%------------------------------------------------------------------------------
% 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 07:07:12 PM UTC 2026
% Result : Theorem 0.30s 0.50s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 3 RR)
% Number of literals : 12 ( 11 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 12 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
proj1S(s(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
cnf(2,axiom,
z != s(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
cnf(3,axiom,
x2(z,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
cnf(4,axiom,
x2(s(X),Y) = s(x2(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
cnf(5,axiom,
x22(z,X) = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
cnf(6,axiom,
x22(s(X),Y) = x2(Y,x22(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
cnf(7,negated_conjecture,
x22(X,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_007) ).
cnf(8,plain,
s(x2(X,x22(X,s(X)))) = s(X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[7,6,theory(equality)]),4,theory(equality)]) ).
cnf(9,plain,
X = x2(X,x22(X,s(X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1,8,theory(equality)]),1,theory(equality)]) ).
cnf(10,plain,
s(X) = s(x2(X,s(s(x2(X,x22(X,s(s(X)))))))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4,9,theory(equality)]),4,6,theory(equality)]) ).
cnf(11,plain,
s(z) = s(s(s(z))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,5,theory(equality)]),3,theory(equality)]) ).
cnf(13,plain,
$false,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1,11,theory(equality)]),2,1,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX204+1 : TPTP v9.3.0. Released v9.3.0.
% 0.11/0.13 % Command : run-snark %s %d
% 0.16/0.34 % Computer : n005.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 11:28:15 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 2026-05-05T11:28:15
% 0.30/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n005.cluster.edu at 2026-05-05T11:28:15
% 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 Theorem for /export/starexec/sandbox/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 ; 51 formulas have been input or derived (from 12 formulas).
% 0.30/0.50 ; 13 (25%) were retained. Of these,
% 0.30/0.50 ; 2 (15%) were simplified or subsumed later,
% 0.30/0.50 ; 11 (85%) are still being kept.
% 0.30/0.50 ;
% 0.30/0.50 ; Run time in seconds excluding printing time:
% 0.30/0.50 ; 0.002 7% Read assertion file (1 call)
% 0.30/0.50 ; 0.000 0% Assert (7 calls)
% 0.30/0.50 ; 0.002 7% Process new row (48 calls)
% 0.30/0.50 ; 0.000 0% Resolution (22 calls)
% 0.30/0.50 ; 0.001 4% Paramodulation (11 calls)
% 0.30/0.50 ; 0.002 7% Forward simplification (36 calls)
% 0.30/0.50 ; 0.000 0% Backward simplification (13 calls)
% 0.30/0.50 ; 0.000 0% Ordering (92 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 ; 0.021 75% Other
% 0.30/0.50 ; 0.028 Total
% 0.30/0.50 ; 0.030 Real time
% 0.30/0.50 ;
% 0.30/0.50 ; Term-hash-array has 36 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 33 entries (35 at peak, 37 added, 4 deleted).
% 0.30/0.50 ; Path-index has 155 nodes (161 at peak, 165 added, 10 deleted).
% 0.30/0.50 ; Trie-index has 33 entries (35 at peak, 37 added, 4 deleted).
% 0.30/0.50 ; Trie-index has 120 nodes (142 at peak, 155 added, 35 deleted).
% 0.30/0.50 ; Retrieved 35 generalization terms in 114 calls.
% 0.30/0.50 ; Retrieved 15 instance terms in 12 calls.
% 0.30/0.50 ; Retrieved 67 unifiable terms in 65 calls.
% 0.30/0.50 ;
% 0.30/0.50 ; The agenda of rows to process has 3 entries:
% 0.30/0.50 ; 1 with value 21 1 with value 22 1 with value 24
% 0.30/0.50 ; The agenda of rows to give has 1 entry:
% 0.30/0.50 ; 1 with value (4 25)
% 0.30/0.50 Evaluation took:
% 0.30/0.50 0.03 seconds of real time
% 0.30/0.50 0.028325 seconds of user run time
% 0.30/0.50 0.00209 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 2,103,872 bytes consed.
% 0.30/0.50 :PROOF-FOUND
% 0.30/0.50 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2026-05-05T11:28:15
% 0.30/0.50 :PROOF-FOUND
% 0.30/0.50 *
%------------------------------------------------------------------------------