%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : SWX204-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n005.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 07:07:13 PM UTC 2026
% Result : Unsatisfiable 0.30s 0.50s
% Output : Refutation 0.30s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named axiom_ory(equal_001)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom,axiom,
x2(z,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
cnf(axiom_001,axiom,
x2(s(X),Y) = s(x2(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
cnf(axiom_002,axiom,
x22(z,X) = z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
cnf(axiom_003,axiom,
x22(s(X),Y) = x2(Y,x22(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
cnf(axiom_004,axiom,
mul_idem(X) = eq(x22(X,X),X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
cnf(axiom_007,axiom,
eq(s(X),s(Y)) = eq(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
cnf(axiom_009,axiom,
eq(s(X),z) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
cnf(axiom_011,axiom,
eq2(X,X) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
cnf(goal,negated_conjecture,
eq2(mul_idem(X),bfalse) != btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(15,plain,
mul_idem(s(X)) = eq(x2(X,x22(X,s(X))),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[axiom_004,axiom_003,theory(equality)]),axiom_007,axiom_001,theory(equality)]) ).
cnf(18,plain,
mul_idem(s(s(X))) = eq(x2(X,s(s(x2(X,x22(X,s(s(X))))))),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,axiom_001,theory(equality)]),axiom_007,axiom_001,axiom_003,theory(equality)]) ).
cnf(19,plain,
mul_idem(s(s(z))) = bfalse,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[18,axiom_002,theory(equality)]),axiom_009,axiom,theory(equality)]) ).
cnf(21,plain,
$false,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[goal,19,theory(equality)]),axiom_011,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWX204-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run-snark %s %d
% 0.16/0.33 % Computer : n005.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 11:29:30 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.20/0.45 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.30/0.46 *
% 0.30/0.46 *
% 0.30/0.46 #<PACKAGE "SNARK-USER">
% 0.30/0.46 *
% 0.30/0.46 SNARK-TPTP-OPTIONS
% 0.30/0.46 *
% 0.30/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.30/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.30/0.46 (USE-FACTORING :POS)
% 0.30/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.30/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.30/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.30/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.30/0.46 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.30/0.46 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.30/0.46 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.30/0.46 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.30/0.46 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.30/0.46 (DECLARE-TPTP-SYMBOLS2))
% 0.30/0.46 *
% 0.30/0.46 "."
% 0.30/0.46 *
% 0.30/0.46 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2026-05-05T11:29:30
% 0.30/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n005.cluster.edu at 2026-05-05T11:29:30
% 0.30/0.48
% 0.30/0.50 ; Recognized left identity assertion (= (|x2| |z| ?X) ?X).
% 0.30/0.50
% 0.30/0.50 #||
% 0.30/0.50 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.30/0.50 % SZS output start Refutation
% See solution above
% 0.30/0.50 ||#
% 0.30/0.50
% 0.30/0.50 ; Summary of computation:
% 0.30/0.50 ; 46 formulas have been input or derived (from 20 formulas).
% 0.30/0.50 ; 21 (46%) were retained. Of these,
% 0.30/0.50 ; 21 (100%) are still being kept.
% 0.30/0.50 ;
% 0.30/0.50 ; Run time in seconds excluding printing time:
% 0.30/0.50 ; 0.001 3% Read assertion file (1 call)
% 0.30/0.50 ; 0.000 0% Assert (13 calls)
% 0.30/0.50 ; 0.004 13% Process new row (46 calls)
% 0.30/0.50 ; 0.001 3% Resolution (38 calls)
% 0.30/0.50 ; 0.003 10% Paramodulation (19 calls)
% 0.30/0.50 ; 0.000 0% Forward simplification (46 calls)
% 0.30/0.50 ; 0.000 0% Backward simplification (21 calls)
% 0.30/0.50 ; 0.000 0% Ordering (118 calls)
% 0.30/0.50 ; 0.000 0% Sortal reasoning (32 calls)
% 0.30/0.50 ; 0.000 0% Purity testing (1 call)
% 0.30/0.50 ; 0.022 71% Other
% 0.30/0.50 ; 0.031 Total
% 0.30/0.50 ; 0.033 Real time
% 0.30/0.50 ;
% 0.30/0.50 ; Term-hash-array has 72 terms in all.
% 0.30/0.50 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.30/0.50 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.30/0.50 ; Path-index has 75 entries (75 at peak, 75 added, 0 deleted).
% 0.30/0.50 ; Path-index has 363 nodes (363 at peak, 363 added, 0 deleted).
% 0.30/0.50 ; Trie-index has 75 entries (75 at peak, 75 added, 0 deleted).
% 0.30/0.50 ; Trie-index has 317 nodes (317 at peak, 317 added, 0 deleted).
% 0.30/0.50 ; Retrieved 57 generalization terms in 121 calls.
% 0.30/0.50 ; Retrieved 27 instance terms in 20 calls.
% 0.30/0.50 ; Retrieved 77 unifiable terms in 111 calls.
% 0.30/0.50 ;
% 0.30/0.50 ; The agenda of rows to give has 1 entry:
% 0.30/0.50 ; 1 with value (4 44)
% 0.30/0.50 Evaluation took:
% 0.30/0.50 0.033 seconds of real time
% 0.30/0.50 0.025568 seconds of user run time
% 0.30/0.50 0.007047 seconds of system run time
% 0.30/0.50 0 calls to %EVAL
% 0.30/0.50 0 page faults and
% 0.30/0.50 2,272,424 bytes consed.
% 0.30/0.50 :PROOF-FOUND
% 0.30/0.50 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2026-05-05T11:29:30
% 0.30/0.50 :PROOF-FOUND
% 0.30/0.50 *
%------------------------------------------------------------------------------