%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC104-1 : 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 : n017.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 08:56:50 AM UTC 2026
% Result : Unsatisfiable 92.08s 13.14s
% Output : CNFRefutation 92.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of formulae : 60 ( 34 unt; 0 def)
% Number of atoms : 111 ( 48 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 115 ( 64 ~; 51 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 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 : 28 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_13,axiom,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
file('theBenchmark.p',co1_13) ).
cnf(c_51,plain,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(clausify,[status(thm)],[co1_13]) ).
fof(co1_12,axiom,
( nil != sk3
| nil = sk4 ),
file('theBenchmark.p',co1_12) ).
cnf(c_52,plain,
( nil != sk3
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_12]) ).
cnf(c_18577,plain,
( nil != sk3
| sk4 = nil ),
inference(copy,[status(thm)],[c_52]) ).
cnf(c_53,plain,
( sk3 != nil
| sk4 = nil ),
inference(copy,[status(thm)],[c_18577]) ).
fof(co1_9,axiom,
app(sk3,sk5) = sk4,
file('theBenchmark.p',co1_9) ).
cnf(c_56,plain,
app(sk3,sk5) = sk4,
inference(clausify,[status(thm)],[co1_9]) ).
fof(co1_8,axiom,
ssList(sk5),
file('theBenchmark.p',co1_8) ).
cnf(c_57,plain,
ssList(sk5),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
neq(sk2,nil),
file('theBenchmark.p',co1_7) ).
cnf(c_58,plain,
neq(sk2,nil),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_59,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_60,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_61,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_62,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(co1_2,axiom,
ssList(sk2),
file('theBenchmark.p',co1_2) ).
cnf(c_63,plain,
ssList(sk2),
inference(clausify,[status(thm)],[co1_2]) ).
fof(co1_1,axiom,
ssList(sk1),
file('theBenchmark.p',co1_1) ).
cnf(c_64,plain,
ssList(sk1),
inference(clausify,[status(thm)],[co1_1]) ).
fof(clause144,axiom,
! [VAR_0,VAR_1,VAR_2] :
( frontsegP(VAR_2,VAR_0)
| ~ ssList(VAR_2)
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| app(VAR_0,VAR_1) != VAR_2 ),
file('theBenchmark.p',clause144) ).
cnf(c_98,plain,
( frontsegP(C,A)
| ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| app(A,B) != C ),
inference(clausify,[status(thm)],[clause144]) ).
fof(clause119,axiom,
! [VAR_0,VAR_1] :
( nil = VAR_1
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| app(VAR_0,VAR_1) != nil ),
file('theBenchmark.p',clause119) ).
cnf(c_121,plain,
( nil = B
| ~ ssList(A)
| ~ ssList(B)
| app(A,B) != nil ),
inference(clausify,[status(thm)],[clause119]) ).
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(clause74,axiom,
! [VAR_0] :
( app(nil,VAR_0) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause74) ).
cnf(c_157,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause74]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_217,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_831,plain,
neq(sk4,nil),
inference(paramod,[status(thm)],[c_60,c_58]) ).
cnf(c_1001,plain,
( frontsegP(B,sk1)
| ~ ssList(B)
| ~ ssList(A)
| app(sk1,A) != B ),
inference(resolve,[status(thm)],[c_98,c_64]) ).
cnf(c_18578,plain,
( nil = sk3
| ~ ssList(A)
| app(A,sk3) != nil ),
inference(resolve,[status(thm)],[c_121,c_62]) ).
cnf(c_1068,plain,
( sk3 = nil
| ~ ssList(A)
| app(A,sk3) != nil ),
inference(copy,[status(thm)],[c_18578]) ).
cnf(c_1108,plain,
( sk1 = A
| neq(sk1,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_140,c_64]) ).
cnf(c_1145,plain,
app(nil,sk1) = sk1,
inference(resolve,[status(thm)],[c_157,c_64]) ).
cnf(c_18579,plain,
( ~ ssList(sk4)
| ~ ssList(nil)
| sk4 != nil ),
inference(resolve,[status(thm)],[c_831,c_125]) ).
cnf(c_18580,plain,
( ~ ssList(sk4)
| sk4 != nil ),
inference(resolve,[status(thm)],[c_217,c_18579]) ).
cnf(c_4889,plain,
sk4 != nil,
inference(resolve,[status(thm)],[c_61,c_18580]) ).
cnf(c_4902,plain,
sk3 != nil,
inference(resolve,[status(thm)],[c_4889,c_53]) ).
cnf(c_4911,plain,
( ~ ssList(A)
| app(A,sk3) != nil ),
inference(resolve,[status(thm)],[c_4902,c_1068]) ).
cnf(c_10324,plain,
app(nil,sk3) != nil,
inference(resolve,[status(thm)],[c_4911,c_217]) ).
cnf(c_11623,plain,
app(nil,sk3) = sk1,
inference(paramod,[status(thm)],[c_59,c_1145]) ).
cnf(c_13942,plain,
sk1 != nil,
inference(paramod,[status(thm)],[c_11623,c_10324]) ).
cnf(c_18581,plain,
( sk1 = nil
| neq(sk1,nil) ),
inference(resolve,[status(thm)],[c_1108,c_217]) ).
cnf(c_14934,plain,
neq(sk1,nil),
inference(resolve,[status(thm)],[c_13942,c_18581]) ).
cnf(c_14962,plain,
~ frontsegP(sk2,sk1),
inference(resolve,[status(thm)],[c_14934,c_51]) ).
cnf(c_18582,plain,
( frontsegP(sk2,sk1)
| ~ ssList(A)
| app(sk1,A) != sk2 ),
inference(resolve,[status(thm)],[c_1001,c_63]) ).
cnf(c_16582,plain,
( ~ ssList(A)
| app(sk1,A) != sk2 ),
inference(resolve,[status(thm)],[c_14962,c_18582]) ).
cnf(c_18107,plain,
app(sk1,sk5) != sk2,
inference(resolve,[status(thm)],[c_16582,c_57]) ).
cnf(c_18275,plain,
app(sk3,sk5) != sk2,
inference(paramod,[status(thm)],[c_59,c_18107]) ).
cnf(c_18583,plain,
sk4 != sk2,
inference(paramod,[status(thm)],[c_56,c_18275]) ).
cnf(c_18584,plain,
sk2 != sk4,
inference(copy,[status(thm)],[c_18583]) ).
cnf(c_18576,plain,
$false,
inference(resolve,[status(thm)],[c_60,c_18584]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC104-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n017.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 12:10:48 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 675302 was started by sandbox2 on n017,
% 0.15/0.43 % Sat Sep 26 12:10:48 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.45
% 0.15/0.45 % From the command line: assign(max_seconds, 300).
% 92.08/13.14
% 92.08/13.14 % given #500 (I,wt=35): 556 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(294,e,f),merge(g)].
% 92.08/13.14
% 92.08/13.14 % given #1000 (W,wt=8): 3062 segmentP(skaf77(A),nil). [resolve(207,a,169,a)].
% 92.08/13.14
% 92.08/13.14 % given #1500 (T,wt=7): 13956 ssList(tl(sk1)). [back_unit_del(1140),unit_del(b,13942)].
% 92.08/13.14
% 92.08/13.14 % SZS status Unsatisfiable for theBenchmark
% 92.08/13.14
% 92.08/13.14 % Proof 1 at 3.36 (+ 1.21) seconds.
% 92.08/13.14 % Length of proof is 35.
% 92.08/13.14 % Level of proof is 12.
% 92.08/13.14 % Maximum clause weight is 18.000.
% 92.08/13.14 % Given clauses 1894.
% 92.08/13.14
% 92.08/13.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------