%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC206-1 : 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 : n017.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 08:57:09 AM UTC 2026
% Result : Unsatisfiable 26.07s 4.14s
% Output : CNFRefutation 26.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 45 ( 24 unt; 0 def)
% Number of atoms : 85 ( 21 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 84 ( 44 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 15 ( 0 sgn 7 !; 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_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_8,axiom,
~ neq(sk1,nil),
file('theBenchmark.p',co1_8) ).
cnf(c_57,plain,
~ neq(sk1,nil),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
neq(sk2,nil),
file('theBenchmark.p',co1_7) ).
cnf(c_58,plain,
neq(sk2,nil),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_59,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_60,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_1,axiom,
ssList(sk1),
file('theBenchmark.p',co1_1) ).
cnf(c_64,plain,
ssList(sk1),
inference(clausify,[status(thm)],[co1_1]) ).
fof(clause127,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| ~ ssList(VAR_1)
| ~ ssList(VAR_0)
| ~ segmentP(VAR_1,VAR_0)
| ~ segmentP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause127) ).
cnf(c_114,plain,
( B = A
| ~ ssList(B)
| ~ ssList(A)
| ~ segmentP(B,A)
| ~ segmentP(A,B) ),
inference(clausify,[status(thm)],[clause127]) ).
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_125,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_140,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause56,axiom,
! [VAR_0] :
( segmentP(VAR_0,nil)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause56) ).
cnf(c_169,plain,
( segmentP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause56]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_217,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_829,plain,
neq(sk4,nil),
inference(paramod,[status(thm)],[c_60,c_58]) ).
cnf(c_830,plain,
ssList(sk5),
inference(resolve,[status(thm)],[c_829,c_54]) ).
cnf(c_831,plain,
neq(sk5,nil),
inference(resolve,[status(thm)],[c_829,c_53]) ).
cnf(c_833,plain,
segmentP(sk3,sk5),
inference(resolve,[status(thm)],[c_829,c_51]) ).
cnf(c_1057,plain,
( sk1 = A
| neq(sk1,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_140,c_64]) ).
cnf(c_6965,plain,
segmentP(sk5,nil),
inference(resolve,[status(thm)],[c_830,c_169]) ).
cnf(c_19113,plain,
( ~ ssList(sk5)
| ~ ssList(nil)
| sk5 != nil ),
inference(resolve,[status(thm)],[c_831,c_125]) ).
cnf(c_19114,plain,
( ~ ssList(sk5)
| sk5 != nil ),
inference(resolve,[status(thm)],[c_217,c_19113]) ).
cnf(c_7016,plain,
sk5 != nil,
inference(resolve,[status(thm)],[c_830,c_19114]) ).
cnf(c_19115,plain,
( sk5 = nil
| ~ ssList(sk5)
| ~ ssList(nil)
| ~ segmentP(nil,sk5) ),
inference(resolve,[status(thm)],[c_6965,c_114]) ).
cnf(c_19116,plain,
( sk5 = nil
| ~ ssList(sk5)
| ~ segmentP(nil,sk5) ),
inference(resolve,[status(thm)],[c_217,c_19115]) ).
cnf(c_19117,plain,
( sk5 = nil
| ~ segmentP(nil,sk5) ),
inference(resolve,[status(thm)],[c_830,c_19116]) ).
cnf(c_10736,plain,
~ segmentP(nil,sk5),
inference(resolve,[status(thm)],[c_7016,c_19117]) ).
cnf(c_19118,plain,
( sk1 = nil
| neq(sk1,nil) ),
inference(resolve,[status(thm)],[c_1057,c_217]) ).
cnf(c_18772,plain,
sk1 = nil,
inference(resolve,[status(thm)],[c_57,c_19118]) ).
cnf(c_19119,plain,
nil = sk3,
inference(paramod,[status(thm)],[c_18772,c_59]) ).
cnf(c_18865,plain,
sk3 = nil,
inference(copy,[status(thm)],[c_19119]) ).
cnf(c_19120,plain,
segmentP(nil,sk5),
inference(paramod,[status(thm)],[c_18865,c_833]) ).
cnf(c_19112,plain,
$false,
inference(resolve,[status(thm)],[c_10736,c_19120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC206-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n017.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 26 12:26:33 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 704223 was started by sandbox2 on n017,
% 0.09/0.35 % Sat Sep 26 12:26:33 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 26.07/4.14
% 26.07/4.14 % given #500 (I,wt=41): 561 app(app(A,cons(B,C)),cons(D,C)) != A | -ssList(C) | -ssList(A) | -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(299,c,f)].
% 26.07/4.14
% 26.07/4.14 % given #1000 (F,wt=5): 12414 app(sk5,sk4) != nil. [para(60(a,1),12383(a,1,2))].
% 26.07/4.14
% 26.07/4.14 % given #1500 (A,wt=10): 1026 app(sk1,A) != nil | -ssList(A) | nil = A. [resolve(121,c,64,a)].
% 26.07/4.14
% 26.07/4.14 % SZS status Unsatisfiable for theBenchmark
% 26.07/4.14
% 26.07/4.14 % Proof 1 at 2.98 (+ 0.68) seconds.
% 26.07/4.14 % Length of proof is 24.
% 26.07/4.14 % Level of proof is 5.
% 26.07/4.14 % Maximum clause weight is 13.000.
% 26.07/4.14 % Given clauses 1601.
% 26.07/4.14
% 26.07/4.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------