%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC256-1 : 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 : 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 08:57:17 AM UTC 2026
% Result : Unsatisfiable 70.53s 19.30s
% Output : CNFRefutation 70.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 36 ( 20 unt; 0 def)
% Number of atoms : 64 ( 23 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 60 ( 32 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 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 : 8 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_7,axiom,
neq(sk2,nil),
file('theBenchmark.p',co1_7) ).
cnf(c_30,plain,
neq(sk2,nil),
inference(clausify,[status(thm)],[co1_7]) ).
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_31,plain,
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(A,B)
| A != B ),
inference(clausify,[status(thm)],[clause115]) ).
cnf(c_34,plain,
( ~ ssList(sk2)
| ~ ssList(nil)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_31,c_30]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_52,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
fof(clause116,axiom,
! [VAR_0,VAR_1] :
( singletonP(VAR_1)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0)
| cons(VAR_0,nil) != VAR_1 ),
file('theBenchmark.p',clause116) ).
cnf(c_142,plain,
( singletonP(B)
| ~ ssList(B)
| ~ ssItem(A)
| cons(A,nil) != B ),
inference(clausify,[status(thm)],[clause116]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_203,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_204,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_205,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_206,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_8,axiom,
~ singletonP(sk1),
file('theBenchmark.p',co1_8) ).
cnf(c_207,plain,
~ singletonP(sk1),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_208,plain,
~ singletonP(sk3),
inference(paramod,[status(thm)],[c_206,c_207]) ).
fof(co1_9,axiom,
( nil = sk4
| ssItem(sk5) ),
file('theBenchmark.p',co1_9) ).
cnf(c_209,plain,
( nil = sk4
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_210,plain,
( sk4 = nil
| ssItem(sk5) ),
inference(copy,[status(thm)],[c_209]) ).
fof(co1_11,axiom,
( nil = sk4
| cons(sk5,nil) = sk3 ),
file('theBenchmark.p',co1_11) ).
cnf(c_213,plain,
( nil = sk4
| cons(sk5,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_11]) ).
cnf(c_214,plain,
( sk4 = nil
| cons(sk5,nil) = sk3 ),
inference(copy,[status(thm)],[c_213]) ).
cnf(c_9705,plain,
( ~ ssList(sk2)
| ~ ssList(nil)
| sk4 != nil ),
inference(paramod,[status(thm)],[c_205,c_34]) ).
cnf(c_9706,plain,
( ~ ssList(sk4)
| ~ ssList(nil)
| sk4 != nil ),
inference(paramod,[status(thm)],[c_205,c_9705]) ).
cnf(c_9707,plain,
( ~ ssList(sk4)
| sk4 != nil ),
inference(resolve,[status(thm)],[c_52,c_9706]) ).
cnf(c_305,plain,
sk4 != nil,
inference(resolve,[status(thm)],[c_204,c_9707]) ).
cnf(c_524,plain,
cons(sk5,nil) = sk3,
inference(resolve,[status(thm)],[c_305,c_214]) ).
cnf(c_525,plain,
ssItem(sk5),
inference(resolve,[status(thm)],[c_305,c_210]) ).
cnf(c_9708,plain,
( singletonP(sk3)
| ~ ssList(sk3)
| ~ ssItem(sk5) ),
inference(resolve,[status(thm)],[c_524,c_142]) ).
cnf(c_9709,plain,
( singletonP(sk3)
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_525,c_9708]) ).
cnf(c_9710,plain,
singletonP(sk3),
inference(resolve,[status(thm)],[c_203,c_9709]) ).
cnf(c_9704,plain,
$false,
inference(resolve,[status(thm)],[c_208,c_9710]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC256-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n017.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Sat Sep 26 12:33:09 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.37 % Process 716135 was started by sandbox on n017,
% 0.08/5.37 % Sat Sep 26 12:33:09 2026
% 0.08/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/5.38
% 0.08/5.38 % From the command line: assign(max_seconds, 300).
% 70.53/19.30
% 70.53/19.30 % SZS status Unsatisfiable for theBenchmark
% 70.53/19.30
% 70.53/19.30 % Proof 1 at 2.47 (+ 0.60) seconds.
% 70.53/19.30 % Length of proof is 19.
% 70.53/19.30 % Level of proof is 4.
% 70.53/19.30 % Maximum clause weight is 15.000.
% 70.53/19.30 % Given clauses 454.
% 70.53/19.30
% 70.53/19.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------