TSTP Solution File: GRP184-4 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n024.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 11:37:24 EDT 2022
% Result : Unsatisfiable 0.20s 0.57s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 12
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 6 RR)
% Number of literals : 20 ( 19 equ; 4 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X,X) = X,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).
cnf(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
cnf(p21x_1,hypothesis,
inverse(identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21x_1) ).
cnf(p21x_2,hypothesis,
inverse(inverse(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21x_2) ).
cnf(p21x_3,hypothesis,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21x_3) ).
cnf(p21x_4,hypothesis,
inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21x_4) ).
cnf(prove_p21x,negated_conjecture,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p21x) ).
cnf(23,plain,
least_upper_bound(multiply(a,inverse(greatest_lower_bound(a,identity))),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),a),multiply(inverse(greatest_lower_bound(a,identity)),identity)),
inference('REWRITE',[status(thm)],[prove_p21x,monotony_lub1,left_identity,monotony_lub2,theory(equality)]) ).
cnf(24,plain,
multiply(X,inverse(X)) = identity,
inference('PARAMODULATE',[status(thm)],[left_inverse,p21x_2,theory(equality)]) ).
cnf(62,plain,
inverse(X) = multiply(inverse(X),identity),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[p21x_3,p21x_1,theory(equality)]),left_identity,theory(equality)]) ).
cnf(63,plain,
least_upper_bound(multiply(a,inverse(greatest_lower_bound(a,identity))),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),a),inverse(greatest_lower_bound(a,identity))),
inference('REWRITE',[status(thm)],[23,62,theory(equality)]) ).
cnf(64,plain,
inverse(multiply(X,inverse(Y))) = multiply(Y,inverse(X)),
inference('PARAMODULATE',[status(thm)],[p21x_3,p21x_2,theory(equality)]) ).
cnf(65,plain,
inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(a),identity))) != least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),a),inverse(greatest_lower_bound(a,identity))),
inference('REWRITE',[status(thm)],[63,idempotence_of_gld,p21x_4,left_identity,24,monotony_glb2,64,theory(equality)]) ).
cnf(66,plain,
inverse(multiply(inverse(X),Y)) = multiply(inverse(Y),X),
inference('PARAMODULATE',[status(thm)],[p21x_3,p21x_2,theory(equality)]) ).
cnf(67,plain,
$false,
inference('REWRITE',[status(thm)],[65,idempotence_of_gld,p21x_4,62,left_inverse,monotony_glb1,66,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : run-snark %s %d
% 0.13/0.35 % Computer : n024.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 : Mon Jun 13 10:46:48 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 *
% 0.20/0.48 #<PACKAGE "SNARK-USER">
% 0.20/0.48 *
% 0.20/0.48 SNARK-TPTP-OPTIONS
% 0.20/0.48 *
% 0.20/0.48 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.48 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.48 (USE-FACTORING :POS)
% 0.20/0.48 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.48 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.48 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.48 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.48 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.48 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.48 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.48 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.48 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.48 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.48 *
% 0.20/0.48 "."
% 0.20/0.48 *
% 0.20/0.48 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T10:46:48
% 0.20/0.49 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n024.cluster.edu at 2022-06-13T10:46:48
% 0.20/0.50
% 0.20/0.50 ; Recognized left identity assertion (= (|multiply| |identity| ?X) ?X).
% 0.20/0.50 ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |identity|).
% 0.20/0.50 ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 0.20/0.50 ; Recognized commutativity assertion (= (|greatest_lower_bound| ?X ?Y) (|greatest_lower_bound| ?Y ?X)).
% 0.20/0.50 ; Recognized commutativity assertion (= (|least_upper_bound| ?X ?Y) (|least_upper_bound| ?Y ?X)).
% 0.20/0.50 ; Recognized associativity assertion (= (|greatest_lower_bound| ?X (|greatest_lower_bound| ?Y ?Z)) (|greatest_lower_bound| (|greatest_lower_bound| ?X ?Y) ?Z)).
% 0.20/0.50 ; Recognized associativity assertion (= (|least_upper_bound| ?X (|least_upper_bound| ?Y ?Z)) (|least_upper_bound| (|least_upper_bound| ?X ?Y) ?Z)).
% 0.20/0.50 ; Declaring greatest_lower_bound to be commutative.
% 0.20/0.50 ; Declaring greatest_lower_bound to be associative-commutative.
% 0.20/0.50 ; Declaring least_upper_bound to be commutative.
% 0.20/0.57 ; Declaring least_upper_bound to be associative-commutative.
% 0.20/0.57
% 0.20/0.57 #||
% 0.20/0.57 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.57 % SZS output start Refutation
% See solution above
% 0.20/0.57 ||#
% 0.20/0.57
% 0.20/0.57 ; Summary of computation:
% 0.20/0.57 ; 276 formulas have been input or derived (from 14 formulas).
% 0.20/0.57 ; 67 (24%) were retained. Of these,
% 0.20/0.57 ; 4 ( 6%) were simplified or subsumed later,
% 0.20/0.57 ; 63 (94%) are still being kept.
% 0.20/0.57 ;
% 0.20/0.57 ; Run time in seconds excluding printing time:
% 0.20/0.57 ; 0.004 5% Read assertion file (1 call)
% 0.20/0.57 ; 0.001 1% Assert (21 calls)
% 0.20/0.57 ; 0.008 10% Process new row (265 calls)
% 0.20/0.57 ; 0.000 0% Resolution (26 calls)
% 0.20/0.57 ; 0.006 8% Paramodulation (13 calls)
% 0.20/0.57 ; 0.001 1% Embedding (28 calls)
% 0.20/0.57 ; 0.027 34% Forward simplification (242 calls)
% 0.20/0.57 ; 0.004 5% Backward simplification (43 calls)
% 0.20/0.57 ; 0.000 0% Ordering (181 calls)
% 0.20/0.57 ; 0.002 2% Ordering ac (60 calls)
% 0.20/0.57 ; 0.000 0% Sortal reasoning (32 calls)
% 0.20/0.57 ; 0.000 0% Purity testing (1 call)
% 0.20/0.57 ; 0.027 34% Other
% 0.20/0.57 ; 0.080 Total
% 0.20/0.57 ; 0.083 Real time
% 0.20/0.57 ;
% 0.20/0.57 ; Term-hash-array has 211 terms in all.
% 0.20/0.57 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.20/0.57 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.20/0.57 ; Path-index has 199 entries (207 at peak, 225 added, 26 deleted).
% 0.20/0.57 ; Path-index has 186 nodes (209 at peak, 266 added, 80 deleted).
% 0.20/0.57 ; Trie-index has 199 entries (207 at peak, 225 added, 26 deleted).
% 0.20/0.57 ; Trie-index has 127 nodes (130 at peak, 144 added, 17 deleted).
% 0.20/0.57 ; Retrieved 5,902 generalization terms in 1,338 calls.
% 0.20/0.57 ; Retrieved 188 instance terms in 48 calls.
% 0.20/0.57 ; Retrieved 183 unifiable terms in 60 calls.
% 0.20/0.57 ;
% 0.20/0.57 ; The agenda of input rows to give has 8 entries:
% 0.20/0.57 ; 3 with value 13 1 with value 14 4 with value 16
% 0.20/0.57 ; The agenda of rows to give has 41 entries:
% 0.20/0.57 ; 1 with value (4 10) 4 with value (4 21) 4 with value (4 27)
% 0.20/0.57 ; 2 with value (4 11) 4 with value (4 22) 4 with value (4 30)
% 0.20/0.57 ; 2 with value (4 15) 4 with value (4 24) 4 with value (4 31)
% 0.20/0.57 ; 4 with value (4 20) 4 with value (4 25) 4 with value (4 33)
% 0.20/0.57 Evaluation took:
% 0.20/0.57 0.084 seconds of real time
% 0.20/0.57 0.077747 seconds of user run time
% 0.20/0.57 0.006094 seconds of system run time
% 0.20/0.57 0 calls to %EVAL
% 0.20/0.57 0 page faults and
% 0.20/0.57 5,757,440 bytes consed.
% 0.20/0.57 :PROOF-FOUND
% 0.20/0.57 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T10:46:49
% 0.20/0.57 :PROOF-FOUND
% 0.20/0.57 *
%------------------------------------------------------------------------------