%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC067-1 : 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 : n020.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 08:56:43 AM UTC 2026
% Result : Unsatisfiable 29.58s 4.37s
% Output : CNFRefutation 29.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 69 ( 27 unt; 0 def)
% Number of atoms : 152 ( 50 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 163 ( 80 ~; 83 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_16,axiom,
( neq(sk2,nil)
| nil != sk1 ),
file('theBenchmark.p',co1_16) ).
cnf(c_53,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(clausify,[status(thm)],[co1_16]) ).
cnf(c_54,plain,
( neq(sk2,nil)
| sk1 != nil ),
inference(copy,[status(thm)],[c_53]) ).
fof(co1_15,axiom,
! [VAR_0] :
( ~ segmentP(sk1,VAR_0)
| ~ segmentP(sk2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil = sk2 ),
file('theBenchmark.p',co1_15) ).
cnf(c_55,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_15]) ).
cnf(c_56,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sk2 = nil ),
inference(copy,[status(thm)],[c_55]) ).
fof(co1_14,axiom,
( neq(sk2,nil)
| nil = sk2 ),
file('theBenchmark.p',co1_14) ).
cnf(c_57,plain,
( neq(sk2,nil)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_14]) ).
cnf(c_58,plain,
( neq(sk2,nil)
| sk2 = nil ),
inference(copy,[status(thm)],[c_57]) ).
fof(co1_13,axiom,
( nil != sk3
| nil = sk4 ),
file('theBenchmark.p',co1_13) ).
cnf(c_59,plain,
( nil != sk3
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_21089,plain,
( nil != sk3
| sk4 = nil ),
inference(copy,[status(thm)],[c_59]) ).
cnf(c_60,plain,
( sk3 != nil
| sk4 = nil ),
inference(copy,[status(thm)],[c_21089]) ).
fof(co1_9,axiom,
app(app(sk5,sk3),sk6) = sk4,
file('theBenchmark.p',co1_9) ).
cnf(c_64,plain,
app(app(sk5,sk3),sk6) = sk4,
inference(clausify,[status(thm)],[co1_9]) ).
fof(co1_8,axiom,
ssList(sk6),
file('theBenchmark.p',co1_8) ).
cnf(c_65,plain,
ssList(sk6),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
ssList(sk5),
file('theBenchmark.p',co1_7) ).
cnf(c_66,plain,
ssList(sk5),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_67,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_68,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_69,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_68]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_70,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
cnf(c_71,plain,
ssList(sk2),
inference(paramod,[status(thm)],[c_69,c_70]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_72,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_81,plain,
( segmentP(D,B)
| ~ ssList(D)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != D ),
inference(clausify,[status(thm)],[clause173]) ).
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_134,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_149,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause80,axiom,
! [VAR_0] :
( nil = VAR_0
| ~ ssList(VAR_0)
| ~ segmentP(nil,VAR_0) ),
file('theBenchmark.p',clause80) ).
cnf(c_162,plain,
( nil = A
| ~ ssList(A)
| ~ segmentP(nil,A) ),
inference(clausify,[status(thm)],[clause80]) ).
fof(clause57,axiom,
! [VAR_0] :
( segmentP(VAR_0,VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause57) ).
cnf(c_177,plain,
( segmentP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause57]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_226,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_332,plain,
( ~ segmentP(sk3,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sk2 = nil ),
inference(paramod,[status(thm)],[c_67,c_56]) ).
cnf(c_333,plain,
( neq(sk2,nil)
| sk3 != nil ),
inference(paramod,[status(thm)],[c_67,c_54]) ).
cnf(c_335,plain,
app(app(sk5,sk3),sk6) = sk2,
inference(paramod,[status(thm)],[c_69,c_64]) ).
cnf(c_336,plain,
( sk3 != nil
| sk2 = nil ),
inference(paramod,[status(thm)],[c_69,c_60]) ).
cnf(c_1496,plain,
( sk3 = A
| neq(sk3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_149,c_72]) ).
cnf(c_21090,plain,
( nil = sk3
| ~ segmentP(nil,sk3) ),
inference(resolve,[status(thm)],[c_162,c_72]) ).
cnf(c_1555,plain,
( sk3 = nil
| ~ segmentP(nil,sk3) ),
inference(copy,[status(thm)],[c_21090]) ).
cnf(c_1597,plain,
segmentP(sk3,sk3),
inference(resolve,[status(thm)],[c_177,c_72]) ).
cnf(c_21091,plain,
( ~ segmentP(sk3,sk3)
| ~ segmentP(sk2,sk3)
| ~ neq(sk3,nil)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_332,c_72]) ).
cnf(c_8447,plain,
( ~ segmentP(sk2,sk3)
| ~ neq(sk3,nil)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_1597,c_21091]) ).
cnf(c_21092,plain,
( segmentP(sk2,sk3)
| ~ ssList(sk2)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssList(sk6) ),
inference(resolve,[status(thm)],[c_335,c_81]) ).
cnf(c_21093,plain,
( segmentP(sk2,sk3)
| ~ ssList(sk2)
| ~ ssList(sk3)
| ~ ssList(sk5) ),
inference(resolve,[status(thm)],[c_65,c_21092]) ).
cnf(c_21094,plain,
( segmentP(sk2,sk3)
| ~ ssList(sk2)
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_66,c_21093]) ).
cnf(c_21095,plain,
( segmentP(sk2,sk3)
| ~ ssList(sk2) ),
inference(resolve,[status(thm)],[c_72,c_21094]) ).
cnf(c_8486,plain,
segmentP(sk2,sk3),
inference(resolve,[status(thm)],[c_71,c_21095]) ).
cnf(c_8497,plain,
( ~ neq(sk3,nil)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_8486,c_8447]) ).
cnf(c_10883,plain,
( segmentP(nil,sk3)
| neq(sk2,nil) ),
inference(paramod,[status(thm)],[c_58,c_8486]) ).
cnf(c_13209,plain,
( sk3 = nil
| neq(sk2,nil) ),
inference(resolve,[status(thm)],[c_10883,c_1555]) ).
cnf(c_21096,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(resolve,[status(thm)],[c_13209,c_333]) ).
cnf(c_13326,plain,
neq(sk2,nil),
inference(copy,[status(thm)],[c_21096]) ).
cnf(c_21097,plain,
( ~ ssList(sk2)
| ~ ssList(nil)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_13326,c_134]) ).
cnf(c_21098,plain,
( ~ ssList(sk2)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_226,c_21097]) ).
cnf(c_13328,plain,
sk2 != nil,
inference(resolve,[status(thm)],[c_71,c_21098]) ).
cnf(c_13336,plain,
~ neq(sk3,nil),
inference(resolve,[status(thm)],[c_13328,c_8497]) ).
cnf(c_13384,plain,
sk3 != nil,
inference(resolve,[status(thm)],[c_13328,c_336]) ).
cnf(c_21099,plain,
( sk3 = nil
| neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_1496,c_226]) ).
cnf(c_21100,plain,
sk3 = nil,
inference(resolve,[status(thm)],[c_13336,c_21099]) ).
cnf(c_21088,plain,
$false,
inference(resolve,[status(thm)],[c_13384,c_21100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC067-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.58 % Computer : n020.cluster.edu
% 0.11/0.58 % Model : x86_64 x86_64
% 0.11/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.58 % Memory : 8046.5625MB
% 0.11/0.58 % OS : Linux 6.8.0-71-generic
% 0.11/0.58 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Sat Sep 26 12:11:05 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.58 % Process 1505015 was started by sandbox on n020,
% 0.11/0.58 % Sat Sep 26 12:11:05 2026
% 0.11/0.58 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.59
% 0.11/0.59 % From the command line: assign(max_seconds, 300).
% 29.58/4.37
% 29.58/4.37 % given #500 (I,wt=40): 567 app(app(A,cons(B,C)),cons(D,A)) != C | -ssList(A) | -ssList(C) | -ssItem(D) | -ssItem(B) | lt(B,D) | lt(D,B) | -lt(skaf59(C),skaf60(C)). [factor(302,c,f)].
% 29.58/4.37
% 29.58/4.37 % given #1000 (T,wt=8): 6084 rearsegP(skaf73(A),nil). [resolve(212,a,176,a)].
% 29.58/4.37
% 29.58/4.37 % given #1500 (F,wt=9): 16283 -segmentP(sk2,app(sk2,sk2)). [resolve(15864,a,123,b),unit_del(b,71),unit_del(c,9845),unit_del(d,14185)].
% 29.58/4.37
% 29.58/4.37 % given #2000 (T,wt=8): 20247 segmentP(tl(sk6),nil). [resolve(20150,a,178,a)].
% 29.58/4.37
% 29.58/4.37 % SZS status Unsatisfiable for theBenchmark
% 29.58/4.37
% 29.58/4.37 % Proof 1 at 2.82 (+ 0.92) seconds.
% 29.58/4.37 % Length of proof is 40.
% 29.58/4.37 % Level of proof is 9.
% 29.58/4.37 % Maximum clause weight is 26.000.
% 29.58/4.37 % Given clauses 2021.
% 29.58/4.37
% 29.58/4.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------