%------------------------------------------------------------------------------
% 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 : 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 : 300s
% DateTime : Tue May 5 07:07:14 PM UTC 2026
% Result : Unsatisfiable 0.54s 0.78s
% Output : Refutation 0.54s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 40ory(equality))
% Comments :
%------------------------------------------------------------------------------
cnf(axiom,axiom,
aux(X,btrue) = cons(o,shw(half(suc(X)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
cnf(axiom_001,axiom,
aux(X,bfalse) = cons(i,shw(half(suc(X)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
cnf(axiom_002,axiom,
notb(btrue) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
cnf(axiom_003,axiom,
notb(bfalse) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
cnf(axiom_004,axiom,
half(zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
cnf(axiom_005,axiom,
half(suc(zero)) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
cnf(axiom_006,axiom,
half(suc(suc(X))) = suc(half(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
cnf(axiom_007,axiom,
evenNat(zero) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
cnf(axiom_008,axiom,
evenNat(suc(X)) = notb(evenNat(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
cnf(axiom_009,axiom,
shw(zero) = nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
cnf(axiom_010,axiom,
shw(suc(X)) = aux(X,evenNat(suc(X))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
cnf(12,plain,
shw(suc(X)) = aux(X,notb(evenNat(X))),
inference('REWRITE',[status(thm)],[axiom_010,axiom_008,theory(equality)]) ).
cnf(axiom_011,axiom,
append(nil,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
cnf(axiom_012,axiom,
append(cons(X,Y),Z) = cons(X,append(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
cnf(axiom_013,axiom,
addNat(zero,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
cnf(axiom_014,axiom,
addNat(suc(X),Y) = suc(addNat(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
cnf(axiom_015,axiom,
double(X) = addNat(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
cnf(axiom_016,axiom,
rd(nil) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
cnf(axiom_017,axiom,
rd(cons(i,X)) = suc(double(rd(X))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
cnf(axiom_018,axiom,
rd(cons(o,X)) = double(rd(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
cnf(axiom_019,axiom,
x(X,Y) = rd(append(shw(X),shw(Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
cnf(axiom_020,axiom,
sat_comm(X,Y) = eq(x(X,Y),x(Y,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
cnf(23,plain,
sat_comm(X,Y) = eq(rd(append(shw(X),shw(Y))),rd(append(shw(Y),shw(X)))),
inference('REWRITE',[status(thm)],[axiom_020,axiom_019,theory(equality)]) ).
cnf(axiom_025,axiom,
eq(suc(X),suc(Y)) = eq(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_025) ).
cnf(axiom_026,axiom,
eq(zero,suc(X)) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
cnf(axiom_029,axiom,
eq2(X,X) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
cnf(goal,negated_conjecture,
eq2(sat_comm(X,Y),bfalse) != btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(35,plain,
eq2(eq(rd(append(shw(X),shw(Y))),rd(append(shw(Y),shw(X)))),bfalse) != btrue,
inference('REWRITE',[status(thm)],[goal,23,theory(equality)]) ).
cnf(36,plain,
double(zero) = zero,
inference('PARAMODULATE',[status(thm)],[axiom_013,axiom_015,theory(equality)]) ).
cnf(37,plain,
double(suc(X)) = suc(addNat(X,suc(X))),
inference('PARAMODULATE',[status(thm)],[axiom_015,axiom_014,theory(equality)]) ).
cnf(38,plain,
shw(suc(zero)) = aux(zero,bfalse),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,axiom_007,theory(equality)]),axiom_002,theory(equality)]) ).
cnf(39,plain,
shw(suc(suc(X))) = aux(suc(X),notb(notb(evenNat(X)))),
inference('PARAMODULATE',[status(thm)],[12,axiom_008,theory(equality)]) ).
cnf(40,plain,
append(cons(X,nil),Y) = cons(X,Y),
inference('PARAMODULATE',[status(thm)],[axiom_012,axiom_011,theory(equality)]) ).
cnf(41,plain,
aux(X,bfalse) = append(cons(i,nil),shw(half(suc(X)))),
inference('REWRITE',[status(thm)],[axiom_001,40,theory(equality)]) ).
cnf(42,plain,
aux(X,btrue) = append(cons(o,nil),shw(half(suc(X)))),
inference('REWRITE',[status(thm)],[axiom,40,theory(equality)]) ).
cnf(43,plain,
append(cons(X,Y),Z) = append(cons(X,nil),append(Y,Z)),
inference('REWRITE',[status(thm)],[axiom_012,40,theory(equality)]) ).
cnf(46,plain,
shw(suc(zero)) = cons(i,nil),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[41,axiom_005,theory(equality)]),40,axiom_009,38,theory(equality)]) ).
cnf(49,plain,
aux(zero,btrue) = cons(o,nil),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[42,axiom_005,theory(equality)]),40,axiom_009,theory(equality)]) ).
cnf(50,plain,
aux(X,btrue) = append(aux(zero,btrue),shw(half(suc(X)))),
inference('REWRITE',[status(thm)],[42,49,theory(equality)]) ).
cnf(57,plain,
append(cons(o,X),Y) = append(aux(zero,btrue),append(X,Y)),
inference('PARAMODULATE',[status(thm)],[43,49,theory(equality)]) ).
cnf(58,plain,
rd(shw(suc(zero))) = suc(zero),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[axiom_017,46,theory(equality)]),36,axiom_016,theory(equality)]) ).
cnf(60,plain,
append(aux(zero,btrue),X) = cons(o,X),
inference('PARAMODULATE',[status(thm)],[40,49,theory(equality)]) ).
cnf(61,plain,
rd(append(aux(zero,btrue),X)) = double(rd(X)),
inference('REWRITE',[status(thm)],[axiom_018,60,theory(equality)]) ).
cnf(62,plain,
append(append(aux(zero,btrue),X),Y) = append(aux(zero,btrue),append(X,Y)),
inference('REWRITE',[status(thm)],[57,60,theory(equality)]) ).
cnf(63,plain,
append(shw(suc(zero)),X) = cons(i,X),
inference('PARAMODULATE',[status(thm)],[40,46,theory(equality)]) ).
cnf(64,plain,
rd(append(shw(suc(zero)),X)) = suc(double(rd(X))),
inference('REWRITE',[status(thm)],[axiom_017,63,theory(equality)]) ).
cnf(69,plain,
eq2(eq(suc(double(rd(shw(X)))),rd(append(shw(X),shw(suc(zero))))),bfalse) != btrue,
inference('PARAMODULATE',[status(thm)],[35,64,theory(equality)]) ).
cnf(71,plain,
double(suc(zero)) = suc(suc(zero)),
inference('PARAMODULATE',[status(thm)],[37,axiom_013,theory(equality)]) ).
cnf(77,plain,
eq(suc(X),double(suc(Y))) = eq(X,addNat(Y,suc(Y))),
inference('PARAMODULATE',[status(thm)],[axiom_025,37,theory(equality)]) ).
cnf(80,plain,
half(double(suc(zero))) = suc(zero),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[axiom_006,71,theory(equality)]),axiom_004,theory(equality)]) ).
cnf(82,plain,
eq(double(suc(zero)),suc(X)) = eq(suc(zero),X),
inference('PARAMODULATE',[status(thm)],[axiom_025,71,theory(equality)]) ).
cnf(83,plain,
addNat(double(suc(zero)),X) = suc(suc(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[axiom_014,71,theory(equality)]),axiom_013,axiom_014,theory(equality)]) ).
cnf(85,plain,
eq(suc(X),double(suc(zero))) = eq(X,suc(zero)),
inference('PARAMODULATE',[status(thm)],[axiom_025,71,theory(equality)]) ).
cnf(86,plain,
double(double(suc(zero))) = suc(suc(double(suc(zero)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[37,71,theory(equality)]),axiom_013,axiom_014,theory(equality)]) ).
cnf(93,plain,
shw(double(suc(zero))) = append(aux(zero,btrue),shw(suc(zero))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[39,axiom_007,theory(equality)]),80,50,axiom_003,axiom_002,71,theory(equality)]) ).
cnf(107,plain,
eq(double(double(suc(zero))),suc(X)) = eq(suc(double(suc(zero))),X),
inference('PARAMODULATE',[status(thm)],[axiom_025,86,theory(equality)]) ).
cnf(110,plain,
eq(suc(X),double(double(suc(zero)))) = eq(X,suc(double(suc(zero)))),
inference('PARAMODULATE',[status(thm)],[axiom_025,86,theory(equality)]) ).
cnf(115,plain,
rd(shw(double(suc(zero)))) = double(suc(zero)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[61,93,theory(equality)]),58,theory(equality)]) ).
cnf(152,plain,
eq(suc(X),double(suc(double(suc(zero))))) = eq(X,suc(double(double(suc(zero))))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[77,83,theory(equality)]),86,theory(equality)]) ).
cnf(239,plain,
rd(append(append(aux(zero,btrue),X),Y)) = double(rd(append(X,Y))),
inference('PARAMODULATE',[status(thm)],[61,62,theory(equality)]) ).
cnf(425,plain,
rd(append(shw(double(suc(zero))),X)) = double(suc(double(rd(X)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[239,93,theory(equality)]),64,theory(equality)]) ).
cnf(771,plain,
$false,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[69,425,theory(equality)]),axiom_029,axiom_026,85,82,110,107,152,58,115,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX217-1 : TPTP v9.3.0. Released v9.3.0.
% 0.13/0.13 % Command : run-snark %s %d
% 0.16/0.34 % Computer : n029.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
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 12:15:59 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.30/0.46 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.30/0.47 *
% 0.30/0.47 *
% 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 2026-05-05T12:15:59
% 0.30/0.48 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n029.cluster.edu at 2026-05-05T12:15:59
% 0.30/0.49
% 0.30/0.49 ; Recognized left identity assertion (= (|append| |nil| ?X) ?X).
% 0.54/0.78 ; Recognized left identity assertion (= (|addNat| |zero| ?X) ?X).
% 0.54/0.78
% 0.54/0.78 #||
% 0.54/0.78 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.54/0.78 % SZS output start Refutation
% See solution above
% 0.54/0.78 ||#
% 0.54/0.78
% 0.54/0.78 ; Summary of computation:
% 0.54/0.78 ; 1864 formulas have been input or derived (from 190 formulas).
% 0.54/0.78 ; 771 (41%) were retained. Of these,
% 0.54/0.78 ; 67 ( 9%) were simplified or subsumed later,
% 0.54/0.78 ; 704 (91%) are still being kept.
% 0.54/0.78 ;
% 0.54/0.78 ; Run time in seconds excluding printing time:
% 0.54/0.78 ; 0.004 1% Read assertion file (1 call)
% 0.54/0.78 ; 0.001 0% Assert (32 calls)
% 0.54/0.78 ; 0.093 31% Process new row (1,851 calls)
% 0.54/0.78 ; 0.007 2% Resolution (378 calls)
% 0.54/0.78 ; 0.026 9% Paramodulation (189 calls)
% 0.54/0.78 ; 0.078 26% Forward simplification (1,838 calls)
% 0.54/0.78 ; 0.012 4% Backward simplification (768 calls)
% 0.54/0.78 ; 0.043 14% Ordering (9,470 calls)
% 0.54/0.78 ; 0.001 0% Sortal reasoning (32 calls)
% 0.54/0.78 ; 0.000 0% Purity testing (1 call)
% 0.54/0.78 ; 0.038 13% Other
% 0.54/0.78 ; 0.303 Total
% 0.54/0.78 ; 0.309 Real time
% 0.54/0.78 ;
% 0.54/0.78 ; Term-hash-array has 2,247 terms in all.
% 0.54/0.78 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.54/0.78 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.54/0.78 ; Path-index has 2,100 entries (2,100 at peak, 2,284 added, 184 deleted).
% 0.54/0.78 ; Path-index has 8,613 nodes (8,613 at peak, 8,813 added, 200 deleted).
% 0.54/0.78 ; Trie-index has 2,100 entries (2,100 at peak, 2,284 added, 184 deleted).
% 0.54/0.78 ; Trie-index has 12,360 nodes (12,360 at peak, 13,367 added, 1,007 deleted).
% 0.54/0.78 ; Retrieved 7,990 generalization terms in 18,638 calls.
% 0.54/0.78 ; Retrieved 1,317 instance terms in 1,067 calls.
% 0.54/0.78 ; Retrieved 2,032 unifiable terms in 1,626 calls.
% 0.54/0.78 ;
% 0.54/0.78 ; The agenda of rows to process has 1 entry:
% 0.54/0.78 ; 1 with value 36
% 0.54/0.78 ; The agenda of rows to give has 523 entries:
% 0.54/0.78 ; 44 with value (4 25) 20 with value (4 32) 15 with value (4 39)
% 0.54/0.78 ; 48 with value (4 26) 16 with value (4 33) 2 with value (4 40)
% 0.54/0.78 ; 57 with value (4 27) 33 with value (4 34) 3 with value (4 41)
% 0.54/0.78 ; 44 with value (4 28) 8 with value (4 35) 1 with value (4 43)
% 0.54/0.78 ; 71 with value (4 29) 7 with value (4 36) 1 with value (4 44)
% 0.54/0.78 ; 73 with value (4 30) 11 with value (4 37) 2 with value (4 45)
% 0.54/0.78 ; 51 with value (4 31) 15 with value (4 38) 1 with value (4 46)
% 0.54/0.78 Evaluation took:
% 0.54/0.78 0.309 seconds of real time
% 0.54/0.78 0.266186 seconds of user run time
% 0.54/0.78 0.042531 seconds of system run time
% 0.54/0.78 [Run times include 0.014 seconds GC run time.]
% 0.54/0.78 0 calls to %EVAL
% 0.54/0.78 0 page faults and
% 0.54/0.78 22,526,808 bytes consed.
% 0.54/0.78 :PROOF-FOUND
% 0.54/0.78 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2026-05-05T12:15:59
% 0.54/0.78 :PROOF-FOUND
% 0.54/0.78 *
%------------------------------------------------------------------------------