%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : SWX228-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n007.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 07:07:16 PM UTC 2026
% Result : Unsatisfiable 0.40s 0.57s
% Output : Refutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 15
% Syntax : Number of clauses : 24 ( 23 unt; 0 nHn; 3 RR)
% Number of literals : 25 ( 24 equ; 2 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-4 aty)
% Number of variables : 44 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom,axiom,
aux(X,Y,Z,btrue) = union(Z,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
cnf(axiom_001,axiom,
aux(X,Y,Z,bfalse) = cons(Y,union(Z,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
cnf(axiom_002,axiom,
barbar(btrue,X) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
cnf(axiom_003,axiom,
barbar(bfalse,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
cnf(axiom_005,axiom,
eqNat(s(X),z) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
cnf(axiom_007,axiom,
eqNat(z,z) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
cnf(axiom_008,axiom,
elem(X,nil) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
cnf(axiom_009,axiom,
elem(X,cons(Y,Z)) = barbar(eqNat(X,Y),elem(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
cnf(axiom_010,axiom,
union(nil,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
cnf(axiom_011,axiom,
union(cons(X,Y),Z) = aux(Z,X,Y,elem(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
cnf(axiom_012,axiom,
prop_union_comm(X,Y) = eq(union(X,Y),union(Y,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
cnf(axiom_016,axiom,
eq2(s(X),z) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
cnf(axiom_020,axiom,
eq3(X,X) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
cnf(axiom_021,axiom,
( eq2(X,Y) != bfalse
| eq(cons(X,Z),cons(Y,U)) = bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
cnf(goal,negated_conjecture,
eq3(prop_union_comm(X,Y),bfalse) != btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(30,plain,
elem(z,cons(z,X)) = btrue,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[axiom_009,axiom_007,theory(equality)]),axiom_002,theory(equality)]) ).
cnf(33,plain,
elem(s(X),cons(z,Y)) = elem(s(X),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[axiom_009,axiom_005,theory(equality)]),axiom_003,theory(equality)]) ).
cnf(38,plain,
eq(cons(s(X),Y),cons(z,Z)) = bfalse,
inference('HYPERRESOLVE',[status(thm)],[axiom_021,axiom_016]) ).
cnf(47,plain,
union(cons(z,X),cons(z,Y)) = union(X,cons(z,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[axiom_011,30,theory(equality)]),axiom,theory(equality)]) ).
cnf(52,plain,
union(cons(s(X),Y),cons(z,Z)) = aux(cons(z,Z),s(X),Y,elem(s(X),Z)),
inference('PARAMODULATE',[status(thm)],[axiom_011,33,theory(equality)]) ).
cnf(55,plain,
prop_union_comm(cons(z,X),cons(z,Y)) = eq(union(X,cons(z,Y)),union(Y,cons(z,X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[axiom_012,47,theory(equality)]),47,theory(equality)]) ).
cnf(144,plain,
union(cons(s(X),Y),cons(z,nil)) = cons(s(X),union(Y,cons(z,nil))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[52,axiom_008,theory(equality)]),axiom_001,theory(equality)]) ).
cnf(162,plain,
prop_union_comm(cons(z,cons(s(X),Y)),cons(z,nil)) = bfalse,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[55,144,theory(equality)]),38,axiom_010,theory(equality)]) ).
cnf(164,plain,
$false,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[goal,162,theory(equality)]),axiom_020,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX228-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.13 % Command : run-snark %s %d
% 0.16/0.34 % Computer : n007.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 12:55:08 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.31/0.46 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.31/0.47 *
% 0.31/0.47 *
% 0.31/0.48 #<PACKAGE "SNARK-USER">
% 0.31/0.48 *
% 0.31/0.48 SNARK-TPTP-OPTIONS
% 0.31/0.48 *
% 0.31/0.48 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.31/0.48 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.31/0.48 (USE-FACTORING :POS)
% 0.31/0.48 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.31/0.48 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.31/0.48 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.31/0.48 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.31/0.48 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.31/0.48 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.31/0.48 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.31/0.48 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.31/0.48 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.31/0.48 (DECLARE-TPTP-SYMBOLS2))
% 0.31/0.48 *
% 0.31/0.48 "."
% 0.31/0.48 *
% 0.31/0.48 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2026-05-05T12:55:08
% 0.31/0.48 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n007.cluster.edu at 2026-05-05T12:55:08
% 0.31/0.49
% 0.31/0.49 ; Recognized left identity assertion (= (|barbar| |bfalse| ?X) ?X).
% 0.40/0.57 ; Recognized left identity assertion (= (|union| |nil| ?X) ?X).
% 0.40/0.57
% 0.40/0.57 #||
% 0.40/0.57 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.40/0.57 % SZS output start Refutation
% See solution above
% 0.40/0.58 ||#
% 0.40/0.58
% 0.40/0.58 ; Summary of computation:
% 0.40/0.58 ; 399 formulas have been input or derived (from 68 formulas).
% 0.40/0.58 ; 164 (41%) were retained. Of these,
% 0.40/0.58 ; 6 ( 4%) were simplified or subsumed later,
% 0.40/0.58 ; 158 (96%) are still being kept.
% 0.40/0.58 ;
% 0.40/0.58 ; Run time in seconds excluding printing time:
% 0.40/0.58 ; 0.004 4% Read assertion file (1 call)
% 0.40/0.58 ; 0.001 1% Assert (26 calls)
% 0.40/0.58 ; 0.025 26% Process new row (397 calls)
% 0.40/0.58 ; 0.003 3% Resolution (134 calls)
% 0.40/0.58 ; 0.011 11% Paramodulation (67 calls)
% 0.40/0.58 ; 0.000 0% Condensing (10 calls)
% 0.40/0.58 ; 0.000 0% Forward subsumption (10 calls)
% 0.40/0.58 ; 0.001 1% Backward subsumption (8 calls)
% 0.40/0.58 ; 0.000 0% Clause clause subsumption (8 calls)
% 0.40/0.58 ; 0.011 11% Forward simplification (358 calls)
% 0.40/0.58 ; 0.003 3% Backward simplification (164 calls)
% 0.40/0.58 ; 0.013 13% Ordering (1,426 calls)
% 0.40/0.58 ; 0.000 0% Sortal reasoning (32 calls)
% 0.40/0.58 ; 0.000 0% Purity testing (1 call)
% 0.40/0.58 ; 0.026 27% Other
% 0.40/0.58 ; 0.098 Total
% 0.40/0.58 ; 0.100 Real time
% 0.40/0.58 ;
% 0.40/0.58 ; Term-hash-array has 627 terms in all.
% 0.40/0.58 ; Feature-vector-row-index has 6 entries (6 at peak, 8 added, 2 deleted).
% 0.40/0.58 ; Feature-vector-row-index has 51 nodes (51 at peak, 68 added, 17 deleted).
% 0.40/0.58 ; Retrieved 8 possibly forward subsuming rows in 10 calls.
% 0.40/0.58 ; Retrieved 0 possibly backward subsumed rows in 8 calls.
% 0.40/0.58 ; Path-index has 619 entries (619 at peak, 633 added, 14 deleted).
% 0.40/0.58 ; Path-index has 1,182 nodes (1,182 at peak, 1,182 added, 0 deleted).
% 0.40/0.58 ; Trie-index has 619 entries (619 at peak, 633 added, 14 deleted).
% 0.40/0.58 ; Trie-index has 3,456 nodes (3,456 at peak, 3,505 added, 49 deleted).
% 0.40/0.58 ; Retrieved 976 generalization terms in 1,379 calls.
% 0.40/0.58 ; Retrieved 275 instance terms in 223 calls.
% 0.40/0.58 ; Retrieved 780 unifiable terms in 477 calls.
% 0.40/0.58 ;
% 0.40/0.58 ; The agenda of rows to give has 92 entries:
% 0.40/0.58 ; 1 with value (4 21) 7 with value (4 32) 2 with value (4 40)
% 0.40/0.58 ; 2 with value (4 25) 6 with value (4 33) 3 with value (4 41)
% 0.40/0.58 ; 2 with value (4 26) 6 with value (4 34) 2 with value (4 42)
% 0.40/0.58 ; 4 with value (4 27) 3 with value (4 35) 5 with value (4 43)
% 0.40/0.58 ; 4 with value (4 28) 5 with value (4 36) 2 with value (4 44)
% 0.40/0.58 ; 3 with value (4 29) 8 with value (4 37) 1 with value (4 45)
% 0.40/0.58 ; 10 with value (4 30) 4 with value (4 38) 2 with value (4 47)
% 0.40/0.58 ; 4 with value (4 31) 5 with value (4 39) 1 with value (4 48)
% 0.40/0.58 Evaluation took:
% 0.40/0.58 0.101 seconds of real time
% 0.40/0.58 0.087693 seconds of user run time
% 0.40/0.58 0.012913 seconds of system run time
% 0.40/0.58 0 calls to %EVAL
% 0.40/0.58 0 page faults and
% 0.40/0.58 6,117,416 bytes consed.
% 0.40/0.58 :PROOF-FOUND
% 0.40/0.58 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2026-05-05T12:55:08
% 0.40/0.58 :PROOF-FOUND
% 0.40/0.58 *
%------------------------------------------------------------------------------