TSTP Solution File: BOO015-2 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : BOO015-2 : TPTP v8.1.0. Bugfixed v1.0.1.
% 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 23:48:57 EDT 2022
% Result : Unsatisfiable 0.43s 0.61s
% Output : Refutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 46 ( 46 unt; 0 nHn; 18 RR)
% Number of literals : 46 ( 45 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 44 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity1,axiom,
add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity1) ).
cnf(distributivity3,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity3) ).
cnf(additive_inverse1,axiom,
add(X,inverse(X)) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_inverse1) ).
cnf(multiplicative_inverse1,axiom,
multiply(X,inverse(X)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_inverse1) ).
cnf(multiplicative_id1,axiom,
multiply(X,multiplicative_identity) = X,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_id1) ).
cnf(additive_id1,axiom,
add(X,additive_identity) = X,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_id1) ).
cnf(a_times_b_is_c,hypothesis,
multiply(a,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(a_inverse_plus_b_inverse_is_d,hypothesis,
add(inverse(a),inverse(b)) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_plus_b_inverse_is_d) ).
cnf(prove_c_inverse_is_d,negated_conjecture,
inverse(c) != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_inverse_is_d) ).
cnf(10,plain,
add(multiply(X,Y),Z) = add(add(multiply(X,Y),multiply(X,Z)),add(multiply(Y,Z),multiply(Z,Z))),
inference('REWRITE',[status(thm)],[distributivity1,distributivity3,theory(equality)]) ).
cnf(13,plain,
multiply(X,Y) = add(multiply(X,Y),multiply(additive_identity,Y)),
inference('PARAMODULATE',[status(thm)],[distributivity3,additive_id1,theory(equality)]) ).
cnf(14,plain,
X = add(multiply(X,Y),multiply(inverse(Y),X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[distributivity3,additive_inverse1,theory(equality)]),multiplicative_id1,theory(equality)]) ).
cnf(15,plain,
multiply(d,X) = add(multiply(inverse(a),X),multiply(inverse(b),X)),
inference('PARAMODULATE',[status(thm)],[distributivity3,a_inverse_plus_b_inverse_is_d,theory(equality)]) ).
cnf(19,plain,
add(c,X) = add(add(c,multiply(a,X)),add(multiply(b,X),multiply(X,X))),
inference('PARAMODULATE',[status(thm)],[10,a_times_b_is_c,theory(equality)]) ).
cnf(23,plain,
X = add(multiply(X,Y),add(multiply(inverse(Y),X),multiply(X,X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(31,plain,
add(multiply(inverse(Y),X),Y) = add(multiply(Y,Y),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,multiplicative_inverse1,theory(equality)]),additive_id1,14,theory(equality)]) ).
cnf(42,plain,
additive_identity = multiply(additive_identity,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[13,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(45,plain,
X = add(multiply(X,Y),multiply(X,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,42,theory(equality)]),42,additive_id1,theory(equality)]) ).
cnf(48,plain,
X = add(X,multiply(X,Y)),
inference('REWRITE',[status(thm)],[23,45,theory(equality)]) ).
cnf(51,plain,
add(multiply(X,Y),Z) = add(add(multiply(X,Y),multiply(X,Z)),Z),
inference('REWRITE',[status(thm)],[10,45,theory(equality)]) ).
cnf(55,plain,
add(c,X) = add(add(c,multiply(a,X)),X),
inference('REWRITE',[status(thm)],[19,45,theory(equality)]) ).
cnf(61,plain,
a = add(a,c),
inference('PARAMODULATE',[status(thm)],[48,a_times_b_is_c,theory(equality)]) ).
cnf(62,plain,
b = add(b,c),
inference('PARAMODULATE',[status(thm)],[48,a_times_b_is_c,theory(equality)]) ).
cnf(69,plain,
multiply(a,X) = add(multiply(a,X),multiply(c,X)),
inference('PARAMODULATE',[status(thm)],[distributivity3,61,theory(equality)]) ).
cnf(70,plain,
multiply(b,X) = add(multiply(b,X),multiply(c,X)),
inference('PARAMODULATE',[status(thm)],[distributivity3,62,theory(equality)]) ).
cnf(76,plain,
X = multiply(X,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[14,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(77,plain,
add(multiply(inverse(X),Y),X) = add(X,Y),
inference('REWRITE',[status(thm)],[31,76,theory(equality)]) ).
cnf(78,plain,
a = add(c,multiply(inverse(b),a)),
inference('PARAMODULATE',[status(thm)],[14,a_times_b_is_c,theory(equality)]) ).
cnf(80,plain,
X = multiply(inverse(inverse(X)),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[14,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(81,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[14,multiplicative_inverse1,theory(equality)]),additive_id1,80,theory(equality)]) ).
cnf(109,plain,
multiplicative_identity = add(X,inverse(multiply(X,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[51,77,theory(equality)]),48,additive_inverse1,theory(equality)]) ).
cnf(132,plain,
additive_identity = multiply(c,inverse(a)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[69,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(138,plain,
inverse(a) = multiply(inverse(c),inverse(a)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[14,132,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(145,plain,
additive_identity = multiply(c,inverse(b)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[70,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(151,plain,
inverse(b) = multiply(inverse(c),inverse(b)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[14,145,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(158,plain,
multiply(d,a) = multiply(inverse(b),a),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(159,plain,
a = add(c,multiply(d,a)),
inference('REWRITE',[status(thm)],[78,158,theory(equality)]) ).
cnf(167,plain,
multiply(d,inverse(a)) = inverse(a),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,76,theory(equality)]),48,theory(equality)]) ).
cnf(169,plain,
multiply(d,inverse(c)) = d,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,138,theory(equality)]),a_inverse_plus_b_inverse_is_d,151,theory(equality)]) ).
cnf(172,plain,
add(c,d) = add(a,d),
inference('PARAMODULATE',[status(thm)],[55,159,theory(equality)]) ).
cnf(178,plain,
add(multiply(a,X),multiply(d,X)) = add(multiply(c,X),multiply(d,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[distributivity3,172,theory(equality)]),distributivity3,theory(equality)]) ).
cnf(201,plain,
multiplicative_identity = add(a,d),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[109,167,theory(equality)]),81,theory(equality)]) ).
cnf(202,plain,
add(c,d) = multiplicative_identity,
inference('REWRITE',[status(thm)],[172,201,theory(equality)]) ).
cnf(207,plain,
X = add(multiply(a,X),multiply(d,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[distributivity3,202,theory(equality)]),178,multiplicative_id1,theory(equality)]) ).
cnf(208,plain,
X = add(multiply(c,X),multiply(d,X)),
inference('REWRITE',[status(thm)],[178,207,theory(equality)]) ).
cnf(246,plain,
$false,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[208,multiplicative_inverse1,theory(equality)]),prove_c_inverse_is_d,additive_id1,169,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : BOO015-2 : TPTP v8.1.0. Bugfixed v1.0.1.
% 0.11/0.12 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 1 23:47:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.44 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 *
% 0.18/0.45 *
% 0.18/0.46 #<PACKAGE "SNARK-USER">
% 0.18/0.46 *
% 0.18/0.46 SNARK-TPTP-OPTIONS
% 0.18/0.46 *
% 0.18/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.46 (USE-FACTORING :POS)
% 0.18/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.46 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.46 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.46 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.46 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.46 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.46 (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.46 *
% 0.18/0.46 "."
% 0.18/0.46 *
% 0.18/0.46 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-01T23:47:23
% 0.18/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n020.cluster.edu at 2022-06-01T23:47:23
% 0.18/0.47
% 0.18/0.47 ; Recognized commutativity assertion (= (|add| ?X ?Y) (|add| ?Y ?X)).
% 0.18/0.47 ; Recognized commutativity assertion (= (|multiply| ?X ?Y) (|multiply| ?Y ?X)).
% 0.18/0.47 ; Recognized possible right inverse assertion (= (|add| ?X (|inverse| ?X)) |multiplicative_identity|).
% 0.18/0.47 ; Recognized possible left inverse assertion (= (|add| (|inverse| ?X) ?X) |multiplicative_identity|).
% 0.18/0.47 ; Recognized possible right inverse assertion (= (|multiply| ?X (|inverse| ?X)) |additive_identity|).
% 0.18/0.47 ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |additive_identity|).
% 0.18/0.47 ; Recognized right identity assertion (= (|multiply| ?X |multiplicative_identity|) ?X).
% 0.18/0.47 ; Recognized left identity assertion (= (|multiply| |multiplicative_identity| ?X) ?X).
% 0.18/0.47 ; Recognized right identity assertion (= (|add| ?X |additive_identity|) ?X).
% 0.18/0.47 ; Recognized left identity assertion (= (|add| |additive_identity| ?X) ?X).
% 0.18/0.47 ; Declaring add to be commutative.
% 0.43/0.61 ; Declaring multiply to be commutative.
% 0.43/0.61
% 0.43/0.61 #||
% 0.43/0.61 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.43/0.61 % SZS output start Refutation
% See solution above
% 0.43/0.62 ||#
% 0.43/0.62
% 0.43/0.62 ; Summary of computation:
% 0.43/0.62 ; 1157 formulas have been input or derived (from 83 formulas).
% 0.43/0.62 ; 246 (21%) were retained. Of these,
% 0.43/0.62 ; 52 (21%) were simplified or subsumed later,
% 0.43/0.62 ; 194 (79%) are still being kept.
% 0.43/0.62 ;
% 0.43/0.62 ; Run time in seconds excluding printing time:
% 0.43/0.62 ; 0.003 2% Read assertion file (1 call)
% 0.43/0.62 ; 0.001 1% Assert (17 calls)
% 0.43/0.62 ; 0.028 18% Process new row (1,064 calls)
% 0.43/0.62 ; 0.002 1% Resolution (164 calls)
% 0.43/0.62 ; 0.021 14% Paramodulation (82 calls)
% 0.43/0.62 ; 0.052 34% Forward simplification (1,042 calls)
% 0.43/0.62 ; 0.008 5% Backward simplification (246 calls)
% 0.43/0.62 ; 0.008 5% Ordering (2,496 calls)
% 0.43/0.62 ; 0.000 0% Sortal reasoning (32 calls)
% 0.43/0.62 ; 0.000 0% Purity testing (1 call)
% 0.43/0.62 ; 0.029 19% Other
% 0.43/0.62 ; 0.152 Total
% 0.43/0.62 ; 0.161 Real time
% 0.43/0.62 ;
% 0.43/0.62 ; Term-hash-array has 684 terms in all.
% 0.43/0.62 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.43/0.62 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.43/0.62 ; Path-index has 553 entries (557 at peak, 713 added, 160 deleted).
% 0.43/0.62 ; Path-index has 277 nodes (277 at peak, 305 added, 28 deleted).
% 0.43/0.62 ; Trie-index has 553 entries (557 at peak, 713 added, 160 deleted).
% 0.43/0.62 ; Trie-index has 2,434 nodes (2,445 at peak, 3,076 added, 642 deleted).
% 0.43/0.62 ; Retrieved 4,792 generalization terms in 4,747 calls.
% 0.43/0.62 ; Retrieved 684 instance terms in 249 calls.
% 0.43/0.62 ; Retrieved 3,864 unifiable terms in 568 calls.
% 0.43/0.62 ;
% 0.43/0.62 ; The agenda of rows to process has 8 entries:
% 0.43/0.62 ; 1 with value 18 2 with value 20 2 with value 26
% 0.43/0.62 ; 2 with value 19 1 with value 24
% 0.43/0.62 ; The agenda of rows to give has 122 entries:
% 0.43/0.62 ; 2 with value (4 16) 10 with value (4 22) 4 with value (4 28)
% 0.43/0.62 ; 7 with value (4 17) 10 with value (4 23) 2 with value (4 29)
% 0.43/0.62 ; 14 with value (4 18) 19 with value (4 24) 4 with value (4 31)
% 0.43/0.62 ; 12 with value (4 19) 12 with value (4 25) 1 with value (4 33)
% 0.43/0.62 ; 11 with value (4 20) 5 with value (4 26) 1 with value (4 34)
% 0.43/0.62 ; 4 with value (4 21) 2 with value (4 27) 2 with value (4 36)
% 0.43/0.62 Evaluation took:
% 0.43/0.62 0.161 seconds of real time
% 0.43/0.62 0.143168 seconds of user run time
% 0.43/0.62 0.017895 seconds of system run time
% 0.43/0.62 [Run times include 0.005 seconds GC run time.]
% 0.43/0.62 0 calls to %EVAL
% 0.43/0.62 0 page faults and
% 0.43/0.62 13,588,720 bytes consed.
% 0.43/0.62 :PROOF-FOUND
% 0.43/0.62 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-01T23:47:23
% 0.43/0.62 :PROOF-FOUND
% 0.43/0.62 *
%------------------------------------------------------------------------------