%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : SWX058+1 : TPTP v9.1.0. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n020.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 Apr 1 02:16:18 AM UTC 2025
% Result : Theorem 2.55s 2.75s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of clauses : 16 ( 11 unt; 0 nHn; 9 RR)
% Number of literals : 26 ( 6 equ; 11 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 17 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(357,axiom,
( ~ nat_succeeds(X)
| ~ nat_succeeds(Y)
| '@+'(X,Y) = '@+'(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(plus:commutative)') ).
cnf(449,axiom,
( ~ list_succeeds(X)
| ~ list_succeeds(Y)
| list_succeeds('**'(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(app:types:1)') ).
cnf(546,axiom,
( ~ list_succeeds(X)
| nat_succeeds(occ(Y,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary-(occ:types)') ).
cnf(547,axiom,
( ~ list_succeeds(X)
| ~ list_succeeds(Y)
| occ(Z,'**'(X,Y)) = '@+'(occ(Z,X),occ(Z,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(occ:app)') ).
cnf(555,axiom,
( ~ list_succeeds(X)
| ~ list_succeeds(Y)
| occ('SKOLEMAAAV130'(Y,X),Y) != occ('SKOLEMAAAV130'(Y,X),X)
| permutation_succeeds(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','theorem-(occ:permutation)') ).
cnf(567,negated_conjecture,
list_succeeds('SKOLEMAAAV135'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','theorem-(permutation:app:commutative)') ).
cnf(568,negated_conjecture,
list_succeeds('SKOLEMAAAV136'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','theorem-(permutation:app:commutative)') ).
cnf(569,negated_conjecture,
~ permutation_succeeds('**'('SKOLEMAAAV135','SKOLEMAAAV136'),'**'('SKOLEMAAAV136','SKOLEMAAAV135')),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','theorem-(permutation:app:commutative)') ).
cnf(628,plain,
nat_succeeds(occ(X,'SKOLEMAAAV136')),
inference('HYPERRESOLVE',[status(thm)],[546,568]) ).
cnf(629,plain,
nat_succeeds(occ(X,'SKOLEMAAAV135')),
inference('HYPERRESOLVE',[status(thm)],[546,567]) ).
cnf(733,plain,
list_succeeds('**'('SKOLEMAAAV136','SKOLEMAAAV135')),
inference('HYPERRESOLVE',[status(thm)],[449,568,567]) ).
cnf(734,plain,
list_succeeds('**'('SKOLEMAAAV135','SKOLEMAAAV136')),
inference('HYPERRESOLVE',[status(thm)],[449,567,568]) ).
cnf(1378,plain,
occ(X,'**'('SKOLEMAAAV136','SKOLEMAAAV135')) = '@+'(occ(X,'SKOLEMAAAV136'),occ(X,'SKOLEMAAAV135')),
inference('HYPERRESOLVE',[status(thm)],[547,568,567]) ).
cnf(1379,plain,
occ(X,'**'('SKOLEMAAAV135','SKOLEMAAAV136')) = '@+'(occ(X,'SKOLEMAAAV135'),occ(X,'SKOLEMAAAV136')),
inference('HYPERRESOLVE',[status(thm)],[547,567,568]) ).
cnf(3776,plain,
'@+'(occ(X,'SKOLEMAAAV135'),occ(Y,'SKOLEMAAAV136')) = '@+'(occ(Y,'SKOLEMAAAV136'),occ(X,'SKOLEMAAAV135')),
inference('HYPERRESOLVE',[status(thm)],[357,629,628]) ).
cnf(4760,plain,
$false,
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[555,734,733,569]),3776,1379,1378,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWX058+1 : TPTP v9.1.0. Released v9.1.0.
% 0.04/0.14 % Command : run-snark %s %d
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Mar 31 15:21:34 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.20/0.47 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.49 *
% 0.20/0.49 *
% 0.20/0.49 #<PACKAGE "SNARK-USER">
% 0.20/0.49 *
% 0.20/0.49 SNARK-TPTP-OPTIONS
% 0.20/0.49 *
% 0.20/0.49 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.49 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.49 (USE-FACTORING :POS)
% 0.20/0.49 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.49 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.49 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.49 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.49 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.49 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.49 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.49 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.49 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.49 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.49 *
% 0.20/0.49 "."
% 0.20/0.49 *
% 0.20/0.49 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2025-03-31T15:21:34
% 0.20/0.49 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n020.cluster.edu at 2025-03-31T15:21:34
% 0.39/0.59
% 0.39/0.59 ; Recognized relation functionality assertion (OR (NOT (|plus_succeeds| ?X ?Y ?Z)) (NOT (|plus_succeeds| ?X ?Y ?U)) (= ?Z ?U)).
% 0.39/0.59 ; Recognized left identity assertion (= (@+ |0| ?X) ?X).
% 0.39/0.59 ; Recognized relation functionality assertion (OR (NOT (|times_succeeds| ?X ?Y ?Z)) (NOT (|times_succeeds| ?X ?Y ?U)) (= ?Z ?U)).
% 0.39/0.59 ; Recognized relation functionality assertion (OR (NOT (|append_succeeds| ?X ?Y ?Z)) (NOT (|append_succeeds| ?X ?Y ?U)) (= ?Z ?U)).
% 0.39/0.59 ; Recognized left identity assertion (= (** |nil| ?X) ?X).
% 0.39/0.59 ; Recognized relation functionality assertion (OR (NOT (|occ_succeeds| ?X ?Y ?Z)) (NOT (|occ_succeeds| ?X ?Y ?U)) (= ?Z ?U)).
% 0.39/0.59 ; Recognized commutativity assertion (OR (NOT (|permutation_succeeds| ?X ?Y)) (|permutation_succeeds| ?Y ?X)).
% 2.55/2.75 ; Declaring permutation_succeeds to be commutative.
% 2.55/2.75
% 2.55/2.75 #||
% 2.55/2.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.55/2.75 % SZS output start Refutation
% See solution above
% 2.58/2.76 ||#
% 2.58/2.76
% 2.58/2.76 ; Summary of computation:
% 2.58/2.76 ; 16404 formulas have been input or derived (from 819 formulas).
% 2.58/2.76 ; 4760 (29%) were retained. Of these,
% 2.58/2.76 ; 1082 (23%) were simplified or subsumed later,
% 2.58/2.76 ; 3678 (77%) are still being kept.
% 2.58/2.76 ;
% 2.58/2.76 ; Run time in seconds excluding printing time:
% 2.58/2.76 ; 0.069 3% Read assertion file (1 call)
% 2.58/2.76 ; 0.017 1% Assert (307 calls)
% 2.58/2.76 ; 0.388 17% Process new row (15,053 calls)
% 2.58/2.76 ; 0.812 36% Resolution (1,636 calls)
% 2.58/2.76 ; 0.034 2% Paramodulation (818 calls)
% 2.58/2.76 ; 0.001 0% Factoring (81 calls)
% 2.58/2.76 ; 0.034 2% Condensing (2,730 calls)
% 2.58/2.76 ; 0.162 7% Forward subsumption (2,730 calls)
% 2.58/2.77 ; 0.053 2% Backward subsumption (1,353 calls)
% 2.58/2.77 ; 0.014 1% Clause clause subsumption (2,725 calls)
% 2.58/2.77 ; 0.365 16% Forward simplification (14,775 calls)
% 2.58/2.77 ; 0.122 5% Backward simplification (4,760 calls)
% 2.58/2.77 ; 0.103 5% Ordering (31,815 calls)
% 2.58/2.77 ; 0.001 0% Sortal reasoning (32 calls)
% 2.58/2.77 ; 0.001 0% Purity testing (1 call)
% 2.58/2.77 ; 0.077 3% Other
% 2.58/2.77 ; 2.253 Total
% 2.58/2.77 ; 2.272 Real time
% 2.58/2.77 ;
% 2.58/2.77 ; Term-hash-array has 8,815 terms in all.
% 2.58/2.77 ; Feature-vector-row-index has 1,102 entries (1,102 at peak, 1,353 added, 251 deleted).
% 2.58/2.77 ; Feature-vector-row-index has 7,803 nodes (7,803 at peak, 9,950 added, 2,147 deleted).
% 2.58/2.77 ; Retrieved 3,892 possibly forward subsuming rows in 2,730 calls.
% 2.58/2.77 ; Retrieved 496 possibly backward subsumed rows in 1,353 calls.
% 2.58/2.77 ; Path-index has 6,830 entries (6,883 at peak, 9,337 added, 2,507 deleted).
% 2.58/2.77 ; Path-index has 16,317 nodes (16,343 at peak, 19,139 added, 2,822 deleted).
% 2.58/2.77 ; Trie-index has 6,830 entries (6,883 at peak, 9,337 added, 2,507 deleted).
% 2.58/2.77 ; Trie-index has 28,244 nodes (28,607 at peak, 41,001 added, 12,757 deleted).
% 2.58/2.77 ; Retrieved 46,140 generalization terms in 93,752 calls.
% 2.58/2.77 ; Retrieved 4,253 instance terms in 3,630 calls.
% 2.58/2.77 ; Retrieved 1,345,726 unifiable terms in 32,160 calls.
% 2.58/2.77 ;
% 2.58/2.77 ; The agenda of rows to process has 225 entries:
% 2.58/2.77 ; 6 with value 29 4 with value 37 9 with value 51
% 2.58/2.77 ; 4 with value 30 48 with value 38 16 with value 52
% 2.58/2.77 ; 4 with value 31 4 with value 42 24 with value 56
% 2.58/2.77 ; 32 with value 33 4 with value 43 1 with value 72
% 2.58/2.77 ; 64 with value 34 4 with value 45 1 with value 74
% 2.58/2.77 ; The agenda of rows to give has 2934 entries:
% 2.58/2.77 ; 100 with value (4 7) 5 with value (4 36) 1 with value (4 69)
% 2.58/2.77 ; 154 with value (4 8) 5 with value (4 37) 1 with value (4 70)
% 2.58/2.77 ; 157 with value (4 9) 17 with value (4 38) 2 with value (4 72)
% 2.58/2.77 ; 187 with value (4 10) 7 with value (4 39) 2 with value (4 74)
% 2.58/2.77 ; 161 with value (4 11) 3 with value (4 40) 1 with value (4 75)
% 2.58/2.77 ; 154 with value (4 12) 7 with value (4 41) 2 with value (4 76)
% 2.58/2.77 ; 123 with value (4 13) 10 with value (4 42) 1 with value (4 78)
% 2.58/2.77 ; 100 with value (4 14) 4 with value (4 43) 2 with value (4 79)
% 2.58/2.77 ; 165 with value (4 15) 5 with value (4 44) 4 with value (4 88)
% 2.58/2.77 ; 121 with value (4 16) 3 with value (4 45) 4 with value (4 91)
% 2.58/2.77 ; 131 with value (4 17) 4 with value (4 46) 4 with value (4 96)
% 2.58/2.77 ; 145 with value (4 18) 7 with value (4 47) 12 with value (4 99)
% 2.58/2.77 ; 88 with value (4 19) 4 with value (4 48) 12 with value (4 102)
% 2.58/2.77 ; 117 with value (4 20) 5 with value (4 50) 4 with value (4 105)
% 2.58/2.77 ; 114 with value (4 21) 14 with value (4 51) 1 with value (4 108)
% 2.58/2.77 ; 70 with value (4 22) 7 with value (4 52) 2 with value (4 112)
% 2.58/2.77 ; 60 with value (4 23) 1 with value (4 53) 2 with value (4 115)
% 2.58/2.77 ; 71 with value (4 24) 3 with value (4 54) 2 with value (4 118)
% 2.58/2.77 ; 81 with value (4 25) 4 with value (4 55) 2 with value (4 120)
% 2.58/2.77 ; 45 with value (4 26) 1 with value (4 56) 2 with value (4 121)
% 2.58/2.77 ; 57 with value (4 27) 1 with value (4 57) 2 with value (4 123)
% 2.58/2.77 ; 63 with value (4 28) 5 with value (4 58) 2 with value (4 126)
% 2.58/2.77 ; 41 with value (4 29) 1 with value (4 59) 2 with value (4 129)
% 2.58/2.77 ; 27 with value (4 30) 1 with value (4 60) 4 with value (4 139)
% 2.58/2.77 ; 54 with value (4 31) 2 with value (4 61) 16 with value (4 142)
% 2.58/2.77 ; 31 with value (4 32) 2 with value (4 62) 24 with value (4 145)
% 2.58/2.77 ; 24 with value (4 33) 1 with value (4 64) 16 with value (4 148)
% 2.58/2.77 ; 26 with value (4 34) 1 with value (4 67) 4 with value (4 151)
% 2.58/2.77 ; 3 with value (4 35) 1 with value (4 68)
% 2.58/2.77 Evaluation took:
% 2.58/2.77 2.274 seconds of real time
% 2.58/2.77 2.125635 seconds of user run time
% 2.58/2.77 0.148056 seconds of system run time
% 2.58/2.77 [Run times include 0.223 seconds GC run time.]
% 2.58/2.77 0 calls to %EVAL
% 2.58/2.77 0 page faults and
% 2.58/2.77 164,221,696 bytes consed.
% 2.58/2.77 :PROOF-FOUND
% 2.58/2.77 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2025-03-31T15:21:36
% 2.58/2.77 :PROOF-FOUND
% 2.58/2.77 *
%------------------------------------------------------------------------------