TSTP Solution File: ALG007-1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : ALG007-1 : TPTP v8.1.0. Released v2.2.0.
% 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 : Thu Jul 14 17:59:36 EDT 2022
% Result : Unsatisfiable 1.73s 1.93s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 2 RR)
% Number of literals : 40 ( 39 equ; 1 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 120 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(set_difference_1,axiom,
difference(X,difference(Y,X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_1) ).
cnf(set_difference_2,axiom,
difference(X,difference(X,Y)) = difference(Y,difference(Y,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_2) ).
cnf(set_difference_3_simplified,axiom,
difference(difference(X,Y),Z) = difference(difference(X,Z),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_3_simplified) ).
cnf(prove_set_difference_3,negated_conjecture,
difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_set_difference_3) ).
cnf(8,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(9,plain,
difference(X,difference(difference(Y,X),Z)) = X,
inference('PARAMODULATE',[status(thm)],[set_difference_1,set_difference_3_simplified,theory(equality)]) ).
cnf(10,plain,
difference(X,Y) = difference(difference(X,Y),difference(Z,X)),
inference('PARAMODULATE',[status(thm)],[set_difference_3_simplified,set_difference_1,theory(equality)]) ).
cnf(12,plain,
difference(difference(X,difference(X,Y)),Z) = difference(difference(Y,Z),difference(Y,X)),
inference('PARAMODULATE',[status(thm)],[set_difference_3_simplified,set_difference_2,theory(equality)]) ).
cnf(13,plain,
difference(X,difference(X,difference(Y,Z))) = difference(difference(Y,Z),difference(difference(Y,X),Z)),
inference('PARAMODULATE',[status(thm)],[set_difference_2,set_difference_3_simplified,theory(equality)]) ).
cnf(16,plain,
difference(X,difference(difference(difference(Y,X),Z),U)) = X,
inference('PARAMODULATE',[status(thm)],[9,set_difference_3_simplified,theory(equality)]) ).
cnf(25,plain,
difference(X,Y) = difference(X,difference(X,difference(X,Y))),
inference('PARAMODULATE',[status(thm)],[set_difference_2,10,theory(equality)]) ).
cnf(26,plain,
difference(X,Y) = difference(X,difference(Y,difference(Y,X))),
inference('REWRITE',[status(thm)],[8,25,theory(equality)]) ).
cnf(29,plain,
difference(X,difference(X,Y)) = difference(difference(X,difference(X,Y)),difference(Z,Y)),
inference('PARAMODULATE',[status(thm)],[10,set_difference_2,theory(equality)]) ).
cnf(41,plain,
difference(difference(X,Y),Z) = difference(difference(X,Z),difference(Y,difference(Y,X))),
inference('PARAMODULATE',[status(thm)],[set_difference_3_simplified,26,theory(equality)]) ).
cnf(43,plain,
difference(difference(X,Y),Z) = difference(difference(X,Z),difference(X,difference(X,Y))),
inference('PARAMODULATE',[status(thm)],[set_difference_3_simplified,25,theory(equality)]) ).
cnf(163,plain,
difference(difference(X,Y),difference(X,Z)) = difference(difference(Z,Y),difference(Z,X)),
inference('PARAMODULATE',[status(thm)],[set_difference_3_simplified,12,theory(equality)]) ).
cnf(164,plain,
difference(X,difference(X,Y)) = difference(difference(Y,difference(Z,X)),difference(Y,X)),
inference('PARAMODULATE',[status(thm)],[10,12,theory(equality)]) ).
cnf(165,plain,
difference(X,difference(difference(Y,Z),difference(Y,difference(U,X)))) = X,
inference('PARAMODULATE',[status(thm)],[16,12,theory(equality)]) ).
cnf(166,plain,
difference(difference(X,difference(X,Y)),Z) = difference(difference(Y,difference(Y,X)),Z),
inference('PARAMODULATE',[status(thm)],[set_difference_3_simplified,12,theory(equality)]) ).
cnf(203,plain,
difference(difference(X,Y),difference(X,Z)) = difference(difference(X,Y),difference(difference(X,Z),difference(difference(Y,difference(Y,X)),Z))),
inference('PARAMODULATE',[status(thm)],[26,12,theory(equality)]) ).
cnf(252,plain,
difference(difference(X,Y),difference(difference(X,Y),Z)) = difference(difference(Z,difference(U,X)),difference(Z,difference(X,Y))),
inference('PARAMODULATE',[status(thm)],[163,10,theory(equality)]) ).
cnf(313,plain,
difference(difference(X,Y),difference(difference(Z,Y),difference(Z,X))) = difference(difference(difference(X,Y),difference(difference(Z,Y),difference(Z,X))),difference(U,difference(X,Z))),
inference('PARAMODULATE',[status(thm)],[29,163,theory(equality)]) ).
cnf(352,plain,
difference(difference(X,difference(Y,Z)),U) = difference(difference(X,U),difference(difference(Y,Z),difference(difference(Y,X),Z))),
inference('PARAMODULATE',[status(thm)],[41,set_difference_3_simplified,theory(equality)]) ).
cnf(356,plain,
difference(difference(X,difference(X,Y)),difference(difference(X,difference(X,Y)),difference(Y,Z))) = difference(difference(Y,Z),difference(difference(Y,X),Z)),
inference('PARAMODULATE',[status(thm)],[set_difference_2,41,theory(equality)]) ).
cnf(503,plain,
difference(difference(difference(X,Y),Z),difference(difference(U,V),difference(U,Y))) = difference(difference(X,Y),Z),
inference('PARAMODULATE',[status(thm)],[165,9,theory(equality)]) ).
cnf(565,plain,
difference(difference(difference(X,Y),difference(difference(Z,Y),difference(Z,X))),U) = difference(difference(difference(X,Z),difference(difference(X,Z),difference(X,Y))),U),
inference('PARAMODULATE',[status(thm)],[166,163,theory(equality)]) ).
cnf(601,plain,
difference(difference(X,Y),difference(difference(Z,difference(Z,X)),Y)) = difference(difference(X,Z),difference(difference(X,difference(X,Y)),Z)),
inference('PARAMODULATE',[status(thm)],[13,12,theory(equality)]) ).
cnf(605,plain,
difference(difference(X,Y),difference(difference(Z,Y),difference(Z,X))) = difference(difference(X,Z),difference(difference(X,difference(X,Y)),Z)),
inference('PARAMODULATE',[status(thm)],[13,163,theory(equality)]) ).
cnf(669,plain,
difference(difference(X,Y),difference(difference(X,Y),difference(X,Z))) = difference(difference(X,Y),Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[164,43,theory(equality)]),503,theory(equality)]) ).
cnf(673,plain,
difference(difference(difference(X,Y),difference(difference(Z,Y),difference(Z,X))),U) = difference(difference(difference(X,Z),Y),U),
inference('REWRITE',[status(thm)],[565,669,theory(equality)]) ).
cnf(674,plain,
difference(difference(X,Y),difference(difference(Z,Y),difference(Z,X))) = difference(difference(X,Z),Y),
inference('REWRITE',[status(thm)],[313,10,673,theory(equality)]) ).
cnf(675,plain,
difference(difference(X,Y),Z) = difference(difference(X,Y),difference(difference(X,difference(X,Z)),Y)),
inference('REWRITE',[status(thm)],[605,674,theory(equality)]) ).
cnf(676,plain,
difference(difference(X,Y),difference(difference(Z,difference(Z,X)),Y)) = difference(difference(X,Z),Y),
inference('REWRITE',[status(thm)],[601,675,theory(equality)]) ).
cnf(681,plain,
difference(difference(X,Y),difference(X,Z)) = difference(difference(X,Y),difference(difference(X,Y),Z)),
inference('REWRITE',[status(thm)],[203,676,theory(equality)]) ).
cnf(685,plain,
difference(difference(X,difference(X,Y)),difference(X,difference(Y,Z))) = difference(difference(Y,Z),difference(difference(Y,X),Z)),
inference('REWRITE',[status(thm)],[356,681,theory(equality)]) ).
cnf(703,plain,
difference(difference(X,Y),difference(X,Z)) = difference(difference(Z,difference(U,X)),difference(Z,difference(X,Y))),
inference('REWRITE',[status(thm)],[252,681,theory(equality)]) ).
cnf(704,plain,
difference(difference(X,Y),difference(X,Z)) = difference(difference(X,Y),difference(difference(X,Z),Y)),
inference('REWRITE',[status(thm)],[685,703,theory(equality)]) ).
cnf(824,plain,
difference(difference(X,difference(Y,Z)),U) = difference(difference(X,U),difference(difference(Y,Z),difference(Y,X))),
inference('REWRITE',[status(thm)],[352,704,theory(equality)]) ).
cnf(826,plain,
difference(difference(X,Y),difference(Z,Y)) = difference(difference(X,Z),Y),
inference('REWRITE',[status(thm)],[674,set_difference_3_simplified,824,theory(equality)]) ).
cnf(827,plain,
$false,
inference('REWRITE',[status(thm)],[prove_set_difference_3,826,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG007-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n029.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 : Wed Jun 8 13:03:06 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 *
% 0.18/0.45 #<PACKAGE "SNARK-USER">
% 0.18/0.45 *
% 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 2022-06-08T13:03:06
% 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 2022-06-08T13:03:06
% 1.73/1.93
% 1.73/1.93
% 1.73/1.93 #||
% 1.73/1.93 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.73/1.93 % SZS output start Refutation
% See solution above
% 1.73/1.94 ||#
% 1.73/1.94
% 1.73/1.94 ; Summary of computation:
% 1.73/1.94 ; 6345 formulas have been input or derived (from 41 formulas).
% 1.73/1.94 ; 827 (13%) were retained. Of these,
% 1.73/1.94 ; 361 (44%) were simplified or subsumed later,
% 1.73/1.94 ; 466 (56%) are still being kept.
% 1.73/1.94 ;
% 1.73/1.94 ; Run time in seconds excluding printing time:
% 1.73/1.94 ; 0.001 0% Read assertion file (1 call)
% 1.73/1.94 ; 0.000 0% Assert (4 calls)
% 1.73/1.94 ; 0.083 6% Process new row (5,824 calls)
% 1.73/1.94 ; 0.004 0% Resolution (80 calls)
% 1.73/1.94 ; 0.083 6% Paramodulation (40 calls)
% 1.73/1.94 ; 0.547 37% Forward simplification (5,824 calls)
% 1.73/1.94 ; 0.107 7% Backward simplification (827 calls)
% 1.73/1.94 ; 0.606 41% Ordering (85,180 calls)
% 1.73/1.94 ; 0.000 0% Sortal reasoning (32 calls)
% 1.73/1.94 ; 0.001 0% Purity testing (1 call)
% 1.73/1.94 ; 0.040 3% Other
% 1.73/1.94 ; 1.472 Total
% 1.73/1.94 ; 1.480 Real time
% 1.73/1.94 ;
% 1.73/1.94 ; Term-hash-array has 2,284 terms in all.
% 1.73/1.94 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 1.73/1.94 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 1.73/1.94 ; Path-index has 1,345 entries (1,896 at peak, 2,371 added, 1,026 deleted).
% 1.73/1.94 ; Path-index has 413 nodes (447 at peak, 457 added, 44 deleted).
% 1.73/1.94 ; Trie-index has 1,345 entries (1,896 at peak, 2,371 added, 1,026 deleted).
% 1.73/1.94 ; Trie-index has 3,270 nodes (5,014 at peak, 6,242 added, 2,972 deleted).
% 1.73/1.94 ; Retrieved 243,389 generalization terms in 48,859 calls.
% 1.73/1.94 ; Retrieved 31,266 instance terms in 1,351 calls.
% 1.73/1.94 ; Retrieved 21,647 unifiable terms in 281 calls.
% 1.73/1.94 ;
% 1.73/1.94 ; The agenda of backward simplifiable rows to process has 30 entries:
% 1.73/1.94 ; 30 with value 0
% 1.73/1.94 ; The agenda of rows to process has 98 entries:
% 1.73/1.94 ; 12 with value 33 4 with value 37 25 with value 41
% 1.73/1.94 ; 19 with value 34 8 with value 38 2 with value 42
% 1.73/1.94 ; 3 with value 35 4 with value 39 4 with value 43
% 1.73/1.94 ; 13 with value 36 4 with value 40
% 1.73/1.94 ; The agenda of rows to give has 429 entries:
% 1.73/1.94 ; 1 with value (4 19) 24 with value (4 28) 19 with value (4 36)
% 1.73/1.94 ; 1 with value (4 21) 29 with value (4 29) 11 with value (4 37)
% 1.73/1.94 ; 6 with value (4 22) 24 with value (4 30) 3 with value (4 38)
% 1.73/1.94 ; 10 with value (4 23) 58 with value (4 31) 5 with value (4 40)
% 1.73/1.94 ; 14 with value (4 24) 54 with value (4 32) 7 with value (4 41)
% 1.73/1.94 ; 20 with value (4 25) 19 with value (4 33) 3 with value (4 42)
% 1.73/1.94 ; 39 with value (4 26) 19 with value (4 34) 1 with value (4 53)
% 1.73/1.94 ; 38 with value (4 27) 24 with value (4 35)
% 1.73/1.94 Evaluation took:
% 1.73/1.94 1.48 seconds of real time
% 1.73/1.94 1.356654 seconds of user run time
% 1.73/1.94 0.12386 seconds of system run time
% 1.73/1.94 [Run times include 0.042 seconds GC run time.]
% 1.73/1.94 0 calls to %EVAL
% 1.73/1.94 0 page faults and
% 1.73/1.94 113,724,536 bytes consed.
% 1.73/1.94 :PROOF-FOUND
% 1.73/1.94 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-08T13:03:07
% 1.73/1.94 :PROOF-FOUND
% 1.73/1.94 *
%------------------------------------------------------------------------------