%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC317-1 : 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 : n006.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 08:57:28 AM UTC 2026
% Result : Unsatisfiable 15.07s 22.32s
% Output : CNFRefutation 15.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 12 unt; 0 def)
% Number of atoms : 74 ( 26 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 85 ( 46 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_18,axiom,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
file('theBenchmark.p',co1_18) ).
cnf(c_51,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
inference(clausify,[status(thm)],[co1_18]) ).
fof(co1_17,axiom,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk3 ),
file('theBenchmark.p',co1_17) ).
cnf(c_52,plain,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk3 ),
inference(clausify,[status(thm)],[co1_17]) ).
fof(co1_16,axiom,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('theBenchmark.p',co1_16) ).
cnf(c_53,plain,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(clausify,[status(thm)],[co1_16]) ).
fof(co1_15,axiom,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('theBenchmark.p',co1_15) ).
cnf(c_54,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_15]) ).
fof(co1_14,axiom,
! [VAR_0,VAR_1] :
( ~ neq(sk4,nil)
| app(VAR_1,cons(VAR_0,nil)) != sk2
| app(cons(VAR_0,nil),VAR_1) != sk1
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_14) ).
cnf(c_55,plain,
( ~ neq(sk4,nil)
| app(B,cons(A,nil)) != sk2
| app(cons(A,nil),B) != sk1
| ~ ssList(B)
| ~ ssItem(A) ),
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]) ).
cnf(c_8228,plain,
( ~ neq(sk4,nil)
| app(B,cons(A,nil)) != sk2
| app(cons(A,nil),B) != sk3
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_64,c_55]) ).
cnf(c_8229,plain,
( ~ neq(sk2,nil)
| app(B,cons(A,nil)) != sk2
| app(cons(A,nil),B) != sk3
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_66,c_8228]) ).
cnf(c_327,plain,
( app(B,cons(A,nil)) != sk2
| app(cons(A,nil),B) != sk3
| ~ ssList(B)
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_63,c_8229]) ).
cnf(c_8230,plain,
( ~ neq(sk2,nil)
| ssItem(sk5) ),
inference(paramod,[status(thm)],[c_66,c_54]) ).
cnf(c_328,plain,
ssItem(sk5),
inference(resolve,[status(thm)],[c_63,c_8230]) ).
cnf(c_8231,plain,
( ~ neq(sk2,nil)
| ssList(sk6) ),
inference(paramod,[status(thm)],[c_66,c_53]) ).
cnf(c_329,plain,
ssList(sk6),
inference(resolve,[status(thm)],[c_63,c_8231]) ).
cnf(c_8232,plain,
( ~ neq(sk2,nil)
| app(cons(sk5,nil),sk6) = sk3 ),
inference(paramod,[status(thm)],[c_66,c_52]) ).
cnf(c_330,plain,
app(cons(sk5,nil),sk6) = sk3,
inference(resolve,[status(thm)],[c_63,c_8232]) ).
cnf(c_8233,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk2 ),
inference(paramod,[status(thm)],[c_66,c_51]) ).
cnf(c_8234,plain,
( ~ neq(sk2,nil)
| app(sk6,cons(sk5,nil)) = sk2 ),
inference(paramod,[status(thm)],[c_66,c_8233]) ).
cnf(c_331,plain,
app(sk6,cons(sk5,nil)) = sk2,
inference(resolve,[status(thm)],[c_63,c_8234]) ).
cnf(c_8235,plain,
( app(sk6,cons(sk5,nil)) != sk2
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(resolve,[status(thm)],[c_330,c_327]) ).
cnf(c_8236,plain,
( sk2 != sk2
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(paramod,[status(thm)],[c_331,c_8235]) ).
cnf(c_8237,plain,
( ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(copy,[status(thm)],[c_8236]) ).
cnf(c_8238,plain,
~ ssList(sk6),
inference(resolve,[status(thm)],[c_328,c_8237]) ).
cnf(c_8227,plain,
$false,
inference(resolve,[status(thm)],[c_329,c_8238]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC317-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/20.40 % Computer : n006.cluster.edu
% 0.11/20.40 % Model : x86_64 x86_64
% 0.11/20.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/20.40 % Memory : 8046.5625MB
% 0.11/20.40 % OS : Linux 6.8.0-71-generic
% 0.11/20.40 % CPULimit : 300
% 0.11/20.40 % WCLimit : 300
% 0.11/20.40 % DateTime : Sat Sep 26 12:46:47 UTC 2026
% 0.11/20.40 % CPUTime :
% 0.11/20.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/20.40 % Process 1293085 was started by sandbox2 on n006,
% 0.11/20.40 % Sat Sep 26 12:46:47 2026
% 0.11/20.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/20.41
% 0.11/20.41 % From the command line: assign(max_seconds, 300).
% 15.07/22.32
% 15.07/22.32 % SZS status Unsatisfiable for theBenchmark
% 15.07/22.32
% 15.07/22.32 % Proof 1 at 1.38 (+ 0.44) seconds.
% 15.07/22.32 % Length of proof is 16.
% 15.07/22.32 % Level of proof is 3.
% 15.07/22.32 % Maximum clause weight is 27.000.
% 15.07/22.32 % Given clauses 268.
% 15.07/22.32
% 15.07/22.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------