TSTP Solution File: BOO014-2 by SNARK---20120808r022
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : BOO014-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n023.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 0.77s 0.93s
% Output : Refutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 13 RR)
% Number of literals : 35 ( 34 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 : 38 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity1,axiom,
add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity1) ).
cnf(distributivity3,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity3) ).
cnf(additive_inverse1,axiom,
add(X,inverse(X)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_inverse1) ).
cnf(multiplicative_inverse1,axiom,
multiply(X,inverse(X)) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_inverse1) ).
cnf(multiplicative_id1,axiom,
multiply(X,multiplicative_identity) = X,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_id1) ).
cnf(additive_id1,axiom,
add(X,additive_identity) = X,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_id1) ).
cnf(a_plus_b_is_c,hypothesis,
add(a,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_plus_b_is_c) ).
cnf(a_inverse_times_b_inverse_is_d,hypothesis,
multiply(inverse(a),inverse(b)) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_inverse_times_b_inverse_is_d) ).
cnf(prove_c_inverse_is_d,negated_conjecture,
inverse(c) != d,
file('/export/starexec/sandbox/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(c,X) = add(multiply(a,X),multiply(b,X)),
inference('PARAMODULATE',[status(thm)],[distributivity3,a_plus_b_is_c,theory(equality)]) ).
cnf(14,plain,
multiply(X,Y) = add(multiply(X,Y),multiply(additive_identity,Y)),
inference('PARAMODULATE',[status(thm)],[distributivity3,additive_id1,theory(equality)]) ).
cnf(15,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(20,plain,
add(X,Y) = add(add(X,Y),add(multiply(X,Y),multiply(Y,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,multiplicative_id1,theory(equality)]),multiplicative_id1,theory(equality)]) ).
cnf(21,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(39,plain,
add(multiply(a,inverse(c)),multiply(b,inverse(c))) = additive_identity,
inference('PARAMODULATE',[status(thm)],[multiplicative_inverse1,13,theory(equality)]) ).
cnf(41,plain,
additive_identity = multiply(additive_identity,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[14,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(44,plain,
X = add(multiply(X,Y),multiply(X,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,41,theory(equality)]),41,additive_id1,theory(equality)]) ).
cnf(51,plain,
X = add(X,multiply(X,Y)),
inference('REWRITE',[status(thm)],[21,44,theory(equality)]) ).
cnf(53,plain,
add(X,Y) = add(add(X,Y),Y),
inference('REWRITE',[status(thm)],[20,44,theory(equality)]) ).
cnf(69,plain,
multiply(X,Y) = add(multiply(X,Y),multiply(multiply(X,Z),Y)),
inference('PARAMODULATE',[status(thm)],[distributivity3,51,theory(equality)]) ).
cnf(80,plain,
X = multiply(inverse(inverse(X)),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(83,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,multiplicative_inverse1,theory(equality)]),additive_id1,80,theory(equality)]) ).
cnf(84,plain,
X = add(add(multiply(a,X),multiply(b,X)),multiply(inverse(c),X)),
inference('PARAMODULATE',[status(thm)],[15,13,theory(equality)]) ).
cnf(127,plain,
additive_identity = multiply(b,inverse(c)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[53,39,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(128,plain,
multiply(a,inverse(c)) = additive_identity,
inference('REWRITE',[status(thm)],[39,additive_id1,127,theory(equality)]) ).
cnf(130,plain,
inverse(c) = multiply(inverse(a),inverse(c)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,128,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(132,plain,
inverse(c) = multiply(inverse(b),inverse(c)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,127,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(198,plain,
additive_identity = multiply(multiply(X,Y),inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[69,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(203,plain,
d = add(d,multiply(multiply(inverse(a),X),inverse(b))),
inference('PARAMODULATE',[status(thm)],[69,a_inverse_times_b_inverse_is_d,theory(equality)]) ).
cnf(215,plain,
additive_identity = multiply(d,a),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[198,a_inverse_times_b_inverse_is_d,theory(equality)]),83,theory(equality)]) ).
cnf(216,plain,
additive_identity = multiply(d,b),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[198,a_inverse_times_b_inverse_is_d,theory(equality)]),83,theory(equality)]) ).
cnf(411,plain,
d = add(d,inverse(c)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[203,130,theory(equality)]),132,theory(equality)]) ).
cnf(483,plain,
d = multiply(inverse(c),d),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[84,215,theory(equality)]),additive_id1,216,theory(equality)]) ).
cnf(499,plain,
$false,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[51,483,theory(equality)]),prove_c_inverse_is_d,411,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : BOO014-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : run-snark %s %d
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 1 17:20:41 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.47 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.48 *
% 0.20/0.48 *
% 0.20/0.49 #<PACKAGE "SNARK-USER">
% 0.20/0.49 *
% 0.20/0.49 SNARK-TPTP-OPTIONS
% 0.20/0.49 *
% 0.20/0.49 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.49 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.49 (USE-FACTORING :POS)
% 0.20/0.49 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.49 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.49 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.49 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.49 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.49 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.49 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.49 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.49 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.49 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.49 *
% 0.20/0.49 "."
% 0.20/0.49 *
% 0.20/0.49 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-01T17:20:41
% 0.20/0.49 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n023.cluster.edu at 2022-06-01T17:20:41
% 0.20/0.50
% 0.20/0.50 ; Recognized commutativity assertion (= (|add| ?X ?Y) (|add| ?Y ?X)).
% 0.20/0.50 ; Recognized commutativity assertion (= (|multiply| ?X ?Y) (|multiply| ?Y ?X)).
% 0.20/0.50 ; Recognized possible right inverse assertion (= (|add| ?X (|inverse| ?X)) |multiplicative_identity|).
% 0.20/0.50 ; Recognized possible left inverse assertion (= (|add| (|inverse| ?X) ?X) |multiplicative_identity|).
% 0.20/0.50 ; Recognized possible right inverse assertion (= (|multiply| ?X (|inverse| ?X)) |additive_identity|).
% 0.20/0.50 ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |additive_identity|).
% 0.20/0.50 ; Recognized right identity assertion (= (|multiply| ?X |multiplicative_identity|) ?X).
% 0.20/0.50 ; Recognized left identity assertion (= (|multiply| |multiplicative_identity| ?X) ?X).
% 0.20/0.50 ; Recognized right identity assertion (= (|add| ?X |additive_identity|) ?X).
% 0.20/0.50 ; Recognized left identity assertion (= (|add| |additive_identity| ?X) ?X).
% 0.20/0.50 ; Declaring add to be commutative.
% 0.77/0.93 ; Declaring multiply to be commutative.
% 0.77/0.93
% 0.77/0.93 #||
% 0.77/0.93 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.77/0.93 % SZS output start Refutation
% See solution above
% 0.77/0.94 ||#
% 0.77/0.94
% 0.77/0.94 ; Summary of computation:
% 0.77/0.94 ; 5672 formulas have been input or derived (from 134 formulas).
% 0.77/0.94 ; 499 ( 9%) were retained. Of these,
% 0.77/0.94 ; 75 (15%) were simplified or subsumed later,
% 0.77/0.94 ; 424 (85%) are still being kept.
% 0.77/0.94 ;
% 0.77/0.94 ; Run time in seconds excluding printing time:
% 0.77/0.94 ; 0.003 1% Read assertion file (1 call)
% 0.77/0.94 ; 0.001 0% Assert (17 calls)
% 0.77/0.94 ; 0.050 11% Process new row (4,584 calls)
% 0.77/0.94 ; 0.004 1% Resolution (266 calls)
% 0.77/0.94 ; 0.081 18% Paramodulation (133 calls)
% 0.77/0.94 ; 0.220 49% Forward simplification (4,553 calls)
% 0.77/0.94 ; 0.025 6% Backward simplification (499 calls)
% 0.77/0.94 ; 0.017 4% Ordering (8,020 calls)
% 0.77/0.94 ; 0.001 0% Sortal reasoning (32 calls)
% 0.77/0.94 ; 0.000 0% Purity testing (1 call)
% 0.77/0.94 ; 0.043 10% Other
% 0.77/0.94 ; 0.445 Total
% 0.77/0.94 ; 0.448 Real time
% 0.77/0.94 ;
% 0.77/0.94 ; Term-hash-array has 1,401 terms in all.
% 0.77/0.94 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.77/0.94 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.77/0.94 ; Path-index has 1,171 entries (1,171 at peak, 1,434 added, 263 deleted).
% 0.77/0.94 ; Path-index has 567 nodes (567 at peak, 639 added, 72 deleted).
% 0.77/0.94 ; Trie-index has 1,171 entries (1,171 at peak, 1,434 added, 263 deleted).
% 0.77/0.94 ; Trie-index has 5,738 nodes (5,738 at peak, 7,083 added, 1,345 deleted).
% 0.77/0.94 ; Retrieved 27,902 generalization terms in 24,673 calls.
% 0.77/0.94 ; Retrieved 1,206 instance terms in 502 calls.
% 0.77/0.94 ; Retrieved 11,411 unifiable terms in 1,002 calls.
% 0.77/0.94 ;
% 0.77/0.94 ; The agenda of rows to process has 46 entries:
% 0.77/0.94 ; 8 with value 16 6 with value 20 1 with value 24
% 0.77/0.94 ; 9 with value 17 4 with value 21 1 with value 25
% 0.77/0.94 ; 3 with value 18 2 with value 22 1 with value 26
% 0.77/0.94 ; 4 with value 19 7 with value 23
% 0.77/0.94 ; The agenda of rows to give has 298 entries:
% 0.77/0.94 ; 2 with value (4 16) 15 with value (4 25) 6 with value (4 33)
% 0.77/0.94 ; 1 with value (4 19) 20 with value (4 26) 3 with value (4 34)
% 0.77/0.94 ; 16 with value (4 20) 29 with value (4 27) 6 with value (4 35)
% 0.77/0.94 ; 21 with value (4 21) 23 with value (4 28) 7 with value (4 36)
% 0.77/0.94 ; 29 with value (4 22) 21 with value (4 29) 1 with value (4 37)
% 0.77/0.94 ; 45 with value (4 23) 12 with value (4 30) 1 with value (4 39)
% 0.77/0.94 ; 28 with value (4 24) 11 with value (4 31) 1 with value (4 50)
% 0.77/0.94 Evaluation took:
% 0.77/0.94 0.448 seconds of real time
% 0.77/0.94 0.415011 seconds of user run time
% 0.77/0.94 0.034002 seconds of system run time
% 0.77/0.94 [Run times include 0.012 seconds GC run time.]
% 0.77/0.94 0 calls to %EVAL
% 0.77/0.94 0 page faults and
% 0.77/0.94 37,377,864 bytes consed.
% 0.77/0.94 :PROOF-FOUND
% 0.77/0.94 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-01T17:20:41
% 0.77/0.94 :PROOF-FOUND
% 0.77/0.94 *
%------------------------------------------------------------------------------