%------------------------------------------------------------------------------
% 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 : n031.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 : Unsatisfiable 0.40s 0.60s
% Output : Refutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of clauses : 26 ( 24 unt; 0 nHn; 7 RR)
% Number of literals : 28 ( 27 equ; 8 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-5 aty)
% Number of variables : 61 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom,axiom,
aux(X,Y,Z,U,btrue) = cons(X,merge(Y,cons(Z,U))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
cnf(axiom_002,axiom,
leqNat(z,X) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
cnf(axiom_004,axiom,
leqNat(s(X),s(Y)) = leqNat(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
cnf(axiom_005,axiom,
merge(nil,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
cnf(axiom_006,axiom,
merge(cons(X,Y),nil) = cons(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
cnf(axiom_007,axiom,
merge(cons(X,Y),cons(Z,U)) = aux(X,Y,Z,U,leqNat(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
cnf(axiom_008,axiom,
impl(btrue,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
cnf(axiom_010,axiom,
prop_merge_comm(X,Y,Z) = impl(eq(merge(X,Y),merge(Y,X)),impl(eq(merge(X,Z),merge(Z,X)),eq(merge(Y,Z),merge(Z,Y)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
cnf(axiom_015,axiom,
eq2(s(X),z) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
cnf(axiom_016,axiom,
eq(X,X) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
cnf(axiom_017,axiom,
eq2(X,X) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
cnf(axiom_018,axiom,
eq3(X,X) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
cnf(axiom_019,axiom,
( eq2(X,Y) != bfalse
| eq(cons(X,Z),cons(Y,U)) = bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
cnf(axiom_020,axiom,
( eq2(X,Y) != btrue
| eq(cons(X,Z),cons(Y,U)) = eq(Z,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
cnf(goal,negated_conjecture,
eq3(prop_merge_comm(X,Y,Z),bfalse) != btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(25,plain,
eq3(impl(eq(merge(X,Y),merge(Y,X)),impl(eq(merge(X,Z),merge(Z,X)),eq(merge(Y,Z),merge(Z,Y)))),bfalse) != btrue,
inference('REWRITE',[status(thm)],[goal,axiom_010,theory(equality)]) ).
cnf(26,plain,
merge(cons(z,X),cons(Y,Z)) = cons(z,merge(X,cons(Y,Z))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[axiom_007,axiom_002,theory(equality)]),axiom,theory(equality)]) ).
cnf(28,plain,
merge(cons(s(X),Y),cons(s(Z),U)) = aux(s(X),Y,s(Z),U,leqNat(X,Z)),
inference('PARAMODULATE',[status(thm)],[axiom_007,axiom_004,theory(equality)]) ).
cnf(29,plain,
eq(cons(s(X),Y),cons(z,Z)) = bfalse,
inference('HYPERRESOLVE',[status(thm)],[axiom_019,axiom_015]) ).
cnf(33,plain,
eq(cons(X,Y),cons(X,Z)) = eq(Y,Z),
inference('HYPERRESOLVE',[status(thm)],[axiom_020,axiom_017]) ).
cnf(43,plain,
eq3(impl(eq(X,merge(X,nil)),eq(merge(cons(Y,Z),X),merge(X,cons(Y,Z)))),bfalse) != btrue,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[25,axiom_006,theory(equality)]),axiom_008,axiom_016,33,axiom_005,theory(equality)]) ).
cnf(63,plain,
merge(cons(s(z),X),cons(s(Y),Z)) = cons(s(z),merge(X,cons(s(Y),Z))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[28,axiom_002,theory(equality)]),axiom,theory(equality)]) ).
cnf(107,plain,
eq3(eq(cons(s(z),merge(X,cons(s(Y),Z))),merge(cons(s(Y),Z),cons(s(z),X))),bfalse) != btrue,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[43,63,theory(equality)]),axiom_008,axiom_016,33,axiom_006,theory(equality)]) ).
cnf(175,plain,
eq3(eq(merge(X,cons(s(z),Y)),merge(Y,cons(s(z),X))),bfalse) != btrue,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[107,63,theory(equality)]),33,theory(equality)]) ).
cnf(179,plain,
eq3(eq(cons(s(z),X),merge(X,cons(s(z),nil))),bfalse) != btrue,
inference('PARAMODULATE',[status(thm)],[175,axiom_005,theory(equality)]) ).
cnf(186,plain,
$false,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[179,26,theory(equality)]),axiom_018,29,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX199-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.13 % Command : run-snark %s %d
% 0.16/0.34 % Computer : n031.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 11:15:23 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 *
% 0.30/0.48 #<PACKAGE "SNARK-USER">
% 0.30/0.48 *
% 0.30/0.48 SNARK-TPTP-OPTIONS
% 0.30/0.48 *
% 0.30/0.48 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.30/0.48 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.30/0.48 (USE-FACTORING :POS)
% 0.30/0.48 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.30/0.48 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.30/0.48 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.30/0.48 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.30/0.48 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.30/0.48 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.30/0.48 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.30/0.48 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.30/0.48 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.30/0.48 (DECLARE-TPTP-SYMBOLS2))
% 0.30/0.48 *
% 0.30/0.48 "."
% 0.30/0.48 *
% 0.30/0.48 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2026-05-05T11:15:24
% 0.30/0.48 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n031.cluster.edu at 2026-05-05T11:15:24
% 0.30/0.49
% 0.30/0.49 ; Recognized left identity assertion (= (|merge| |nil| ?X) ?X).
% 0.40/0.60 ; Recognized left identity assertion (= (|impl| |btrue| ?X) ?X).
% 0.40/0.60
% 0.40/0.60 #||
% 0.40/0.60 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.40/0.60 % SZS output start Refutation
% See solution above
% 0.40/0.61 ||#
% 0.40/0.61
% 0.40/0.61 ; Summary of computation:
% 0.40/0.61 ; 577 formulas have been input or derived (from 96 formulas).
% 0.40/0.61 ; 186 (32%) were retained. Of these,
% 0.40/0.61 ; 6 ( 3%) were simplified or subsumed later,
% 0.40/0.61 ; 180 (97%) are still being kept.
% 0.40/0.61 ;
% 0.40/0.61 ; Run time in seconds excluding printing time:
% 0.40/0.61 ; 0.004 3% Read assertion file (1 call)
% 0.40/0.61 ; 0.001 1% Assert (24 calls)
% 0.40/0.61 ; 0.031 25% Process new row (570 calls)
% 0.40/0.61 ; 0.008 6% Resolution (190 calls)
% 0.40/0.61 ; 0.012 10% Paramodulation (95 calls)
% 0.40/0.61 ; 0.000 0% Condensing (16 calls)
% 0.40/0.61 ; 0.001 1% Forward subsumption (16 calls)
% 0.40/0.61 ; 0.000 0% Backward subsumption (11 calls)
% 0.40/0.61 ; 0.000 0% Clause clause subsumption (21 calls)
% 0.40/0.61 ; 0.026 21% Forward simplification (570 calls)
% 0.40/0.61 ; 0.008 6% Backward simplification (185 calls)
% 0.40/0.61 ; 0.005 4% Ordering (828 calls)
% 0.40/0.61 ; 0.000 0% Sortal reasoning (32 calls)
% 0.40/0.61 ; 0.000 0% Purity testing (1 call)
% 0.40/0.61 ; 0.030 24% Other
% 0.40/0.61 ; 0.126 Total
% 0.40/0.61 ; 0.128 Real time
% 0.40/0.61 ;
% 0.40/0.61 ; Term-hash-array has 843 terms in all.
% 0.40/0.61 ; Feature-vector-row-index has 9 entries (9 at peak, 11 added, 2 deleted).
% 0.40/0.61 ; Feature-vector-row-index has 76 nodes (76 at peak, 93 added, 17 deleted).
% 0.40/0.61 ; Retrieved 21 possibly forward subsuming rows in 16 calls.
% 0.40/0.61 ; Retrieved 0 possibly backward subsumed rows in 11 calls.
% 0.40/0.61 ; Path-index has 831 entries (831 at peak, 851 added, 20 deleted).
% 0.40/0.61 ; Path-index has 2,701 nodes (2,701 at peak, 2,719 added, 18 deleted).
% 0.40/0.61 ; Trie-index has 831 entries (831 at peak, 851 added, 20 deleted).
% 0.40/0.61 ; Trie-index has 7,907 nodes (7,907 at peak, 8,027 added, 120 deleted).
% 0.40/0.61 ; Retrieved 2,615 generalization terms in 3,969 calls.
% 0.40/0.61 ; Retrieved 190 instance terms in 173 calls.
% 0.40/0.61 ; Retrieved 1,316 unifiable terms in 966 calls.
% 0.40/0.61 ;
% 0.40/0.61 ; The agenda of rows to process has 2 entries:
% 0.40/0.61 ; 1 with value 34 1 with value 37
% 0.40/0.61 ; The agenda of rows to give has 85 entries:
% 0.40/0.61 ; 1 with value (4 26) 3 with value (4 41) 6 with value (4 61)
% 0.40/0.61 ; 7 with value (4 33) 2 with value (4 42) 2 with value (4 62)
% 0.40/0.61 ; 1 with value (4 34) 4 with value (4 44) 4 with value (4 63)
% 0.40/0.61 ; 7 with value (4 35) 2 with value (4 47) 4 with value (4 64)
% 0.40/0.61 ; 6 with value (4 36) 2 with value (4 52) 2 with value (4 67)
% 0.40/0.61 ; 2 with value (4 37) 10 with value (4 53) 2 with value (4 72)
% 0.40/0.61 ; 5 with value (4 38) 4 with value (4 54) 4 with value (4 73)
% 0.40/0.61 ; 3 with value (4 39) 2 with value (4 57)
% 0.40/0.61 Evaluation took:
% 0.40/0.61 0.128 seconds of real time
% 0.40/0.61 0.109601 seconds of user run time
% 0.40/0.61 0.018922 seconds of system run time
% 0.40/0.61 0 calls to %EVAL
% 0.40/0.61 0 page faults and
% 0.40/0.61 9,344,232 bytes consed.
% 0.40/0.61 :PROOF-FOUND
% 0.40/0.61 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2026-05-05T11:15:24
% 0.40/0.61 :PROOF-FOUND
% 0.40/0.61 *
%------------------------------------------------------------------------------