TSTP Solution File: RNG008-7 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : RNG008-7 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n019.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 : Mon Jul 18 20:40:33 EDT 2022
% Result : Unsatisfiable 0.50s 0.70s
% Output : Refutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of clauses : 51 ( 51 unt; 0 nHn; 11 RR)
% Number of literals : 51 ( 50 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 67 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_additive_identity,axiom,
add(additive_identity,X) = X,
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',left_additive_identity) ).
cnf(left_additive_inverse,axiom,
add(additive_inverse(X),X) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',left_additive_inverse) ).
cnf(3,plain,
add(additive_inverse(X),add(X,Y)) = add(additive_identity,Y),
inference('EMBED',[status(thm)],[left_additive_inverse]) ).
cnf(associativity_for_multiplication,axiom,
multiply(X,multiply(Y,Z)) = multiply(multiply(X,Y),Z),
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',associativity_for_multiplication) ).
cnf(distribute1,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',distribute1) ).
cnf(distribute2,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',distribute2) ).
cnf(boolean_ring,hypothesis,
multiply(X,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boolean_ring) ).
cnf(a_times_b_is_c,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(prove_commutativity,negated_conjecture,
multiply(b,a) != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).
cnf(10,plain,
additive_identity = additive_inverse(additive_identity),
inference('PARAMODULATE',[status(thm)],[left_additive_identity,left_additive_inverse,theory(equality)]) ).
cnf(11,plain,
X = additive_inverse(additive_inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,3,theory(equality)]),left_additive_identity,theory(equality)]) ).
cnf(12,plain,
additive_inverse(X) = add(additive_inverse(add(X,Y)),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,3,theory(equality)]),left_additive_identity,theory(equality)]) ).
cnf(14,plain,
multiply(X,c) = multiply(multiply(X,a),b),
inference('PARAMODULATE',[status(thm)],[associativity_for_multiplication,a_times_b_is_c,theory(equality)]) ).
cnf(15,plain,
multiply(X,Y) = multiply(multiply(X,Y),Y),
inference('PARAMODULATE',[status(thm)],[associativity_for_multiplication,boolean_ring,theory(equality)]) ).
cnf(18,plain,
multiply(X,multiply(multiply(Y,Z),U)) = multiply(multiply(X,Y),multiply(Z,U)),
inference('PARAMODULATE',[status(thm)],[associativity_for_multiplication,associativity_for_multiplication,theory(equality)]) ).
cnf(23,plain,
multiply(X,Y) = add(multiply(X,Y),multiply(X,additive_identity)),
inference('PARAMODULATE',[status(thm)],[distribute1,left_additive_identity,theory(equality)]) ).
cnf(25,plain,
multiply(X,additive_identity) = add(multiply(X,Y),multiply(X,additive_inverse(Y))),
inference('PARAMODULATE',[status(thm)],[distribute1,left_additive_inverse,theory(equality)]) ).
cnf(27,plain,
add(X,add(multiply(Y,X),add(multiply(X,Y),Y))) = add(X,Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[boolean_ring,distribute1,theory(equality)]),boolean_ring,distribute2,theory(equality)]) ).
cnf(33,plain,
multiply(X,Y) = add(multiply(X,Y),multiply(additive_identity,Y)),
inference('PARAMODULATE',[status(thm)],[distribute2,left_additive_identity,theory(equality)]) ).
cnf(35,plain,
multiply(additive_identity,X) = add(multiply(Y,X),multiply(additive_inverse(Y),X)),
inference('PARAMODULATE',[status(thm)],[distribute2,left_additive_inverse,theory(equality)]) ).
cnf(39,plain,
multiply(a,c) = c,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[14,boolean_ring,theory(equality)]),a_times_b_is_c,theory(equality)]) ).
cnf(40,plain,
multiply(multiply(X,a),multiply(b,Y)) = multiply(multiply(X,c),Y),
inference('PARAMODULATE',[status(thm)],[associativity_for_multiplication,14,theory(equality)]) ).
cnf(41,plain,
multiply(X,c) = multiply(multiply(X,a),c),
inference('PARAMODULATE',[status(thm)],[associativity_for_multiplication,39,theory(equality)]) ).
cnf(43,plain,
c = multiply(c,b),
inference('PARAMODULATE',[status(thm)],[15,a_times_b_is_c,theory(equality)]) ).
cnf(44,plain,
multiply(multiply(X,Y),multiply(Y,Z)) = multiply(multiply(X,Y),Z),
inference('PARAMODULATE',[status(thm)],[associativity_for_multiplication,15,theory(equality)]) ).
cnf(55,plain,
additive_inverse(add(X,Y)) = add(additive_inverse(Y),additive_inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,3,theory(equality)]),left_additive_identity,theory(equality)]) ).
cnf(73,plain,
additive_inverse(multiply(X,additive_identity)) = additive_identity,
inference('PARAMODULATE',[status(thm)],[12,23,theory(equality)]) ).
cnf(86,plain,
multiply(X,additive_identity) = additive_identity,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11,73,theory(equality)]),10,theory(equality)]) ).
cnf(87,plain,
additive_identity = add(multiply(X,Y),multiply(X,additive_inverse(Y))),
inference('REWRITE',[status(thm)],[25,86,theory(equality)]) ).
cnf(98,plain,
additive_inverse(multiply(additive_identity,X)) = additive_identity,
inference('PARAMODULATE',[status(thm)],[12,33,theory(equality)]) ).
cnf(109,plain,
multiply(additive_identity,X) = additive_identity,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11,98,theory(equality)]),10,theory(equality)]) ).
cnf(110,plain,
additive_identity = add(multiply(X,Y),multiply(additive_inverse(X),Y)),
inference('REWRITE',[status(thm)],[35,109,theory(equality)]) ).
cnf(112,plain,
multiply(multiply(X,a),multiply(c,Y)) = multiply(multiply(X,c),Y),
inference('PARAMODULATE',[status(thm)],[associativity_for_multiplication,41,theory(equality)]) ).
cnf(125,plain,
additive_inverse(multiply(X,Y)) = multiply(X,additive_inverse(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,87,theory(equality)]),left_additive_identity,10,theory(equality)]) ).
cnf(126,plain,
additive_inverse(multiply(additive_inverse(X),X)) = additive_inverse(X),
inference('PARAMODULATE',[status(thm)],[boolean_ring,125,theory(equality)]) ).
cnf(138,plain,
additive_identity = additive_inverse(add(X,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[110,boolean_ring,theory(equality)]),55,boolean_ring,125,theory(equality)]) ).
cnf(139,plain,
additive_inverse(multiply(X,Y)) = multiply(additive_inverse(X),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,110,theory(equality)]),left_additive_identity,10,theory(equality)]) ).
cnf(143,plain,
X = additive_inverse(X),
inference('REWRITE',[status(thm)],[126,11,boolean_ring,139,theory(equality)]) ).
cnf(144,plain,
additive_identity = add(X,X),
inference('REWRITE',[status(thm)],[138,143,theory(equality)]) ).
cnf(145,plain,
add(X,add(X,Y)) = add(additive_identity,Y),
inference('EMBED',[status(thm)],[144]) ).
cnf(160,plain,
multiply(multiply(b,a),multiply(c,a)) = multiply(b,a),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[boolean_ring,40,theory(equality)]),112,theory(equality)]) ).
cnf(180,plain,
multiply(multiply(b,c),multiply(a,X)) = multiply(multiply(b,a),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity_for_multiplication,160,theory(equality)]),41,18,theory(equality)]) ).
cnf(222,plain,
add(multiply(c,a),a) = add(c,a),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[27,39,theory(equality)]),left_additive_identity,144,theory(equality)]) ).
cnf(223,plain,
add(multiply(c,a),add(a,X)) = add(c,add(a,X)),
inference('EMBED',[status(thm)],[222]) ).
cnf(224,plain,
add(b,multiply(b,c)) = add(b,c),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[27,43,theory(equality)]),left_additive_identity,144,theory(equality)]) ).
cnf(225,plain,
add(b,add(multiply(b,c),X)) = add(b,add(c,X)),
inference('EMBED',[status(thm)],[224]) ).
cnf(244,plain,
c = multiply(c,a),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,223,theory(equality)]),left_additive_identity,144,theory(equality)]) ).
cnf(247,plain,
multiply(c,multiply(a,X)) = multiply(c,X),
inference('PARAMODULATE',[status(thm)],[44,244,theory(equality)]) ).
cnf(252,plain,
c = multiply(b,c),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[145,225,theory(equality)]),left_additive_identity,144,theory(equality)]) ).
cnf(253,plain,
multiply(c,X) = multiply(multiply(b,a),X),
inference('REWRITE',[status(thm)],[180,247,252,theory(equality)]) ).
cnf(256,plain,
$false,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,253,theory(equality)]),prove_commutativity,244,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : RNG008-7 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n019.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 : Mon May 30 11:33:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.45 /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p 2022-05-30T11:33:41
% 0.20/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n019.cluster.edu at 2022-05-30T11:33:41
% 0.20/0.48
% 0.20/0.48 ; Recognized left identity assertion (= (|add| |additive_identity| ?X) ?X).
% 0.20/0.48 ; Recognized right identity assertion (= (|add| ?X |additive_identity|) ?X).
% 0.20/0.48 ; Recognized possible left inverse assertion (= (|add| (|additive_inverse| ?X) ?X) |additive_identity|).
% 0.20/0.48 ; Recognized possible right inverse assertion (= (|add| ?X (|additive_inverse| ?X)) |additive_identity|).
% 0.20/0.48 ; Recognized associativity assertion (= (|add| ?X (|add| ?Y ?Z)) (|add| (|add| ?X ?Y) ?Z)).
% 0.20/0.48 ; Recognized commutativity assertion (= (|add| ?X ?Y) (|add| ?Y ?X)).
% 0.20/0.48 ; Recognized associativity assertion (= (|multiply| ?X (|multiply| ?Y ?Z)) (|multiply| (|multiply| ?X ?Y) ?Z)).
% 0.20/0.48 ; Declaring add to be commutative.
% 0.50/0.70 ; Declaring add to be associative-commutative.
% 0.50/0.70
% 0.50/0.70 #||
% 0.50/0.70 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.50/0.70 % SZS output start Refutation
% See solution above
% 0.50/0.71 ||#
% 0.50/0.71
% 0.50/0.71 ; Summary of computation:
% 0.50/0.71 ; 1426 formulas have been input or derived (from 52 formulas).
% 0.50/0.71 ; 256 (18%) were retained. Of these,
% 0.50/0.71 ; 136 (53%) were simplified or subsumed later,
% 0.50/0.71 ; 120 (47%) are still being kept.
% 0.50/0.71 ;
% 0.50/0.71 ; Run time in seconds excluding printing time:
% 0.50/0.71 ; 0.002 1% Read assertion file (1 call)
% 0.50/0.71 ; 0.000 0% Assert (12 calls)
% 0.50/0.71 ; 0.031 14% Process new row (1,376 calls)
% 0.50/0.71 ; 0.002 1% Resolution (102 calls)
% 0.50/0.71 ; 0.025 11% Paramodulation (51 calls)
% 0.50/0.71 ; 0.000 0% Embedding (73 calls)
% 0.50/0.71 ; 0.099 43% Forward simplification (1,104 calls)
% 0.50/0.71 ; 0.007 3% Backward simplification (188 calls)
% 0.50/0.71 ; 0.019 8% Ordering (5,035 calls)
% 0.50/0.71 ; 0.016 7% Ordering ac (1,290 calls)
% 0.50/0.71 ; 0.000 0% Sortal reasoning (32 calls)
% 0.50/0.71 ; 0.000 0% Purity testing (1 call)
% 0.50/0.71 ; 0.027 12% Other
% 0.50/0.71 ; 0.228 Total
% 0.50/0.71 ; 0.237 Real time
% 0.50/0.71 ;
% 0.50/0.71 ; Term-hash-array has 687 terms in all.
% 0.50/0.71 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.50/0.71 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.50/0.71 ; Path-index has 347 entries (393 at peak, 711 added, 364 deleted).
% 0.50/0.71 ; Path-index has 300 nodes (304 at peak, 461 added, 161 deleted).
% 0.50/0.71 ; Trie-index has 347 entries (393 at peak, 711 added, 364 deleted).
% 0.50/0.71 ; Trie-index has 861 nodes (976 at peak, 1,261 added, 400 deleted).
% 0.50/0.71 ; Retrieved 53,616 generalization terms in 9,942 calls.
% 0.50/0.71 ; Retrieved 771 instance terms in 271 calls.
% 0.50/0.71 ; Retrieved 2,298 unifiable terms in 313 calls.
% 0.50/0.71 ;
% 0.50/0.71 ; The agenda of rows to process has 23 entries:
% 0.50/0.71 ; 4 with value 17 4 with value 22 4 with value 24
% 0.50/0.71 ; 6 with value 19 1 with value 23 2 with value 26
% 0.50/0.71 ; 2 with value 21
% 0.50/0.71 ; The agenda of rows to give has 91 entries:
% 0.50/0.71 ; 1 with value (4 16) 6 with value (4 22) 1 with value (4 30)
% 0.50/0.71 ; 4 with value (4 17) 24 with value (4 24) 8 with value (4 33)
% 0.50/0.71 ; 2 with value (4 18) 5 with value (4 26) 8 with value (4 34)
% 0.50/0.71 ; 4 with value (4 19) 4 with value (4 27) 4 with value (4 38)
% 0.50/0.71 ; 5 with value (4 20) 9 with value (4 28) 2 with value (4 46)
% 0.50/0.71 ; 4 with value (4 21)
% 0.50/0.71 Evaluation took:
% 0.50/0.71 0.237 seconds of real time
% 0.50/0.71 0.211362 seconds of user run time
% 0.50/0.71 0.025936 seconds of system run time
% 0.50/0.71 [Run times include 0.005 seconds GC run time.]
% 0.50/0.71 0 calls to %EVAL
% 0.50/0.71 0 page faults and
% 0.50/0.71 16,354,288 bytes consed.
% 0.50/0.71 :PROOF-FOUND
% 0.50/0.71 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-30T11:33:41
% 0.50/0.71 :PROOF-FOUND
% 0.50/0.71 *
%------------------------------------------------------------------------------