%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC001-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:56:29 AM UTC 2026
% Result : Unsatisfiable 41.33s 6.42s
% Output : CNFRefutation 41.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 61 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 56 ( 27 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 5 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_12,axiom,
( ~ duplicatefreeP(sk1)
| ~ memberP(sk1,sk5)
| ~ memberP(sk2,sk5) ),
file('theBenchmark.p',co1_12) ).
cnf(c_42,plain,
( ~ duplicatefreeP(sk1)
| ~ memberP(sk1,sk5)
| ~ memberP(sk2,sk5) ),
inference(clausify,[status(thm)],[co1_12]) ).
fof(co1_11,axiom,
( ~ duplicatefreeP(sk1)
| memberP(sk1,sk5)
| memberP(sk2,sk5) ),
file('theBenchmark.p',co1_11) ).
cnf(c_43,plain,
( ~ duplicatefreeP(sk1)
| memberP(sk1,sk5)
| memberP(sk2,sk5) ),
inference(clausify,[status(thm)],[co1_11]) ).
fof(co1_10,axiom,
( ~ duplicatefreeP(sk1)
| ssItem(sk5) ),
file('theBenchmark.p',co1_10) ).
cnf(c_44,plain,
( ~ duplicatefreeP(sk1)
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_10]) ).
fof(co1_9,axiom,
! [VAR_0] :
( ~ memberP(sk4,VAR_0)
| memberP(sk3,VAR_0)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_9) ).
cnf(c_45,plain,
( ~ memberP(sk4,A)
| memberP(sk3,A)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_9]) ).
fof(co1_8,axiom,
! [VAR_0] :
( ~ memberP(sk3,VAR_0)
| memberP(sk4,VAR_0)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_8) ).
cnf(c_46,plain,
( ~ memberP(sk3,A)
| memberP(sk4,A)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
duplicatefreeP(sk3),
file('theBenchmark.p',co1_7) ).
cnf(c_47,plain,
duplicatefreeP(sk3),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_48,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
cnf(c_49,plain,
sk3 = sk1,
inference(copy,[status(thm)],[c_48]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_50,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_823,plain,
( ~ memberP(sk1,A)
| memberP(sk4,A)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_49,c_46]) ).
cnf(c_824,plain,
duplicatefreeP(sk1),
inference(paramod,[status(thm)],[c_49,c_47]) ).
cnf(c_825,plain,
ssItem(sk5),
inference(resolve,[status(thm)],[c_824,c_44]) ).
cnf(c_826,plain,
( memberP(sk1,sk5)
| memberP(sk2,sk5) ),
inference(resolve,[status(thm)],[c_824,c_43]) ).
cnf(c_827,plain,
( ~ memberP(sk1,sk5)
| ~ memberP(sk2,sk5) ),
inference(resolve,[status(thm)],[c_824,c_42]) ).
cnf(c_10626,plain,
( ~ memberP(sk1,sk5)
| ~ memberP(sk4,sk5) ),
inference(paramod,[status(thm)],[c_50,c_827]) ).
cnf(c_10704,plain,
( memberP(sk1,sk5)
| memberP(sk4,sk5) ),
inference(paramod,[status(thm)],[c_50,c_826]) ).
cnf(c_14486,plain,
( memberP(sk3,sk5)
| ~ ssItem(sk5)
| memberP(sk1,sk5) ),
inference(resolve,[status(thm)],[c_10704,c_45]) ).
cnf(c_14239,plain,
( memberP(sk3,sk5)
| memberP(sk1,sk5) ),
inference(resolve,[status(thm)],[c_825,c_14486]) ).
cnf(c_14487,plain,
( memberP(sk1,sk5)
| memberP(sk1,sk5) ),
inference(paramod,[status(thm)],[c_49,c_14239]) ).
cnf(c_14482,plain,
memberP(sk1,sk5),
inference(copy,[status(thm)],[c_14487]) ).
cnf(c_14483,plain,
~ memberP(sk4,sk5),
inference(resolve,[status(thm)],[c_14482,c_10626]) ).
cnf(c_14488,plain,
( memberP(sk4,sk5)
| ~ ssItem(sk5) ),
inference(resolve,[status(thm)],[c_14482,c_823]) ).
cnf(c_14489,plain,
memberP(sk4,sk5),
inference(resolve,[status(thm)],[c_825,c_14488]) ).
cnf(c_14485,plain,
$false,
inference(resolve,[status(thm)],[c_14483,c_14489]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC001-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n002.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 12:04:50 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 1671233 was started by sandbox2 on n002,
% 0.10/0.36 % Sat Sep 26 12:04:50 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 41.33/6.42
% 41.33/6.42 % given #500 (I,wt=53): 559 -ssItem(A) | app(app(B,cons(C,B)),cons(A,D)) != cons(A,nil) | -ssList(D) | -ssList(B) | -ssItem(C) | -ssList(cons(A,nil)) | lt(C,A) | lt(A,C). [factor(370,d,e)].
% 41.33/6.42
% 41.33/6.42 % SZS status Unsatisfiable for theBenchmark
% 41.33/6.42
% 41.33/6.42 % Proof 1 at 5.14 (+ 0.83) seconds.
% 41.33/6.42 % Length of proof is 20.
% 41.33/6.42 % Level of proof is 8.
% 41.33/6.42 % Maximum clause weight is 13.000.
% 41.33/6.42 % Given clauses 933.
% 41.33/6.42
% 41.33/6.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------