TSTP Solution File: GRP486-1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP486-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n011.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 11:39:06 EDT 2022
% Result : Unsatisfiable 0.39s 0.56s
% Output : Refutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of clauses : 42 ( 42 unt; 0 nHn; 6 RR)
% Number of literals : 42 ( 41 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 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 : 72 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(X,double_divide(double_divide(double_divide(X,Y),Z),double_divide(Y,identity))),double_divide(identity,identity)) = Z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(multiply,axiom,
multiply(X,Y) = double_divide(double_divide(Y,X),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(inverse,axiom,
inverse(X) = double_divide(X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
cnf(identity,axiom,
identity = double_divide(X,inverse(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(6,plain,
multiply(X,Y) = inverse(double_divide(Y,X)),
inference('REWRITE',[status(thm)],[multiply,inverse,theory(equality)]) ).
cnf(7,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference('REWRITE',[status(thm)],[prove_these_axioms_3,6,theory(equality)]) ).
cnf(8,plain,
double_divide(double_divide(X,double_divide(double_divide(double_divide(X,Y),Z),inverse(Y))),inverse(identity)) = Z,
inference('REWRITE',[status(thm)],[single_axiom,inverse,theory(equality)]) ).
cnf(9,plain,
double_divide(double_divide(X,double_divide(identity,inverse(Y))),inverse(identity)) = inverse(double_divide(X,Y)),
inference('PARAMODULATE',[status(thm)],[8,identity,theory(equality)]) ).
cnf(10,plain,
double_divide(double_divide(X,double_divide(double_divide(inverse(X),Y),inverse(identity))),inverse(identity)) = Y,
inference('PARAMODULATE',[status(thm)],[8,inverse,theory(equality)]) ).
cnf(16,plain,
double_divide(inverse(X),inverse(identity)) = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9,identity,theory(equality)]),inverse,theory(equality)]) ).
cnf(17,plain,
double_divide(double_divide(X,inverse(double_divide(inverse(X),Y))),inverse(identity)) = double_divide(identity,inverse(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,9,theory(equality)]),inverse,theory(equality)]) ).
cnf(21,plain,
double_divide(double_divide(X,inverse(inverse(inverse(X)))),inverse(identity)) = identity,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,inverse,theory(equality)]),16,theory(equality)]) ).
cnf(23,plain,
identity = inverse(identity),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,16,theory(equality)]),21,16,theory(equality)]) ).
cnf(24,plain,
inverse(double_divide(X,double_divide(double_divide(double_divide(X,Y),Z),inverse(Y)))) = Z,
inference('REWRITE',[status(thm)],[8,inverse,23,theory(equality)]) ).
cnf(26,plain,
inverse(double_divide(X,inverse(double_divide(inverse(X),Y)))) = Y,
inference('REWRITE',[status(thm)],[10,inverse,23,theory(equality)]) ).
cnf(32,plain,
X = double_divide(identity,inverse(X)),
inference('REWRITE',[status(thm)],[17,26,inverse,23,theory(equality)]) ).
cnf(33,plain,
inverse(double_divide(X,inverse(inverse(inverse(X))))) = identity,
inference('REWRITE',[status(thm)],[21,inverse,23,theory(equality)]) ).
cnf(36,plain,
inverse(double_divide(X,double_divide(double_divide(double_divide(X,double_divide(Y,double_divide(double_divide(double_divide(Y,Z),U),inverse(Z)))),V),U))) = V,
inference('PARAMODULATE',[status(thm)],[24,24,theory(equality)]) ).
cnf(37,plain,
inverse(double_divide(identity,double_divide(double_divide(X,Y),inverse(inverse(X))))) = Y,
inference('PARAMODULATE',[status(thm)],[24,32,theory(equality)]) ).
cnf(38,plain,
double_divide(X,double_divide(double_divide(double_divide(X,Y),Z),inverse(Y))) = double_divide(identity,Z),
inference('PARAMODULATE',[status(thm)],[32,24,theory(equality)]) ).
cnf(39,plain,
inverse(double_divide(X,double_divide(double_divide(double_divide(X,double_divide(identity,Y)),Z),Y))) = Z,
inference('REWRITE',[status(thm)],[36,38,theory(equality)]) ).
cnf(40,plain,
inverse(double_divide(identity,X)) = X,
inference('REWRITE',[status(thm)],[24,38,theory(equality)]) ).
cnf(41,plain,
double_divide(double_divide(X,Y),inverse(inverse(X))) = Y,
inference('REWRITE',[status(thm)],[37,40,theory(equality)]) ).
cnf(45,plain,
double_divide(X,inverse(inverse(double_divide(Y,X)))) = inverse(inverse(Y)),
inference('PARAMODULATE',[status(thm)],[41,41,theory(equality)]) ).
cnf(46,plain,
double_divide(X,inverse(double_divide(inverse(X),Y))) = double_divide(identity,Y),
inference('PARAMODULATE',[status(thm)],[32,26,theory(equality)]) ).
cnf(47,plain,
double_divide(X,inverse(inverse(inverse(X)))) = identity,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[32,33,theory(equality)]),23,inverse,theory(equality)]) ).
cnf(49,plain,
inverse(X) = inverse(inverse(inverse(X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[41,47,theory(equality)]),32,theory(equality)]) ).
cnf(50,plain,
X = inverse(inverse(X)),
inference('PARAMODULATE',[status(thm)],[49,40,theory(equality)]) ).
cnf(51,plain,
double_divide(X,double_divide(Y,X)) = Y,
inference('REWRITE',[status(thm)],[45,50,theory(equality)]) ).
cnf(52,plain,
double_divide(double_divide(X,Y),X) = Y,
inference('REWRITE',[status(thm)],[41,50,theory(equality)]) ).
cnf(53,plain,
inverse(X) = double_divide(identity,X),
inference('PARAMODULATE',[status(thm)],[32,50,theory(equality)]) ).
cnf(57,plain,
inverse(double_divide(X,double_divide(double_divide(double_divide(X,inverse(Y)),Z),Y))) = Z,
inference('REWRITE',[status(thm)],[39,53,theory(equality)]) ).
cnf(58,plain,
double_divide(X,inverse(double_divide(inverse(X),Y))) = inverse(Y),
inference('REWRITE',[status(thm)],[46,53,theory(equality)]) ).
cnf(63,plain,
double_divide(inverse(X),Y) = inverse(double_divide(inverse(Y),X)),
inference('PARAMODULATE',[status(thm)],[52,58,theory(equality)]) ).
cnf(64,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != double_divide(inverse(a3),double_divide(c3,b3)),
inference('REWRITE',[status(thm)],[7,63,theory(equality)]) ).
cnf(65,plain,
double_divide(X,inverse(Y)) = inverse(double_divide(Y,inverse(X))),
inference('PARAMODULATE',[status(thm)],[58,51,theory(equality)]) ).
cnf(67,plain,
double_divide(double_divide(b3,a3),inverse(c3)) != double_divide(inverse(a3),double_divide(c3,b3)),
inference('REWRITE',[status(thm)],[64,65,theory(equality)]) ).
cnf(68,plain,
double_divide(inverse(X),inverse(Y)) = inverse(double_divide(Y,X)),
inference('PARAMODULATE',[status(thm)],[63,50,theory(equality)]) ).
cnf(87,plain,
inverse(double_divide(X,double_divide(Y,Z))) = double_divide(Y,double_divide(X,inverse(Z))),
inference('PARAMODULATE',[status(thm)],[57,51,theory(equality)]) ).
cnf(134,plain,
inverse(double_divide(X,inverse(double_divide(Y,Z)))) = double_divide(inverse(Z),double_divide(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[87,68,theory(equality)]),50,theory(equality)]) ).
cnf(135,plain,
$false,
inference('REWRITE',[status(thm)],[67,50,65,134,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP486-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 10:27:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.44 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 *
% 0.18/0.45 *
% 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/sandbox2/benchmark/theBenchmark.p 2022-06-13T10:27:48
% 0.18/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n011.cluster.edu at 2022-06-13T10:27:48
% 0.18/0.47
% 0.39/0.56 ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.39/0.56
% 0.39/0.56 #||
% 0.39/0.56 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.56 % SZS output start Refutation
% See solution above
% 0.39/0.57 ||#
% 0.39/0.57
% 0.39/0.57 ; Summary of computation:
% 0.39/0.57 ; 529 formulas have been input or derived (from 36 formulas).
% 0.39/0.57 ; 135 (26%) were retained. Of these,
% 0.39/0.57 ; 67 (50%) were simplified or subsumed later,
% 0.39/0.57 ; 68 (50%) are still being kept.
% 0.39/0.57 ;
% 0.39/0.57 ; Run time in seconds excluding printing time:
% 0.39/0.57 ; 0.001 1% Read assertion file (1 call)
% 0.39/0.57 ; 0.001 1% Assert (5 calls)
% 0.39/0.57 ; 0.019 18% Process new row (501 calls)
% 0.39/0.57 ; 0.000 0% Resolution (70 calls)
% 0.39/0.57 ; 0.007 7% Paramodulation (35 calls)
% 0.39/0.57 ; 0.022 21% Forward simplification (432 calls)
% 0.39/0.57 ; 0.014 14% Backward simplification (135 calls)
% 0.39/0.57 ; 0.016 16% Ordering (2,277 calls)
% 0.39/0.57 ; 0.000 0% Sortal reasoning (32 calls)
% 0.39/0.57 ; 0.000 0% Purity testing (1 call)
% 0.39/0.57 ; 0.023 22% Other
% 0.39/0.57 ; 0.103 Total
% 0.39/0.57 ; 0.109 Real time
% 0.39/0.57 ;
% 0.39/0.57 ; Term-hash-array has 446 terms in all.
% 0.39/0.57 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.39/0.57 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.39/0.57 ; Path-index has 250 entries (260 at peak, 524 added, 274 deleted).
% 0.39/0.57 ; Path-index has 701 nodes (719 at peak, 1,182 added, 481 deleted).
% 0.39/0.57 ; Trie-index has 250 entries (260 at peak, 524 added, 274 deleted).
% 0.39/0.57 ; Trie-index has 995 nodes (1,029 at peak, 2,379 added, 1,384 deleted).
% 0.39/0.57 ; Retrieved 2,245 generalization terms in 2,709 calls.
% 0.39/0.57 ; Retrieved 572 instance terms in 214 calls.
% 0.39/0.57 ; Retrieved 917 unifiable terms in 258 calls.
% 0.39/0.57 ;
% 0.39/0.57 ; The agenda of rows to process has 24 entries:
% 0.39/0.57 ; 2 with value 28 7 with value 30 2 with value 32
% 0.39/0.57 ; 2 with value 29 8 with value 31 3 with value 33
% 0.39/0.57 ; The agenda of rows to give has 53 entries:
% 0.39/0.57 ; 4 with value (4 23) 4 with value (4 27) 1 with value (4 31)
% 0.39/0.57 ; 3 with value (4 24) 4 with value (4 28) 1 with value (4 32)
% 0.39/0.57 ; 13 with value (4 25) 2 with value (4 29) 1 with value (4 33)
% 0.39/0.57 ; 12 with value (4 26) 8 with value (4 30)
% 0.39/0.57 Evaluation took:
% 0.39/0.57 0.109 seconds of real time
% 0.39/0.57 0.093785 seconds of user run time
% 0.39/0.57 0.014847 seconds of system run time
% 0.39/0.57 0 calls to %EVAL
% 0.39/0.57 0 page faults and
% 0.39/0.57 7,955,328 bytes consed.
% 0.39/0.57 :PROOF-FOUND
% 0.39/0.57 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T10:27:49
% 0.39/0.57 :PROOF-FOUND
% 0.39/0.57 *
%------------------------------------------------------------------------------