%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC039-1 : 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 : n001.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 08:56:37 AM UTC 2026
% Result : Unsatisfiable 11.19s 1.86s
% Output : CNFRefutation 11.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 43 ( 23 unt; 0 def)
% Number of atoms : 79 ( 34 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 67 ( 31 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_49,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
fof(clause80,axiom,
! [VAR_0] :
( nil = VAR_0
| ~ ssList(VAR_0)
| ~ segmentP(nil,VAR_0) ),
file('theBenchmark.p',clause80) ).
cnf(c_113,plain,
( nil = A
| ~ ssList(A)
| ~ segmentP(nil,A) ),
inference(clausify,[status(thm)],[clause80]) ).
fof(clause173,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( segmentP(VAR_3,VAR_1)
| ~ ssList(VAR_3)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0)
| ~ ssList(VAR_2)
| app(app(VAR_0,VAR_1),VAR_2) != VAR_3 ),
file('theBenchmark.p',clause173) ).
cnf(c_190,plain,
( segmentP(D,B)
| ~ ssList(D)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != D ),
inference(clausify,[status(thm)],[clause173]) ).
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_7614,plain,
nil = sk4,
inference(paramod,[status(thm)],[c_203,c_204]) ).
cnf(c_205,plain,
sk4 = nil,
inference(copy,[status(thm)],[c_7614]) ).
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_7615,plain,
nil != sk3,
inference(paramod,[status(thm)],[c_206,c_207]) ).
cnf(c_208,plain,
sk3 != nil,
inference(copy,[status(thm)],[c_7615]) ).
fof(co1_17,axiom,
( nil = sk3
| ssList(sk6) ),
file('theBenchmark.p',co1_17) ).
cnf(c_218,plain,
( nil = sk3
| ssList(sk6) ),
inference(clausify,[status(thm)],[co1_17]) ).
cnf(c_7616,plain,
( sk3 = nil
| ssList(sk6) ),
inference(copy,[status(thm)],[c_218]) ).
cnf(c_219,plain,
ssList(sk6),
inference(resolve,[status(thm)],[c_208,c_7616]) ).
fof(co1_18,axiom,
( nil = sk3
| ssList(sk7) ),
file('theBenchmark.p',co1_18) ).
cnf(c_220,plain,
( nil = sk3
| ssList(sk7) ),
inference(clausify,[status(thm)],[co1_18]) ).
cnf(c_7617,plain,
( sk3 = nil
| ssList(sk7) ),
inference(copy,[status(thm)],[c_220]) ).
cnf(c_221,plain,
ssList(sk7),
inference(resolve,[status(thm)],[c_208,c_7617]) ).
fof(co1_20,axiom,
( nil = sk3
| app(app(sk6,sk3),sk7) = sk4 ),
file('theBenchmark.p',co1_20) ).
cnf(c_224,plain,
( nil = sk3
| app(app(sk6,sk3),sk7) = sk4 ),
inference(clausify,[status(thm)],[co1_20]) ).
cnf(c_7618,plain,
( nil = sk3
| app(app(sk6,sk3),sk7) = nil ),
inference(paramod,[status(thm)],[c_205,c_224]) ).
cnf(c_7619,plain,
( sk3 = nil
| app(app(sk6,sk3),sk7) = nil ),
inference(copy,[status(thm)],[c_7618]) ).
cnf(c_225,plain,
app(app(sk6,sk3),sk7) = nil,
inference(resolve,[status(thm)],[c_208,c_7619]) ).
cnf(c_7620,plain,
( nil = sk3
| ~ segmentP(nil,sk3) ),
inference(resolve,[status(thm)],[c_200,c_113]) ).
cnf(c_7621,plain,
( sk3 = nil
| ~ segmentP(nil,sk3) ),
inference(copy,[status(thm)],[c_7620]) ).
cnf(c_7072,plain,
~ segmentP(nil,sk3),
inference(resolve,[status(thm)],[c_208,c_7621]) ).
cnf(c_7622,plain,
( segmentP(nil,sk3)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_225,c_190]) ).
cnf(c_7623,plain,
( segmentP(nil,sk3)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk6) ),
inference(resolve,[status(thm)],[c_221,c_7622]) ).
cnf(c_7624,plain,
( segmentP(nil,sk3)
| ~ ssList(nil)
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_219,c_7623]) ).
cnf(c_7625,plain,
( segmentP(nil,sk3)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_200,c_7624]) ).
cnf(c_7626,plain,
segmentP(nil,sk3),
inference(resolve,[status(thm)],[c_49,c_7625]) ).
cnf(c_7613,plain,
$false,
inference(resolve,[status(thm)],[c_7072,c_7626]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC039-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 12:12:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1752368 was started by sandbox2 on n001,
% 0.10/0.37 % Sat Sep 26 12:12:58 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 11.19/1.86
% 11.19/1.86 % SZS status Unsatisfiable for theBenchmark
% 11.19/1.86
% 11.19/1.86 % Proof 1 at 1.21 (+ 0.25) seconds.
% 11.19/1.86 % Length of proof is 19.
% 11.19/1.86 % Level of proof is 4.
% 11.19/1.86 % Maximum clause weight is 26.000.
% 11.19/1.86 % Given clauses 167.
% 11.19/1.86
% 11.19/1.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------