%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC387-1 : 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 : n009.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 08:57:40 AM UTC 2026
% Result : Unsatisfiable 102.13s 14.25s
% Output : CNFRefutation 102.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 53 ( 16 unt; 0 def)
% Number of atoms : 107 ( 48 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 118 ( 64 ~; 54 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_12,axiom,
( ~ neq(sk4,nil)
| memberP(sk4,sk5) ),
file('theBenchmark.p',co1_12) ).
cnf(c_51,plain,
( ~ neq(sk4,nil)
| memberP(sk4,sk5) ),
inference(clausify,[status(thm)],[co1_12]) ).
fof(co1_11,axiom,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk3 ),
file('theBenchmark.p',co1_11) ).
cnf(c_52,plain,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_11]) ).
fof(co1_10,axiom,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('theBenchmark.p',co1_10) ).
cnf(c_53,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_10]) ).
fof(co1_9,axiom,
( nil != sk1
| nil != sk2 ),
file('theBenchmark.p',co1_9) ).
cnf(c_54,plain,
( nil != sk1
| nil != sk2 ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_16612,plain,
( nil != sk1
| sk2 != nil ),
inference(copy,[status(thm)],[c_54]) ).
cnf(c_55,plain,
( sk1 != nil
| sk2 != nil ),
inference(copy,[status(thm)],[c_16612]) ).
fof(co1_8,axiom,
( nil != sk4
| nil = sk3 ),
file('theBenchmark.p',co1_8) ).
cnf(c_56,plain,
( nil != sk4
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_16613,plain,
( nil != sk4
| sk3 = nil ),
inference(copy,[status(thm)],[c_56]) ).
cnf(c_57,plain,
( sk4 != nil
| sk3 = nil ),
inference(copy,[status(thm)],[c_16613]) ).
fof(co1_7,axiom,
! [VAR_0] :
( ~ memberP(sk2,VAR_0)
| cons(VAR_0,nil) != sk1
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_7) ).
cnf(c_58,plain,
( ~ memberP(sk2,A)
| cons(A,nil) != sk1
| ~ ssItem(A) ),
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(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(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_217,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_16614,plain,
( ~ memberP(sk2,A)
| cons(A,nil) != sk3
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_59,c_58]) ).
cnf(c_321,plain,
( ~ memberP(sk4,A)
| cons(A,nil) != sk3
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_60,c_16614]) ).
cnf(c_16615,plain,
( sk1 != nil
| sk4 != nil ),
inference(paramod,[status(thm)],[c_60,c_55]) ).
cnf(c_322,plain,
( sk3 != nil
| sk4 != nil ),
inference(paramod,[status(thm)],[c_59,c_16615]) ).
cnf(c_16616,plain,
( ~ ssList(A)
| ~ neq(A,sk4)
| A != sk4 ),
inference(resolve,[status(thm)],[c_125,c_61]) ).
cnf(c_1135,plain,
( ~ ssList(A)
| ~ neq(A,sk4)
| sk4 != A ),
inference(copy,[status(thm)],[c_16616]) ).
cnf(c_16617,plain,
( A = sk4
| neq(A,sk4)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_140,c_61]) ).
cnf(c_1149,plain,
( sk4 = A
| neq(A,sk4)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_16617]) ).
cnf(c_1151,plain,
( sk4 = A
| neq(sk4,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_140,c_61]) ).
cnf(c_12438,plain,
( ~ neq(nil,sk4)
| sk4 != nil ),
inference(resolve,[status(thm)],[c_1135,c_217]) ).
cnf(c_14570,plain,
( sk4 = nil
| neq(nil,sk4) ),
inference(resolve,[status(thm)],[c_1149,c_217]) ).
cnf(c_14605,plain,
( sk3 != nil
| neq(nil,sk4) ),
inference(resolve,[status(thm)],[c_14570,c_322]) ).
cnf(c_14608,plain,
( sk3 = nil
| neq(nil,sk4) ),
inference(resolve,[status(thm)],[c_14570,c_57]) ).
cnf(c_16618,plain,
( neq(nil,sk4)
| neq(nil,sk4) ),
inference(resolve,[status(thm)],[c_14608,c_14605]) ).
cnf(c_14860,plain,
neq(nil,sk4),
inference(copy,[status(thm)],[c_16618]) ).
cnf(c_14865,plain,
sk4 != nil,
inference(resolve,[status(thm)],[c_14860,c_12438]) ).
cnf(c_16619,plain,
( sk4 = nil
| neq(sk4,nil) ),
inference(resolve,[status(thm)],[c_1151,c_217]) ).
cnf(c_16377,plain,
neq(sk4,nil),
inference(resolve,[status(thm)],[c_14865,c_16619]) ).
cnf(c_16405,plain,
ssItem(sk5),
inference(resolve,[status(thm)],[c_16377,c_53]) ).
cnf(c_16406,plain,
cons(sk5,nil) = sk3,
inference(resolve,[status(thm)],[c_16377,c_52]) ).
cnf(c_16407,plain,
memberP(sk4,sk5),
inference(resolve,[status(thm)],[c_16377,c_51]) ).
cnf(c_16620,plain,
( ~ memberP(sk4,sk5)
| cons(sk5,nil) != sk3 ),
inference(resolve,[status(thm)],[c_16405,c_321]) ).
cnf(c_16621,plain,
( ~ memberP(sk4,sk5)
| sk3 != sk3 ),
inference(paramod,[status(thm)],[c_16406,c_16620]) ).
cnf(c_16622,plain,
~ memberP(sk4,sk5),
inference(copy,[status(thm)],[c_16621]) ).
cnf(c_16611,plain,
$false,
inference(resolve,[status(thm)],[c_16407,c_16622]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC387-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.58 % Computer : n009.cluster.edu
% 0.15/0.58 % Model : x86_64 x86_64
% 0.15/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.58 % Memory : 8046.5625MB
% 0.15/0.58 % OS : Linux 6.8.0-71-generic
% 0.15/0.58 % CPULimit : 300
% 0.15/0.58 % WCLimit : 300
% 0.15/0.58 % DateTime : Sat Sep 26 12:56:30 UTC 2026
% 0.15/0.58 % CPUTime :
% 0.15/0.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.58 % Process 180202 was started by sandbox2 on n009,
% 0.15/0.58 % Sat Sep 26 12:56:30 2026
% 0.15/0.58 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.60
% 0.15/0.60 % From the command line: assign(max_seconds, 300).
% 102.13/14.25
% 102.13/14.25 % given #500 (I,wt=37): 560 app(app(A,cons(B,C)),cons(B,D)) != A | -ssList(D) | -ssList(C) | -ssList(A) | -ssItem(B) | lt(B,B) | -lt(skaf59(A),skaf60(A)). [factor(297,e,f),merge(g)].
% 102.13/14.25
% 102.13/14.25 % given #1000 (F,wt=9): 9380 -neq(skaf57(A),skaf57(A)). [resolve(387,b,187,a)].
% 102.13/14.25
% 102.13/14.25 % given #1500 (W,wt=8): 15822 neq(sk3,nil) | -memberP(nil,sk5). [resolve(15666,b,159,b)].
% 102.13/14.25
% 102.13/14.25 % SZS status Unsatisfiable for theBenchmark
% 102.13/14.25
% 102.13/14.25 % Proof 1 at 4.11 (+ 1.42) seconds.
% 102.13/14.25 % Length of proof is 30.
% 102.13/14.25 % Level of proof is 8.
% 102.13/14.25 % Maximum clause weight is 14.000.
% 102.13/14.25 % Given clauses 1555.
% 102.13/14.25
% 102.13/14.25 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------