%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : NUN135-1.006 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n001.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 06:48:43 PM UTC 2026
% Result : Unsatisfiable 0.71s 0.92s
% Output : Refutation 0.71s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 1ory(1)
% Comments :
%------------------------------------------------------------------------------
cnf(rule1,axiom,
minus(X,zero) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule1) ).
cnf(rule2,axiom,
minus(s(X),s(Y)) = minus(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule2) ).
cnf(rule3,axiom,
'<='(zero,X) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule3) ).
cnf(rule4,axiom,
'<='(s(X),zero) = false,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule4) ).
cnf(rule5,axiom,
'<='(s(X),s(Y)) = '<='(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule5) ).
cnf(rule6,axiom,
if(true,X,Y) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule6) ).
cnf(rule7,axiom,
if(false,X,Y) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule7) ).
cnf(rule9,axiom,
perfectp(s(X)) = f(X,s(zero),s(X),s(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule9) ).
cnf(rule10,axiom,
f(zero,X,zero,Y) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule10) ).
cnf(rule12,axiom,
f(s(X),zero,Y,Z) = f(X,Z,minus(Y,s(X)),Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule12) ).
cnf(rule13,axiom,
f(s(X),s(Y),Z,U) = if('<='(X,Y),f(s(X),minus(Y,X),Z,U),f(X,U,Z,U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule13) ).
cnf(goal,negated_conjecture,
perfectp(X) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(17,plain,
f(s(X),zero,s(Y),Z) = f(X,Z,minus(Y,X),Z),
inference('PARAMODULATE',[status(thm)],[rule12,rule2,theory(equality)]) ).
cnf(19,plain,
f(s(zero),s(X),Y,Z) = f(s(zero),X,Y,Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[rule13,rule3,theory(equality)]),rule6,rule1,theory(equality)]) ).
cnf(20,plain,
f(s(s(X)),s(zero),Y,Z) = f(s(X),Z,Y,Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[rule13,rule4,theory(equality)]),rule7,theory(equality)]) ).
cnf(21,plain,
f(s(s(X)),s(s(Y)),Z,U) = if('<='(X,Y),f(s(s(X)),minus(Y,X),Z,U),f(s(X),U,Z,U)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[rule13,rule5,theory(equality)]),rule2,theory(equality)]) ).
cnf(27,plain,
f(s(zero),zero,s(X),Y) = f(zero,Y,X,Y),
inference('PARAMODULATE',[status(thm)],[17,rule1,theory(equality)]) ).
cnf(28,plain,
f(s(s(X)),zero,s(s(Y)),Z) = f(s(X),Z,minus(Y,X),Z),
inference('PARAMODULATE',[status(thm)],[17,rule2,theory(equality)]) ).
cnf(32,plain,
f(s(zero),zero,s(zero),X) = true,
inference('PARAMODULATE',[status(thm)],[rule10,27,theory(equality)]) ).
cnf(39,plain,
f(s(s(zero)),s(zero),X,s(Y)) = f(s(zero),Y,X,s(Y)),
inference('PARAMODULATE',[status(thm)],[19,20,theory(equality)]) ).
cnf(47,plain,
f(s(s(zero)),s(zero),X,s(s(Y))) = f(s(zero),Y,X,s(s(Y))),
inference('PARAMODULATE',[status(thm)],[19,39,theory(equality)]) ).
cnf(51,plain,
f(s(s(zero)),zero,s(s(X)),Y) = f(s(zero),Y,X,Y),
inference('PARAMODULATE',[status(thm)],[28,rule1,theory(equality)]) ).
cnf(54,plain,
f(s(s(s(X))),zero,s(s(s(Y))),Z) = f(s(s(X)),Z,minus(Y,X),Z),
inference('PARAMODULATE',[status(thm)],[28,rule2,theory(equality)]) ).
cnf(57,plain,
f(s(s(zero)),s(zero),X,Y) = f(s(s(zero)),zero,s(s(X)),Y),
inference('PARAMODULATE',[status(thm)],[20,51,theory(equality)]) ).
cnf(61,plain,
f(s(s(zero)),s(zero),X,s(s(s(Y)))) = f(s(zero),Y,X,s(s(s(Y)))),
inference('PARAMODULATE',[status(thm)],[19,47,theory(equality)]) ).
cnf(67,plain,
f(s(s(s(zero))),zero,s(s(s(X))),Y) = f(s(s(zero)),Y,X,Y),
inference('PARAMODULATE',[status(thm)],[54,rule1,theory(equality)]) ).
cnf(71,plain,
f(s(s(s(zero))),s(zero),X,Y) = f(s(s(s(zero))),zero,s(s(s(X))),Y),
inference('PARAMODULATE',[status(thm)],[20,67,theory(equality)]) ).
cnf(74,plain,
f(s(s(zero)),s(zero),X,s(s(s(s(Y))))) = f(s(zero),Y,X,s(s(s(s(Y))))),
inference('PARAMODULATE',[status(thm)],[19,61,theory(equality)]) ).
cnf(88,plain,
f(s(s(zero)),s(zero),X,s(s(s(s(s(Y)))))) = f(s(zero),Y,X,s(s(s(s(s(Y)))))),
inference('PARAMODULATE',[status(thm)],[19,74,theory(equality)]) ).
cnf(89,plain,
f(s(s(zero)),s(s(X)),Y,Z) = f(s(s(zero)),X,Y,Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[21,rule3,theory(equality)]),rule6,rule1,theory(equality)]) ).
cnf(91,plain,
f(s(s(s(X))),s(s(zero)),Y,Z) = f(s(s(X)),Z,Y,Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[21,rule4,theory(equality)]),rule7,theory(equality)]) ).
cnf(92,plain,
f(s(s(s(X))),s(s(s(Y))),Z,U) = if('<='(X,Y),f(s(s(s(X))),minus(Y,X),Z,U),f(s(s(X)),U,Z,U)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[21,rule5,theory(equality)]),rule2,theory(equality)]) ).
cnf(113,plain,
f(s(s(s(zero))),s(zero),X,s(s(Y))) = f(s(s(zero)),Y,X,s(s(Y))),
inference('PARAMODULATE',[status(thm)],[20,89,theory(equality)]) ).
cnf(119,plain,
f(s(s(s(X))),s(zero),Y,Z) = f(s(s(s(X))),s(s(zero)),Y,Z),
inference('PARAMODULATE',[status(thm)],[20,91,theory(equality)]) ).
cnf(125,plain,
f(s(s(s(zero))),s(zero),X,s(s(s(s(Y))))) = f(s(s(zero)),Y,X,s(s(s(s(Y))))),
inference('PARAMODULATE',[status(thm)],[89,113,theory(equality)]) ).
cnf(139,plain,
f(s(s(s(zero))),s(zero),X,s(s(s(s(s(s(Y))))))) = f(s(s(zero)),Y,X,s(s(s(s(s(s(Y))))))),
inference('PARAMODULATE',[status(thm)],[89,125,theory(equality)]) ).
cnf(162,plain,
f(s(s(zero)),s(zero),X,s(s(s(s(s(s(Y))))))) = f(s(zero),Y,X,s(s(s(s(s(s(Y))))))),
inference('PARAMODULATE',[status(thm)],[19,88,theory(equality)]) ).
cnf(211,plain,
f(s(s(s(zero))),s(s(s(X))),Y,Z) = f(s(s(s(zero))),X,Y,Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[92,rule3,theory(equality)]),rule6,rule1,theory(equality)]) ).
cnf(214,plain,
f(s(s(s(s(X)))),s(s(s(s(Y)))),Z,U) = if('<='(X,Y),f(s(s(s(s(X)))),minus(Y,X),Z,U),f(s(s(s(X))),U,Z,U)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[92,rule5,theory(equality)]),rule2,theory(equality)]) ).
cnf(240,plain,
f(s(s(s(s(zero)))),s(zero),X,s(s(s(Y)))) = f(s(s(s(zero))),Y,X,s(s(s(Y)))),
inference('PARAMODULATE',[status(thm)],[20,211,theory(equality)]) ).
cnf(255,plain,
f(s(s(s(s(zero)))),s(zero),X,s(s(s(s(s(s(Y))))))) = f(s(s(s(zero))),Y,X,s(s(s(s(s(s(Y))))))),
inference('PARAMODULATE',[status(thm)],[211,240,theory(equality)]) ).
cnf(421,plain,
f(s(s(s(s(zero)))),s(s(s(s(X)))),Y,Z) = f(s(s(s(s(zero)))),X,Y,Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[214,rule3,theory(equality)]),rule6,rule1,theory(equality)]) ).
cnf(456,plain,
f(s(s(s(s(s(zero))))),s(zero),X,s(s(s(s(Y))))) = f(s(s(s(s(zero)))),Y,X,s(s(s(s(Y))))),
inference('PARAMODULATE',[status(thm)],[20,421,theory(equality)]) ).
cnf(473,plain,
$false,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[rule9,456,theory(equality)]),goal,32,162,57,139,71,255,119,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN135-1.006 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : run-snark %s %d
% 0.16/0.34 % Computer : n001.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 04:49:18 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.27/0.47 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.27/0.48 *
% 0.27/0.48 *
% 0.27/0.49 #<PACKAGE "SNARK-USER">
% 0.27/0.49 *
% 0.27/0.49 SNARK-TPTP-OPTIONS
% 0.27/0.49 *
% 0.27/0.49 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.27/0.49 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.27/0.49 (USE-FACTORING :POS)
% 0.27/0.49 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.27/0.49 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.27/0.49 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.27/0.49 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.27/0.49 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.27/0.49 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.27/0.49 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.27/0.49 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.27/0.49 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.27/0.49 (DECLARE-TPTP-SYMBOLS2))
% 0.27/0.49 *
% 0.27/0.49 "."
% 0.27/0.49 *
% 0.27/0.49 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2026-05-05T04:49:18
% 0.27/0.49 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n001.cluster.edu at 2026-05-05T04:49:18
% 0.27/0.50
% 0.27/0.50 WARNING: <= is being used as a 2-ary FUNCTION in (= (<= |zero| ?Y) |true|); it is also a LOGICAL-SYMBOL.
% 0.71/0.92 ; Recognized right identity assertion (= (|minus| ?X |zero|) ?X).
% 0.71/0.92
% 0.71/0.92 #||
% 0.71/0.92 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.71/0.92 % SZS output start Refutation
% See solution above
% 0.71/0.93 ||#
% 0.71/0.93
% 0.71/0.93 ; Summary of computation:
% 0.71/0.93 ; 2177 formulas have been input or derived (from 159 formulas).
% 0.71/0.93 ; 473 (22%) were retained. Of these,
% 0.71/0.93 ; 18 ( 4%) were simplified or subsumed later,
% 0.71/0.93 ; 455 (96%) are still being kept.
% 0.71/0.93 ;
% 0.71/0.93 ; Run time in seconds excluding printing time:
% 0.71/0.93 ; 0.002 0% Read assertion file (1 call)
% 0.71/0.93 ; 0.001 0% Assert (14 calls)
% 0.71/0.93 ; 0.095 22% Process new row (2,136 calls)
% 0.71/0.93 ; 0.010 2% Resolution (316 calls)
% 0.71/0.93 ; 0.069 16% Paramodulation (158 calls)
% 0.71/0.93 ; 0.155 36% Forward simplification (1,862 calls)
% 0.71/0.93 ; 0.015 3% Backward simplification (473 calls)
% 0.71/0.93 ; 0.053 12% Ordering (8,356 calls)
% 0.71/0.93 ; 0.000 0% Sortal reasoning (32 calls)
% 0.71/0.93 ; 0.000 0% Purity testing (1 call)
% 0.71/0.93 ; 0.036 8% Other
% 0.71/0.93 ; 0.436 Total
% 0.71/0.93 ; 0.441 Real time
% 0.71/0.93 ;
% 0.71/0.93 ; Term-hash-array has 1,943 terms in all.
% 0.71/0.93 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.71/0.93 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.71/0.93 ; Path-index has 1,902 entries (1,902 at peak, 1,950 added, 48 deleted).
% 0.71/0.93 ; Path-index has 1,313 nodes (1,313 at peak, 1,333 added, 20 deleted).
% 0.71/0.93 ; Trie-index has 1,902 entries (1,902 at peak, 1,950 added, 48 deleted).
% 0.71/0.93 ; Trie-index has 24,103 nodes (24,103 at peak, 24,555 added, 452 deleted).
% 0.71/0.93 ; Retrieved 24,335 generalization terms in 15,657 calls.
% 0.71/0.93 ; Retrieved 1,582 instance terms in 562 calls.
% 0.71/0.93 ; Retrieved 10,085 unifiable terms in 1,721 calls.
% 0.71/0.93 ;
% 0.71/0.93 ; The agenda of rows to process has 41 entries:
% 0.71/0.93 ; 7 with value 48 1 with value 72 1 with value 85
% 0.71/0.93 ; 2 with value 49 2 with value 75 1 with value 88
% 0.71/0.93 ; 5 with value 50 1 with value 78 1 with value 89
% 0.71/0.93 ; 1 with value 51 3 with value 79 2 with value 90
% 0.71/0.93 ; 1 with value 53 3 with value 80 1 with value 92
% 0.71/0.93 ; 1 with value 69 1 with value 81 1 with value 93
% 0.71/0.93 ; 2 with value 70 1 with value 83 1 with value 94
% 0.71/0.93 ; 2 with value 71
% 0.71/0.93 ; The agenda of rows to give has 305 entries:
% 0.71/0.93 ; 1 with value (4 45) 5 with value (4 61) 8 with value (4 76)
% 0.71/0.93 ; 6 with value (4 47) 5 with value (4 62) 8 with value (4 77)
% 0.71/0.93 ; 8 with value (4 48) 6 with value (4 63) 7 with value (4 78)
% 0.71/0.93 ; 14 with value (4 49) 5 with value (4 64) 11 with value (4 79)
% 0.71/0.93 ; 11 with value (4 50) 3 with value (4 65) 7 with value (4 80)
% 0.71/0.93 ; 7 with value (4 51) 14 with value (4 66) 4 with value (4 81)
% 0.71/0.93 ; 6 with value (4 52) 9 with value (4 67) 4 with value (4 82)
% 0.71/0.93 ; 8 with value (4 53) 9 with value (4 68) 5 with value (4 83)
% 0.71/0.93 ; 7 with value (4 54) 7 with value (4 69) 3 with value (4 84)
% 0.71/0.93 ; 9 with value (4 55) 9 with value (4 70) 3 with value (4 85)
% 0.71/0.93 ; 6 with value (4 56) 10 with value (4 71) 1 with value (4 86)
% 0.71/0.93 ; 7 with value (4 57) 6 with value (4 72) 3 with value (4 87)
% 0.71/0.93 ; 12 with value (4 58) 9 with value (4 73) 1 with value (4 88)
% 0.71/0.93 ; 11 with value (4 59) 9 with value (4 74) 1 with value (4 89)
% 0.71/0.93 ; 10 with value (4 60) 9 with value (4 75) 1 with value (4 94)
% 0.71/0.93 Evaluation took:
% 0.71/0.93 0.441 seconds of real time
% 0.71/0.93 0.408839 seconds of user run time
% 0.71/0.93 0.032057 seconds of system run time
% 0.71/0.93 [Run times include 0.018 seconds GC run time.]
% 0.71/0.93 0 calls to %EVAL
% 0.71/0.93 0 page faults and
% 0.71/0.93 34,481,896 bytes consed.
% 0.71/0.93 :PROOF-FOUND
% 0.71/0.93 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2026-05-05T04:49:19
% 0.71/0.93 :PROOF-FOUND
% 0.71/0.93 *
%------------------------------------------------------------------------------