%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC415-1 : 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 : 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 08:57:45 AM UTC 2026
% Result : Unsatisfiable 52.62s 8.18s
% Output : CNFRefutation 52.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 19 unt; 0 def)
% Number of atoms : 130 ( 49 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 161 ( 82 ~; 79 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 23 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_12,axiom,
! [VAR_0] :
( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| sk1 != VAR_0
| tl(sk2) != VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',co1_12) ).
cnf(c_51,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| sk1 != A
| tl(sk2) != A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[co1_12]) ).
fof(co1_11,axiom,
! [VAR_0] :
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| tl(sk4) != VAR_0
| sk3 = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',co1_11) ).
cnf(c_52,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| tl(sk4) != A
| sk3 = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[co1_11]) ).
fof(co1_7,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('theBenchmark.p',co1_7) ).
cnf(c_56,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_57,plain,
neq(sk2,nil),
inference(copy,[status(thm)],[c_56]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_58,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_59,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_60,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_59]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_61,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
cnf(c_62,plain,
ssList(sk2),
inference(paramod,[status(thm)],[c_60,c_61]) ).
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_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(clause77,axiom,
! [VAR_0] :
( nil = VAR_0
| ssList(tl(VAR_0))
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause77) ).
cnf(c_156,plain,
( nil = A
| ssList(tl(A))
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause77]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_217,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_14878,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| sk3 != A
| tl(sk2) != A
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_58,c_51]) ).
cnf(c_14879,plain,
( ~ neq(sk2,nil)
| ~ neq(nil,sk2)
| sk3 != A
| tl(sk2) != A
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_60,c_14878]) ).
cnf(c_321,plain,
( ~ neq(nil,sk2)
| sk3 != A
| tl(sk2) != A
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_57,c_14879]) ).
cnf(c_14880,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| tl(sk2) != A
| sk3 = A
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_60,c_52]) ).
cnf(c_14881,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| tl(sk2) != A
| sk3 = A
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_60,c_14880]) ).
cnf(c_14882,plain,
( ~ neq(sk2,nil)
| ~ neq(nil,sk2)
| tl(sk2) != A
| sk3 = A
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_60,c_14881]) ).
cnf(c_322,plain,
( ~ neq(nil,sk2)
| tl(sk2) != A
| sk3 = A
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_57,c_14882]) ).
cnf(c_14883,plain,
( ~ ssList(sk2)
| ~ ssList(nil)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_125,c_57]) ).
cnf(c_14884,plain,
( ~ ssList(sk2)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_217,c_14883]) ).
cnf(c_1135,plain,
sk2 != nil,
inference(resolve,[status(thm)],[c_62,c_14884]) ).
cnf(c_14885,plain,
( A = sk2
| neq(A,sk2)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_140,c_62]) ).
cnf(c_1160,plain,
( sk2 = A
| neq(A,sk2)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_14885]) ).
cnf(c_14886,plain,
( nil = sk2
| ssList(tl(sk2)) ),
inference(resolve,[status(thm)],[c_156,c_62]) ).
cnf(c_14887,plain,
( sk2 = nil
| ssList(tl(sk2)) ),
inference(copy,[status(thm)],[c_14886]) ).
cnf(c_1196,plain,
ssList(tl(sk2)),
inference(resolve,[status(thm)],[c_1135,c_14887]) ).
cnf(c_14888,plain,
( ~ neq(nil,sk2)
| sk3 != sk3
| tl(sk2) != sk3 ),
inference(resolve,[status(thm)],[c_321,c_63]) ).
cnf(c_7907,plain,
( ~ neq(nil,sk2)
| tl(sk2) != sk3 ),
inference(copy,[status(thm)],[c_14888]) ).
cnf(c_14889,plain,
( ~ neq(nil,sk2)
| sk3 = tl(sk2)
| ~ ssList(tl(sk2)) ),
inference(xxres,[status(thm)],[c_322]) ).
cnf(c_14890,plain,
( ~ neq(nil,sk2)
| tl(sk2) = sk3
| ~ ssList(tl(sk2)) ),
inference(copy,[status(thm)],[c_14889]) ).
cnf(c_7938,plain,
( ~ neq(nil,sk2)
| tl(sk2) = sk3 ),
inference(resolve,[status(thm)],[c_1196,c_14890]) ).
cnf(c_14891,plain,
( sk2 = nil
| neq(nil,sk2) ),
inference(resolve,[status(thm)],[c_1160,c_217]) ).
cnf(c_14838,plain,
neq(nil,sk2),
inference(resolve,[status(thm)],[c_1135,c_14891]) ).
cnf(c_14875,plain,
tl(sk2) = sk3,
inference(resolve,[status(thm)],[c_14838,c_7938]) ).
cnf(c_14892,plain,
( ~ neq(nil,sk2)
| sk3 != sk3 ),
inference(paramod,[status(thm)],[c_14875,c_7907]) ).
cnf(c_14893,plain,
~ neq(nil,sk2),
inference(copy,[status(thm)],[c_14892]) ).
cnf(c_14877,plain,
$false,
inference(resolve,[status(thm)],[c_14838,c_14893]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC415-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % 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 13:06:13 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 1863949 was started by sandbox on n001,
% 0.10/0.38 % Sat Sep 26 13:06:13 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 52.62/8.18
% 52.62/8.18 % given #500 (I,wt=55): 563 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)].
% 52.62/8.18
% 52.62/8.18 % given #1000 (T,wt=9): 1378 segmentP(skaf43(A,B),nil). [resolve(173,a,169,a)].
% 52.62/8.18
% 52.62/8.18 % SZS status Unsatisfiable for theBenchmark
% 52.62/8.18
% 52.62/8.18 % Proof 1 at 5.71 (+ 1.91) seconds.
% 52.62/8.18 % Length of proof is 24.
% 52.62/8.18 % Level of proof is 7.
% 52.62/8.18 % Maximum clause weight is 19.000.
% 52.62/8.18 % Given clauses 1361.
% 52.62/8.18
% 52.62/8.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------