%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : ALG005-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n018.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 : Thu Jul 14 17:59:35 EDT 2022
% Result : Unsatisfiable 0.56s 0.75s
% Output : Refutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of clauses : 43 ( 43 unt; 0 nHn; 5 RR)
% Number of literals : 43 ( 42 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 104 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(set_difference_1,axiom,
difference(X,difference(Y,X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_1) ).
cnf(set_difference_2,axiom,
difference(X,difference(X,Y)) = difference(Y,difference(Y,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_2) ).
cnf(set_difference_3,axiom,
difference(difference(X,Y),Z) = difference(difference(X,Z),difference(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_3) ).
cnf(intersection,axiom,
multiply(X,Y) = difference(X,difference(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
cnf(prove_associativity_of_multiply,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity_of_multiply) ).
cnf(6,plain,
difference(c,difference(c,difference(a,difference(a,b)))) != difference(a,difference(a,difference(b,difference(b,c)))),
inference('REWRITE',[status(thm)],[prove_associativity_of_multiply,set_difference_2,intersection,theory(equality)]) ).
cnf(7,plain,
difference(difference(X,Y),Y) = difference(X,Y),
inference('PARAMODULATE',[status(thm)],[set_difference_1,set_difference_1,theory(equality)]) ).
cnf(9,plain,
difference(X,X) = difference(difference(Y,X),difference(Y,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[set_difference_2,set_difference_1,theory(equality)]),7,theory(equality)]) ).
cnf(10,plain,
difference(X,difference(X,difference(X,Y))) = difference(X,difference(Y,difference(Y,X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[set_difference_2,set_difference_2,theory(equality)]),set_difference_2,theory(equality)]) ).
cnf(12,plain,
difference(difference(X,Y),difference(difference(Z,X),Y)) = difference(X,Y),
inference('PARAMODULATE',[status(thm)],[set_difference_1,set_difference_3,theory(equality)]) ).
cnf(14,plain,
difference(difference(X,Y),difference(Z,X)) = difference(X,difference(Y,difference(Z,X))),
inference('PARAMODULATE',[status(thm)],[set_difference_3,set_difference_1,theory(equality)]) ).
cnf(15,plain,
difference(X,difference(X,difference(X,Y))) = difference(difference(X,Y),difference(Y,X)),
inference('REWRITE',[status(thm)],[10,14,theory(equality)]) ).
cnf(16,plain,
difference(difference(X,Y),difference(Z,Y)) = difference(difference(X,difference(Z,Y)),Y),
inference('PARAMODULATE',[status(thm)],[set_difference_3,set_difference_1,theory(equality)]) ).
cnf(18,plain,
difference(X,difference(X,difference(Y,Z))) = difference(difference(Y,Z),difference(difference(Y,X),difference(Z,X))),
inference('PARAMODULATE',[status(thm)],[set_difference_2,set_difference_3,theory(equality)]) ).
cnf(19,plain,
difference(c,difference(c,difference(a,difference(a,b)))) != difference(difference(b,difference(b,c)),difference(difference(b,a),difference(difference(b,a),difference(c,a)))),
inference('REWRITE',[status(thm)],[6,set_difference_3,18,theory(equality)]) ).
cnf(24,plain,
difference(difference(X,Y),difference(X,Z)) = difference(difference(Z,difference(Z,X)),difference(Y,difference(X,Z))),
inference('PARAMODULATE',[status(thm)],[set_difference_3,set_difference_2,theory(equality)]) ).
cnf(27,plain,
difference(difference(X,Y),difference(difference(X,Y),difference(Z,Y))) = difference(difference(Z,Y),difference(difference(Z,X),Y)),
inference('PARAMODULATE',[status(thm)],[set_difference_2,set_difference_3,theory(equality)]) ).
cnf(30,plain,
difference(difference(X,Y),Z) = difference(difference(difference(X,Y),Z),difference(Y,Z)),
inference('PARAMODULATE',[status(thm)],[set_difference_3,7,theory(equality)]) ).
cnf(31,plain,
difference(difference(difference(X,Y),Z),Y) = difference(difference(X,Y),difference(Z,Y)),
inference('PARAMODULATE',[status(thm)],[set_difference_3,7,theory(equality)]) ).
cnf(34,plain,
difference(difference(X,Y),X) = difference(X,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[7,9,theory(equality)]),set_difference_3,theory(equality)]) ).
cnf(37,plain,
difference(X,X) = difference(Y,Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9,set_difference_2,theory(equality)]),9,theory(equality)]) ).
cnf(38,plain,
difference(X,difference(Y,Y)) = X,
inference('PARAMODULATE',[status(thm)],[set_difference_1,37,theory(equality)]) ).
cnf(39,plain,
difference(difference(X,X),Y) = difference(X,X),
inference('PARAMODULATE',[status(thm)],[7,37,theory(equality)]) ).
cnf(40,plain,
difference(difference(X,Y),difference(Y,X)) = difference(X,Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[set_difference_2,34,theory(equality)]),38,15,theory(equality)]) ).
cnf(41,plain,
difference(X,difference(X,difference(X,Y))) = difference(X,Y),
inference('REWRITE',[status(thm)],[15,40,theory(equality)]) ).
cnf(42,plain,
difference(X,X) = difference(difference(difference(X,Y),Z),difference(X,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[set_difference_3,34,theory(equality)]),39,theory(equality)]) ).
cnf(44,plain,
difference(difference(X,difference(Y,Z)),Y) = difference(X,Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[set_difference_3,34,theory(equality)]),7,set_difference_3,theory(equality)]) ).
cnf(88,plain,
difference(difference(X,Y),difference(X,difference(Y,Z))) = difference(difference(X,difference(Y,Z)),difference(X,difference(Y,Z))),
inference('PARAMODULATE',[status(thm)],[34,44,theory(equality)]) ).
cnf(90,plain,
difference(difference(difference(X,Y),difference(Z,X)),U) = difference(difference(X,U),difference(difference(Y,difference(Z,X)),U)),
inference('PARAMODULATE',[status(thm)],[set_difference_3,14,theory(equality)]) ).
cnf(102,plain,
difference(X,X) = difference(difference(X,Y),difference(X,difference(Y,Z))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[34,16,theory(equality)]),88,42,theory(equality)]) ).
cnf(130,plain,
difference(difference(X,difference(X,Y)),Z) = difference(difference(difference(X,difference(X,Y)),Z),difference(difference(Y,X),Z)),
inference('PARAMODULATE',[status(thm)],[30,set_difference_2,theory(equality)]) ).
cnf(139,plain,
difference(difference(difference(X,difference(X,Y)),Z),difference(Y,X)) = difference(difference(Y,Z),difference(Y,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[31,set_difference_2,theory(equality)]),24,theory(equality)]) ).
cnf(142,plain,
difference(difference(X,Y),Z) = difference(difference(X,Y),difference(Z,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[41,31,theory(equality)]),38,102,theory(equality)]) ).
cnf(146,plain,
difference(difference(X,difference(X,Y)),Z) = difference(difference(Y,Z),difference(Y,X)),
inference('REWRITE',[status(thm)],[130,139,142,theory(equality)]) ).
cnf(157,plain,
difference(difference(difference(X,Y),difference(Z,X)),U) = difference(difference(X,U),difference(Y,difference(Z,X))),
inference('REWRITE',[status(thm)],[90,142,theory(equality)]) ).
cnf(180,plain,
difference(X,difference(X,difference(Y,Z))) = difference(difference(Y,Z),difference(Y,X)),
inference('REWRITE',[status(thm)],[18,142,theory(equality)]) ).
cnf(188,plain,
difference(difference(X,Y),difference(difference(X,Y),Z)) = difference(difference(Z,Y),difference(Z,X)),
inference('REWRITE',[status(thm)],[27,142,theory(equality)]) ).
cnf(194,plain,
difference(difference(X,Y),difference(Z,X)) = difference(X,Y),
inference('REWRITE',[status(thm)],[12,142,theory(equality)]) ).
cnf(199,plain,
difference(difference(X,Y),Z) = difference(difference(X,Z),difference(Y,difference(U,X))),
inference('REWRITE',[status(thm)],[157,194,theory(equality)]) ).
cnf(200,plain,
difference(difference(X,Y),difference(X,Z)) = difference(difference(Z,Y),difference(Z,X)),
inference('REWRITE',[status(thm)],[24,199,theory(equality)]) ).
cnf(204,plain,
difference(difference(a,difference(a,b)),difference(a,c)) != difference(difference(a,difference(a,b)),difference(b,c)),
inference('REWRITE',[status(thm)],[19,set_difference_2,146,200,188,180,142,theory(equality)]) ).
cnf(255,plain,
difference(difference(X,difference(X,Y)),difference(X,Z)) = difference(difference(X,difference(X,Y)),difference(Y,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[180,set_difference_2,theory(equality)]),180,theory(equality)]) ).
cnf(256,plain,
$false,
inference('REWRITE',[status(thm)],[204,255,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG005-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : run-snark %s %d
% 0.13/0.33 % Computer : n018.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 : Wed Jun 8 11:06:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.45 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 *
% 0.19/0.46 *
% 0.19/0.47 #<PACKAGE "SNARK-USER">
% 0.19/0.47 *
% 0.19/0.47 SNARK-TPTP-OPTIONS
% 0.19/0.47 *
% 0.19/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.47 (USE-FACTORING :POS)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.47 *
% 0.19/0.47 "."
% 0.19/0.47 *
% 0.19/0.47 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-08T11:06:07
% 0.19/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n018.cluster.edu at 2022-06-08T11:06:07
% 0.56/0.75
% 0.56/0.75
% 0.56/0.75 #||
% 0.56/0.75 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.56/0.75 % SZS output start Refutation
% See solution above
% 0.56/0.75 ||#
% 0.56/0.75
% 0.56/0.75 ; Summary of computation:
% 0.56/0.75 ; 1824 formulas have been input or derived (from 34 formulas).
% 0.56/0.75 ; 256 (14%) were retained. Of these,
% 0.56/0.75 ; 162 (63%) were simplified or subsumed later,
% 0.56/0.75 ; 94 (37%) are still being kept.
% 0.56/0.75 ;
% 0.56/0.75 ; Run time in seconds excluding printing time:
% 0.56/0.75 ; 0.001 0% Read assertion file (1 call)
% 0.56/0.75 ; 0.000 0% Assert (5 calls)
% 0.56/0.75 ; 0.027 10% Process new row (1,716 calls)
% 0.56/0.75 ; 0.001 0% Resolution (66 calls)
% 0.56/0.75 ; 0.035 12% Paramodulation (33 calls)
% 0.56/0.75 ; 0.105 38% Forward simplification (1,701 calls)
% 0.56/0.75 ; 0.017 6% Backward simplification (255 calls)
% 0.56/0.75 ; 0.064 23% Ordering (9,110 calls)
% 0.56/0.75 ; 0.000 0% Sortal reasoning (32 calls)
% 0.56/0.75 ; 0.000 0% Purity testing (1 call)
% 0.56/0.75 ; 0.030 11% Other
% 0.56/0.75 ; 0.280 Total
% 0.56/0.75 ; 0.283 Real time
% 0.56/0.75 ;
% 0.56/0.75 ; Term-hash-array has 658 terms in all.
% 0.56/0.75 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.56/0.75 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.56/0.75 ; Path-index has 272 entries (379 at peak, 747 added, 475 deleted).
% 0.56/0.75 ; Path-index has 175 nodes (228 at peak, 295 added, 120 deleted).
% 0.56/0.75 ; Trie-index has 272 entries (379 at peak, 747 added, 475 deleted).
% 0.56/0.75 ; Trie-index has 757 nodes (1,345 at peak, 2,328 added, 1,571 deleted).
% 0.56/0.75 ; Retrieved 39,940 generalization terms in 13,816 calls.
% 0.56/0.75 ; Retrieved 3,040 instance terms in 314 calls.
% 0.56/0.75 ; Retrieved 5,004 unifiable terms in 218 calls.
% 0.56/0.75 ;
% 0.56/0.75 ; The agenda of rows to process has 37 entries:
% 0.56/0.75 ; 1 with value 26 9 with value 30 4 with value 34
% 0.56/0.75 ; 3 with value 27 2 with value 31 1 with value 38
% 0.56/0.75 ; 1 with value 28 5 with value 32 1 with value 39
% 0.56/0.75 ; 7 with value 29 3 with value 33
% 0.56/0.75 ; The agenda of rows to give has 74 entries:
% 0.56/0.75 ; 4 with value (4 20) 6 with value (4 24) 5 with value (4 28)
% 0.56/0.75 ; 9 with value (4 21) 9 with value (4 25) 2 with value (4 29)
% 0.56/0.75 ; 4 with value (4 22) 14 with value (4 26) 7 with value (4 31)
% 0.56/0.75 ; 5 with value (4 23) 7 with value (4 27) 2 with value (4 33)
% 0.56/0.75 Evaluation took:
% 0.56/0.75 0.283 seconds of real time
% 0.56/0.75 0.258224 seconds of user run time
% 0.56/0.75 0.025116 seconds of system run time
% 0.56/0.75 [Run times include 0.006 seconds GC run time.]
% 0.56/0.75 0 calls to %EVAL
% 0.56/0.75 0 page faults and
% 0.56/0.75 20,390,736 bytes consed.
% 0.56/0.75 :PROOF-FOUND
% 0.56/0.75 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-08T11:06:07
% 0.56/0.75 :PROOF-FOUND
% 0.56/0.75 *
%------------------------------------------------------------------------------