TSTP Solution File: GRP169-2 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP169-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n015.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 11:37:15 EDT 2022
% Result : Unsatisfiable 0.83s 1.07s
% Output : Refutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 6 RR)
% Number of literals : 23 ( 22 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; 3 con; 0-2 aty)
% Number of variables : 30 ( 2 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(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
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_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(p02b_1,hypothesis,
greatest_lower_bound(inverse(a),inverse(b)) = inverse(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p02b_1) ).
cnf(prove_p02b,negated_conjecture,
greatest_lower_bound(a,b) != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p02b) ).
cnf(68,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(69,plain,
multiply(multiply(X,inverse(Y)),Y) = multiply(X,identity),
inference('PARAMODULATE',[status(thm)],[associativity,left_inverse,theory(equality)]) ).
cnf(93,plain,
multiply(inverse(a),X) = greatest_lower_bound(multiply(inverse(a),X),multiply(inverse(b),X)),
inference('PARAMODULATE',[status(thm)],[monotony_glb2,p02b_1,theory(equality)]) ).
cnf(110,plain,
X = multiply(inverse(inverse(X)),identity),
inference('PARAMODULATE',[status(thm)],[68,left_inverse,theory(equality)]) ).
cnf(111,plain,
multiply(X,Y) = multiply(inverse(inverse(X)),Y),
inference('PARAMODULATE',[status(thm)],[68,68,theory(equality)]) ).
cnf(112,plain,
X = multiply(X,identity),
inference('REWRITE',[status(thm)],[110,111,theory(equality)]) ).
cnf(113,plain,
multiply(multiply(X,inverse(Y)),Y) = X,
inference('REWRITE',[status(thm)],[69,112,theory(equality)]) ).
cnf(121,plain,
X = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[113,left_inverse,theory(equality)]),left_identity,theory(equality)]) ).
cnf(129,plain,
X = multiply(Y,multiply(inverse(Y),X)),
inference('PARAMODULATE',[status(thm)],[68,121,theory(equality)]) ).
cnf(292,plain,
multiply(inverse(a),b) = greatest_lower_bound(multiply(inverse(a),b),identity),
inference('PARAMODULATE',[status(thm)],[93,left_inverse,theory(equality)]) ).
cnf(360,plain,
least_upper_bound(identity,multiply(inverse(a),b)) = identity,
inference('PARAMODULATE',[status(thm)],[lub_absorbtion,292,theory(equality)]) ).
cnf(368,plain,
X = least_upper_bound(X,multiply(X,multiply(inverse(a),b))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[monotony_lub1,360,theory(equality)]),112,theory(equality)]) ).
cnf(528,plain,
a = least_upper_bound(a,b),
inference('PARAMODULATE',[status(thm)],[368,129,theory(equality)]) ).
cnf(550,plain,
$false,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[glb_absorbtion,528,theory(equality)]),prove_p02b]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP169-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n015.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 Jun 13 12:11:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.46 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47 *
% 0.19/0.47 *
% 0.19/0.48 #<PACKAGE "SNARK-USER">
% 0.19/0.48 *
% 0.19/0.48 SNARK-TPTP-OPTIONS
% 0.19/0.48 *
% 0.19/0.48 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.48 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.48 (USE-FACTORING :POS)
% 0.19/0.48 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.48 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.48 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.48 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.48 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.48 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.48 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.48 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.48 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.48 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.48 *
% 0.19/0.48 "."
% 0.19/0.48 *
% 0.19/0.48 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T12:11:38
% 0.19/0.48 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n015.cluster.edu at 2022-06-13T12:11:38
% 0.19/0.49
% 0.19/0.49 ; Recognized left identity assertion (= (|multiply| |identity| ?X) ?X).
% 0.19/0.49 ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |identity|).
% 0.19/0.49 ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 0.19/0.49 ; Recognized commutativity assertion (= (|greatest_lower_bound| ?X ?Y) (|greatest_lower_bound| ?Y ?X)).
% 0.19/0.49 ; Recognized commutativity assertion (= (|least_upper_bound| ?X ?Y) (|least_upper_bound| ?Y ?X)).
% 0.19/0.49 ; Recognized associativity assertion (= (|greatest_lower_bound| ?X (|greatest_lower_bound| ?Y ?Z)) (|greatest_lower_bound| (|greatest_lower_bound| ?X ?Y) ?Z)).
% 0.19/0.49 ; Recognized associativity assertion (= (|least_upper_bound| ?X (|least_upper_bound| ?Y ?Z)) (|least_upper_bound| (|least_upper_bound| ?X ?Y) ?Z)).
% 0.19/0.49 ; Declaring greatest_lower_bound to be commutative.
% 0.19/0.49 ; Declaring greatest_lower_bound to be associative-commutative.
% 0.19/0.49 ; Declaring least_upper_bound to be commutative.
% 0.83/1.07 ; Declaring least_upper_bound to be associative-commutative.
% 0.83/1.07
% 0.83/1.07 #||
% 0.83/1.07 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.83/1.07 % SZS output start Refutation
% See solution above
% 0.83/1.07 ||#
% 0.83/1.07
% 0.83/1.07 ; Summary of computation:
% 0.83/1.07 ; 2648 formulas have been input or derived (from 66 formulas).
% 0.83/1.07 ; 550 (21%) were retained. Of these,
% 0.83/1.07 ; 49 ( 9%) were simplified or subsumed later,
% 0.83/1.07 ; 501 (91%) are still being kept.
% 0.83/1.07 ;
% 0.83/1.07 ; Run time in seconds excluding printing time:
% 0.83/1.07 ; 0.004 1% Read assertion file (1 call)
% 0.83/1.07 ; 0.000 0% Assert (17 calls)
% 0.83/1.07 ; 0.064 11% Process new row (2,592 calls)
% 0.83/1.07 ; 0.002 0% Resolution (130 calls)
% 0.83/1.07 ; 0.055 9% Paramodulation (65 calls)
% 0.83/1.07 ; 0.002 0% Embedding (242 calls)
% 0.83/1.07 ; 0.363 61% Forward simplification (2,294 calls)
% 0.83/1.07 ; 0.016 3% Backward simplification (312 calls)
% 0.83/1.07 ; 0.045 8% Ordering (10,362 calls)
% 0.83/1.07 ; 0.007 1% Ordering ac (865 calls)
% 0.83/1.07 ; 0.001 0% Sortal reasoning (32 calls)
% 0.83/1.07 ; 0.000 0% Purity testing (1 call)
% 0.83/1.07 ; 0.035 6% Other
% 0.83/1.07 ; 0.594 Total
% 0.83/1.07 ; 0.596 Real time
% 0.83/1.07 ;
% 0.83/1.07 ; Term-hash-array has 1,642 terms in all.
% 0.83/1.07 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.83/1.07 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.83/1.07 ; Path-index has 1,515 entries (1,515 at peak, 1,656 added, 141 deleted).
% 0.83/1.07 ; Path-index has 1,534 nodes (1,534 at peak, 1,558 added, 24 deleted).
% 0.83/1.07 ; Trie-index has 1,515 entries (1,515 at peak, 1,656 added, 141 deleted).
% 0.83/1.07 ; Trie-index has 1,036 nodes (1,036 at peak, 1,168 added, 132 deleted).
% 0.83/1.07 ; Retrieved 480,118 generalization terms in 26,693 calls.
% 0.83/1.07 ; Retrieved 1,118 instance terms in 394 calls.
% 0.83/1.08 ; Retrieved 8,379 unifiable terms in 396 calls.
% 0.83/1.08 ;
% 0.83/1.08 ; The agenda of rows to process has 2 entries:
% 0.83/1.08 ; 2 with value 20
% 0.83/1.08 ; The agenda of rows to give has 438 entries:
% 0.83/1.08 ; 1 with value (4 12) 40 with value (4 25) 16 with value (4 32)
% 0.83/1.08 ; 7 with value (4 19) 37 with value (4 26) 6 with value (4 33)
% 0.83/1.08 ; 28 with value (4 20) 58 with value (4 27) 6 with value (4 34)
% 0.83/1.08 ; 20 with value (4 21) 44 with value (4 28) 4 with value (4 35)
% 0.83/1.08 ; 22 with value (4 22) 22 with value (4 29) 10 with value (4 36)
% 0.83/1.08 ; 35 with value (4 23) 26 with value (4 30) 2 with value (4 40)
% 0.83/1.08 ; 34 with value (4 24) 18 with value (4 31) 2 with value (4 42)
% 0.83/1.08 Evaluation took:
% 0.83/1.08 0.596 seconds of real time
% 0.83/1.08 0.561606 seconds of user run time
% 0.83/1.08 0.034629 seconds of system run time
% 0.83/1.08 [Run times include 0.012 seconds GC run time.]
% 0.83/1.08 0 calls to %EVAL
% 0.83/1.08 0 page faults and
% 0.83/1.08 33,597,520 bytes consed.
% 0.83/1.08 :PROOF-FOUND
% 0.83/1.08 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T12:11:38
% 0.83/1.08 :PROOF-FOUND
% 0.83/1.08 *
%------------------------------------------------------------------------------