| ?X |multiplicative_identity| ?X).
% 0.20/0.50 ; Recognized possible left inverse assertion (|sum| (|inverse| ?X) ?X |multiplicative_identity|).
% 0.20/0.50 ; Recognized possible right inverse assertion (|sum| ?X (|inverse| ?X) |multiplicative_identity|).
% 0.20/0.50 ; Recognized possible left inverse assertion (|product| (|inverse| ?X) ?X |additive_identity|).
% 0.20/0.50 ; Recognized possible right inverse assertion (|product| ?X (|inverse| ?X) |additive_identity|).
% 0.20/0.50 ; Recognized relation functionality assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?X ?Y ?U)) (= ?Z ?U)).
% 0.20/0.50 ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.20/0.50 ; Declaring sum to be commutative.
% 0.20/0.50 ; Declaring add to be commutative.
% 0.20/0.50 ; Declaring product to be commutative.
% 6.53/6.77 ; Declaring multiply to be commutative.
% 6.53/6.77
% 6.53/6.77 #||
% 6.53/6.77 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.53/6.77 % SZS output start Refutation
% See solution above
% 6.53/6.78 ||#
% 6.53/6.78
% 6.53/6.78 ; Summary of computation:
% 6.53/6.78 ; 191457 formulas have been input or derived (from 123 formulas).
% 6.53/6.78 ; 1938 ( 1%) were retained. Of these,
% 6.53/6.78 ; 701 (36%) were simplified or subsumed later,
% 6.53/6.78 ; 1237 (64%) are still being kept.
% 6.53/6.78 ;
% 6.53/6.78 ; Run time in seconds excluding printing time:
% 6.53/6.78 ; 0.006 0% Read assertion file (1 call)
% 6.53/6.78 ; 0.001 0% Assert (27 calls)
% 6.53/6.78 ; 0.278 4% Process new row (100,977 calls)
% 6.53/6.78 ; 4.631 74% Resolution (244 calls)
% 6.53/6.78 ; 0.003 0% Paramodulation (122 calls)
% 6.53/6.78 ; 0.003 0% Condensing (11 calls)
% 6.53/6.78 ; 0.000 0% Forward subsumption (11 calls)
% 6.53/6.78 ; 0.000 0% Backward subsumption (7 calls)
% 6.53/6.78 ; 0.002 0% Clause clause subsumption (6 calls)
% 6.53/6.78 ; 1.056 17% Forward simplification (86,548 calls)
% 6.53/6.78 ; 0.050 1% Backward simplification (1,938 calls)
% 6.53/6.78 ; 0.000 0% Ordering (281 calls)
% 6.53/6.78 ; 0.000 0% Sortal reasoning (32 calls)
% 6.53/6.78 ; 0.000 0% Purity testing (1 call)
% 6.53/6.78 ; 0.261 4% Other
% 6.53/6.78 ; 6.291 Total
% 6.53/6.78 ; 6.295 Real time
% 6.53/6.78 ;
% 6.53/6.78 ; Term-hash-array has 3,138 terms in all.
% 6.53/6.78 ; Feature-vector-row-index has 7 entries (7 at peak, 7 added, 0 deleted).
% 6.53/6.78 ; Feature-vector-row-index has 20 nodes (20 at peak, 20 added, 0 deleted).
% 6.53/6.78 ; Retrieved 6 possibly forward subsuming rows in 11 calls.
% 6.53/6.78 ; Retrieved 0 possibly backward subsumed rows in 7 calls.
% 6.53/6.78 ; Path-index has 2,078 entries (2,090 at peak, 3,163 added, 1,085 deleted).
% 6.53/6.78 ; Path-index has 861 nodes (861 at peak, 1,128 added, 267 deleted).
% 6.53/6.78 ; Trie-index has 2,078 entries (2,090 at peak, 3,163 added, 1,085 deleted).
% 6.53/6.78 ; Trie-index has 8,701 nodes (8,741 at peak, 12,788 added, 4,087 deleted).
% 6.53/6.78 ; Retrieved 321,786 generalization terms in 250,215 calls.
% 6.53/6.78 ; Retrieved 3,318 instance terms in 1,930 calls.
% 6.53/6.78 ; Retrieved 5,883,593 unifiable terms in 339,513 calls.
% 6.53/6.78 ;
% 6.53/6.78 ; The agenda of backward simplifiable rows to process has 4 entries:
% 6.53/6.78 ; 4 with value 0
% 6.53/6.78 ; The agenda of rows to process has 3529 entries:
% 6.53/6.78 ; 248 with value 12 437 with value 19 28 with value 25
% 6.53/6.78 ; 190 with value 13 239 with value 20 28 with value 26
% 6.53/6.78 ; 82 with value 14 204 with value 21 8 with value 27
% 6.53/6.78 ; 257 with value 15 188 with value 22 1 with value 28
% 6.53/6.78 ; 535 with value 16 66 with value 23 8 with value 29
% 6.53/6.78 ; 580 with value 17 59 with value 24 4 with value 30
% 6.53/6.78 ; 367 with value 18
% 6.53/6.78 ; The agenda of rows to give has 1137 entries:
% 6.53/6.78 ; 1 with value (4 10) 119 with value (4 18) 22 with value (4 25)
% 6.53/6.78 ; 43 with value (4 12) 100 with value (4 19) 8 with value (4 26)
% 6.53/6.78 ; 40 with value (4 13) 122 with value (4 20) 9 with value (4 27)
% 6.53/6.78 ; 94 with value (4 14) 80 with value (4 21) 5 with value (4 28)
% 6.53/6.78 ; 107 with value (4 15) 54 with value (4 22) 6 with value (4 29)
% 6.53/6.78 ; 116 with value (4 16) 39 with value (4 23) 3 with value (4 30)
% 6.53/6.78 ; 117 with value (4 17) 52 with value (4 24)
% 6.53/6.78 Evaluation took:
% 6.53/6.78 6.295 seconds of real time
% 6.53/6.78 6.004459 seconds of user run time
% 6.53/6.78 0.290185 seconds of system run time
% 6.53/6.78 [Run times include 0.283 seconds GC run time.]
% 6.53/6.78 0 calls to %EVAL
% 6.53/6.78 0 page faults and
% 6.53/6.78 521,391,376 bytes consed.
% 6.53/6.78 :PROOF-FOUND
% 6.53/6.78 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-01T22:03:48
% 6.53/6.78 :PROOF-FOUND
% 6.53/6.78 *
%------------------------------------------------------------------------------