%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC030-1 : 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 : 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 08:56:36 AM UTC 2026
% Result : Unsatisfiable 36.42s 5.64s
% Output : CNFRefutation 36.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 66 ( 30 unt; 0 def)
% Number of atoms : 125 ( 91 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 117 ( 58 ~; 59 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause73,axiom,
! [VAR_0] :
( app(VAR_0,nil) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause73) ).
cnf(c_108,plain,
( app(A,nil) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause73]) ).
fof(clause74,axiom,
! [VAR_0] :
( app(nil,VAR_0) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause74) ).
cnf(c_109,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause74]) ).
fof(clause118,axiom,
! [VAR_0,VAR_1] :
( nil = VAR_0
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| app(VAR_0,VAR_1) != nil ),
file('theBenchmark.p',clause118) ).
cnf(c_140,plain,
( nil = A
| ~ ssList(A)
| ~ ssList(B)
| app(A,B) != nil ),
inference(clausify,[status(thm)],[clause118]) ).
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_141,plain,
( nil = B
| ~ ssList(A)
| ~ ssList(B)
| app(A,B) != nil ),
inference(clausify,[status(thm)],[clause119]) ).
fof(co1_1,axiom,
ssList(sk1),
file('theBenchmark.p',co1_1) ).
cnf(c_198,plain,
ssList(sk1),
inference(clausify,[status(thm)],[co1_1]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_202,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_203,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_202]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_204,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
cnf(c_205,plain,
sk3 = sk1,
inference(copy,[status(thm)],[c_204]) ).
fof(co1_7,axiom,
ssList(sk5),
file('theBenchmark.p',co1_7) ).
cnf(c_206,plain,
ssList(sk5),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_8,axiom,
ssList(sk6),
file('theBenchmark.p',co1_8) ).
cnf(c_207,plain,
ssList(sk6),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_9,axiom,
app(sk5,sk6) = sk4,
file('theBenchmark.p',co1_9) ).
cnf(c_208,plain,
app(sk5,sk6) = sk4,
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_209,plain,
app(sk5,sk6) = sk2,
inference(paramod,[status(thm)],[c_203,c_208]) ).
fof(co1_10,axiom,
app(sk6,sk5) = sk3,
file('theBenchmark.p',co1_10) ).
cnf(c_210,plain,
app(sk6,sk5) = sk3,
inference(clausify,[status(thm)],[co1_10]) ).
cnf(c_211,plain,
app(sk6,sk5) = sk1,
inference(paramod,[status(thm)],[c_205,c_210]) ).
fof(co1_11,axiom,
( nil = sk1
| nil = sk2 ),
file('theBenchmark.p',co1_11) ).
cnf(c_212,plain,
( nil = sk1
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_11]) ).
cnf(c_12023,plain,
( nil = sk1
| sk2 = nil ),
inference(copy,[status(thm)],[c_212]) ).
cnf(c_213,plain,
( sk1 = nil
| sk2 = nil ),
inference(copy,[status(thm)],[c_12023]) ).
fof(co1_14,axiom,
( nil != sk2
| nil != sk1 ),
file('theBenchmark.p',co1_14) ).
cnf(c_216,plain,
( nil != sk2
| nil != sk1 ),
inference(clausify,[status(thm)],[co1_14]) ).
cnf(c_12024,plain,
( nil != sk2
| sk1 != nil ),
inference(copy,[status(thm)],[c_216]) ).
cnf(c_217,plain,
( sk2 != nil
| sk1 != nil ),
inference(copy,[status(thm)],[c_12024]) ).
cnf(c_7071,plain,
app(nil,sk1) = sk1,
inference(resolve,[status(thm)],[c_198,c_109]) ).
cnf(c_7594,plain,
app(sk6,nil) = sk6,
inference(resolve,[status(thm)],[c_207,c_108]) ).
cnf(c_12025,plain,
( nil = sk5
| ~ ssList(sk5)
| ~ ssList(sk6)
| sk2 != nil ),
inference(paramod,[status(thm)],[c_209,c_140]) ).
cnf(c_12026,plain,
( sk5 = nil
| ~ ssList(sk5)
| ~ ssList(sk6)
| sk2 != nil ),
inference(copy,[status(thm)],[c_12025]) ).
cnf(c_12027,plain,
( sk5 = nil
| ~ ssList(sk5)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_207,c_12026]) ).
cnf(c_7657,plain,
( sk5 = nil
| sk2 != nil ),
inference(resolve,[status(thm)],[c_206,c_12027]) ).
cnf(c_12028,plain,
( nil = sk6
| ~ ssList(sk6)
| ~ ssList(sk5)
| sk1 != nil ),
inference(paramod,[status(thm)],[c_211,c_140]) ).
cnf(c_12029,plain,
( sk6 = nil
| ~ ssList(sk6)
| ~ ssList(sk5)
| sk1 != nil ),
inference(copy,[status(thm)],[c_12028]) ).
cnf(c_12030,plain,
( sk6 = nil
| ~ ssList(sk6)
| sk1 != nil ),
inference(resolve,[status(thm)],[c_206,c_12029]) ).
cnf(c_7668,plain,
( sk6 = nil
| sk1 != nil ),
inference(resolve,[status(thm)],[c_207,c_12030]) ).
cnf(c_12031,plain,
( nil = sk5
| ~ ssList(sk6)
| ~ ssList(sk5)
| sk1 != nil ),
inference(paramod,[status(thm)],[c_211,c_141]) ).
cnf(c_12032,plain,
( sk5 = nil
| ~ ssList(sk6)
| ~ ssList(sk5)
| sk1 != nil ),
inference(copy,[status(thm)],[c_12031]) ).
cnf(c_12033,plain,
( sk5 = nil
| ~ ssList(sk6)
| sk1 != nil ),
inference(resolve,[status(thm)],[c_206,c_12032]) ).
cnf(c_7669,plain,
( sk5 = nil
| sk1 != nil ),
inference(resolve,[status(thm)],[c_207,c_12033]) ).
cnf(c_11279,plain,
( sk1 = nil
| sk5 = nil ),
inference(resolve,[status(thm)],[c_7657,c_213]) ).
cnf(c_11281,plain,
( sk2 = nil
| sk6 = nil ),
inference(resolve,[status(thm)],[c_7668,c_213]) ).
cnf(c_12034,plain,
( sk5 = nil
| sk5 = nil ),
inference(resolve,[status(thm)],[c_11279,c_7669]) ).
cnf(c_11951,plain,
sk5 = nil,
inference(copy,[status(thm)],[c_12034]) ).
cnf(c_12035,plain,
app(sk6,nil) = sk1,
inference(paramod,[status(thm)],[c_11951,c_211]) ).
cnf(c_11965,plain,
sk6 = sk1,
inference(paramod,[status(thm)],[c_7594,c_12035]) ).
cnf(c_12036,plain,
app(nil,sk6) = sk2,
inference(paramod,[status(thm)],[c_11951,c_209]) ).
cnf(c_12037,plain,
app(nil,sk1) = sk2,
inference(paramod,[status(thm)],[c_11965,c_12036]) ).
cnf(c_12038,plain,
sk1 = sk2,
inference(paramod,[status(thm)],[c_7071,c_12037]) ).
cnf(c_11966,plain,
sk2 = sk1,
inference(copy,[status(thm)],[c_12038]) ).
cnf(c_12039,plain,
( sk2 = nil
| sk1 = nil ),
inference(paramod,[status(thm)],[c_11965,c_11281]) ).
cnf(c_12040,plain,
( sk1 = nil
| sk1 = nil ),
inference(paramod,[status(thm)],[c_11966,c_12039]) ).
cnf(c_12021,plain,
sk1 = nil,
inference(copy,[status(thm)],[c_12040]) ).
cnf(c_12041,plain,
( sk2 != nil
| nil != nil ),
inference(paramod,[status(thm)],[c_12021,c_217]) ).
cnf(c_12042,plain,
( sk1 != nil
| nil != nil ),
inference(paramod,[status(thm)],[c_11966,c_12041]) ).
cnf(c_12043,plain,
( nil != nil
| nil != nil ),
inference(paramod,[status(thm)],[c_12021,c_12042]) ).
cnf(c_12044,plain,
nil != nil,
inference(copy,[status(thm)],[c_12043]) ).
cnf(c_12022,plain,
$false,
inference(copy,[status(thm)],[c_12044]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC030-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n018.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 12:08:08 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 401106 was started by sandbox2 on n018,
% 0.07/0.35 % Sat Sep 26 12:08:08 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.36
% 0.11/0.36 % From the command line: assign(max_seconds, 300).
% 36.42/5.64
% 36.42/5.64 % given #500 (I,wt=34): 562 app(A,cons(B,cons(C,A))) != cons(B,nil) | -ssList(A) | -ssItem(C) | -ssItem(B) | -ssList(cons(B,nil)) | B = C. [factor(374,d,g)].
% 36.42/5.64
% 36.42/5.64 % given #1000 (F,wt=11): 7054 cons(A,sk1) != sk1 | -ssItem(A). [resolve(198,a,125,c)].
% 36.42/5.64
% 36.42/5.64 % SZS status Unsatisfiable for theBenchmark
% 36.42/5.64
% 36.42/5.64 % Proof 1 at 4.19 (+ 1.01) seconds.
% 36.42/5.64 % Length of proof is 31.
% 36.42/5.64 % Level of proof is 9.
% 36.42/5.64 % Maximum clause weight is 16.000.
% 36.42/5.64 % Given clauses 1094.
% 36.42/5.64
% 36.42/5.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------