TSTP Solution File: BOO008-4 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : BOO008-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n027.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 23:48:54 EDT 2022
% Result : Unsatisfiable 0.77s 1.01s
% Output : Refutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of clauses : 55 ( 55 unt; 0 nHn; 3 RR)
% Number of literals : 55 ( 54 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 110 ( 19 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity1,axiom,
add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',distributivity1) ).
cnf(distributivity2,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',distributivity2) ).
cnf(additive_id1,axiom,
add(X,additive_identity) = X,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',additive_id1) ).
cnf(multiplicative_id1,axiom,
multiply(X,multiplicative_identity) = X,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_id1) ).
cnf(additive_inverse1,axiom,
add(X,inverse(X)) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',additive_inverse1) ).
cnf(multiplicative_inverse1,axiom,
multiply(X,inverse(X)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_inverse1) ).
cnf(prove_associativity,negated_conjecture,
add(a,add(b,c)) != add(add(a,b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity) ).
cnf(8,plain,
add(X,multiply(Y,Z)) = add(add(multiply(X,X),multiply(X,Y)),add(multiply(X,Z),multiply(Y,Z))),
inference('REWRITE',[status(thm)],[distributivity1,distributivity2,theory(equality)]) ).
cnf(10,plain,
additive_identity = inverse(multiplicative_identity),
inference('PARAMODULATE',[status(thm)],[multiplicative_id1,multiplicative_inverse1,theory(equality)]) ).
cnf(11,plain,
multiply(X,Y) = add(multiply(X,Y),multiply(X,additive_identity)),
inference('PARAMODULATE',[status(thm)],[distributivity2,additive_id1,theory(equality)]) ).
cnf(12,plain,
X = add(multiply(X,Y),multiply(X,inverse(Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[distributivity2,additive_inverse1,theory(equality)]),multiplicative_id1,theory(equality)]) ).
cnf(13,plain,
add(multiply(inverse(add(X,Y)),X),multiply(inverse(add(X,Y)),Y)) = additive_identity,
inference('PARAMODULATE',[status(thm)],[multiplicative_inverse1,distributivity2,theory(equality)]) ).
cnf(16,plain,
add(X,Y) = add(add(multiply(X,X),multiply(X,Y)),add(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,multiplicative_id1,theory(equality)]),multiplicative_id1,theory(equality)]) ).
cnf(20,plain,
X = add(add(multiply(X,X),multiply(X,inverse(Y))),multiply(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(21,plain,
add(X,multiply(inverse(X),Y)) = add(Y,multiply(X,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,multiplicative_inverse1,theory(equality)]),12,additive_id1,theory(equality)]) ).
cnf(23,plain,
add(inverse(X),multiply(X,Y)) = add(multiply(inverse(X),inverse(X)),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,multiplicative_inverse1,theory(equality)]),12,additive_id1,theory(equality)]) ).
cnf(30,plain,
additive_identity = multiply(X,additive_identity),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(31,plain,
X = add(multiply(X,X),multiply(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,30,theory(equality)]),30,additive_id1,theory(equality)]) ).
cnf(32,plain,
X = add(X,multiply(X,Y)),
inference('REWRITE',[status(thm)],[20,31,theory(equality)]) ).
cnf(34,plain,
add(X,multiply(Y,Z)) = add(X,add(multiply(X,Z),multiply(Y,Z))),
inference('REWRITE',[status(thm)],[8,31,theory(equality)]) ).
cnf(35,plain,
add(X,Y) = add(X,add(X,Y)),
inference('REWRITE',[status(thm)],[16,31,theory(equality)]) ).
cnf(46,plain,
multiply(X,Y) = add(multiply(X,Y),multiply(X,multiply(Y,Z))),
inference('PARAMODULATE',[status(thm)],[distributivity2,32,theory(equality)]) ).
cnf(49,plain,
X = multiply(X,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(50,plain,
add(inverse(X),multiply(X,Y)) = add(inverse(X),Y),
inference('REWRITE',[status(thm)],[23,49,theory(equality)]) ).
cnf(51,plain,
add(X,multiply(inverse(X),Y)) = add(X,Y),
inference('REWRITE',[status(thm)],[21,49,theory(equality)]) ).
cnf(52,plain,
X = multiply(X,inverse(inverse(X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(53,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,multiplicative_inverse1,theory(equality)]),additive_id1,52,theory(equality)]) ).
cnf(69,plain,
multiplicative_identity = add(inverse(multiply(X,Y)),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[34,51,theory(equality)]),32,additive_inverse1,theory(equality)]) ).
cnf(86,plain,
additive_identity = multiply(inverse(X),multiply(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[46,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(87,plain,
additive_identity = multiply(X,multiply(inverse(X),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[46,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(94,plain,
inverse(X) = multiply(inverse(multiply(X,Y)),inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,86,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(98,plain,
X = multiply(inverse(multiply(inverse(X),Y)),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,87,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(124,plain,
add(X,Y) = add(X,add(multiply(X,inverse(multiply(inverse(Y),Z))),Y)),
inference('PARAMODULATE',[status(thm)],[34,98,theory(equality)]) ).
cnf(163,plain,
additive_identity = multiply(inverse(add(X,Y)),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[35,13,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(166,plain,
inverse(X) = add(inverse(X),inverse(add(X,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[50,163,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(170,plain,
additive_identity = multiply(multiply(inverse(add(X,Y)),Z),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[46,163,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(171,plain,
inverse(add(X,Y)) = multiply(inverse(add(X,Y)),inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,163,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(224,plain,
additive_identity = multiply(inverse(add(add(X,Y),Z)),X),
inference('PARAMODULATE',[status(thm)],[170,171,theory(equality)]) ).
cnf(227,plain,
inverse(X) = add(multiply(inverse(X),Y),inverse(add(X,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,171,theory(equality)]),additive_id1,multiplicative_inverse1,distributivity2,theory(equality)]) ).
cnf(241,plain,
add(add(X,Y),Z) = add(add(add(X,Y),Z),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[51,224,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(277,plain,
inverse(multiply(X,Y)) = add(inverse(X),inverse(add(inverse(X),Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[227,94,theory(equality)]),50,theory(equality)]) ).
cnf(296,plain,
add(X,Y) = add(X,add(Y,multiply(X,inverse(add(Y,Z))))),
inference('REWRITE',[status(thm)],[124,34,distributivity2,53,277,theory(equality)]) ).
cnf(303,plain,
multiplicative_identity = add(add(inverse(X),inverse(add(inverse(X),Y))),Y),
inference('REWRITE',[status(thm)],[69,277,theory(equality)]) ).
cnf(332,plain,
multiplicative_identity = add(add(X,inverse(add(X,Y))),Y),
inference('PARAMODULATE',[status(thm)],[303,53,theory(equality)]) ).
cnf(335,plain,
multiplicative_identity = add(add(inverse(X),inverse(Y)),multiply(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[332,12,theory(equality)]),50,theory(equality)]) ).
cnf(349,plain,
add(inverse(X),inverse(add(inverse(X),Y))) = add(inverse(X),inverse(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[227,335,theory(equality)]),10,227,171,additive_id1,163,49,distributivity2,277,theory(equality)]) ).
cnf(355,plain,
inverse(multiply(X,Y)) = add(inverse(X),inverse(Y)),
inference('REWRITE',[status(thm)],[277,349,theory(equality)]) ).
cnf(368,plain,
inverse(add(inverse(X),inverse(Y))) = multiply(X,Y),
inference('PARAMODULATE',[status(thm)],[53,355,theory(equality)]) ).
cnf(380,plain,
add(X,Y) = add(X,add(Y,inverse(add(inverse(X),add(Y,Z))))),
inference('REWRITE',[status(thm)],[296,53,368,theory(equality)]) ).
cnf(382,plain,
add(X,inverse(add(X,inverse(Y)))) = add(X,Y),
inference('REWRITE',[status(thm)],[51,53,368,theory(equality)]) ).
cnf(471,plain,
add(X,inverse(add(X,Y))) = add(X,inverse(Y)),
inference('PARAMODULATE',[status(thm)],[382,53,theory(equality)]) ).
cnf(530,plain,
add(X,Y) = add(X,add(Y,inverse(add(inverse(X),Z)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[380,241,theory(equality)]),471,theory(equality)]) ).
cnf(532,plain,
add(add(X,Y),Z) = add(add(X,Y),add(X,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[530,166,theory(equality)]),53,theory(equality)]) ).
cnf(556,plain,
add(add(X,Y),Z) = add(add(X,Z),Y),
inference('PARAMODULATE',[status(thm)],[532,532,theory(equality)]) ).
cnf(557,plain,
$false,
inference('REWRITE',[status(thm)],[prove_associativity,556,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : BOO008-4 : TPTP v8.1.0. Released v1.1.0.
% 0.10/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n027.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 16:43:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.45 /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p 2022-06-01T16:43:34
% 0.20/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n027.cluster.edu at 2022-06-01T16:43:34
% 0.20/0.48
% 0.20/0.48 ; Recognized commutativity assertion (= (|add| ?X ?Y) (|add| ?Y ?X)).
% 0.20/0.48 ; Recognized commutativity assertion (= (|multiply| ?X ?Y) (|multiply| ?Y ?X)).
% 0.20/0.48 ; Recognized right identity assertion (= (|add| ?X |additive_identity|) ?X).
% 0.20/0.48 ; Recognized right identity assertion (= (|multiply| ?X |multiplicative_identity|) ?X).
% 0.20/0.48 ; Recognized possible right inverse assertion (= (|add| ?X (|inverse| ?X)) |multiplicative_identity|).
% 0.20/0.48 ; Recognized possible right inverse assertion (= (|multiply| ?X (|inverse| ?X)) |additive_identity|).
% 0.20/0.48 ; Declaring add to be commutative.
% 0.77/1.01 ; Declaring multiply to be commutative.
% 0.77/1.01
% 0.77/1.01 #||
% 0.77/1.01 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.77/1.01 % SZS output start Refutation
% See solution above
% 0.77/1.02 ||#
% 0.77/1.02
% 0.77/1.02 ; Summary of computation:
% 0.77/1.02 ; 6572 formulas have been input or derived (from 85 formulas).
% 0.77/1.02 ; 557 ( 8%) were retained. Of these,
% 0.77/1.02 ; 460 (83%) were simplified or subsumed later,
% 0.77/1.02 ; 97 (17%) are still being kept.
% 0.77/1.02 ;
% 0.77/1.02 ; Run time in seconds excluding printing time:
% 0.77/1.02 ; 0.002 0% Read assertion file (1 call)
% 0.77/1.02 ; 0.001 0% Assert (9 calls)
% 0.77/1.02 ; 0.052 10% Process new row (5,430 calls)
% 0.77/1.02 ; 0.004 1% Resolution (168 calls)
% 0.77/1.02 ; 0.090 17% Paramodulation (84 calls)
% 0.77/1.02 ; 0.269 50% Forward simplification (4,985 calls)
% 0.77/1.02 ; 0.053 10% Backward simplification (557 calls)
% 0.77/1.02 ; 0.019 4% Ordering (6,558 calls)
% 0.77/1.02 ; 0.000 0% Sortal reasoning (32 calls)
% 0.77/1.02 ; 0.000 0% Purity testing (1 call)
% 0.77/1.02 ; 0.048 9% Other
% 0.77/1.02 ; 0.538 Total
% 0.77/1.02 ; 0.547 Real time
% 0.77/1.02 ;
% 0.77/1.02 ; Term-hash-array has 1,744 terms in all.
% 0.77/1.02 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.77/1.02 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.77/1.02 ; Path-index has 374 entries (641 at peak, 1,829 added, 1,455 deleted).
% 0.77/1.02 ; Path-index has 512 nodes (582 at peak, 903 added, 391 deleted).
% 0.77/1.02 ; Trie-index has 374 entries (641 at peak, 1,829 added, 1,455 deleted).
% 0.77/1.02 ; Trie-index has 2,462 nodes (3,857 at peak, 11,406 added, 8,944 deleted).
% 0.77/1.02 ; Retrieved 43,040 generalization terms in 36,580 calls.
% 0.77/1.02 ; Retrieved 4,248 instance terms in 569 calls.
% 0.77/1.02 ; Retrieved 9,035 unifiable terms in 588 calls.
% 0.77/1.02 ;
% 0.77/1.02 ; The agenda of backward simplifiable rows to process has 29 entries:
% 0.77/1.02 ; 29 with value 0
% 0.77/1.02 ; The agenda of rows to process has 159 entries:
% 0.77/1.02 ; 9 with value 22 13 with value 29 5 with value 35
% 0.77/1.02 ; 11 with value 23 8 with value 30 3 with value 36
% 0.77/1.02 ; 10 with value 24 12 with value 31 4 with value 37
% 0.77/1.02 ; 22 with value 25 11 with value 32 1 with value 38
% 0.77/1.02 ; 14 with value 26 12 with value 33 1 with value 39
% 0.77/1.02 ; 12 with value 27 4 with value 34 2 with value 40
% 0.77/1.02 ; 5 with value 28
% 0.77/1.02 ; The agenda of rows to give has 74 entries:
% 0.77/1.02 ; 1 with value (4 22) 7 with value (4 34) 3 with value (4 43)
% 0.77/1.02 ; 2 with value (4 26) 2 with value (4 35) 2 with value (4 45)
% 0.77/1.02 ; 6 with value (4 27) 7 with value (4 36) 2 with value (4 46)
% 0.77/1.02 ; 5 with value (4 28) 3 with value (4 37) 1 with value (4 48)
% 0.77/1.02 ; 4 with value (4 29) 5 with value (4 38) 2 with value (4 51)
% 0.77/1.02 ; 2 with value (4 30) 2 with value (4 39) 2 with value (4 57)
% 0.77/1.02 ; 4 with value (4 31) 1 with value (4 41) 1 with value (4 59)
% 0.77/1.02 ; 2 with value (4 32) 2 with value (4 42) 1 with value (4 62)
% 0.77/1.02 ; 5 with value (4 33)
% 0.77/1.02 Evaluation took:
% 0.77/1.02 0.547 seconds of real time
% 0.77/1.02 0.507109 seconds of user run time
% 0.77/1.02 0.03983 seconds of system run time
% 0.77/1.02 [Run times include 0.022 seconds GC run time.]
% 0.77/1.02 0 calls to %EVAL
% 0.77/1.02 0 page faults and
% 0.77/1.02 54,779,192 bytes consed.
% 0.77/1.02 :PROOF-FOUND
% 0.77/1.02 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-01T16:43:34
% 0.77/1.02 :PROOF-FOUND
% 0.77/1.02 *
%------------------------------------------------------------------------------