%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP167-5 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n017.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 : Sat Jul 16 11:37:14 EDT 2022
% Result : Unsatisfiable 11.38s 11.66s
% Output : Refutation 11.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 44 ( 44 unt; 0 nHn; 8 RR)
% Number of literals : 44 ( 43 equ; 6 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; 2 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
cnf(monotony_glb1,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
cnf(p10,axiom,
inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
cnf(lat4_1,axiom,
positive_part(X) = least_upper_bound(X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_1) ).
cnf(lat4_2,axiom,
negative_part(X) = greatest_lower_bound(X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_2) ).
cnf(lat4_3,axiom,
least_upper_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(X,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_3) ).
cnf(prove_lat4,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lat4) ).
cnf(46,plain,
inverse(positive_part(X)) = greatest_lower_bound(inverse(X),inverse(identity)),
inference('PARAMODULATE',[status(thm)],[p10,lat4_1,theory(equality)]) ).
cnf(58,plain,
X = multiply(inverse(Y),multiply(Y,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity,left_inverse,theory(equality)]),left_identity,theory(equality)]) ).
cnf(59,plain,
multiply(multiply(X,inverse(Y)),Y) = multiply(X,identity),
inference('PARAMODULATE',[status(thm)],[associativity,left_inverse,theory(equality)]) ).
cnf(65,plain,
multiply(X,positive_part(Y)) = least_upper_bound(multiply(X,Y),multiply(X,identity)),
inference('PARAMODULATE',[status(thm)],[monotony_lub1,lat4_1,theory(equality)]) ).
cnf(72,plain,
multiply(X,negative_part(Y)) = greatest_lower_bound(multiply(X,Y),multiply(X,identity)),
inference('PARAMODULATE',[status(thm)],[monotony_glb1,lat4_2,theory(equality)]) ).
cnf(73,plain,
a != greatest_lower_bound(multiply(positive_part(a),a),multiply(positive_part(a),identity)),
inference('REWRITE',[status(thm)],[prove_lat4,72,theory(equality)]) ).
cnf(80,plain,
multiply(positive_part(X),Y) = least_upper_bound(multiply(X,Y),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[monotony_lub2,lat4_1,theory(equality)]),left_identity,theory(equality)]) ).
cnf(81,plain,
a != greatest_lower_bound(least_upper_bound(multiply(a,a),a),positive_part(multiply(a,identity))),
inference('REWRITE',[status(thm)],[73,lat4_1,80,theory(equality)]) ).
cnf(94,plain,
least_upper_bound(X,negative_part(Y)) = greatest_lower_bound(least_upper_bound(X,Y),positive_part(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[lat4_3,lat4_2,theory(equality)]),lat4_1,theory(equality)]) ).
cnf(108,plain,
X = multiply(inverse(inverse(X)),identity),
inference('PARAMODULATE',[status(thm)],[58,left_inverse,theory(equality)]) ).
cnf(109,plain,
multiply(X,Y) = multiply(inverse(inverse(X)),Y),
inference('PARAMODULATE',[status(thm)],[58,58,theory(equality)]) ).
cnf(110,plain,
X = multiply(X,identity),
inference('REWRITE',[status(thm)],[108,109,theory(equality)]) ).
cnf(111,plain,
a != greatest_lower_bound(least_upper_bound(multiply(a,a),a),positive_part(a)),
inference('REWRITE',[status(thm)],[81,110,theory(equality)]) ).
cnf(112,plain,
multiply(multiply(X,inverse(Y)),Y) = X,
inference('REWRITE',[status(thm)],[59,110,theory(equality)]) ).
cnf(113,plain,
multiply(X,positive_part(Y)) = least_upper_bound(multiply(X,Y),X),
inference('REWRITE',[status(thm)],[65,110,theory(equality)]) ).
cnf(114,plain,
multiply(X,negative_part(Y)) = greatest_lower_bound(multiply(X,Y),X),
inference('REWRITE',[status(thm)],[72,110,theory(equality)]) ).
cnf(121,plain,
inverse(identity) = identity,
inference('PARAMODULATE',[status(thm)],[left_inverse,110,theory(equality)]) ).
cnf(122,plain,
inverse(positive_part(X)) = negative_part(inverse(X)),
inference('REWRITE',[status(thm)],[46,lat4_2,121,theory(equality)]) ).
cnf(154,plain,
X = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[112,left_inverse,theory(equality)]),left_identity,theory(equality)]) ).
cnf(156,plain,
greatest_lower_bound(least_upper_bound(X,multiply(X,inverse(Y))),least_upper_bound(multiply(X,Y),X)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[112,122,theory(equality)]),112,113,monotony_glb2,114,theory(equality)]) ).
cnf(164,plain,
multiply(X,inverse(X)) = identity,
inference('PARAMODULATE',[status(thm)],[left_inverse,154,theory(equality)]) ).
cnf(166,plain,
positive_part(X) = inverse(negative_part(inverse(X))),
inference('PARAMODULATE',[status(thm)],[154,122,theory(equality)]) ).
cnf(221,plain,
least_upper_bound(X,negative_part(Y)) = greatest_lower_bound(least_upper_bound(X,Y),inverse(negative_part(inverse(X)))),
inference('REWRITE',[status(thm)],[94,166,theory(equality)]) ).
cnf(223,plain,
a != greatest_lower_bound(least_upper_bound(multiply(a,a),a),inverse(negative_part(inverse(a)))),
inference('REWRITE',[status(thm)],[111,166,theory(equality)]) ).
cnf(225,plain,
least_upper_bound(X,Y) = inverse(greatest_lower_bound(inverse(X),inverse(Y))),
inference('PARAMODULATE',[status(thm)],[154,p10,theory(equality)]) ).
cnf(248,plain,
greatest_lower_bound(inverse(greatest_lower_bound(inverse(X),inverse(multiply(X,inverse(Y))))),inverse(greatest_lower_bound(inverse(multiply(X,Y)),inverse(X)))) = X,
inference('REWRITE',[status(thm)],[156,225,theory(equality)]) ).
cnf(272,plain,
inverse(greatest_lower_bound(inverse(X),inverse(greatest_lower_bound(Y,Z)))) = greatest_lower_bound(inverse(greatest_lower_bound(inverse(X),inverse(Y))),inverse(greatest_lower_bound(inverse(X),inverse(Z)))),
inference('REWRITE',[status(thm)],[lat4_3,225,theory(equality)]) ).
cnf(278,plain,
inverse(greatest_lower_bound(inverse(X),inverse(greatest_lower_bound(multiply(X,inverse(Y)),multiply(X,Y))))) = X,
inference('REWRITE',[status(thm)],[248,272,theory(equality)]) ).
cnf(288,plain,
inverse(greatest_lower_bound(inverse(X),inverse(negative_part(Y)))) = greatest_lower_bound(inverse(greatest_lower_bound(inverse(X),inverse(Y))),inverse(negative_part(inverse(X)))),
inference('REWRITE',[status(thm)],[221,225,theory(equality)]) ).
cnf(290,plain,
a != inverse(greatest_lower_bound(inverse(a),inverse(negative_part(multiply(a,a))))),
inference('REWRITE',[status(thm)],[223,288,225,theory(equality)]) ).
cnf(1979,plain,
inverse(greatest_lower_bound(inverse(X),inverse(negative_part(multiply(X,X))))) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[278,164,theory(equality)]),lat4_2,theory(equality)]) ).
cnf(1980,plain,
$false,
inference('REWRITE',[status(thm)],[290,1979,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP167-5 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.00/0.09 % Command : run-snark %s %d
% 0.09/0.29 % Computer : n017.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.14/0.29 % WCLimit : 600
% 0.14/0.29 % DateTime : Tue Jun 14 13:19:24 EDT 2022
% 0.14/0.29 % CPUTime :
% 0.14/0.38 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.38 *
% 0.14/0.38 *
% 0.14/0.39 #<PACKAGE "SNARK-USER">
% 0.14/0.39 *
% 0.14/0.39 SNARK-TPTP-OPTIONS
% 0.14/0.39 *
% 0.14/0.39 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.14/0.39 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.14/0.39 (USE-FACTORING :POS)
% 0.14/0.39 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.14/0.39 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.14/0.39 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.14/0.39 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.14/0.39 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.14/0.39 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.14/0.39 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.14/0.39 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.14/0.39 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.14/0.39 (DECLARE-TPTP-SYMBOLS2))
% 0.14/0.39 *
% 0.14/0.39 "."
% 0.14/0.39 *
% 0.14/0.39 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T13:19:24
% 0.14/0.39 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n017.cluster.edu at 2022-06-14T13:19:24
% 0.14/0.40
% 0.14/0.40 ; Recognized left identity assertion (= (|multiply| |identity| ?X) ?X).
% 0.14/0.40 ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |identity|).
% 0.14/0.40 ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 0.14/0.40 ; Recognized commutativity assertion (= (|greatest_lower_bound| ?X ?Y) (|greatest_lower_bound| ?Y ?X)).
% 0.14/0.40 ; Recognized commutativity assertion (= (|least_upper_bound| ?X ?Y) (|least_upper_bound| ?Y ?X)).
% 0.14/0.40 ; Recognized associativity assertion (= (|greatest_lower_bound| ?X (|greatest_lower_bound| ?Y ?Z)) (|greatest_lower_bound| (|greatest_lower_bound| ?X ?Y) ?Z)).
% 0.14/0.40 ; Recognized associativity assertion (= (|least_upper_bound| ?X (|least_upper_bound| ?Y ?Z)) (|least_upper_bound| (|least_upper_bound| ?X ?Y) ?Z)).
% 0.14/0.40 ; Declaring greatest_lower_bound to be commutative.
% 0.14/0.40 ; Declaring greatest_lower_bound to be associative-commutative.
% 0.14/0.40 ; Declaring least_upper_bound to be commutative.
% 11.38/11.66 ; Declaring least_upper_bound to be associative-commutative.
% 11.38/11.66
% 11.38/11.66 #||
% 11.38/11.66 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.38/11.66 % SZS output start Refutation
% See solution above
% 11.48/11.68 ||#
% 11.48/11.68
% 11.48/11.68 ; Summary of computation:
% 11.48/11.68 ; 12513 formulas have been input or derived (from 125 formulas).
% 11.48/11.68 ; 1980 (16%) were retained. Of these,
% 11.48/11.68 ; 556 (28%) were simplified or subsumed later,
% 11.48/11.68 ; 1424 (72%) are still being kept.
% 11.48/11.68 ;
% 11.48/11.68 ; Run time in seconds excluding printing time:
% 11.48/11.68 ; 0.002 0% Read assertion file (1 call)
% 11.48/11.68 ; 0.001 0% Assert (21 calls)
% 11.48/11.68 ; 0.410 4% Process new row (12,235 calls)
% 11.48/11.68 ; 0.008 0% Resolution (248 calls)
% 11.48/11.68 ; 0.386 3% Paramodulation (124 calls)
% 11.48/11.68 ; 0.041 0% Embedding (612 calls)
% 11.48/11.68 ; 8.589 76% Forward simplification (11,331 calls)
% 11.48/11.68 ; 0.272 2% Backward simplification (1,421 calls)
% 11.48/11.68 ; 0.568 5% Ordering (59,107 calls)
% 11.48/11.68 ; 0.898 8% Ordering ac (4,655 calls)
% 11.48/11.68 ; 0.000 0% Sortal reasoning (32 calls)
% 11.48/11.68 ; 0.000 0% Purity testing (1 call)
% 11.48/11.68 ; 0.092 1% Other
% 11.48/11.68 ; 11.267 Total
% 11.48/11.68 ; 11.290 Real time
% 11.48/11.68 ;
% 11.48/11.68 ; Term-hash-array has 5,884 terms in all.
% 11.48/11.68 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 11.48/11.68 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 11.48/11.68 ; Path-index has 4,028 entries (4,035 at peak, 6,079 added, 2,051 deleted).
% 11.48/11.68 ; Path-index has 3,781 nodes (3,798 at peak, 4,400 added, 619 deleted).
% 11.48/11.68 ; Trie-index has 4,028 entries (4,035 at peak, 6,079 added, 2,051 deleted).
% 11.48/11.68 ; Trie-index has 6,549 nodes (6,559 at peak, 7,536 added, 987 deleted).
% 11.48/11.68 ; Retrieved 8,538,980 generalization terms in 167,830 calls.
% 11.48/11.68 ; Retrieved 13,072 instance terms in 2,642 calls.
% 11.48/11.68 ; Retrieved 30,287 unifiable terms in 780 calls.
% 11.48/11.68 ;
% 11.48/11.68 ; The agenda of rows to process has 106 entries:
% 11.48/11.68 ; 1 with value 22 4 with value 31 4 with value 40
% 11.48/11.68 ; 2 with value 23 4 with value 32 1 with value 41
% 11.48/11.68 ; 2 with value 24 6 with value 33 11 with value 42
% 11.48/11.68 ; 2 with value 25 11 with value 34 3 with value 43
% 11.48/11.68 ; 3 with value 26 11 with value 35 4 with value 45
% 11.48/11.68 ; 3 with value 27 2 with value 36 1 with value 46
% 11.48/11.68 ; 1 with value 28 2 with value 37 1 with value 60
% 11.48/11.68 ; 7 with value 29 9 with value 38 1 with value 61
% 11.48/11.68 ; 5 with value 30 5 with value 39
% 11.48/11.68 ; The agenda of rows to give has 1345 entries:
% 11.48/11.68 ; 1 with value (4 21) 42 with value (4 36) 7 with value (4 49)
% 11.48/11.68 ; 9 with value (4 24) 29 with value (4 37) 4 with value (4 50)
% 11.48/11.68 ; 41 with value (4 25) 71 with value (4 38) 8 with value (4 51)
% 11.48/11.68 ; 57 with value (4 26) 44 with value (4 39) 7 with value (4 52)
% 11.48/11.68 ; 43 with value (4 27) 36 with value (4 40) 4 with value (4 53)
% 11.48/11.68 ; 51 with value (4 28) 28 with value (4 41) 2 with value (4 55)
% 11.48/11.68 ; 65 with value (4 29) 21 with value (4 42) 1 with value (4 56)
% 11.48/11.68 ; 131 with value (4 30) 11 with value (4 43) 2 with value (4 57)
% 11.48/11.68 ; 184 with value (4 31) 13 with value (4 44) 2 with value (4 59)
% 11.48/11.68 ; 124 with value (4 32) 12 with value (4 45) 2 with value (4 63)
% 11.48/11.68 ; 87 with value (4 33) 14 with value (4 46) 2 with value (4 67)
% 11.48/11.68 ; 95 with value (4 34) 24 with value (4 47) 2 with value (4 69)
% 11.48/11.68 ; 58 with value (4 35) 9 with value (4 48) 2 with value (4 77)
% 11.48/11.68 Evaluation took:
% 11.48/11.68 11.291 seconds of real time
% 11.48/11.68 11.030119 seconds of user run time
% 11.48/11.68 0.254918 seconds of system run time
% 11.48/11.68 [Run times include 0.268 seconds GC run time.]
% 11.48/11.68 0 calls to %EVAL
% 11.48/11.68 0 page faults and
% 11.48/11.68 318,337,392 bytes consed.
% 11.48/11.68 :PROOF-FOUND
% 11.48/11.68 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T13:19:35
% 11.48/11.68 :PROOF-FOUND
% 11.48/11.68 *
%------------------------------------------------------------------------------