%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC069-1 : 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 : n005.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 08:56:44 AM UTC 2026
% Result : Unsatisfiable 103.89s 14.48s
% Output : CNFRefutation 103.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 66 ( 19 unt; 0 def)
% Number of atoms : 142 ( 46 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 158 ( 82 ~; 76 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 17 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_13,axiom,
( ~ neq(sk4,nil)
| segmentP(sk3,sk5) ),
file('theBenchmark.p',co1_13) ).
cnf(c_51,plain,
( ~ neq(sk4,nil)
| segmentP(sk3,sk5) ),
inference(clausify,[status(thm)],[co1_13]) ).
fof(co1_12,axiom,
( ~ neq(sk4,nil)
| segmentP(sk4,sk5) ),
file('theBenchmark.p',co1_12) ).
cnf(c_52,plain,
( ~ neq(sk4,nil)
| segmentP(sk4,sk5) ),
inference(clausify,[status(thm)],[co1_12]) ).
fof(co1_11,axiom,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
file('theBenchmark.p',co1_11) ).
cnf(c_53,plain,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
inference(clausify,[status(thm)],[co1_11]) ).
fof(co1_10,axiom,
( ~ neq(sk4,nil)
| ssList(sk5) ),
file('theBenchmark.p',co1_10) ).
cnf(c_54,plain,
( ~ neq(sk4,nil)
| ssList(sk5) ),
inference(clausify,[status(thm)],[co1_10]) ).
fof(co1_9,axiom,
( nil != sk1
| nil != sk2 ),
file('theBenchmark.p',co1_9) ).
cnf(c_55,plain,
( nil != sk1
| nil != sk2 ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_13899,plain,
( nil != sk1
| sk2 != nil ),
inference(copy,[status(thm)],[c_55]) ).
cnf(c_56,plain,
( sk1 != nil
| sk2 != nil ),
inference(copy,[status(thm)],[c_13899]) ).
fof(co1_8,axiom,
( nil != sk4
| nil = sk3 ),
file('theBenchmark.p',co1_8) ).
cnf(c_57,plain,
( nil != sk4
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_13900,plain,
( nil != sk4
| sk3 = nil ),
inference(copy,[status(thm)],[c_57]) ).
cnf(c_58,plain,
( sk4 != nil
| sk3 = nil ),
inference(copy,[status(thm)],[c_13900]) ).
fof(co1_7,axiom,
! [VAR_0] :
( ~ segmentP(sk1,VAR_0)
| ~ segmentP(sk2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',co1_7) ).
cnf(c_59,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_60,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_61,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_62,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_63,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
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_126,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_141,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_218,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_13901,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(sk4,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_61,c_59]) ).
cnf(c_322,plain,
( ~ segmentP(sk3,A)
| ~ segmentP(sk4,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_60,c_13901]) ).
cnf(c_13902,plain,
( sk1 != nil
| sk4 != nil ),
inference(paramod,[status(thm)],[c_61,c_56]) ).
cnf(c_323,plain,
( sk3 != nil
| sk4 != nil ),
inference(paramod,[status(thm)],[c_60,c_13902]) ).
cnf(c_13903,plain,
( A = sk3
| neq(A,sk3)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_141,c_63]) ).
cnf(c_937,plain,
( sk3 = A
| neq(A,sk3)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_13903]) ).
cnf(c_13904,plain,
( A = sk4
| neq(A,sk4)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_141,c_62]) ).
cnf(c_938,plain,
( sk4 = A
| neq(A,sk4)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_13904]) ).
cnf(c_940,plain,
( sk4 = A
| neq(sk4,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_141,c_62]) ).
cnf(c_12995,plain,
( sk3 = nil
| neq(nil,sk3) ),
inference(resolve,[status(thm)],[c_937,c_218]) ).
cnf(c_13027,plain,
( sk4 != nil
| neq(nil,sk3) ),
inference(resolve,[status(thm)],[c_12995,c_323]) ).
cnf(c_13135,plain,
( sk4 = nil
| neq(nil,sk4) ),
inference(resolve,[status(thm)],[c_938,c_218]) ).
cnf(c_13164,plain,
( neq(nil,sk3)
| neq(nil,sk4) ),
inference(resolve,[status(thm)],[c_13135,c_13027]) ).
cnf(c_13168,plain,
( sk3 = nil
| neq(nil,sk4) ),
inference(resolve,[status(thm)],[c_13135,c_58]) ).
cnf(c_13905,plain,
( ~ ssList(nil)
| ~ ssList(sk3)
| nil != sk3
| neq(nil,sk4) ),
inference(resolve,[status(thm)],[c_13164,c_126]) ).
cnf(c_13906,plain,
( ~ ssList(nil)
| ~ ssList(sk3)
| sk3 != nil
| neq(nil,sk4) ),
inference(copy,[status(thm)],[c_13905]) ).
cnf(c_13907,plain,
( ~ ssList(nil)
| sk3 != nil
| neq(nil,sk4) ),
inference(resolve,[status(thm)],[c_63,c_13906]) ).
cnf(c_13169,plain,
( sk3 != nil
| neq(nil,sk4) ),
inference(resolve,[status(thm)],[c_218,c_13907]) ).
cnf(c_13908,plain,
( neq(nil,sk4)
| neq(nil,sk4) ),
inference(resolve,[status(thm)],[c_13169,c_13168]) ).
cnf(c_13281,plain,
neq(nil,sk4),
inference(copy,[status(thm)],[c_13908]) ).
cnf(c_13909,plain,
( ~ ssList(nil)
| ~ ssList(sk4)
| nil != sk4 ),
inference(resolve,[status(thm)],[c_13281,c_126]) ).
cnf(c_13910,plain,
( ~ ssList(nil)
| ~ ssList(sk4)
| sk4 != nil ),
inference(copy,[status(thm)],[c_13909]) ).
cnf(c_13911,plain,
( ~ ssList(nil)
| sk4 != nil ),
inference(resolve,[status(thm)],[c_62,c_13910]) ).
cnf(c_13282,plain,
sk4 != nil,
inference(resolve,[status(thm)],[c_218,c_13911]) ).
cnf(c_13912,plain,
( sk4 = nil
| neq(sk4,nil) ),
inference(resolve,[status(thm)],[c_940,c_218]) ).
cnf(c_13610,plain,
neq(sk4,nil),
inference(resolve,[status(thm)],[c_13282,c_13912]) ).
cnf(c_13638,plain,
ssList(sk5),
inference(resolve,[status(thm)],[c_13610,c_54]) ).
cnf(c_13639,plain,
neq(sk5,nil),
inference(resolve,[status(thm)],[c_13610,c_53]) ).
cnf(c_13640,plain,
segmentP(sk4,sk5),
inference(resolve,[status(thm)],[c_13610,c_52]) ).
cnf(c_13641,plain,
segmentP(sk3,sk5),
inference(resolve,[status(thm)],[c_13610,c_51]) ).
cnf(c_13913,plain,
( ~ segmentP(sk3,sk5)
| ~ segmentP(sk4,sk5)
| ~ ssList(sk5) ),
inference(resolve,[status(thm)],[c_13639,c_322]) ).
cnf(c_13914,plain,
( ~ segmentP(sk3,sk5)
| ~ segmentP(sk4,sk5) ),
inference(resolve,[status(thm)],[c_13638,c_13913]) ).
cnf(c_13915,plain,
~ segmentP(sk3,sk5),
inference(resolve,[status(thm)],[c_13640,c_13914]) ).
cnf(c_13898,plain,
$false,
inference(resolve,[status(thm)],[c_13641,c_13915]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC069-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.57 % Computer : n005.cluster.edu
% 0.17/0.57 % Model : x86_64 x86_64
% 0.17/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.57 % Memory : 8046.5625MB
% 0.17/0.57 % OS : Linux 6.8.0-71-generic
% 0.17/0.58 % CPULimit : 300
% 0.17/0.58 % WCLimit : 300
% 0.17/0.58 % DateTime : Sat Sep 26 12:10:17 UTC 2026
% 0.17/0.58 % CPUTime :
% 0.17/0.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.58 % Process 2090888 was started by sandbox2 on n005,
% 0.17/0.58 % Sat Sep 26 12:10:17 2026
% 0.17/0.58 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.60
% 0.17/0.60 % From the command line: assign(max_seconds, 300).
% 103.89/14.48
% 103.89/14.48 % given #500 (I,wt=66): 566 app(app(A,cons(B,C)),cons(D,A)) != A | -ssList(A) | -ssList(C) | -ssItem(D) | -ssItem(B) | lt(B,D) | lt(D,B) | app(app(skaf61(A),cons(skaf59(A),skaf62(A))),cons(skaf60(A),skaf63(A))) = A. [factor(301,b,f)].
% 103.89/14.48
% 103.89/14.48 % SZS status Unsatisfiable for theBenchmark
% 103.89/14.48
% 103.89/14.48 % Proof 1 at 5.13 (+ 0.63) seconds.
% 103.89/14.48 % Length of proof is 35.
% 103.89/14.48 % Level of proof is 10.
% 103.89/14.48 % Maximum clause weight is 16.000.
% 103.89/14.48 % Given clauses 901.
% 103.89/14.48
% 103.89/14.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------