%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : SWX199+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n016.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 : 300s
% DateTime : Tue May 5 07:07:12 PM UTC 2026
% Result : Theorem 0.48s 0.64s
% Output : Refutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of clauses : 30 ( 23 unt; 1 nHn; 7 RR)
% Number of literals : 39 ( 31 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 66 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
head(cons(X,Y)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
cnf(2,axiom,
tail(cons(X,Y)) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
cnf(5,axiom,
z != s(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
cnf(6,axiom,
leqNat(z,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
cnf(7,axiom,
~ leqNat(s(X),z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
cnf(9,axiom,
( leqNat(s(X),s(Y))
| ~ leqNat(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
cnf(10,axiom,
merge(nil,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
cnf(11,axiom,
merge(cons(X,Y),nil) = cons(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
cnf(12,axiom,
( ~ leqNat(X,Y)
| merge(cons(X,Z),cons(Y,U)) = cons(X,merge(Z,cons(Y,U))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
cnf(13,axiom,
( leqNat(X,Y)
| merge(cons(X,Z),cons(Y,U)) = cons(Y,merge(cons(X,Z),U)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
cnf(14,negated_conjecture,
( merge(X,Y) != merge(Y,X)
| merge(X,Z) != merge(Z,X)
| merge(Y,Z) = merge(Z,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_013) ).
cnf(16,plain,
leqNat(s(z),s(X)),
inference('HYPERRESOLVE',[status(thm)],[9,6]) ).
cnf(17,plain,
merge(cons(z,X),cons(Y,Z)) = cons(z,merge(X,cons(Y,Z))),
inference('HYPERRESOLVE',[status(thm)],[12,6]) ).
cnf(18,plain,
merge(cons(s(X),Y),cons(z,Z)) = cons(z,merge(cons(s(X),Y),Z)),
inference('HYPERRESOLVE',[status(thm)],[7,13]) ).
cnf(22,plain,
( X != merge(X,nil)
| Y != merge(Y,nil)
| merge(X,Y) = merge(Y,X) ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[14,10,theory(equality)]),10,theory(equality)]) ).
cnf(24,plain,
( merge(cons(X,Y),Z) != merge(Z,cons(X,Y))
| Z = merge(Z,nil) ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[14,11,theory(equality)]),10,theory(equality)]) ).
cnf(25,plain,
( X != merge(X,nil)
| merge(cons(Y,Z),X) = merge(X,cons(Y,Z)) ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[14,11,theory(equality)]),10,theory(equality)]) ).
cnf(27,plain,
merge(cons(s(z),X),cons(s(Y),Z)) = cons(s(z),merge(X,cons(s(Y),Z))),
inference('HYPERRESOLVE',[status(thm)],[12,16]) ).
cnf(42,plain,
merge(cons(X,Y),cons(Z,U)) = merge(cons(Z,U),cons(X,Y)),
inference('HYPERRESOLVE',[status(thm)],[25,11]) ).
cnf(43,plain,
merge(cons(X,Y),cons(z,Z)) = cons(z,merge(Z,cons(X,Y))),
inference('PARAMODULATE',[status(thm)],[17,42,theory(equality)]) ).
cnf(46,plain,
cons(z,merge(X,cons(s(Y),Z))) = cons(z,merge(cons(s(Y),Z),X)),
inference('REWRITE',[status(thm)],[18,43,theory(equality)]) ).
cnf(51,plain,
merge(cons(s(X),Y),Z) = merge(Z,cons(s(X),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[2,46,theory(equality)]),2,theory(equality)]) ).
cnf(53,plain,
X = merge(X,nil),
inference('HYPERRESOLVE',[status(thm)],[24,51]) ).
cnf(54,plain,
merge(X,Y) = merge(Y,X),
inference('REWRITE',[status(thm)],[22,53,theory(equality)]) ).
cnf(123,plain,
cons(s(z),merge(X,cons(s(Y),Z))) = merge(cons(s(Y),Z),cons(s(z),X)),
inference('PARAMODULATE',[status(thm)],[54,27,theory(equality)]) ).
cnf(147,plain,
cons(s(z),merge(X,cons(s(z),Y))) = cons(s(z),merge(Y,cons(s(z),X))),
inference('PARAMODULATE',[status(thm)],[27,123,theory(equality)]) ).
cnf(151,plain,
merge(X,cons(s(z),Y)) = merge(Y,cons(s(z),X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[2,147,theory(equality)]),2,theory(equality)]) ).
cnf(160,plain,
merge(X,cons(s(z),nil)) = cons(s(z),X),
inference('PARAMODULATE',[status(thm)],[10,151,theory(equality)]) ).
cnf(171,plain,
cons(s(z),cons(z,X)) = cons(z,cons(s(z),X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[17,160,theory(equality)]),160,theory(equality)]) ).
cnf(190,plain,
$false,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1,171,theory(equality)]),5,1,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX199+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : run-snark %s %d
% 0.16/0.34 % Computer : n016.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue May 5 11:12:21 EDT 2026
% 0.16/0.35 % CPUTime :
% 0.27/0.47 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.27/0.48 *
% 0.27/0.48 *
% 0.27/0.48 #<PACKAGE "SNARK-USER">
% 0.27/0.48 *
% 0.27/0.48 SNARK-TPTP-OPTIONS
% 0.27/0.48 *
% 0.27/0.48 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.27/0.48 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.27/0.48 (USE-FACTORING :POS)
% 0.27/0.48 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.27/0.48 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.27/0.48 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.27/0.48 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.27/0.48 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.27/0.48 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.27/0.48 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.27/0.48 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.27/0.48 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.27/0.48 (DECLARE-TPTP-SYMBOLS2))
% 0.27/0.48 *
% 0.27/0.48 "."
% 0.27/0.48 *
% 0.27/0.49 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2026-05-05T11:12:21
% 0.27/0.49 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n016.cluster.edu at 2026-05-05T11:12:21
% 0.27/0.50
% 0.48/0.64 ; Recognized left identity assertion (= (|merge| |nil| ?X) ?X).
% 0.48/0.64
% 0.48/0.64 #||
% 0.48/0.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.64 % SZS output start Refutation
% See solution above
% 0.48/0.64 ||#
% 0.48/0.64
% 0.48/0.64 ; Summary of computation:
% 0.48/0.64 ; 1070 formulas have been input or derived (from 55 formulas).
% 0.48/0.64 ; 190 (18%) were retained. Of these,
% 0.48/0.64 ; 24 (13%) were simplified or subsumed later,
% 0.48/0.64 ; 166 (87%) are still being kept.
% 0.48/0.64 ;
% 0.48/0.64 ; Run time in seconds excluding printing time:
% 0.48/0.64 ; 0.003 2% Read assertion file (1 call)
% 0.48/0.64 ; 0.001 1% Assert (13 calls)
% 0.48/0.64 ; 0.028 18% Process new row (979 calls)
% 0.48/0.64 ; 0.005 3% Resolution (108 calls)
% 0.48/0.64 ; 0.020 13% Paramodulation (54 calls)
% 0.48/0.64 ; 0.000 0% Factoring (2 calls)
% 0.48/0.64 ; 0.000 0% Condensing (39 calls)
% 0.48/0.64 ; 0.002 1% Forward subsumption (39 calls)
% 0.48/0.64 ; 0.000 0% Backward subsumption (19 calls)
% 0.48/0.64 ; 0.003 2% Clause clause subsumption (29 calls)
% 0.48/0.64 ; 0.030 19% Forward simplification (915 calls)
% 0.48/0.64 ; 0.008 5% Backward simplification (190 calls)
% 0.48/0.64 ; 0.025 16% Ordering (5,640 calls)
% 0.48/0.64 ; 0.000 0% Sortal reasoning (32 calls)
% 0.48/0.64 ; 0.000 0% Purity testing (1 call)
% 0.48/0.64 ; 0.029 19% Other
% 0.48/0.64 ; 0.154 Total
% 0.48/0.64 ; 0.157 Real time
% 0.48/0.64 ;
% 0.48/0.64 ; Term-hash-array has 564 terms in all.
% 0.48/0.64 ; Feature-vector-row-index has 9 entries (14 at peak, 19 added, 10 deleted).
% 0.48/0.64 ; Feature-vector-row-index has 63 nodes (114 at peak, 167 added, 104 deleted).
% 0.48/0.64 ; Retrieved 29 possibly forward subsuming rows in 39 calls.
% 0.48/0.64 ; Retrieved 2 possibly backward subsumed rows in 19 calls.
% 0.48/0.64 ; Path-index has 494 entries (494 at peak, 577 added, 83 deleted).
% 0.48/0.64 ; Path-index has 822 nodes (822 at peak, 857 added, 35 deleted).
% 0.48/0.64 ; Trie-index has 494 entries (494 at peak, 577 added, 83 deleted).
% 0.48/0.64 ; Trie-index has 2,260 nodes (2,260 at peak, 2,488 added, 228 deleted).
% 0.48/0.64 ; Retrieved 3,415 generalization terms in 5,871 calls.
% 0.48/0.64 ; Retrieved 682 instance terms in 354 calls.
% 0.48/0.64 ; Retrieved 3,374 unifiable terms in 529 calls.
% 0.48/0.64 ;
% 0.48/0.64 ; The agenda of rows to process has 25 entries:
% 0.48/0.64 ; 2 with value 24 2 with value 30 2 with value 37
% 0.48/0.64 ; 6 with value 29 13 with value 34
% 0.48/0.64 ; The agenda of rows to give has 117 entries:
% 0.48/0.64 ; 1 with value (4 24) 9 with value (4 34) 3 with value (4 41)
% 0.48/0.64 ; 2 with value (4 27) 13 with value (4 35) 1 with value (4 44)
% 0.48/0.64 ; 4 with value (4 28) 11 with value (4 36) 1 with value (4 45)
% 0.48/0.64 ; 8 with value (4 29) 10 with value (4 37) 1 with value (4 47)
% 0.48/0.64 ; 6 with value (4 30) 5 with value (4 38) 1 with value (4 50)
% 0.48/0.64 ; 12 with value (4 31) 4 with value (4 39) 1 with value (4 53)
% 0.48/0.64 ; 14 with value (4 32) 1 with value (4 40) 1 with value (4 56)
% 0.48/0.64 ; 8 with value (4 33)
% 0.48/0.64 Evaluation took:
% 0.48/0.64 0.157 seconds of real time
% 0.48/0.64 0.131996 seconds of user run time
% 0.48/0.64 0.024952 seconds of system run time
% 0.48/0.64 0 calls to %EVAL
% 0.48/0.64 0 page faults and
% 0.48/0.64 10,192,416 bytes consed.
% 0.48/0.64 :PROOF-FOUND
% 0.48/0.64 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2026-05-05T11:12:21
% 0.48/0.64 :PROOF-FOUND
% 0.48/0.64 *
%------------------------------------------------------------------------------