%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP178-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 : Sat Jul 16 11:37:20 EDT 2022
% Result : Unsatisfiable 0.85s 1.07s
% Output : Refutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 5 RR)
% Number of literals : 21 ( 20 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 27 ( 1 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(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
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_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(p09a_3,hypothesis,
least_upper_bound(identity,c) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p09a_3) ).
cnf(p09a_4,hypothesis,
greatest_lower_bound(a,b) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p09a_4) ).
cnf(prove_p09a,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p09a) ).
cnf(55,plain,
greatest_lower_bound(identity,c) = identity,
inference('PARAMODULATE',[status(thm)],[glb_absorbtion,p09a_3,theory(equality)]) ).
cnf(110,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(129,plain,
multiply(X,identity) = greatest_lower_bound(multiply(X,a),multiply(X,b)),
inference('PARAMODULATE',[status(thm)],[monotony_glb1,p09a_4,theory(equality)]) ).
cnf(151,plain,
X = greatest_lower_bound(multiply(a,X),multiply(b,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[monotony_glb2,p09a_4,theory(equality)]),left_identity,theory(equality)]) ).
cnf(152,plain,
greatest_lower_bound(multiply(a,X),greatest_lower_bound(multiply(b,X),Y)) = greatest_lower_bound(X,Y),
inference('EMBED',[status(thm)],[151]) ).
cnf(163,plain,
greatest_lower_bound(multiply(X,a),multiply(X,b)) = greatest_lower_bound(multiply(X,a),greatest_lower_bound(multiply(X,b),multiply(X,c))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[monotony_glb1,55,theory(equality)]),129,theory(equality)]) ).
cnf(224,plain,
X = greatest_lower_bound(multiply(inverse(inverse(X)),a),multiply(inverse(inverse(X)),b)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[110,left_inverse,theory(equality)]),129,theory(equality)]) ).
cnf(226,plain,
multiply(X,Y) = multiply(inverse(inverse(X)),Y),
inference('PARAMODULATE',[status(thm)],[110,110,theory(equality)]) ).
cnf(227,plain,
X = greatest_lower_bound(multiply(X,a),multiply(X,b)),
inference('REWRITE',[status(thm)],[224,226,theory(equality)]) ).
cnf(235,plain,
X = greatest_lower_bound(multiply(X,c),X),
inference('REWRITE',[status(thm)],[163,227,theory(equality)]) ).
cnf(236,plain,
greatest_lower_bound(multiply(X,c),greatest_lower_bound(X,Y)) = greatest_lower_bound(X,Y),
inference('EMBED',[status(thm)],[235]) ).
cnf(510,plain,
$false,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[236,152,theory(equality)]),prove_p09a]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP178-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : run-snark %s %d
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 07:48:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.45 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46 *
% 0.18/0.46 *
% 0.18/0.47 #<PACKAGE "SNARK-USER">
% 0.18/0.47 *
% 0.18/0.47 SNARK-TPTP-OPTIONS
% 0.18/0.47 *
% 0.18/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.47 (USE-FACTORING :POS)
% 0.18/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.47 *
% 0.18/0.47 "."
% 0.18/0.47 *
% 0.18/0.47 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T07:48:51
% 0.18/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n023.cluster.edu at 2022-06-13T07:48:51
% 0.18/0.48
% 0.18/0.48 ; Recognized left identity assertion (= (|multiply| |identity| ?X) ?X).
% 0.18/0.48 ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |identity|).
% 0.18/0.48 ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 0.18/0.48 ; Recognized commutativity assertion (= (|greatest_lower_bound| ?X ?Y) (|greatest_lower_bound| ?Y ?X)).
% 0.18/0.48 ; Recognized commutativity assertion (= (|least_upper_bound| ?X ?Y) (|least_upper_bound| ?Y ?X)).
% 0.18/0.48 ; Recognized associativity assertion (= (|greatest_lower_bound| ?X (|greatest_lower_bound| ?Y ?Z)) (|greatest_lower_bound| (|greatest_lower_bound| ?X ?Y) ?Z)).
% 0.18/0.48 ; Recognized associativity assertion (= (|least_upper_bound| ?X (|least_upper_bound| ?Y ?Z)) (|least_upper_bound| (|least_upper_bound| ?X ?Y) ?Z)).
% 0.18/0.48 ; Declaring greatest_lower_bound to be commutative.
% 0.18/0.48 ; Declaring greatest_lower_bound to be associative-commutative.
% 0.18/0.48 ; Declaring least_upper_bound to be commutative.
% 0.85/1.07 ; Declaring least_upper_bound to be associative-commutative.
% 0.85/1.07
% 0.85/1.07 #||
% 0.85/1.07 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.85/1.07 % SZS output start Refutation
% See solution above
% 0.85/1.08 ||#
% 0.85/1.08
% 0.85/1.08 ; Summary of computation:
% 0.85/1.08 ; 3285 formulas have been input or derived (from 62 formulas).
% 0.85/1.08 ; 510 (16%) were retained. Of these,
% 0.85/1.08 ; 69 (14%) were simplified or subsumed later,
% 0.85/1.08 ; 441 (86%) are still being kept.
% 0.85/1.08 ;
% 0.85/1.08 ; Run time in seconds excluding printing time:
% 0.85/1.08 ; 0.004 1% Read assertion file (1 call)
% 0.85/1.08 ; 0.001 0% Assert (20 calls)
% 0.85/1.08 ; 0.048 8% Process new row (3,102 calls)
% 0.85/1.08 ; 0.003 0% Resolution (122 calls)
% 0.85/1.08 ; 0.055 9% Paramodulation (61 calls)
% 0.85/1.08 ; 0.002 0% Embedding (248 calls)
% 0.85/1.08 ; 0.414 68% Forward simplification (2,860 calls)
% 0.85/1.08 ; 0.020 3% Backward simplification (268 calls)
% 0.85/1.08 ; 0.014 2% Ordering (3,737 calls)
% 0.85/1.08 ; 0.012 2% Ordering ac (1,269 calls)
% 0.85/1.08 ; 0.001 0% Sortal reasoning (32 calls)
% 0.85/1.08 ; 0.000 0% Purity testing (1 call)
% 0.85/1.08 ; 0.032 5% Other
% 0.85/1.08 ; 0.606 Total
% 0.85/1.08 ; 0.608 Real time
% 0.85/1.08 ;
% 0.85/1.08 ; Term-hash-array has 1,338 terms in all.
% 0.85/1.08 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.85/1.08 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.85/1.08 ; Path-index has 1,183 entries (1,183 at peak, 1,358 added, 175 deleted).
% 0.85/1.08 ; Path-index has 473 nodes (473 at peak, 507 added, 34 deleted).
% 0.85/1.08 ; Trie-index has 1,183 entries (1,183 at peak, 1,358 added, 175 deleted).
% 0.85/1.08 ; Trie-index has 372 nodes (372 at peak, 418 added, 46 deleted).
% 0.85/1.08 ; Retrieved 766,629 generalization terms in 30,704 calls.
% 0.85/1.08 ; Retrieved 724 instance terms in 291 calls.
% 0.85/1.08 ; Retrieved 7,280 unifiable terms in 314 calls.
% 0.85/1.08 ;
% 0.85/1.08 ; The agenda of rows to process has 81 entries:
% 0.85/1.08 ; 1 with value 15 6 with value 23 8 with value 29
% 0.85/1.08 ; 4 with value 16 3 with value 24 8 with value 30
% 0.85/1.08 ; 2 with value 18 1 with value 25 1 with value 31
% 0.85/1.08 ; 5 with value 20 13 with value 26 1 with value 32
% 0.85/1.08 ; 4 with value 21 4 with value 27 4 with value 33
% 0.85/1.08 ; 13 with value 22 3 with value 28
% 0.85/1.08 ; The agenda of rows to give has 379 entries:
% 0.85/1.08 ; 23 with value (4 13) 27 with value (4 20) 4 with value (4 27)
% 0.85/1.08 ; 20 with value (4 14) 46 with value (4 21) 12 with value (4 28)
% 0.85/1.08 ; 31 with value (4 15) 32 with value (4 22) 4 with value (4 30)
% 0.85/1.08 ; 56 with value (4 16) 26 with value (4 23) 4 with value (4 31)
% 0.85/1.08 ; 18 with value (4 17) 12 with value (4 24) 4 with value (4 33)
% 0.85/1.08 ; 14 with value (4 18) 12 with value (4 25) 4 with value (4 36)
% 0.85/1.08 ; 26 with value (4 19) 4 with value (4 26)
% 0.85/1.08 Evaluation took:
% 0.85/1.08 0.608 seconds of real time
% 0.85/1.08 0.580967 seconds of user run time
% 0.85/1.08 0.027089 seconds of system run time
% 0.85/1.08 [Run times include 0.009 seconds GC run time.]
% 0.85/1.08 0 calls to %EVAL
% 0.85/1.08 0 page faults and
% 0.85/1.08 34,818,896 bytes consed.
% 0.85/1.08 :PROOF-FOUND
% 0.85/1.08 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T07:48:52
% 0.85/1.08 :PROOF-FOUND
% 0.85/1.08 *
%------------------------------------------------------------------------------