TSTP Solution File: BOO014-4 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : BOO014-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n025.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 0.63s 0.86s
% Output : Refutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of clauses : 41 ( 41 unt; 0 nHn; 3 RR)
% Number of literals : 41 ( 40 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 73 ( 8 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_c_inverse_is_d,negated_conjecture,
inverse(add(a,b)) != multiply(inverse(a),inverse(b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_inverse_is_d) ).
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(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(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(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(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(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(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(369,plain,
$false,
inference('REWRITE',[status(thm)],[prove_c_inverse_is_d,53,368,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : BOO014-4 : TPTP v8.1.0. Released v1.1.0.
% 0.10/0.13 % Command : run-snark %s %d
% 0.12/0.32 % Computer : n025.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Wed Jun 1 22:08:14 EDT 2022
% 0.17/0.32 % CPUTime :
% 0.17/0.43 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 *
% 0.17/0.44 *
% 0.17/0.45 #<PACKAGE "SNARK-USER">
% 0.17/0.45 *
% 0.17/0.45 SNARK-TPTP-OPTIONS
% 0.17/0.45 *
% 0.17/0.45 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.17/0.45 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.17/0.45 (USE-FACTORING :POS)
% 0.17/0.45 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.17/0.45 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.17/0.45 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.17/0.45 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.17/0.45 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.17/0.45 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.17/0.45 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.17/0.45 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.17/0.45 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.17/0.45 (DECLARE-TPTP-SYMBOLS2))
% 0.17/0.45 *
% 0.17/0.45 "."
% 0.17/0.45 *
% 0.17/0.45 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-01T22:08:14
% 0.17/0.45 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n025.cluster.edu at 2022-06-01T22:08:14
% 0.17/0.46
% 0.17/0.46 ; Recognized commutativity assertion (= (|add| ?X ?Y) (|add| ?Y ?X)).
% 0.17/0.46 ; Recognized commutativity assertion (= (|multiply| ?X ?Y) (|multiply| ?Y ?X)).
% 0.17/0.46 ; Recognized right identity assertion (= (|add| ?X |additive_identity|) ?X).
% 0.17/0.46 ; Recognized right identity assertion (= (|multiply| ?X |multiplicative_identity|) ?X).
% 0.17/0.46 ; Recognized possible right inverse assertion (= (|add| ?X (|inverse| ?X)) |multiplicative_identity|).
% 0.17/0.46 ; Recognized possible right inverse assertion (= (|multiply| ?X (|inverse| ?X)) |additive_identity|).
% 0.17/0.46 ; Declaring add to be commutative.
% 0.63/0.86 ; Declaring multiply to be commutative.
% 0.63/0.86
% 0.63/0.86 #||
% 0.63/0.86 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.63/0.86 % SZS output start Refutation
% See solution above
% 0.63/0.86 ||#
% 0.63/0.86
% 0.63/0.86 ; Summary of computation:
% 0.63/0.86 ; 3692 formulas have been input or derived (from 62 formulas).
% 0.63/0.86 ; 369 (10%) were retained. Of these,
% 0.63/0.86 ; 342 (93%) were simplified or subsumed later,
% 0.63/0.86 ; 27 ( 7%) are still being kept.
% 0.63/0.86 ;
% 0.63/0.86 ; Run time in seconds excluding printing time:
% 0.63/0.86 ; 0.002 0% Read assertion file (1 call)
% 0.63/0.86 ; 0.001 0% Assert (9 calls)
% 0.63/0.86 ; 0.062 16% Process new row (3,099 calls)
% 0.63/0.86 ; 0.002 0% Resolution (122 calls)
% 0.63/0.86 ; 0.055 14% Paramodulation (61 calls)
% 0.63/0.86 ; 0.190 48% Forward simplification (2,973 calls)
% 0.63/0.86 ; 0.031 8% Backward simplification (369 calls)
% 0.63/0.86 ; 0.014 4% Ordering (3,308 calls)
% 0.63/0.86 ; 0.000 0% Sortal reasoning (32 calls)
% 0.63/0.86 ; 0.000 0% Purity testing (1 call)
% 0.63/0.86 ; 0.043 11% Other
% 0.63/0.86 ; 0.400 Total
% 0.63/0.86 ; 0.407 Real time
% 0.63/0.86 ;
% 0.63/0.86 ; Term-hash-array has 1,113 terms in all.
% 0.63/0.86 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.63/0.86 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.63/0.86 ; Path-index has 79 entries (641 at peak, 1,154 added, 1,075 deleted).
% 0.63/0.86 ; Path-index has 389 nodes (582 at peak, 744 added, 355 deleted).
% 0.63/0.86 ; Trie-index has 79 entries (641 at peak, 1,154 added, 1,075 deleted).
% 0.63/0.86 ; Trie-index has 305 nodes (3,525 at peak, 6,614 added, 6,309 deleted).
% 0.63/0.86 ; Retrieved 24,090 generalization terms in 20,237 calls.
% 0.63/0.86 ; Retrieved 1,374 instance terms in 372 calls.
% 0.63/0.86 ; Retrieved 4,345 unifiable terms in 397 calls.
% 0.63/0.86 ;
% 0.63/0.86 ; The agenda of backward simplifiable rows to process has 158 entries:
% 0.63/0.86 ; 158 with value 0
% 0.63/0.86 ; The agenda of rows to process has 39 entries:
% 0.63/0.86 ; 3 with value 21 6 with value 25 2 with value 29
% 0.63/0.86 ; 6 with value 22 7 with value 26 1 with value 30
% 0.63/0.86 ; 2 with value 23 4 with value 27 1 with value 31
% 0.63/0.86 ; 5 with value 24 2 with value 28
% 0.63/0.86 ; The agenda of rows to give has 12 entries:
% 0.63/0.86 ; 1 with value (4 20) 1 with value (4 23) 1 with value (4 27)
% 0.63/0.86 ; 1 with value (4 21) 1 with value (4 24) 2 with value (4 32)
% 0.63/0.86 ; 4 with value (4 22) 1 with value (4 25)
% 0.63/0.86 Evaluation took:
% 0.63/0.86 0.407 seconds of real time
% 0.63/0.86 0.377536 seconds of user run time
% 0.63/0.86 0.026366 seconds of system run time
% 0.63/0.86 [Run times include 0.015 seconds GC run time.]
% 0.63/0.86 0 calls to %EVAL
% 0.63/0.86 0 page faults and
% 0.63/0.86 31,031,664 bytes consed.
% 0.63/0.86 :PROOF-FOUND
% 0.63/0.86 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-01T22:08:14
% 0.63/0.86 :PROOF-FOUND
% 0.63/0.86 *
%------------------------------------------------------------------------------