%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC042-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 08:56:38 AM UTC 2026
% Result : Unsatisfiable 10.10s 1.76s
% Output : CNFRefutation 10.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 25 unt; 0 def)
% Number of atoms : 54 ( 22 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 45 ( 25 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_49,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
fof(clause84,axiom,
! [VAR_0] :
( nil = VAR_0
| ~ ssList(VAR_0)
| ~ frontsegP(nil,VAR_0) ),
file('theBenchmark.p',clause84) ).
cnf(c_117,plain,
( nil = A
| ~ ssList(A)
| ~ frontsegP(nil,A) ),
inference(clausify,[status(thm)],[clause84]) ).
fof(clause144,axiom,
! [VAR_0,VAR_1,VAR_2] :
( frontsegP(VAR_2,VAR_0)
| ~ ssList(VAR_2)
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| app(VAR_0,VAR_1) != VAR_2 ),
file('theBenchmark.p',clause144) ).
cnf(c_164,plain,
( frontsegP(C,A)
| ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| app(A,B) != C ),
inference(clausify,[status(thm)],[clause144]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_200,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(co1_5,axiom,
nil = sk2,
file('theBenchmark.p',co1_5) ).
cnf(c_202,plain,
nil = sk2,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_203,plain,
sk2 = nil,
inference(copy,[status(thm)],[c_202]) ).
fof(co1_6,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_6) ).
cnf(c_204,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_6]) ).
cnf(c_7297,plain,
nil = sk4,
inference(paramod,[status(thm)],[c_203,c_204]) ).
cnf(c_205,plain,
sk4 = nil,
inference(copy,[status(thm)],[c_7297]) ).
fof(co1_7,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_7) ).
cnf(c_206,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_8,axiom,
nil != sk1,
file('theBenchmark.p',co1_8) ).
cnf(c_207,plain,
nil != sk1,
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_7298,plain,
nil != sk3,
inference(paramod,[status(thm)],[c_206,c_207]) ).
cnf(c_208,plain,
sk3 != nil,
inference(copy,[status(thm)],[c_7298]) ).
fof(co1_9,axiom,
ssList(sk5),
file('theBenchmark.p',co1_9) ).
cnf(c_209,plain,
ssList(sk5),
inference(clausify,[status(thm)],[co1_9]) ).
fof(co1_10,axiom,
app(sk3,sk5) = sk4,
file('theBenchmark.p',co1_10) ).
cnf(c_210,plain,
app(sk3,sk5) = sk4,
inference(clausify,[status(thm)],[co1_10]) ).
cnf(c_211,plain,
app(sk3,sk5) = nil,
inference(paramod,[status(thm)],[c_205,c_210]) ).
cnf(c_7299,plain,
( nil = sk3
| ~ frontsegP(nil,sk3) ),
inference(resolve,[status(thm)],[c_200,c_117]) ).
cnf(c_7300,plain,
( sk3 = nil
| ~ frontsegP(nil,sk3) ),
inference(copy,[status(thm)],[c_7299]) ).
cnf(c_7055,plain,
~ frontsegP(nil,sk3),
inference(resolve,[status(thm)],[c_208,c_7300]) ).
cnf(c_7301,plain,
( frontsegP(nil,sk3)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk5) ),
inference(resolve,[status(thm)],[c_211,c_164]) ).
cnf(c_7302,plain,
( frontsegP(nil,sk3)
| ~ ssList(nil)
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_209,c_7301]) ).
cnf(c_7303,plain,
( frontsegP(nil,sk3)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_200,c_7302]) ).
cnf(c_7304,plain,
frontsegP(nil,sk3),
inference(resolve,[status(thm)],[c_49,c_7303]) ).
cnf(c_7296,plain,
$false,
inference(resolve,[status(thm)],[c_7055,c_7304]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC042-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 12:10:10 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 932973 was started by sandbox on n026,
% 0.09/0.36 % Sat Sep 26 12:10:10 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 10.10/1.76
% 10.10/1.76 % SZS status Unsatisfiable for theBenchmark
% 10.10/1.76
% 10.10/1.76 % Proof 1 at 1.12 (+ 0.24) seconds.
% 10.10/1.76 % Length of proof is 16.
% 10.10/1.76 % Level of proof is 4.
% 10.10/1.76 % Maximum clause weight is 18.000.
% 10.10/1.76 % Given clauses 164.
% 10.10/1.76
% 10.10/1.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------