%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC210-1 : 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 : n018.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 08:57:10 AM UTC 2026
% Result : Unsatisfiable 16.89s 2.92s
% Output : CNFRefutation 16.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 51 ( 28 unt; 0 def)
% Number of atoms : 91 ( 32 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 86 ( 46 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_12,axiom,
( ~ neq(sk4,nil)
| ~ neq(sk1,nil) ),
file('theBenchmark.p',co1_12) ).
cnf(c_51,plain,
( ~ neq(sk4,nil)
| ~ neq(sk1,nil) ),
inference(clausify,[status(thm)],[co1_12]) ).
fof(co1_11,axiom,
( ~ neq(sk4,nil)
| singletonP(sk3) ),
file('theBenchmark.p',co1_11) ).
cnf(c_52,plain,
( ~ neq(sk4,nil)
| singletonP(sk3) ),
inference(clausify,[status(thm)],[co1_11]) ).
fof(co1_7,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('theBenchmark.p',co1_7) ).
cnf(c_56,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_57,plain,
neq(sk2,nil),
inference(copy,[status(thm)],[c_56]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_58,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_59,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_60,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_59]) ).
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(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(clause11,axiom,
~ singletonP(nil),
file('theBenchmark.p',clause11) ).
cnf(c_214,plain,
~ singletonP(nil),
inference(clausify,[status(thm)],[clause11]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_217,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_14296,plain,
( nil = sk2
| ~ ssList(A)
| app(A,sk2) != nil ),
inference(resolve,[status(thm)],[c_121,c_63]) ).
cnf(c_1017,plain,
( sk2 = nil
| ~ ssList(A)
| app(A,sk2) != nil ),
inference(copy,[status(thm)],[c_14296]) ).
cnf(c_14297,plain,
( ~ ssList(sk2)
| ~ ssList(nil)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_125,c_57]) ).
cnf(c_14298,plain,
( ~ ssList(sk2)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_217,c_14297]) ).
cnf(c_1033,plain,
sk2 != nil,
inference(resolve,[status(thm)],[c_63,c_14298]) ).
cnf(c_1035,plain,
( ~ ssList(A)
| app(A,sk2) != nil ),
inference(resolve,[status(thm)],[c_1033,c_1017]) ).
cnf(c_1053,plain,
( sk3 = A
| neq(sk3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_140,c_62]) ).
cnf(c_1054,plain,
( sk4 = A
| neq(sk4,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_140,c_61]) ).
cnf(c_1083,plain,
app(nil,sk4) = sk4,
inference(resolve,[status(thm)],[c_157,c_61]) ).
cnf(c_5405,plain,
app(nil,sk2) != nil,
inference(resolve,[status(thm)],[c_1035,c_217]) ).
cnf(c_10389,plain,
app(nil,sk2) = sk4,
inference(paramod,[status(thm)],[c_60,c_1083]) ).
cnf(c_12626,plain,
sk4 != nil,
inference(paramod,[status(thm)],[c_10389,c_5405]) ).
cnf(c_13787,plain,
( sk3 = nil
| neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_1053,c_217]) ).
cnf(c_14299,plain,
( sk4 = nil
| neq(sk4,nil) ),
inference(resolve,[status(thm)],[c_1054,c_217]) ).
cnf(c_13826,plain,
neq(sk4,nil),
inference(resolve,[status(thm)],[c_12626,c_14299]) ).
cnf(c_13855,plain,
singletonP(sk3),
inference(resolve,[status(thm)],[c_13826,c_52]) ).
cnf(c_13856,plain,
~ neq(sk1,nil),
inference(resolve,[status(thm)],[c_13826,c_51]) ).
cnf(c_14103,plain,
~ neq(sk3,nil),
inference(paramod,[status(thm)],[c_58,c_13856]) ).
cnf(c_14104,plain,
sk3 = nil,
inference(resolve,[status(thm)],[c_14103,c_13787]) ).
cnf(c_14300,plain,
singletonP(nil),
inference(paramod,[status(thm)],[c_14104,c_13855]) ).
cnf(c_14295,plain,
$false,
inference(resolve,[status(thm)],[c_214,c_14300]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC210-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n018.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 26 12:33:51 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 449867 was started by sandbox on n018,
% 0.09/0.35 % Sat Sep 26 12:33:51 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.35
% 0.09/0.35 % From the command line: assign(max_seconds, 300).
% 16.89/2.92
% 16.89/2.92 % given #500 (I,wt=51): 560 app(app(A,cons(B,C)),cons(D,C)) != C | -ssList(C) | -ssList(A) | -ssItem(D) | -ssItem(B) | lt(B,D) | lt(D,B) | app(app(skaf61(C),cons(skaf59(C),skaf62(C))),cons(skaf60(C),skaf63(C))) = C. [factor(299,b,f)].
% 16.89/2.92
% 16.89/2.92 % given #1000 (F,wt=12): 5419 app(skaf62(A),sk2) != nil. [resolve(1035,b,192,a)].
% 16.89/2.92
% 16.89/2.92 % given #1500 (A,wt=17): 952 nil != A | sk1 != nil | -ssList(A) | app(A,sk1) = nil. [resolve(97,c,64,a),flip(b)].
% 16.89/2.92
% 16.89/2.92 % SZS status Unsatisfiable for theBenchmark
% 16.89/2.92
% 16.89/2.92 % Proof 1 at 1.80 (+ 0.53) seconds.
% 16.89/2.92 % Length of proof is 32.
% 16.89/2.92 % Level of proof is 10.
% 16.89/2.92 % Maximum clause weight is 16.000.
% 16.89/2.92 % Given clauses 1570.
% 16.89/2.92
% 16.89/2.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------