TSTP Solution File: GRP177-2 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP177-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 : Sat Jul 16 11:37:20 EDT 2022
% Result : Unsatisfiable 0.69s 0.86s
% Output : Refutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 8 RR)
% Number of literals : 22 ( 21 equ; 4 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 : 22 ( 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(idempotence_of_gld,axiom,
greatest_lower_bound(X,X) = X,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).
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(p08b_1,hypothesis,
greatest_lower_bound(identity,a) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p08b_1) ).
cnf(p08b_2,hypothesis,
greatest_lower_bound(identity,b) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p08b_2) ).
cnf(p08b_3,hypothesis,
greatest_lower_bound(identity,c) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p08b_3) ).
cnf(prove_p08b,negated_conjecture,
greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) != greatest_lower_bound(a,multiply(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p08b) ).
cnf(23,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(multiply(a,c),greatest_lower_bound(multiply(a,a),greatest_lower_bound(a,multiply(b,c))))) != greatest_lower_bound(a,multiply(b,c)),
inference('REWRITE',[status(thm)],[prove_p08b,idempotence_of_gld,monotony_glb1,monotony_glb2,theory(equality)]) ).
cnf(97,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(110,plain,
multiply(X,identity) = greatest_lower_bound(multiply(X,identity),multiply(X,c)),
inference('PARAMODULATE',[status(thm)],[monotony_glb1,p08b_3,theory(equality)]) ).
cnf(128,plain,
X = greatest_lower_bound(X,multiply(b,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[monotony_glb2,p08b_2,theory(equality)]),left_identity,theory(equality)]) ).
cnf(130,plain,
greatest_lower_bound(multiply(a,c),greatest_lower_bound(multiply(a,a),greatest_lower_bound(multiply(b,c),a))) != greatest_lower_bound(a,multiply(b,c)),
inference('REWRITE',[status(thm)],[23,128,theory(equality)]) ).
cnf(131,plain,
X = greatest_lower_bound(X,multiply(a,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[monotony_glb2,p08b_1,theory(equality)]),left_identity,theory(equality)]) ).
cnf(133,plain,
greatest_lower_bound(multiply(a,c),greatest_lower_bound(multiply(b,c),a)) != greatest_lower_bound(a,multiply(b,c)),
inference('REWRITE',[status(thm)],[130,131,theory(equality)]) ).
cnf(337,plain,
X = multiply(inverse(inverse(X)),identity),
inference('PARAMODULATE',[status(thm)],[97,left_inverse,theory(equality)]) ).
cnf(338,plain,
multiply(X,Y) = multiply(inverse(inverse(X)),Y),
inference('PARAMODULATE',[status(thm)],[97,97,theory(equality)]) ).
cnf(339,plain,
X = multiply(X,identity),
inference('REWRITE',[status(thm)],[337,338,theory(equality)]) ).
cnf(341,plain,
X = greatest_lower_bound(X,multiply(X,c)),
inference('REWRITE',[status(thm)],[110,339,theory(equality)]) ).
cnf(343,plain,
$false,
inference('REWRITE',[status(thm)],[133,341,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP177-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.14 % Command : run-snark %s %d
% 0.13/0.35 % Computer : n025.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 14:33:09 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.47 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48 *
% 0.20/0.48 *
% 0.20/0.49 #<PACKAGE "SNARK-USER">
% 0.20/0.49 *
% 0.20/0.49 SNARK-TPTP-OPTIONS
% 0.20/0.49 *
% 0.20/0.49 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.49 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.49 (USE-FACTORING :POS)
% 0.20/0.49 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.49 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.49 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.49 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.49 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.49 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.49 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.49 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.49 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.49 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.49 *
% 0.20/0.49 "."
% 0.20/0.49 *
% 0.20/0.49 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T14:33:09
% 0.20/0.49 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n025.cluster.edu at 2022-06-13T14:33:09
% 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.
% 0.69/0.86 ; Declaring least_upper_bound to be associative-commutative.
% 0.69/0.86
% 0.69/0.86 #||
% 0.69/0.86 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.69/0.86 % SZS output start Refutation
% See solution above
% 0.69/0.86 ||#
% 0.69/0.86
% 0.69/0.86 ; Summary of computation:
% 0.69/0.86 ; 2128 formulas have been input or derived (from 48 formulas).
% 0.69/0.86 ; 343 (16%) were retained. Of these,
% 0.69/0.86 ; 49 (14%) were simplified or subsumed later,
% 0.69/0.86 ; 294 (86%) are still being kept.
% 0.69/0.86 ;
% 0.69/0.86 ; Run time in seconds excluding printing time:
% 0.69/0.86 ; 0.005 1% Read assertion file (1 call)
% 0.69/0.86 ; 0.000 0% Assert (19 calls)
% 0.69/0.86 ; 0.041 11% Process new row (2,014 calls)
% 0.69/0.86 ; 0.001 0% Resolution (94 calls)
% 0.69/0.86 ; 0.049 13% Paramodulation (47 calls)
% 0.69/0.86 ; 0.005 1% Embedding (163 calls)
% 0.69/0.86 ; 0.219 59% Forward simplification (1,855 calls)
% 0.69/0.86 ; 0.011 3% Backward simplification (183 calls)
% 0.69/0.86 ; 0.005 1% Ordering (1,807 calls)
% 0.69/0.86 ; 0.005 1% Ordering ac (629 calls)
% 0.69/0.86 ; 0.000 0% Sortal reasoning (32 calls)
% 0.69/0.86 ; 0.000 0% Purity testing (1 call)
% 0.69/0.86 ; 0.031 8% Other
% 0.69/0.86 ; 0.372 Total
% 0.69/0.86 ; 0.374 Real time
% 0.69/0.86 ;
% 0.69/0.86 ; Term-hash-array has 923 terms in all.
% 0.69/0.86 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.69/0.86 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.69/0.86 ; Path-index has 813 entries (877 at peak, 942 added, 129 deleted).
% 0.69/0.86 ; Path-index has 408 nodes (422 at peak, 428 added, 20 deleted).
% 0.69/0.86 ; Trie-index has 813 entries (877 at peak, 942 added, 129 deleted).
% 0.69/0.86 ; Trie-index has 250 nodes (271 at peak, 291 added, 41 deleted).
% 0.69/0.86 ; Retrieved 385,512 generalization terms in 17,903 calls.
% 0.69/0.86 ; Retrieved 460 instance terms in 206 calls.
% 0.69/0.86 ; Retrieved 4,595 unifiable terms in 243 calls.
% 0.69/0.86 ;
% 0.69/0.86 ; The agenda of backward simplifiable rows to process has 11 entries:
% 0.69/0.86 ; 11 with value 0
% 0.69/0.86 ; The agenda of rows to process has 8 entries:
% 0.69/0.86 ; 4 with value 18 4 with value 20
% 0.69/0.86 ; The agenda of rows to give has 247 entries:
% 0.69/0.86 ; 1 with value (4 9) 12 with value (4 18) 4 with value (4 25)
% 0.69/0.86 ; 3 with value (4 11) 18 with value (4 19) 4 with value (4 27)
% 0.69/0.86 ; 18 with value (4 12) 9 with value (4 20) 12 with value (4 28)
% 0.69/0.86 ; 1 with value (4 13) 32 with value (4 21) 4 with value (4 30)
% 0.69/0.86 ; 6 with value (4 14) 22 with value (4 22) 4 with value (4 31)
% 0.69/0.86 ; 31 with value (4 15) 18 with value (4 23) 4 with value (4 33)
% 0.69/0.86 ; 12 with value (4 16) 4 with value (4 24) 4 with value (4 36)
% 0.69/0.86 ; 24 with value (4 17)
% 0.69/0.86 Evaluation took:
% 0.69/0.87 0.375 seconds of real time
% 0.69/0.87 0.358114 seconds of user run time
% 0.69/0.87 0.016843 seconds of system run time
% 0.69/0.87 [Run times include 0.006 seconds GC run time.]
% 0.69/0.87 0 calls to %EVAL
% 0.69/0.87 0 page faults and
% 0.69/0.87 20,718,968 bytes consed.
% 0.69/0.87 :PROOF-FOUND
% 0.69/0.87 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T14:33:09
% 0.69/0.87 :PROOF-FOUND
% 0.69/0.87 *
%------------------------------------------------------------------------------