%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : SWX217+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n028.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 07:07:14 PM UTC 2026
% Result : Theorem 0.54s 0.80s
% Output : Refutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of clauses : 58 ( 51 unt; 4 nHn; 29 RR)
% Number of literals : 65 ( 43 equ; 10 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
proj1Suc(suc(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
cnf(7,axiom,
half(zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
cnf(8,axiom,
half(suc(zero)) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
cnf(9,axiom,
half(suc(suc(X))) = suc(half(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
cnf(10,axiom,
evenNat(zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
cnf(11,axiom,
( ~ evenNat(suc(X))
| ~ evenNat(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
cnf(12,axiom,
( evenNat(suc(X))
| evenNat(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
cnf(13,axiom,
shw(zero) = nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
cnf(14,axiom,
( ~ evenNat(suc(X))
| shw(suc(X)) = cons(o,shw(half(suc(X)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
cnf(15,axiom,
( evenNat(suc(X))
| shw(suc(X)) = cons(i,shw(half(suc(X)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
cnf(16,axiom,
append(nil,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
cnf(17,axiom,
append(cons(X,Y),Z) = cons(X,append(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
cnf(18,axiom,
addNat(zero,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
cnf(19,axiom,
addNat(suc(X),Y) = suc(addNat(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
cnf(20,axiom,
double(X) = addNat(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
cnf(21,axiom,
rd(nil) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
cnf(22,axiom,
rd(cons(i,X)) = suc(double(rd(X))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
cnf(23,axiom,
rd(cons(o,X)) = double(rd(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_022) ).
cnf(24,axiom,
x(X,Y) = rd(append(shw(X),shw(Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_023) ).
cnf(25,plain,
~ evenNat(suc(zero)),
inference('UR-RESOLVE',[status(thm)],[11,10]) ).
cnf(26,plain,
double(zero) = zero,
inference('PARAMODULATE',[status(thm)],[18,20,theory(equality)]) ).
cnf(27,plain,
double(suc(X)) = suc(addNat(X,suc(X))),
inference('PARAMODULATE',[status(thm)],[20,19,theory(equality)]) ).
cnf(30,plain,
append(cons(X,nil),Y) = cons(X,Y),
inference('PARAMODULATE',[status(thm)],[17,16,theory(equality)]) ).
cnf(31,plain,
( evenNat(suc(X))
| shw(suc(X)) = append(cons(i,nil),shw(half(suc(X)))) ),
inference('REWRITE',[status(thm)],[15,30,theory(equality)]) ).
cnf(32,plain,
( ~ evenNat(suc(X))
| shw(suc(X)) = append(cons(o,nil),shw(half(suc(X)))) ),
inference('REWRITE',[status(thm)],[14,30,theory(equality)]) ).
cnf(33,plain,
append(cons(X,Y),Z) = append(cons(X,nil),append(Y,Z)),
inference('REWRITE',[status(thm)],[17,30,theory(equality)]) ).
cnf(34,plain,
rd(append(shw(X),shw(Y))) = rd(append(shw(Y),shw(X))),
inference('PARAMODULATE',[status(thm)],[24,24,theory(equality)]) ).
cnf(37,plain,
shw(suc(zero)) = cons(i,nil),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[11,31,10]),30,13,8,theory(equality)]) ).
cnf(44,plain,
evenNat(suc(suc(zero))),
inference('UR-RESOLVE',[status(thm)],[12,25]) ).
cnf(45,plain,
~ evenNat(suc(suc(suc(zero)))),
inference('UR-RESOLVE',[status(thm)],[11,44]) ).
cnf(46,plain,
shw(suc(suc(zero))) = append(cons(o,nil),shw(suc(zero))),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[32,44]),7,9,theory(equality)]) ).
cnf(52,plain,
rd(shw(suc(zero))) = suc(zero),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[22,37,theory(equality)]),26,21,theory(equality)]) ).
cnf(54,plain,
evenNat(suc(suc(suc(suc(zero))))),
inference('UR-RESOLVE',[status(thm)],[12,45]) ).
cnf(58,plain,
append(shw(suc(zero)),X) = cons(i,X),
inference('PARAMODULATE',[status(thm)],[30,37,theory(equality)]) ).
cnf(59,plain,
rd(append(shw(suc(zero)),X)) = suc(double(rd(X))),
inference('REWRITE',[status(thm)],[22,58,theory(equality)]) ).
cnf(61,plain,
rd(append(cons(o,nil),X)) = double(rd(X)),
inference('PARAMODULATE',[status(thm)],[23,30,theory(equality)]) ).
cnf(66,plain,
double(suc(zero)) = suc(suc(zero)),
inference('PARAMODULATE',[status(thm)],[27,18,theory(equality)]) ).
cnf(69,plain,
shw(double(suc(zero))) = append(cons(o,nil),shw(suc(zero))),
inference('REWRITE',[status(thm)],[46,66,theory(equality)]) ).
cnf(71,plain,
evenNat(suc(suc(double(suc(zero))))),
inference('REWRITE',[status(thm)],[54,66,theory(equality)]) ).
cnf(72,plain,
proj1Suc(double(suc(X))) = addNat(X,suc(X)),
inference('PARAMODULATE',[status(thm)],[4,27,theory(equality)]) ).
cnf(73,plain,
double(suc(X)) = suc(proj1Suc(double(suc(X)))),
inference('REWRITE',[status(thm)],[27,72,theory(equality)]) ).
cnf(78,plain,
addNat(double(suc(zero)),X) = suc(suc(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[19,66,theory(equality)]),18,19,theory(equality)]) ).
cnf(85,plain,
~ evenNat(suc(suc(suc(double(suc(zero)))))),
inference('UR-RESOLVE',[status(thm)],[11,71]) ).
cnf(89,plain,
proj1Suc(double(double(suc(zero)))) = suc(double(suc(zero))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[72,66,theory(equality)]),18,19,theory(equality)]) ).
cnf(94,plain,
~ evenNat(suc(suc(proj1Suc(double(double(suc(zero))))))),
inference('REWRITE',[status(thm)],[85,89,theory(equality)]) ).
cnf(98,plain,
( evenNat(double(suc(X)))
| evenNat(proj1Suc(double(suc(X)))) ),
inference('PARAMODULATE',[status(thm)],[12,73,theory(equality)]) ).
cnf(100,plain,
double(double(suc(X))) = suc(proj1Suc(double(double(suc(X))))),
inference('PARAMODULATE',[status(thm)],[73,73,theory(equality)]) ).
cnf(102,plain,
~ evenNat(suc(double(double(suc(zero))))),
inference('REWRITE',[status(thm)],[94,100,theory(equality)]) ).
cnf(113,plain,
rd(append(cons(o,X),Y)) = double(rd(append(X,Y))),
inference('PARAMODULATE',[status(thm)],[61,33,theory(equality)]) ).
cnf(114,plain,
proj1Suc(double(proj1Suc(double(double(suc(zero)))))) = suc(double(double(suc(zero)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[72,78,theory(equality)]),100,89,theory(equality)]) ).
cnf(115,plain,
~ evenNat(proj1Suc(double(proj1Suc(double(double(suc(zero))))))),
inference('REWRITE',[status(thm)],[102,114,theory(equality)]) ).
cnf(126,plain,
rd(append(shw(X),shw(suc(zero)))) = suc(double(rd(shw(X)))),
inference('PARAMODULATE',[status(thm)],[59,34,theory(equality)]) ).
cnf(136,plain,
evenNat(double(proj1Suc(double(double(suc(zero)))))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[98,89,theory(equality)]),115]) ).
cnf(158,plain,
rd(append(append(cons(o,nil),X),Y)) = double(rd(append(X,Y))),
inference('PARAMODULATE',[status(thm)],[113,30,theory(equality)]) ).
cnf(159,plain,
rd(shw(double(suc(zero)))) = double(suc(zero)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[113,69,theory(equality)]),52,16,theory(equality)]) ).
cnf(526,plain,
rd(append(shw(double(suc(zero))),X)) = double(suc(double(rd(X)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[158,69,theory(equality)]),59,theory(equality)]) ).
cnf(1042,plain,
double(proj1Suc(double(double(suc(zero))))) = proj1Suc(double(proj1Suc(double(double(suc(zero)))))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[126,526,theory(equality)]),114,159,89,52,theory(equality)]) ).
cnf(1044,plain,
$false,
inference('REWRITE',[status(thm)],[115,136,1042,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX217+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.13 % Command : run-snark %s %d
% 0.16/0.33 % Computer : n028.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 12:14:45 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.19/0.45 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.30/0.46 *
% 0.30/0.46 *
% 0.30/0.47 #<PACKAGE "SNARK-USER">
% 0.30/0.47 *
% 0.30/0.47 SNARK-TPTP-OPTIONS
% 0.30/0.47 *
% 0.30/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.30/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.30/0.47 (USE-FACTORING :POS)
% 0.30/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.30/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.30/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.30/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.30/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.30/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.30/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.30/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.30/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.30/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.30/0.47 *
% 0.30/0.47 "."
% 0.30/0.47 *
% 0.30/0.47 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2026-05-05T12:14:45
% 0.30/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n028.cluster.edu at 2026-05-05T12:14:45
% 0.30/0.49
% 0.30/0.49 ; Recognized left identity assertion (= (|append| |nil| ?X) ?X).
% 0.30/0.49 ; Recognized left identity assertion (= (|addNat| |zero| ?X) ?X).
% 0.30/0.49 ; Recognized commutativity assertion (= (|x| ?X ?Y) (|x| ?Y ?X)).
% 0.54/0.80 ; Declaring x to be commutative.
% 0.54/0.80
% 0.54/0.80 #||
% 0.54/0.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.54/0.80 % SZS output start Refutation
% See solution above
% 0.64/0.81 ||#
% 0.64/0.81
% 0.64/0.81 ; Summary of computation:
% 0.64/0.81 ; 2139 formulas have been input or derived (from 225 formulas).
% 0.64/0.81 ; 1044 (49%) were retained. Of these,
% 0.64/0.81 ; 201 (19%) were simplified or subsumed later,
% 0.64/0.81 ; 843 (81%) are still being kept.
% 0.64/0.81 ;
% 0.64/0.81 ; Run time in seconds excluding printing time:
% 0.64/0.81 ; 0.004 1% Read assertion file (1 call)
% 0.64/0.81 ; 0.000 0% Assert (24 calls)
% 0.64/0.81 ; 0.087 27% Process new row (2,022 calls)
% 0.64/0.81 ; 0.009 3% Resolution (448 calls)
% 0.64/0.81 ; 0.044 14% Paramodulation (224 calls)
% 0.64/0.81 ; 0.000 0% Factoring (7 calls)
% 0.64/0.81 ; 0.000 0% Condensing (111 calls)
% 0.64/0.81 ; 0.009 3% Forward subsumption (111 calls)
% 0.64/0.81 ; 0.001 0% Backward subsumption (75 calls)
% 0.64/0.81 ; 0.000 0% Clause clause subsumption (79 calls)
% 0.64/0.81 ; 0.069 21% Forward simplification (1,927 calls)
% 0.64/0.81 ; 0.027 8% Backward simplification (1,044 calls)
% 0.64/0.81 ; 0.031 10% Ordering (7,617 calls)
% 0.64/0.81 ; 0.001 0% Sortal reasoning (32 calls)
% 0.64/0.81 ; 0.000 0% Purity testing (1 call)
% 0.64/0.81 ; 0.041 13% Other
% 0.64/0.81 ; 0.323 Total
% 0.64/0.81 ; 0.343 Real time
% 0.64/0.81 ;
% 0.64/0.81 ; Term-hash-array has 2,469 terms in all.
% 0.64/0.81 ; Feature-vector-row-index has 68 entries (70 at peak, 75 added, 7 deleted).
% 0.64/0.81 ; Feature-vector-row-index has 709 nodes (737 at peak, 803 added, 94 deleted).
% 0.64/0.81 ; Retrieved 80 possibly forward subsuming rows in 111 calls.
% 0.64/0.81 ; Retrieved 2 possibly backward subsumed rows in 75 calls.
% 0.64/0.81 ; Path-index has 2,037 entries (2,196 at peak, 2,521 added, 484 deleted).
% 0.64/0.81 ; Path-index has 9,340 nodes (9,498 at peak, 9,823 added, 483 deleted).
% 0.64/0.81 ; Trie-index has 2,037 entries (2,196 at peak, 2,521 added, 484 deleted).
% 0.64/0.81 ; Trie-index has 10,245 nodes (11,248 at peak, 13,201 added, 2,956 deleted).
% 0.64/0.81 ; Retrieved 5,429 generalization terms in 17,875 calls.
% 0.64/0.81 ; Retrieved 1,301 instance terms in 1,116 calls.
% 0.64/0.81 ; Retrieved 4,490 unifiable terms in 1,960 calls.
% 0.64/0.81 ;
% 0.64/0.81 ; The agenda of backward simplifiable rows to process has 71 entries:
% 0.64/0.81 ; 71 with value 0
% 0.64/0.81 ; The agenda of rows to give has 647 entries:
% 0.64/0.81 ; 1 with value (4 22) 77 with value (4 31) 6 with value (4 39)
% 0.64/0.81 ; 11 with value (4 24) 40 with value (4 32) 7 with value (4 40)
% 0.64/0.81 ; 50 with value (4 25) 26 with value (4 33) 7 with value (4 41)
% 0.64/0.81 ; 59 with value (4 26) 23 with value (4 34) 3 with value (4 46)
% 0.64/0.81 ; 61 with value (4 27) 6 with value (4 35) 1 with value (4 47)
% 0.64/0.81 ; 72 with value (4 28) 14 with value (4 36) 1 with value (4 53)
% 0.64/0.82 ; 77 with value (4 29) 4 with value (4 37) 1 with value (4 54)
% 0.64/0.82 ; 93 with value (4 30) 7 with value (4 38)
% 0.64/0.82 Evaluation took:
% 0.64/0.82 0.343 seconds of real time
% 0.64/0.82 0.312267 seconds of user run time
% 0.64/0.82 0.030541 seconds of system run time
% 0.64/0.82 [Run times include 0.028 seconds GC run time.]
% 0.64/0.82 0 calls to %EVAL
% 0.64/0.82 0 page faults and
% 0.64/0.82 25,532,176 bytes consed.
% 0.64/0.82 :PROOF-FOUND
% 0.64/0.82 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2026-05-05T12:14:46
% 0.64/0.82 :PROOF-FOUND
% 0.64/0.82 *
%------------------------------------------------------------------------------