TSTP Solution File: GRP184-1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP184-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n029.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 0.38s 0.61s
% Output : Refutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 5 RR)
% Number of literals : 26 ( 25 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 : 41 ( 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(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/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/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(prove_p21,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_p21) ).
cnf(17,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_p21,monotony_lub1,left_identity,monotony_lub2,theory(equality)]) ).
cnf(55,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(56,plain,
multiply(multiply(X,inverse(Y)),Y) = multiply(X,identity),
inference('PARAMODULATE',[status(thm)],[associativity,left_inverse,theory(equality)]) ).
cnf(83,plain,
X = multiply(inverse(inverse(X)),identity),
inference('PARAMODULATE',[status(thm)],[55,left_inverse,theory(equality)]) ).
cnf(84,plain,
multiply(X,Y) = multiply(inverse(inverse(X)),Y),
inference('PARAMODULATE',[status(thm)],[55,55,theory(equality)]) ).
cnf(85,plain,
X = multiply(X,identity),
inference('REWRITE',[status(thm)],[83,84,theory(equality)]) ).
cnf(86,plain,
multiply(multiply(X,inverse(Y)),Y) = X,
inference('REWRITE',[status(thm)],[56,85,theory(equality)]) ).
cnf(87,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)],[17,85,theory(equality)]) ).
cnf(95,plain,
X = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[86,left_inverse,theory(equality)]),left_identity,theory(equality)]) ).
cnf(101,plain,
multiply(X,inverse(X)) = identity,
inference('PARAMODULATE',[status(thm)],[left_inverse,95,theory(equality)]) ).
cnf(102,plain,
multiply(multiply(X,Y),inverse(Y)) = X,
inference('PARAMODULATE',[status(thm)],[86,95,theory(equality)]) ).
cnf(103,plain,
X = multiply(Y,multiply(inverse(Y),X)),
inference('PARAMODULATE',[status(thm)],[55,95,theory(equality)]) ).
cnf(108,plain,
inverse(X) = multiply(inverse(multiply(Y,X)),Y),
inference('PARAMODULATE',[status(thm)],[55,102,theory(equality)]) ).
cnf(109,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference('PARAMODULATE',[status(thm)],[102,55,theory(equality)]) ).
cnf(121,plain,
multiply(inverse(X),Y) = inverse(multiply(inverse(Y),X)),
inference('PARAMODULATE',[status(thm)],[86,108,theory(equality)]) ).
cnf(124,plain,
least_upper_bound(multiply(a,inverse(greatest_lower_bound(a,identity))),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(inverse(greatest_lower_bound(identity,inverse(a))),inverse(greatest_lower_bound(a,identity))),
inference('REWRITE',[status(thm)],[87,85,left_inverse,monotony_glb1,121,theory(equality)]) ).
cnf(127,plain,
inverse(multiply(X,inverse(Y))) = multiply(Y,inverse(X)),
inference('PARAMODULATE',[status(thm)],[103,109,theory(equality)]) ).
cnf(130,plain,
$false,
inference('REWRITE',[status(thm)],[124,left_identity,101,monotony_glb2,127,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP184-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : run-snark %s %d
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 14:02:55 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.18/0.45 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.46 *
% 0.18/0.46 *
% 0.18/0.46 #<PACKAGE "SNARK-USER">
% 0.18/0.46 *
% 0.18/0.46 SNARK-TPTP-OPTIONS
% 0.18/0.46 *
% 0.18/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.46 (USE-FACTORING :POS)
% 0.18/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.46 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.46 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.46 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.46 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.46 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.46 (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.46 *
% 0.18/0.46 "."
% 0.18/0.46 *
% 0.18/0.46 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T14:02:55
% 0.18/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n029.cluster.edu at 2022-06-13T14:02:55
% 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.
% 0.38/0.61 ; Declaring least_upper_bound to be associative-commutative.
% 0.38/0.61
% 0.38/0.61 #||
% 0.38/0.61 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.38/0.61 % SZS output start Refutation
% See solution above
% 0.38/0.61 ||#
% 0.38/0.61
% 0.38/0.61 ; Summary of computation:
% 0.38/0.61 ; 682 formulas have been input or derived (from 29 formulas).
% 0.38/0.61 ; 130 (19%) were retained. Of these,
% 0.38/0.61 ; 20 (15%) were simplified or subsumed later,
% 0.38/0.61 ; 110 (85%) are still being kept.
% 0.38/0.61 ;
% 0.38/0.61 ; Run time in seconds excluding printing time:
% 0.38/0.61 ; 0.004 3% Read assertion file (1 call)
% 0.38/0.61 ; 0.001 1% Assert (16 calls)
% 0.38/0.61 ; 0.014 10% Process new row (655 calls)
% 0.38/0.61 ; 0.002 1% Resolution (56 calls)
% 0.38/0.61 ; 0.016 11% Paramodulation (28 calls)
% 0.38/0.61 ; 0.003 2% Embedding (49 calls)
% 0.38/0.61 ; 0.067 47% Forward simplification (595 calls)
% 0.38/0.61 ; 0.005 3% Backward simplification (84 calls)
% 0.38/0.61 ; 0.005 3% Ordering (906 calls)
% 0.38/0.61 ; 0.001 1% Ordering ac (144 calls)
% 0.38/0.61 ; 0.000 0% Sortal reasoning (32 calls)
% 0.38/0.61 ; 0.000 0% Purity testing (1 call)
% 0.38/0.61 ; 0.026 18% Other
% 0.38/0.61 ; 0.144 Total
% 0.38/0.61 ; 0.147 Real time
% 0.38/0.61 ;
% 0.38/0.61 ; Term-hash-array has 441 terms in all.
% 0.38/0.61 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.38/0.61 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.38/0.61 ; Path-index has 388 entries (403 at peak, 458 added, 70 deleted).
% 0.38/0.61 ; Path-index has 436 nodes (447 at peak, 524 added, 88 deleted).
% 0.38/0.61 ; Trie-index has 388 entries (403 at peak, 458 added, 70 deleted).
% 0.38/0.61 ; Trie-index has 278 nodes (291 at peak, 358 added, 80 deleted).
% 0.38/0.61 ; Retrieved 33,274 generalization terms in 5,921 calls.
% 0.38/0.61 ; Retrieved 328 instance terms in 111 calls.
% 0.38/0.61 ; Retrieved 1,058 unifiable terms in 163 calls.
% 0.38/0.61 ;
% 0.38/0.61 ; The agenda of backward simplifiable rows to process has 1 entry:
% 0.38/0.61 ; 1 with value 0
% 0.38/0.61 ; The agenda of rows to process has 15 entries:
% 0.38/0.61 ; 2 with value 19 3 with value 23 4 with value 25
% 0.38/0.61 ; 2 with value 20 1 with value 24 2 with value 31
% 0.38/0.61 ; 1 with value 22
% 0.38/0.61 ; The agenda of rows to give has 86 entries:
% 0.38/0.61 ; 3 with value (4 18) 8 with value (4 24) 4 with value (4 29)
% 0.38/0.61 ; 2 with value (4 19) 4 with value (4 25) 4 with value (4 30)
% 0.38/0.61 ; 11 with value (4 20) 4 with value (4 26) 4 with value (4 31)
% 0.38/0.61 ; 4 with value (4 21) 10 with value (4 27) 4 with value (4 33)
% 0.38/0.61 ; 4 with value (4 22) 16 with value (4 28) 4 with value (4 36)
% 0.38/0.61 Evaluation took:
% 0.38/0.61 0.147 seconds of real time
% 0.38/0.61 0.129667 seconds of user run time
% 0.38/0.61 0.017135 seconds of system run time
% 0.38/0.61 0 calls to %EVAL
% 0.38/0.61 0 page faults and
% 0.38/0.61 10,262,568 bytes consed.
% 0.38/0.61 :PROOF-FOUND
% 0.38/0.61 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T14:02:55
% 0.38/0.61 :PROOF-FOUND
% 0.38/0.61 *
%------------------------------------------------------------------------------