%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC207-1 : 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 : 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 08:57:09 AM UTC 2026
% Result : Unsatisfiable 23.05s 3.71s
% Output : CNFRefutation 23.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 43 ( 21 unt; 0 def)
% Number of atoms : 83 ( 29 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 80 ( 40 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 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 : 13 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_11,axiom,
( nil = sk4
| cons(sk5,nil) = sk3 ),
file('theBenchmark.p',co1_11) ).
cnf(c_61,plain,
( nil = sk4
| cons(sk5,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_11]) ).
cnf(c_62,plain,
( sk4 = nil
| cons(sk5,nil) = sk3 ),
inference(copy,[status(thm)],[c_61]) ).
fof(co1_9,axiom,
( nil = sk4
| ssItem(sk5) ),
file('theBenchmark.p',co1_9) ).
cnf(c_65,plain,
( nil = sk4
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_66,plain,
( sk4 = nil
| ssItem(sk5) ),
inference(copy,[status(thm)],[c_65]) ).
fof(co1_8,axiom,
~ neq(sk1,nil),
file('theBenchmark.p',co1_8) ).
cnf(c_67,plain,
~ neq(sk1,nil),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
neq(sk2,nil),
file('theBenchmark.p',co1_7) ).
cnf(c_68,plain,
neq(sk2,nil),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_69,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_70,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_71,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_72,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_135,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_150,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause99,axiom,
! [VAR_0,VAR_1] :
( ~ ssList(VAR_1)
| ~ ssItem(VAR_0)
| cons(VAR_0,VAR_1) != VAR_1 ),
file('theBenchmark.p',clause99) ).
cnf(c_151,plain,
( ~ ssList(B)
| ~ ssItem(A)
| cons(A,B) != B ),
inference(clausify,[status(thm)],[clause99]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_227,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_331,plain,
~ neq(sk3,nil),
inference(paramod,[status(thm)],[c_69,c_67]) ).
cnf(c_332,plain,
neq(sk4,nil),
inference(paramod,[status(thm)],[c_70,c_68]) ).
cnf(c_15882,plain,
( ssItem(sk5)
| ~ ssList(sk4)
| ~ ssList(nil)
| ~ neq(sk4,nil) ),
inference(resolve,[status(thm)],[c_135,c_66]) ).
cnf(c_15883,plain,
( ssItem(sk5)
| ~ ssList(sk4)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_332,c_15882]) ).
cnf(c_15884,plain,
( ssItem(sk5)
| ~ ssList(sk4) ),
inference(resolve,[status(thm)],[c_227,c_15883]) ).
cnf(c_1374,plain,
ssItem(sk5),
inference(resolve,[status(thm)],[c_71,c_15884]) ).
cnf(c_15885,plain,
( cons(sk5,nil) = sk3
| ~ ssList(sk4)
| ~ ssList(nil)
| ~ neq(sk4,nil) ),
inference(resolve,[status(thm)],[c_135,c_62]) ).
cnf(c_15886,plain,
( cons(sk5,nil) = sk3
| ~ ssList(sk4)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_332,c_15885]) ).
cnf(c_15887,plain,
( cons(sk5,nil) = sk3
| ~ ssList(sk4) ),
inference(resolve,[status(thm)],[c_227,c_15886]) ).
cnf(c_1375,plain,
cons(sk5,nil) = sk3,
inference(resolve,[status(thm)],[c_71,c_15887]) ).
cnf(c_1429,plain,
( sk3 = A
| neq(sk3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_150,c_72]) ).
cnf(c_15888,plain,
( ~ ssList(nil)
| ~ ssItem(sk5)
| sk3 != nil ),
inference(paramod,[status(thm)],[c_1375,c_151]) ).
cnf(c_15889,plain,
( ~ ssList(nil)
| sk3 != nil ),
inference(resolve,[status(thm)],[c_1374,c_15888]) ).
cnf(c_13026,plain,
sk3 != nil,
inference(resolve,[status(thm)],[c_227,c_15889]) ).
cnf(c_15890,plain,
( sk3 = nil
| neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_1429,c_227]) ).
cnf(c_15891,plain,
sk3 = nil,
inference(resolve,[status(thm)],[c_331,c_15890]) ).
cnf(c_15881,plain,
$false,
inference(resolve,[status(thm)],[c_13026,c_15891]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC207-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n005.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 12:31:01 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2139188 was started by sandbox on n005,
% 0.11/0.37 % Sat Sep 26 12:31:01 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 23.05/3.71
% 23.05/3.71 % given #500 (I,wt=37): 566 app(app(A,cons(B,C)),cons(B,D)) != D | -ssList(D) | -ssList(C) | -ssList(A) | -ssItem(B) | lt(B,B) | -lt(skaf59(D),skaf60(D)). [factor(304,e,f),merge(g)].
% 23.05/3.71
% 23.05/3.71 % given #1000 (A,wt=24): 950 app(app(A,B),C) != sk4 | -ssList(C) | -ssList(A) | -ssList(B) | segmentP(sk4,B). [resolve(82,e,71,a)].
% 23.05/3.71
% 23.05/3.71 % SZS status Unsatisfiable for theBenchmark
% 23.05/3.71
% 23.05/3.71 % Proof 1 at 2.42 (+ 0.76) seconds.
% 23.05/3.71 % Length of proof is 21.
% 23.05/3.71 % Level of proof is 4.
% 23.05/3.71 % Maximum clause weight is 13.000.
% 23.05/3.71 % Given clauses 1394.
% 23.05/3.71
% 23.05/3.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------