%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : SWX190+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n026.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 07:07:11 PM UTC 2026
% Result : Theorem 0.54s 0.76s
% Output : Refutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 19 ( 19 unt; 0 nHn; 7 RR)
% Number of literals : 19 ( 18 equ; 3 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 : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(8,axiom,
n(X) != x(Y,Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
cnf(39,axiom,
d(n(X)) = n(z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_039) ).
cnf(40,axiom,
d(x(X,Y)) = x(d(X),d(Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_040) ).
cnf(42,axiom,
d(x2) = n(s(z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_042) ).
cnf(50,axiom,
opt(x(n(z),X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_050) ).
cnf(54,negated_conjecture,
opt(d(X)) = opt(d(opt(X))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_054) ).
cnf(63,plain,
d(d(n(X))) = d(n(X)),
inference('PARAMODULATE',[status(thm)],[39,39,theory(equality)]) ).
cnf(66,plain,
d(x2) != x(X,Y),
inference('PARAMODULATE',[status(thm)],[8,42,theory(equality)]) ).
cnf(67,plain,
d(d(x2)) = n(z),
inference('PARAMODULATE',[status(thm)],[39,42,theory(equality)]) ).
cnf(72,plain,
d(n(X)) = d(d(x2)),
inference('REWRITE',[status(thm)],[39,67,theory(equality)]) ).
cnf(77,plain,
d(d(d(x2))) = d(d(x2)),
inference('REWRITE',[status(thm)],[63,72,theory(equality)]) ).
cnf(78,plain,
opt(x(d(d(x2)),X)) = X,
inference('REWRITE',[status(thm)],[50,67,theory(equality)]) ).
cnf(108,plain,
opt(d(x(d(x2),X))) = d(X),
inference('PARAMODULATE',[status(thm)],[78,40,theory(equality)]) ).
cnf(109,plain,
opt(d(x(d(d(x2)),X))) = opt(d(X)),
inference('PARAMODULATE',[status(thm)],[54,78,theory(equality)]) ).
cnf(340,plain,
d(x2) != d(x(X,Y)),
inference('PARAMODULATE',[status(thm)],[66,40,theory(equality)]) ).
cnf(618,plain,
d(x(d(d(x2)),X)) = d(x(d(x2),X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[40,77,theory(equality)]),40,theory(equality)]) ).
cnf(619,plain,
d(X) = opt(d(X)),
inference('REWRITE',[status(thm)],[109,108,618,theory(equality)]) ).
cnf(626,plain,
d(x(d(x2),X)) = d(X),
inference('REWRITE',[status(thm)],[108,619,theory(equality)]) ).
cnf(878,plain,
$false,
inference('HYPERRESOLVE',[status(thm)],[340,626]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX190+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : run-snark %s %d
% 0.16/0.34 % Computer : n026.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 09:54:08 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.31/0.46 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.31/0.47 *
% 0.31/0.47 *
% 0.31/0.47 #<PACKAGE "SNARK-USER">
% 0.31/0.47 *
% 0.31/0.47 SNARK-TPTP-OPTIONS
% 0.31/0.47 *
% 0.31/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.31/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.31/0.47 (USE-FACTORING :POS)
% 0.31/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.31/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.31/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.31/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.31/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.31/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.31/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.31/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.31/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.31/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.31/0.47 *
% 0.31/0.47 "."
% 0.31/0.47 *
% 0.31/0.47 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2026-05-05T09:54:08
% 0.31/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n026.cluster.edu at 2026-05-05T09:54:08
% 0.31/0.50
% 0.54/0.76 ; Recognized left identity assertion (= (|addNat| |z| ?X) ?X).
% 0.54/0.76
% 0.54/0.76 #||
% 0.54/0.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.54/0.76 % SZS output start Refutation
% See solution above
% 0.54/0.76 ||#
% 0.54/0.76
% 0.54/0.76 ; Summary of computation:
% 0.54/0.76 ; 1699 formulas have been input or derived (from 152 formulas).
% 0.54/0.76 ; 878 (52%) were retained. Of these,
% 0.54/0.76 ; 135 (15%) were simplified or subsumed later,
% 0.54/0.76 ; 743 (85%) are still being kept.
% 0.54/0.76 ;
% 0.54/0.76 ; Run time in seconds excluding printing time:
% 0.54/0.76 ; 0.010 4% Read assertion file (1 call)
% 0.54/0.76 ; 0.002 1% Assert (54 calls)
% 0.54/0.76 ; 0.081 29% Process new row (1,609 calls)
% 0.54/0.76 ; 0.030 11% Resolution (302 calls)
% 0.54/0.76 ; 0.020 7% Paramodulation (151 calls)
% 0.54/0.76 ; 0.000 0% Factoring (14 calls)
% 0.54/0.76 ; 0.011 4% Condensing (275 calls)
% 0.54/0.76 ; 0.022 8% Forward subsumption (275 calls)
% 0.54/0.76 ; 0.002 1% Backward subsumption (258 calls)
% 0.54/0.76 ; 0.000 0% Clause clause subsumption (67 calls)
% 0.54/0.76 ; 0.038 13% Forward simplification (1,427 calls)
% 0.54/0.76 ; 0.018 6% Backward simplification (878 calls)
% 0.54/0.76 ; 0.013 5% Ordering (3,751 calls)
% 0.54/0.76 ; 0.001 0% Sortal reasoning (32 calls)
% 0.54/0.76 ; 0.000 0% Purity testing (1 call)
% 0.54/0.76 ; 0.034 12% Other
% 0.54/0.76 ; 0.282 Total
% 0.54/0.76 ; 0.283 Real time
% 0.54/0.76 ;
% 0.54/0.76 ; Term-hash-array has 2,166 terms in all.
% 0.54/0.76 ; Feature-vector-row-index has 230 entries (230 at peak, 258 added, 28 deleted).
% 0.54/0.76 ; Feature-vector-row-index has 1,728 nodes (1,728 at peak, 1,983 added, 255 deleted).
% 0.54/0.76 ; Retrieved 93 possibly forward subsuming rows in 275 calls.
% 0.54/0.76 ; Retrieved 6 possibly backward subsumed rows in 258 calls.
% 0.54/0.76 ; Path-index has 1,848 entries (1,848 at peak, 2,279 added, 431 deleted).
% 0.54/0.76 ; Path-index has 6,312 nodes (6,312 at peak, 6,824 added, 512 deleted).
% 0.54/0.76 ; Trie-index has 1,848 entries (1,848 at peak, 2,279 added, 431 deleted).
% 0.54/0.76 ; Trie-index has 8,525 nodes (8,525 at peak, 10,685 added, 2,160 deleted).
% 0.54/0.76 ; Retrieved 1,338 generalization terms in 11,088 calls.
% 0.54/0.76 ; Retrieved 725 instance terms in 634 calls.
% 0.54/0.76 ; Retrieved 20,306 unifiable terms in 1,720 calls.
% 0.54/0.76 ;
% 0.54/0.76 ; The agenda of rows to process has 16 entries:
% 0.54/0.76 ; 1 with value 8 4 with value 11 2 with value 20
% 0.54/0.76 ; 2 with value 9 2 with value 12 1 with value 21
% 0.54/0.76 ; 2 with value 10 1 with value 15 1 with value 27
% 0.54/0.76 ; The agenda of rows to give has 606 entries:
% 0.54/0.76 ; 19 with value (4 13) 23 with value (4 26) 4 with value (4 40)
% 0.54/0.76 ; 33 with value (4 14) 33 with value (4 27) 5 with value (4 41)
% 0.54/0.76 ; 51 with value (4 15) 25 with value (4 28) 1 with value (4 42)
% 0.54/0.76 ; 40 with value (4 16) 12 with value (4 29) 6 with value (4 43)
% 0.54/0.76 ; 39 with value (4 17) 8 with value (4 30) 1 with value (4 45)
% 0.54/0.76 ; 32 with value (4 18) 9 with value (4 31) 1 with value (4 46)
% 0.54/0.76 ; 33 with value (4 19) 12 with value (4 32) 2 with value (4 48)
% 0.54/0.76 ; 43 with value (4 20) 3 with value (4 33) 2 with value (4 49)
% 0.54/0.76 ; 36 with value (4 21) 5 with value (4 34) 1 with value (4 50)
% 0.54/0.76 ; 34 with value (4 22) 3 with value (4 36) 2 with value (4 54)
% 0.54/0.76 ; 25 with value (4 23) 4 with value (4 37) 1 with value (4 72)
% 0.54/0.76 ; 26 with value (4 24) 5 with value (4 39) 1 with value (4 90)
% 0.54/0.76 ; 26 with value (4 25)
% 0.54/0.76 Evaluation took:
% 0.54/0.76 0.284 seconds of real time
% 0.54/0.76 0.257432 seconds of user run time
% 0.54/0.76 0.026902 seconds of system run time
% 0.54/0.76 [Run times include 0.011 seconds GC run time.]
% 0.54/0.76 0 calls to %EVAL
% 0.54/0.76 0 page faults and
% 0.54/0.76 18,407,984 bytes consed.
% 0.54/0.76 :PROOF-FOUND
% 0.54/0.76 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2026-05-05T09:54:08
% 0.54/0.76 :PROOF-FOUND
% 0.54/0.76 *
%------------------------------------------------------------------------------