%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC016-1 : 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 : n013.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 08:56:32 AM UTC 2026
% Result : Unsatisfiable 39.25s 11.34s
% Output : CNFRefutation 39.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 85 ( 21 unt; 0 def)
% Number of atoms : 199 ( 68 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 231 ( 117 ~; 114 |; 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 : 19 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_15,axiom,
! [VAR_0] :
( ~ frontsegP(sk1,VAR_0)
| ~ frontsegP(sk2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil != sk1 ),
file('theBenchmark.p',co1_15) ).
cnf(c_51,plain,
( ~ frontsegP(sk1,A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil != sk1 ),
inference(clausify,[status(thm)],[co1_15]) ).
cnf(c_52,plain,
( ~ frontsegP(sk1,A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sk1 != nil ),
inference(copy,[status(thm)],[c_51]) ).
fof(co1_14,axiom,
( neq(sk2,nil)
| nil != sk1 ),
file('theBenchmark.p',co1_14) ).
cnf(c_53,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(clausify,[status(thm)],[co1_14]) ).
cnf(c_54,plain,
( neq(sk2,nil)
| sk1 != nil ),
inference(copy,[status(thm)],[c_53]) ).
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_55,plain,
( ~ frontsegP(sk1,A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_56,plain,
( ~ frontsegP(sk1,A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sk2 = nil ),
inference(copy,[status(thm)],[c_55]) ).
fof(co1_12,axiom,
( neq(sk2,nil)
| nil = sk2 ),
file('theBenchmark.p',co1_12) ).
cnf(c_57,plain,
( neq(sk2,nil)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_12]) ).
cnf(c_58,plain,
( neq(sk2,nil)
| sk2 = nil ),
inference(copy,[status(thm)],[c_57]) ).
fof(co1_11,axiom,
( ~ neq(sk4,nil)
| frontsegP(sk3,sk5) ),
file('theBenchmark.p',co1_11) ).
cnf(c_59,plain,
( ~ neq(sk4,nil)
| frontsegP(sk3,sk5) ),
inference(clausify,[status(thm)],[co1_11]) ).
fof(co1_10,axiom,
( ~ neq(sk4,nil)
| frontsegP(sk4,sk5) ),
file('theBenchmark.p',co1_10) ).
cnf(c_60,plain,
( ~ neq(sk4,nil)
| frontsegP(sk4,sk5) ),
inference(clausify,[status(thm)],[co1_10]) ).
fof(co1_9,axiom,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
file('theBenchmark.p',co1_9) ).
cnf(c_61,plain,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
inference(clausify,[status(thm)],[co1_9]) ).
fof(co1_8,axiom,
( ~ neq(sk4,nil)
| ssList(sk5) ),
file('theBenchmark.p',co1_8) ).
cnf(c_62,plain,
( ~ neq(sk4,nil)
| ssList(sk5) ),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
( nil != sk4
| nil = sk3 ),
file('theBenchmark.p',co1_7) ).
cnf(c_63,plain,
( nil != sk4
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_13471,plain,
( nil != sk4
| sk3 = nil ),
inference(copy,[status(thm)],[c_63]) ).
cnf(c_64,plain,
( sk4 != nil
| sk3 = nil ),
inference(copy,[status(thm)],[c_13471]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_65,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
cnf(c_66,plain,
sk3 = sk1,
inference(copy,[status(thm)],[c_65]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_67,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_68,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
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_132,plain,
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(A,B)
| A != B ),
inference(clausify,[status(thm)],[clause115]) ).
fof(clause84,axiom,
! [VAR_0] :
( nil = VAR_0
| ~ ssList(VAR_0)
| ~ frontsegP(nil,VAR_0) ),
file('theBenchmark.p',clause84) ).
cnf(c_156,plain,
( nil = A
| ~ ssList(A)
| ~ frontsegP(nil,A) ),
inference(clausify,[status(thm)],[clause84]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_224,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_328,plain,
( sk4 != nil
| sk1 = nil ),
inference(paramod,[status(thm)],[c_66,c_64]) ).
cnf(c_329,plain,
( ~ neq(sk4,nil)
| frontsegP(sk1,sk5) ),
inference(paramod,[status(thm)],[c_66,c_59]) ).
cnf(c_13472,plain,
( neq(sk2,nil)
| sk4 = nil ),
inference(paramod,[status(thm)],[c_67,c_58]) ).
cnf(c_330,plain,
( neq(sk4,nil)
| sk4 = nil ),
inference(paramod,[status(thm)],[c_67,c_13472]) ).
cnf(c_13473,plain,
( ~ frontsegP(sk1,A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sk4 = nil ),
inference(paramod,[status(thm)],[c_67,c_56]) ).
cnf(c_331,plain,
( ~ frontsegP(sk1,A)
| ~ frontsegP(sk4,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sk4 = nil ),
inference(paramod,[status(thm)],[c_67,c_13473]) ).
cnf(c_332,plain,
( neq(sk4,nil)
| sk1 != nil ),
inference(paramod,[status(thm)],[c_67,c_54]) ).
cnf(c_333,plain,
( ~ frontsegP(sk1,A)
| ~ frontsegP(sk4,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sk1 != nil ),
inference(paramod,[status(thm)],[c_67,c_52]) ).
cnf(c_13474,plain,
( ~ ssList(A)
| ~ neq(A,A)
| A != A ),
inference(factor,[status(thm)],[c_132]) ).
cnf(c_398,plain,
( ~ ssList(A)
| ~ neq(A,A) ),
inference(copy,[status(thm)],[c_13474]) ).
cnf(c_13475,plain,
( ~ ssList(A)
| ~ neq(A,sk4)
| A != sk4 ),
inference(resolve,[status(thm)],[c_132,c_68]) ).
cnf(c_1146,plain,
( ~ ssList(A)
| ~ neq(A,sk4)
| sk4 != A ),
inference(copy,[status(thm)],[c_13475]) ).
cnf(c_7882,plain,
( sk1 = nil
| neq(sk4,nil) ),
inference(resolve,[status(thm)],[c_330,c_328]) ).
cnf(c_7898,plain,
( ssList(sk5)
| sk4 = nil ),
inference(resolve,[status(thm)],[c_330,c_62]) ).
cnf(c_9420,plain,
~ neq(nil,nil),
inference(resolve,[status(thm)],[c_398,c_224]) ).
cnf(c_10389,plain,
( sk1 = nil
| ssList(sk5) ),
inference(resolve,[status(thm)],[c_7898,c_328]) ).
cnf(c_13476,plain,
( ~ frontsegP(sk1,sk5)
| ~ frontsegP(sk4,sk5)
| ~ neq(sk5,nil)
| sk4 = nil
| sk4 = nil ),
inference(resolve,[status(thm)],[c_7898,c_331]) ).
cnf(c_10497,plain,
( ~ frontsegP(sk1,sk5)
| ~ frontsegP(sk4,sk5)
| ~ neq(sk5,nil)
| sk4 = nil ),
inference(copy,[status(thm)],[c_13476]) ).
cnf(c_13477,plain,
( nil = sk5
| ~ frontsegP(nil,sk5)
| sk1 = nil ),
inference(resolve,[status(thm)],[c_10389,c_156]) ).
cnf(c_10716,plain,
( sk5 = nil
| ~ frontsegP(nil,sk5)
| sk1 = nil ),
inference(copy,[status(thm)],[c_13477]) ).
cnf(c_10809,plain,
( neq(sk4,nil)
| ssList(sk5) ),
inference(resolve,[status(thm)],[c_10389,c_332]) ).
cnf(c_13478,plain,
( ssList(sk5)
| ssList(sk5) ),
inference(resolve,[status(thm)],[c_10809,c_62]) ).
cnf(c_11744,plain,
ssList(sk5),
inference(copy,[status(thm)],[c_13478]) ).
cnf(c_11874,plain,
( ~ frontsegP(sk1,sk5)
| ~ frontsegP(sk4,sk5)
| ~ neq(sk5,nil)
| sk1 != nil ),
inference(resolve,[status(thm)],[c_11744,c_333]) ).
cnf(c_13479,plain,
( ~ neq(sk5,sk4)
| sk4 != sk5 ),
inference(resolve,[status(thm)],[c_1146,c_11744]) ).
cnf(c_13390,plain,
( ~ neq(sk5,sk4)
| sk5 != sk4 ),
inference(copy,[status(thm)],[c_13479]) ).
cnf(c_13423,plain,
( ~ neq(sk5,nil)
| sk5 != sk4
| neq(sk4,nil) ),
inference(paramod,[status(thm)],[c_330,c_13390]) ).
cnf(c_13427,plain,
( frontsegP(sk4,sk5)
| sk1 = nil ),
inference(resolve,[status(thm)],[c_7882,c_60]) ).
cnf(c_13480,plain,
( neq(sk4,nil)
| neq(sk4,nil) ),
inference(resolve,[status(thm)],[c_7882,c_332]) ).
cnf(c_13433,plain,
neq(sk4,nil),
inference(copy,[status(thm)],[c_13480]) ).
cnf(c_13435,plain,
frontsegP(sk1,sk5),
inference(resolve,[status(thm)],[c_13433,c_329]) ).
cnf(c_13436,plain,
neq(sk5,nil),
inference(resolve,[status(thm)],[c_13433,c_61]) ).
cnf(c_13437,plain,
frontsegP(sk4,sk5),
inference(resolve,[status(thm)],[c_13433,c_60]) ).
cnf(c_13481,plain,
( ~ frontsegP(sk1,sk5)
| ~ frontsegP(sk4,sk5)
| sk1 != nil ),
inference(resolve,[status(thm)],[c_13436,c_11874]) ).
cnf(c_13482,plain,
( ~ frontsegP(sk1,sk5)
| sk1 != nil ),
inference(resolve,[status(thm)],[c_13437,c_13481]) ).
cnf(c_13438,plain,
sk1 != nil,
inference(resolve,[status(thm)],[c_13435,c_13482]) ).
cnf(c_13483,plain,
( ~ frontsegP(sk1,sk5)
| ~ frontsegP(sk4,sk5)
| sk4 = nil ),
inference(resolve,[status(thm)],[c_13436,c_10497]) ).
cnf(c_13484,plain,
( ~ frontsegP(sk1,sk5)
| sk4 = nil ),
inference(resolve,[status(thm)],[c_13437,c_13483]) ).
cnf(c_13441,plain,
sk4 = nil,
inference(resolve,[status(thm)],[c_13435,c_13484]) ).
cnf(c_13485,plain,
( ~ neq(sk5,nil)
| sk5 != sk4
| neq(nil,nil) ),
inference(paramod,[status(thm)],[c_13441,c_13423]) ).
cnf(c_13486,plain,
( ~ neq(sk5,nil)
| sk5 != nil
| neq(nil,nil) ),
inference(paramod,[status(thm)],[c_13441,c_13485]) ).
cnf(c_13487,plain,
( ~ neq(sk5,nil)
| sk5 != nil ),
inference(resolve,[status(thm)],[c_9420,c_13486]) ).
cnf(c_13442,plain,
sk5 != nil,
inference(resolve,[status(thm)],[c_13436,c_13487]) ).
cnf(c_13488,plain,
( frontsegP(nil,sk5)
| sk1 = nil ),
inference(paramod,[status(thm)],[c_13441,c_13427]) ).
cnf(c_13445,plain,
frontsegP(nil,sk5),
inference(resolve,[status(thm)],[c_13438,c_13488]) ).
cnf(c_13489,plain,
( sk5 = nil
| ~ frontsegP(nil,sk5) ),
inference(resolve,[status(thm)],[c_13438,c_10716]) ).
cnf(c_13490,plain,
sk5 = nil,
inference(resolve,[status(thm)],[c_13445,c_13489]) ).
cnf(c_13470,plain,
$false,
inference(resolve,[status(thm)],[c_13442,c_13490]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC016-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.67 % Computer : n013.cluster.edu
% 0.16/5.67 % Model : x86_64 x86_64
% 0.16/5.67 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.67 % Memory : 8046.5625MB
% 0.16/5.67 % OS : Linux 6.8.0-71-generic
% 0.16/5.67 % CPULimit : 300
% 0.16/5.67 % WCLimit : 300
% 0.16/5.67 % DateTime : Sat Sep 26 12:03:42 UTC 2026
% 0.16/5.67 % CPUTime :
% 0.16/5.68 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.68 % Process 2685758 was started by sandbox on n013,
% 0.16/5.68 % Sat Sep 26 12:03:42 2026
% 0.16/5.68 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/5.69
% 0.16/5.69 % From the command line: assign(max_seconds, 300).
% 39.25/11.34
% 39.25/11.34 % given #500 (I,wt=40): 568 app(app(A,cons(B,A)),cons(C,D)) != A | -ssList(D) | -ssList(A) | -ssItem(C) | -ssItem(B) | lt(B,C) | lt(C,B) | -lt(skaf59(A),skaf60(A)). [factor(302,c,f)].
% 39.25/11.34
% 39.25/11.34 % given #1000 (F,wt=9): 9434 -neq(skaf62(A),skaf62(A)). [resolve(398,b,199,a)].
% 39.25/11.34
% 39.25/11.34 % SZS status Unsatisfiable for theBenchmark
% 39.25/11.34
% 39.25/11.34 % Proof 1 at 4.21 (+ 1.38) seconds.
% 39.25/11.34 % Length of proof is 50.
% 39.25/11.34 % Level of proof is 10.
% 39.25/11.34 % Maximum clause weight is 16.000.
% 39.25/11.34 % Given clauses 1037.
% 39.25/11.34
% 39.25/11.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------