%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC071-1 : 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 : 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 08:56:44 AM UTC 2026
% Result : Unsatisfiable 221.08s 30.57s
% Output : CNFRefutation 221.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of formulae : 79 ( 18 unt; 0 def)
% Number of atoms : 188 ( 83 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 199 ( 90 ~; 109 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 33 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_20,axiom,
( nil = sk3
| app(app(sk6,sk3),sk7) = sk4 ),
file('theBenchmark.p',co1_20) ).
cnf(c_55,plain,
( nil = sk3
| app(app(sk6,sk3),sk7) = sk4 ),
inference(clausify,[status(thm)],[co1_20]) ).
cnf(c_56,plain,
( sk3 = nil
| app(app(sk6,sk3),sk7) = sk4 ),
inference(copy,[status(thm)],[c_55]) ).
fof(co1_18,axiom,
( nil = sk3
| ssList(sk7) ),
file('theBenchmark.p',co1_18) ).
cnf(c_59,plain,
( nil = sk3
| ssList(sk7) ),
inference(clausify,[status(thm)],[co1_18]) ).
cnf(c_60,plain,
( sk3 = nil
| ssList(sk7) ),
inference(copy,[status(thm)],[c_59]) ).
fof(co1_17,axiom,
( nil = sk3
| ssList(sk6) ),
file('theBenchmark.p',co1_17) ).
cnf(c_61,plain,
( nil = sk3
| ssList(sk6) ),
inference(clausify,[status(thm)],[co1_17]) ).
cnf(c_62,plain,
( sk3 = nil
| ssList(sk6) ),
inference(copy,[status(thm)],[c_61]) ).
fof(co1_13,axiom,
( nil = sk4
| cons(sk5,nil) = sk3 ),
file('theBenchmark.p',co1_13) ).
cnf(c_69,plain,
( nil = sk4
| cons(sk5,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_70,plain,
( sk4 = nil
| cons(sk5,nil) = sk3 ),
inference(copy,[status(thm)],[c_69]) ).
fof(co1_9,axiom,
( nil = sk4
| ssItem(sk5) ),
file('theBenchmark.p',co1_9) ).
cnf(c_77,plain,
( nil = sk4
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_78,plain,
( sk4 = nil
| ssItem(sk5) ),
inference(copy,[status(thm)],[c_77]) ).
fof(co1_8,axiom,
( nil != sk1
| nil != sk2 ),
file('theBenchmark.p',co1_8) ).
cnf(c_79,plain,
( nil != sk1
| nil != sk2 ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_9729,plain,
( nil != sk1
| sk2 != nil ),
inference(copy,[status(thm)],[c_79]) ).
cnf(c_80,plain,
( sk1 != nil
| sk2 != nil ),
inference(copy,[status(thm)],[c_9729]) ).
fof(co1_7,axiom,
! [VAR_0] :
( ~ segmentP(sk1,VAR_0)
| ~ segmentP(sk2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',co1_7) ).
cnf(c_81,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(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_82,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_83,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_84,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_85,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(clause173,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( segmentP(VAR_3,VAR_1)
| ~ ssList(VAR_3)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0)
| ~ ssList(VAR_2)
| app(app(VAR_0,VAR_1),VAR_2) != VAR_3 ),
file('theBenchmark.p',clause173) ).
cnf(c_95,plain,
( segmentP(D,B)
| ~ ssList(D)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != D ),
inference(clausify,[status(thm)],[clause173]) ).
fof(clause116,axiom,
! [VAR_0,VAR_1] :
( singletonP(VAR_1)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0)
| cons(VAR_0,nil) != VAR_1 ),
file('theBenchmark.p',clause116) ).
cnf(c_147,plain,
( singletonP(B)
| ~ ssList(B)
| ~ ssItem(A)
| cons(A,nil) != B ),
inference(clausify,[status(thm)],[clause116]) ).
fof(clause101,axiom,
! [VAR_0] :
( cons(skaf44(VAR_0),nil) = VAR_0
| ~ ssList(VAR_0)
| ~ singletonP(VAR_0) ),
file('theBenchmark.p',clause101) ).
cnf(c_162,plain,
( cons(skaf44(A),nil) = A
| ~ ssList(A)
| ~ singletonP(A) ),
inference(clausify,[status(thm)],[clause101]) ).
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_163,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause98,axiom,
! [VAR_0,VAR_1] :
( ~ ssList(VAR_1)
| ~ ssItem(VAR_0)
| cons(VAR_0,VAR_1) != nil ),
file('theBenchmark.p',clause98) ).
cnf(c_165,plain,
( ~ ssList(B)
| ~ ssItem(A)
| cons(A,B) != nil ),
inference(clausify,[status(thm)],[clause98]) ).
fof(clause57,axiom,
! [VAR_0] :
( segmentP(VAR_0,VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause57) ).
cnf(c_191,plain,
( segmentP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause57]) ).
fof(clause47,axiom,
! [VAR_0] : ssItem(skaf44(VAR_0)),
file('theBenchmark.p',clause47) ).
cnf(c_201,plain,
ssItem(skaf44(A)),
inference(clausify,[status(thm)],[clause47]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_240,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_9730,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(sk4,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_83,c_81]) ).
cnf(c_344,plain,
( ~ segmentP(sk3,A)
| ~ segmentP(sk4,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_82,c_9730]) ).
cnf(c_9731,plain,
( sk1 != nil
| sk4 != nil ),
inference(paramod,[status(thm)],[c_83,c_80]) ).
cnf(c_345,plain,
( sk3 != nil
| sk4 != nil ),
inference(paramod,[status(thm)],[c_82,c_9731]) ).
cnf(c_9732,plain,
( sk3 = nil
| segmentP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_95,c_56]) ).
cnf(c_9733,plain,
( sk3 = nil
| segmentP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk6)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_85,c_9732]) ).
cnf(c_924,plain,
( sk3 = nil
| segmentP(sk4,sk3)
| ~ ssList(sk6)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_84,c_9733]) ).
cnf(c_9734,plain,
( sk4 = nil
| singletonP(sk3)
| ~ ssList(sk3)
| ~ ssItem(sk5) ),
inference(resolve,[status(thm)],[c_147,c_70]) ).
cnf(c_1511,plain,
( sk4 = nil
| singletonP(sk3)
| ~ ssItem(sk5) ),
inference(resolve,[status(thm)],[c_85,c_9734]) ).
cnf(c_1616,plain,
( sk3 = A
| neq(sk3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_163,c_85]) ).
cnf(c_1783,plain,
segmentP(sk3,sk3),
inference(resolve,[status(thm)],[c_191,c_85]) ).
cnf(c_5168,plain,
( ~ ssItem(A)
| cons(A,nil) != nil ),
inference(resolve,[status(thm)],[c_240,c_165]) ).
cnf(c_9735,plain,
( ~ segmentP(sk3,sk3)
| ~ segmentP(sk4,sk3)
| ~ neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_344,c_85]) ).
cnf(c_5262,plain,
( ~ segmentP(sk4,sk3)
| ~ neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_1783,c_9735]) ).
cnf(c_9736,plain,
( sk4 = nil
| sk4 = nil
| singletonP(sk3) ),
inference(resolve,[status(thm)],[c_1511,c_78]) ).
cnf(c_7156,plain,
( sk4 = nil
| singletonP(sk3) ),
inference(copy,[status(thm)],[c_9736]) ).
cnf(c_9737,plain,
( cons(skaf44(sk3),nil) = sk3
| ~ ssList(sk3)
| sk4 = nil ),
inference(resolve,[status(thm)],[c_7156,c_162]) ).
cnf(c_7171,plain,
( cons(skaf44(sk3),nil) = sk3
| sk4 = nil ),
inference(resolve,[status(thm)],[c_85,c_9737]) ).
cnf(c_7254,plain,
( sk3 = nil
| neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_1616,c_240]) ).
cnf(c_7286,plain,
( ~ segmentP(sk4,sk3)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_7254,c_5262]) ).
cnf(c_8725,plain,
cons(skaf44(A),nil) != nil,
inference(resolve,[status(thm)],[c_5168,c_201]) ).
cnf(c_9738,plain,
( sk3 = nil
| sk3 = nil
| segmentP(sk4,sk3)
| ~ ssList(sk6) ),
inference(resolve,[status(thm)],[c_924,c_60]) ).
cnf(c_9446,plain,
( sk3 = nil
| segmentP(sk4,sk3)
| ~ ssList(sk6) ),
inference(copy,[status(thm)],[c_9738]) ).
cnf(c_9739,plain,
( sk3 = nil
| sk3 = nil
| segmentP(sk4,sk3) ),
inference(resolve,[status(thm)],[c_9446,c_62]) ).
cnf(c_9511,plain,
( sk3 = nil
| segmentP(sk4,sk3) ),
inference(copy,[status(thm)],[c_9739]) ).
cnf(c_9740,plain,
( sk3 = nil
| sk3 = nil ),
inference(resolve,[status(thm)],[c_9511,c_7286]) ).
cnf(c_9512,plain,
sk3 = nil,
inference(copy,[status(thm)],[c_9740]) ).
cnf(c_9741,plain,
( cons(skaf44(nil),nil) = sk3
| sk4 = nil ),
inference(paramod,[status(thm)],[c_9512,c_7171]) ).
cnf(c_9742,plain,
( cons(skaf44(nil),nil) = nil
| sk4 = nil ),
inference(paramod,[status(thm)],[c_9512,c_9741]) ).
cnf(c_9612,plain,
sk4 = nil,
inference(resolve,[status(thm)],[c_8725,c_9742]) ).
cnf(c_9743,plain,
( sk3 != nil
| nil != nil ),
inference(paramod,[status(thm)],[c_9612,c_345]) ).
cnf(c_9744,plain,
( nil != nil
| nil != nil ),
inference(paramod,[status(thm)],[c_9512,c_9743]) ).
cnf(c_9745,plain,
nil != nil,
inference(copy,[status(thm)],[c_9744]) ).
cnf(c_9728,plain,
$false,
inference(copy,[status(thm)],[c_9745]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC071-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 12:10:47 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2092433 was started by sandbox2 on n005,
% 0.08/0.36 % Sat Sep 26 12:10:47 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 221.08/30.57
% 221.08/30.57 % given #500 (I,wt=52): 567 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(skaf60(A),skaf59(A)). [factor(311,c,f)].
% 221.08/30.57
% 221.08/30.57 % given #1000 (T,wt=13): 5085 -lt(A,skac3) | -ssItem(A) | leq(A,skac3). [resolve(239,a,160,b)].
% 221.08/30.57
% 221.08/30.57 % given #1500 (W,wt=11): 9423 sk3 = nil | -neq(nil,sk4). [resolve(9409,a,6421,a)].
% 221.08/30.57
% 221.08/30.57 % SZS status Unsatisfiable for theBenchmark
% 221.08/30.57
% 221.08/30.57 % Proof 1 at 4.21 (+ 1.71) seconds.
% 221.08/30.57 % Length of proof is 43.
% 221.08/30.57 % Level of proof is 7.
% 221.08/30.57 % Maximum clause weight is 35.000.
% 221.08/30.57 % Given clauses 1519.
% 221.08/30.57
% 221.08/30.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------