%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC018-1 : 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 : 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 08:56:33 AM UTC 2026
% Result : Unsatisfiable 28.01s 4.02s
% Output : CNFRefutation 28.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 67 ( 25 unt; 0 def)
% Number of atoms : 152 ( 58 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 168 ( 83 ~; 85 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_14,axiom,
( neq(sk2,nil)
| nil != sk1 ),
file('theBenchmark.p',co1_14) ).
cnf(c_55,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(clausify,[status(thm)],[co1_14]) ).
cnf(c_56,plain,
( neq(sk2,nil)
| sk1 != nil ),
inference(copy,[status(thm)],[c_55]) ).
fof(co1_13,axiom,
! [VAR_0] :
( ~ frontsegP(sk1,VAR_0)
| ~ frontsegP(sk2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil = sk2 ),
file('theBenchmark.p',co1_13) ).
cnf(c_57,plain,
( ~ frontsegP(sk1,A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_58,plain,
( ~ frontsegP(sk1,A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sk2 = nil ),
inference(copy,[status(thm)],[c_57]) ).
fof(co1_12,axiom,
( neq(sk2,nil)
| nil = sk2 ),
file('theBenchmark.p',co1_12) ).
cnf(c_59,plain,
( neq(sk2,nil)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_12]) ).
cnf(c_60,plain,
( neq(sk2,nil)
| sk2 = nil ),
inference(copy,[status(thm)],[c_59]) ).
fof(co1_11,axiom,
( nil != sk3
| nil = sk4 ),
file('theBenchmark.p',co1_11) ).
cnf(c_61,plain,
( nil != sk3
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_11]) ).
cnf(c_18016,plain,
( nil != sk3
| sk4 = nil ),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_62,plain,
( sk3 != nil
| sk4 = nil ),
inference(copy,[status(thm)],[c_18016]) ).
fof(co1_8,axiom,
app(sk3,sk5) = sk4,
file('theBenchmark.p',co1_8) ).
cnf(c_64,plain,
app(sk3,sk5) = sk4,
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
ssList(sk5),
file('theBenchmark.p',co1_7) ).
cnf(c_65,plain,
ssList(sk5),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_66,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_67,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_68,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_67]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_69,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
cnf(c_70,plain,
ssList(sk2),
inference(paramod,[status(thm)],[c_68,c_69]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_71,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
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_106,plain,
( frontsegP(C,A)
| ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| app(A,B) != C ),
inference(clausify,[status(thm)],[clause144]) ).
fof(clause118,axiom,
! [VAR_0,VAR_1] :
( nil = VAR_0
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| app(VAR_0,VAR_1) != nil ),
file('theBenchmark.p',clause118) ).
cnf(c_130,plain,
( nil = A
| ~ ssList(A)
| ~ ssList(B)
| app(A,B) != nil ),
inference(clausify,[status(thm)],[clause118]) ).
fof(clause115,axiom,
! [VAR_0,VAR_1] :
( ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| ~ neq(VAR_0,VAR_1)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',clause115) ).
cnf(c_133,plain,
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(A,B)
| A != B ),
inference(clausify,[status(thm)],[clause115]) ).
fof(clause100,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| neq(VAR_1,VAR_0)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause100) ).
cnf(c_148,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause61,axiom,
! [VAR_0] :
( frontsegP(VAR_0,VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause61) ).
cnf(c_172,plain,
( frontsegP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause61]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_225,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_333,plain,
( ~ frontsegP(sk3,A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sk2 = nil ),
inference(paramod,[status(thm)],[c_66,c_58]) ).
cnf(c_334,plain,
( neq(sk2,nil)
| sk3 != nil ),
inference(paramod,[status(thm)],[c_66,c_56]) ).
cnf(c_336,plain,
app(sk3,sk5) = sk2,
inference(paramod,[status(thm)],[c_68,c_64]) ).
cnf(c_337,plain,
( sk3 != nil
| sk2 = nil ),
inference(paramod,[status(thm)],[c_68,c_62]) ).
cnf(c_1314,plain,
( ~ ssList(A)
| ~ neq(sk2,A)
| sk2 != A ),
inference(resolve,[status(thm)],[c_133,c_70]) ).
cnf(c_1338,plain,
( sk3 = A
| neq(sk3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_148,c_71]) ).
cnf(c_1404,plain,
frontsegP(sk3,sk3),
inference(resolve,[status(thm)],[c_172,c_71]) ).
cnf(c_18017,plain,
( ~ frontsegP(sk3,sk3)
| ~ frontsegP(sk2,sk3)
| ~ neq(sk3,nil)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_333,c_71]) ).
cnf(c_8397,plain,
( ~ frontsegP(sk2,sk3)
| ~ neq(sk3,nil)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_1404,c_18017]) ).
cnf(c_18018,plain,
( frontsegP(sk2,sk3)
| ~ ssList(sk2)
| ~ ssList(sk3)
| ~ ssList(sk5) ),
inference(resolve,[status(thm)],[c_336,c_106]) ).
cnf(c_18019,plain,
( frontsegP(sk2,sk3)
| ~ ssList(sk2)
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_65,c_18018]) ).
cnf(c_18020,plain,
( frontsegP(sk2,sk3)
| ~ ssList(sk2) ),
inference(resolve,[status(thm)],[c_71,c_18019]) ).
cnf(c_8433,plain,
frontsegP(sk2,sk3),
inference(resolve,[status(thm)],[c_70,c_18020]) ).
cnf(c_18021,plain,
( nil = sk3
| ~ ssList(sk3)
| ~ ssList(sk5)
| sk2 != nil ),
inference(paramod,[status(thm)],[c_336,c_130]) ).
cnf(c_18022,plain,
( sk3 = nil
| ~ ssList(sk3)
| ~ ssList(sk5)
| sk2 != nil ),
inference(copy,[status(thm)],[c_18021]) ).
cnf(c_18023,plain,
( sk3 = nil
| ~ ssList(sk3)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_65,c_18022]) ).
cnf(c_8441,plain,
( sk3 = nil
| sk2 != nil ),
inference(resolve,[status(thm)],[c_71,c_18023]) ).
cnf(c_8443,plain,
( ~ neq(sk3,nil)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_8433,c_8397]) ).
cnf(c_12655,plain,
( neq(sk2,nil)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_8441,c_60]) ).
cnf(c_13276,plain,
( ~ neq(sk2,nil)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_1314,c_225]) ).
cnf(c_18024,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(resolve,[status(thm)],[c_12655,c_334]) ).
cnf(c_13311,plain,
neq(sk2,nil),
inference(copy,[status(thm)],[c_18024]) ).
cnf(c_13312,plain,
sk2 != nil,
inference(resolve,[status(thm)],[c_13311,c_13276]) ).
cnf(c_13321,plain,
~ neq(sk3,nil),
inference(resolve,[status(thm)],[c_13312,c_8443]) ).
cnf(c_13368,plain,
sk3 != nil,
inference(resolve,[status(thm)],[c_13312,c_337]) ).
cnf(c_18025,plain,
( sk3 = nil
| neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_1338,c_225]) ).
cnf(c_18026,plain,
sk3 = nil,
inference(resolve,[status(thm)],[c_13321,c_18025]) ).
cnf(c_18015,plain,
$false,
inference(resolve,[status(thm)],[c_13368,c_18026]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC018-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 12:07:26 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 929263 was started by sandbox2 on n026,
% 0.10/0.37 % Sat Sep 26 12:07:26 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 28.01/4.02
% 28.01/4.02 % given #500 (I,wt=40): 569 app(app(A,cons(B,C)),cons(D,A)) != C | -ssList(A) | -ssList(C) | -ssItem(D) | -ssItem(B) | lt(B,D) | lt(D,B) | -lt(skaf59(C),skaf60(C)). [factor(301,c,f)].
% 28.01/4.02
% 28.01/4.02 % given #1000 (T,wt=8): 6886 segmentP(skaf80(A),nil). [resolve(218,a,177,a)].
% 28.01/4.02
% 28.01/4.02 % given #1500 (F,wt=12): 13108 skaf58(A) != sk5 | -neq(skaf58(A),sk5). [resolve(1312,c,196,a),flip(a)].
% 28.01/4.02
% 28.01/4.02 % SZS status Unsatisfiable for theBenchmark
% 28.01/4.02
% 28.01/4.02 % Proof 1 at 2.62 (+ 0.89) seconds.
% 28.01/4.02 % Length of proof is 40.
% 28.01/4.02 % Level of proof is 8.
% 28.01/4.02 % Maximum clause weight is 18.000.
% 28.01/4.02 % Given clauses 1714.
% 28.01/4.02
% 28.01/4.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------