%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC020-1 : 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 : n009.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 08:56:33 AM UTC 2026
% Result : Unsatisfiable 21.49s 8.24s
% Output : CNFRefutation 21.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of formulae : 71 ( 27 unt; 0 def)
% Number of atoms : 161 ( 50 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 168 ( 78 ~; 90 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 24 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_12,axiom,
( frontsegP(sk4,sk3)
| nil = sk3 ),
file('theBenchmark.p',co1_12) ).
cnf(c_51,plain,
( frontsegP(sk4,sk3)
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_12]) ).
cnf(c_52,plain,
( frontsegP(sk4,sk3)
| sk3 = nil ),
inference(copy,[status(thm)],[c_51]) ).
fof(co1_10,axiom,
( frontsegP(sk4,sk3)
| nil = sk4 ),
file('theBenchmark.p',co1_10) ).
cnf(c_55,plain,
( frontsegP(sk4,sk3)
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_10]) ).
cnf(c_56,plain,
( frontsegP(sk4,sk3)
| sk4 = nil ),
inference(copy,[status(thm)],[c_55]) ).
fof(co1_9,axiom,
( neq(sk3,nil)
| nil = sk4 ),
file('theBenchmark.p',co1_9) ).
cnf(c_57,plain,
( neq(sk3,nil)
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_58,plain,
( neq(sk3,nil)
| sk4 = nil ),
inference(copy,[status(thm)],[c_57]) ).
fof(co1_8,axiom,
( nil != sk1
| nil != sk2 ),
file('theBenchmark.p',co1_8) ).
cnf(c_59,plain,
( nil != sk1
| nil != sk2 ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_11325,plain,
( nil != sk1
| sk2 != nil ),
inference(copy,[status(thm)],[c_59]) ).
cnf(c_60,plain,
( sk1 != nil
| sk2 != nil ),
inference(copy,[status(thm)],[c_11325]) ).
fof(co1_7,axiom,
! [VAR_0] :
( ~ frontsegP(sk1,VAR_0)
| ~ frontsegP(sk2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',co1_7) ).
cnf(c_61,plain,
( ~ frontsegP(sk1,A)
| ~ frontsegP(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_62,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_63,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_64,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_65,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(co1_2,axiom,
ssList(sk2),
file('theBenchmark.p',co1_2) ).
cnf(c_66,plain,
ssList(sk2),
inference(clausify,[status(thm)],[co1_2]) ).
fof(co1_1,axiom,
ssList(sk1),
file('theBenchmark.p',co1_1) ).
cnf(c_67,plain,
ssList(sk1),
inference(clausify,[status(thm)],[co1_1]) ).
fof(clause154,axiom,
! [VAR_0,VAR_1,VAR_2] :
( frontsegP(VAR_0,VAR_2)
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| ~ ssList(VAR_2)
| ~ frontsegP(VAR_1,VAR_2)
| ~ frontsegP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause154) ).
cnf(c_91,plain,
( frontsegP(A,C)
| ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ~ frontsegP(B,C)
| ~ frontsegP(A,B) ),
inference(clausify,[status(thm)],[clause154]) ).
fof(clause129,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| ~ ssList(VAR_1)
| ~ ssList(VAR_0)
| ~ frontsegP(VAR_1,VAR_0)
| ~ frontsegP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause129) ).
cnf(c_115,plain,
( B = A
| ~ ssList(B)
| ~ ssList(A)
| ~ frontsegP(B,A)
| ~ frontsegP(A,B) ),
inference(clausify,[status(thm)],[clause129]) ).
fof(clause83,axiom,
! [VAR_0] :
( frontsegP(nil,VAR_0)
| ~ ssList(VAR_0)
| nil != VAR_0 ),
file('theBenchmark.p',clause83) ).
cnf(c_153,plain,
( frontsegP(nil,A)
| ~ ssList(A)
| nil != A ),
inference(clausify,[status(thm)],[clause83]) ).
fof(clause61,axiom,
! [VAR_0] :
( frontsegP(VAR_0,VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause61) ).
cnf(c_167,plain,
( frontsegP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause61]) ).
fof(clause60,axiom,
! [VAR_0] :
( frontsegP(VAR_0,nil)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause60) ).
cnf(c_168,plain,
( frontsegP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause60]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_220,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_11326,plain,
( sk4 = nil
| ~ frontsegP(sk1,sk3)
| ~ frontsegP(sk2,sk3)
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_61,c_58]) ).
cnf(c_831,plain,
( sk4 = nil
| ~ frontsegP(sk1,sk3)
| ~ frontsegP(sk2,sk3) ),
inference(resolve,[status(thm)],[c_65,c_11326]) ).
cnf(c_11327,plain,
( sk4 = nil
| frontsegP(A,sk3)
| ~ ssList(A)
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ frontsegP(A,sk4) ),
inference(resolve,[status(thm)],[c_91,c_56]) ).
cnf(c_11328,plain,
( sk4 = nil
| frontsegP(A,sk3)
| ~ ssList(A)
| ~ ssList(sk4)
| ~ frontsegP(A,sk4) ),
inference(resolve,[status(thm)],[c_65,c_11327]) ).
cnf(c_915,plain,
( sk4 = nil
| frontsegP(A,sk3)
| ~ ssList(A)
| ~ frontsegP(A,sk4) ),
inference(resolve,[status(thm)],[c_64,c_11328]) ).
cnf(c_11329,plain,
( sk3 = nil
| frontsegP(A,sk3)
| ~ ssList(A)
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ frontsegP(A,sk4) ),
inference(resolve,[status(thm)],[c_91,c_52]) ).
cnf(c_11330,plain,
( sk3 = nil
| frontsegP(A,sk3)
| ~ ssList(A)
| ~ ssList(sk4)
| ~ frontsegP(A,sk4) ),
inference(resolve,[status(thm)],[c_65,c_11329]) ).
cnf(c_916,plain,
( sk3 = nil
| frontsegP(A,sk3)
| ~ ssList(A)
| ~ frontsegP(A,sk4) ),
inference(resolve,[status(thm)],[c_64,c_11330]) ).
cnf(c_11331,plain,
( frontsegP(nil,sk4)
| nil != sk4 ),
inference(resolve,[status(thm)],[c_153,c_64]) ).
cnf(c_1080,plain,
( frontsegP(nil,sk4)
| sk4 != nil ),
inference(copy,[status(thm)],[c_11331]) ).
cnf(c_1105,plain,
frontsegP(sk1,sk1),
inference(resolve,[status(thm)],[c_167,c_67]) ).
cnf(c_1106,plain,
frontsegP(sk2,sk2),
inference(resolve,[status(thm)],[c_167,c_66]) ).
cnf(c_1111,plain,
frontsegP(sk3,nil),
inference(resolve,[status(thm)],[c_168,c_65]) ).
cnf(c_4836,plain,
frontsegP(sk1,sk3),
inference(paramod,[status(thm)],[c_62,c_1105]) ).
cnf(c_4838,plain,
( sk4 = nil
| ~ frontsegP(sk2,sk3) ),
inference(resolve,[status(thm)],[c_4836,c_831]) ).
cnf(c_4845,plain,
frontsegP(sk2,sk4),
inference(paramod,[status(thm)],[c_63,c_1106]) ).
cnf(c_11332,plain,
( sk3 = nil
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ frontsegP(nil,sk3) ),
inference(resolve,[status(thm)],[c_1111,c_115]) ).
cnf(c_11333,plain,
( sk3 = nil
| ~ ssList(sk3)
| ~ frontsegP(nil,sk3) ),
inference(resolve,[status(thm)],[c_220,c_11332]) ).
cnf(c_4976,plain,
( sk3 = nil
| ~ frontsegP(nil,sk3) ),
inference(resolve,[status(thm)],[c_65,c_11333]) ).
cnf(c_11334,plain,
( sk4 = nil
| frontsegP(sk2,sk3)
| ~ ssList(sk2) ),
inference(resolve,[status(thm)],[c_915,c_4845]) ).
cnf(c_10993,plain,
( sk4 = nil
| frontsegP(sk2,sk3) ),
inference(resolve,[status(thm)],[c_66,c_11334]) ).
cnf(c_11335,plain,
( sk4 = nil
| sk4 = nil ),
inference(resolve,[status(thm)],[c_10993,c_4838]) ).
cnf(c_11035,plain,
sk4 = nil,
inference(copy,[status(thm)],[c_11335]) ).
cnf(c_11039,plain,
frontsegP(nil,sk4),
inference(resolve,[status(thm)],[c_11035,c_1080]) ).
cnf(c_11048,plain,
sk2 = nil,
inference(paramod,[status(thm)],[c_11035,c_63]) ).
cnf(c_11074,plain,
sk1 != nil,
inference(resolve,[status(thm)],[c_11048,c_60]) ).
cnf(c_11336,plain,
( sk3 = nil
| frontsegP(nil,sk3)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_11039,c_916]) ).
cnf(c_11125,plain,
( sk3 = nil
| frontsegP(nil,sk3) ),
inference(resolve,[status(thm)],[c_220,c_11336]) ).
cnf(c_11292,plain,
sk3 != nil,
inference(paramod,[status(thm)],[c_62,c_11074]) ).
cnf(c_11293,plain,
frontsegP(nil,sk3),
inference(resolve,[status(thm)],[c_11292,c_11125]) ).
cnf(c_11337,plain,
sk3 = nil,
inference(resolve,[status(thm)],[c_11293,c_4976]) ).
cnf(c_11324,plain,
$false,
inference(resolve,[status(thm)],[c_11292,c_11337]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC020-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n009.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 12:04:49 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.39 % Process 53682 was started by sandbox on n009,
% 0.11/5.39 % Sat Sep 26 12:04:49 2026
% 0.11/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/5.40
% 0.16/5.40 % From the command line: assign(max_seconds, 300).
% 21.49/8.24
% 21.49/8.24 % given #500 (I,wt=35): 560 app(app(A,cons(B,C)),cons(B,D)) != C | -ssList(D) | -ssList(C) | -ssList(A) | -ssItem(B) | lt(B,B) | -lt(skaf59(C),skaf60(C)). [factor(299,e,f),merge(g)].
% 21.49/8.24
% 21.49/8.24 % given #1000 (F,wt=13): 4824 cons(skac2,skaf43(A,B)) != nil. [resolve(3365,b,176,a)].
% 21.49/8.24
% 21.49/8.24 % SZS status Unsatisfiable for theBenchmark
% 21.49/8.24
% 21.49/8.24 % Proof 1 at 2.11 (+ 0.68) seconds.
% 21.49/8.24 % Length of proof is 41.
% 21.49/8.24 % Level of proof is 9.
% 21.49/8.24 % Maximum clause weight is 17.000.
% 21.49/8.24 % Given clauses 1288.
% 21.49/8.24
% 21.49/8.24 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------