%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC254-1 : 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 : n004.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 24.25s 3.59s
% Output : CNFRefutation 24.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 13 unt; 0 def)
% Number of atoms : 50 ( 11 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 24 ~; 21 |; 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 : 4 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_18,axiom,
( ~ neq(sk4,nil)
| ~ singletonP(sk1) ),
file('theBenchmark.p',co1_18) ).
cnf(c_51,plain,
( ~ neq(sk4,nil)
| ~ singletonP(sk1) ),
inference(clausify,[status(thm)],[co1_18]) ).
fof(co1_16,axiom,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk3 ),
file('theBenchmark.p',co1_16) ).
cnf(c_53,plain,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_16]) ).
fof(co1_14,axiom,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('theBenchmark.p',co1_14) ).
cnf(c_55,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_14]) ).
fof(co1_7,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('theBenchmark.p',co1_7) ).
cnf(c_62,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_63,plain,
neq(sk2,nil),
inference(copy,[status(thm)],[c_62]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_64,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_65,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_66,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_65]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_69,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
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_130,plain,
( singletonP(B)
| ~ ssList(B)
| ~ ssItem(A)
| cons(A,nil) != B ),
inference(clausify,[status(thm)],[clause116]) ).
cnf(c_8199,plain,
( ~ neq(sk4,nil)
| ~ singletonP(sk3) ),
inference(paramod,[status(thm)],[c_64,c_51]) ).
cnf(c_8200,plain,
( ~ neq(sk2,nil)
| ~ singletonP(sk3) ),
inference(paramod,[status(thm)],[c_66,c_8199]) ).
cnf(c_327,plain,
~ singletonP(sk3),
inference(resolve,[status(thm)],[c_63,c_8200]) ).
cnf(c_8201,plain,
( ~ neq(sk2,nil)
| ssItem(sk5) ),
inference(paramod,[status(thm)],[c_66,c_55]) ).
cnf(c_328,plain,
ssItem(sk5),
inference(resolve,[status(thm)],[c_63,c_8201]) ).
cnf(c_8202,plain,
( ~ neq(sk2,nil)
| cons(sk5,nil) = sk3 ),
inference(paramod,[status(thm)],[c_66,c_53]) ).
cnf(c_330,plain,
cons(sk5,nil) = sk3,
inference(resolve,[status(thm)],[c_63,c_8202]) ).
cnf(c_8203,plain,
( singletonP(sk3)
| ~ ssList(sk3)
| ~ ssItem(sk5) ),
inference(resolve,[status(thm)],[c_330,c_130]) ).
cnf(c_8204,plain,
( singletonP(sk3)
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_328,c_8203]) ).
cnf(c_8205,plain,
singletonP(sk3),
inference(resolve,[status(thm)],[c_69,c_8204]) ).
cnf(c_8198,plain,
$false,
inference(resolve,[status(thm)],[c_327,c_8205]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC254-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n004.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 12:37:06 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 1719286 was started by sandbox on n004,
% 0.19/0.44 % Sat Sep 26 12:37:06 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 24.25/3.59
% 24.25/3.59 % SZS status Unsatisfiable for theBenchmark
% 24.25/3.59
% 24.25/3.59 % Proof 1 at 2.19 (+ 0.58) seconds.
% 24.25/3.59 % Length of proof is 14.
% 24.25/3.59 % Level of proof is 3.
% 24.25/3.59 % Maximum clause weight is 15.000.
% 24.25/3.59 % Given clauses 268.
% 24.25/3.59
% 24.25/3.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------