%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC097-1 : 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 : n013.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 08:56:49 AM UTC 2026
% Result : Unsatisfiable 7.44s 6.34s
% Output : CNFRefutation 7.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 11 unt; 0 def)
% Number of atoms : 43 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 23 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_14,axiom,
( ~ neq(sk4,nil)
| app(sk3,cons(sk5,nil)) = sk4 ),
file('theBenchmark.p',co1_14) ).
cnf(c_51,plain,
( ~ neq(sk4,nil)
| app(sk3,cons(sk5,nil)) = sk4 ),
inference(clausify,[status(thm)],[co1_14]) ).
fof(co1_13,axiom,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('theBenchmark.p',co1_13) ).
cnf(c_52,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_13]) ).
fof(co1_12,axiom,
! [VAR_0] :
( ~ neq(sk4,nil)
| app(sk1,cons(VAR_0,nil)) != sk2
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_12) ).
cnf(c_53,plain,
( ~ neq(sk4,nil)
| app(sk1,cons(A,nil)) != sk2
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_12]) ).
fof(co1_7,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('theBenchmark.p',co1_7) ).
cnf(c_58,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_59,plain,
neq(sk2,nil),
inference(copy,[status(thm)],[c_58]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_60,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_61,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_62,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_61]) ).
cnf(c_7900,plain,
( ~ neq(sk4,nil)
| app(sk3,cons(A,nil)) != sk2
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_60,c_53]) ).
cnf(c_7901,plain,
( ~ neq(sk2,nil)
| app(sk3,cons(A,nil)) != sk2
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_62,c_7900]) ).
cnf(c_323,plain,
( app(sk3,cons(A,nil)) != sk2
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_59,c_7901]) ).
cnf(c_7902,plain,
( ~ neq(sk2,nil)
| ssItem(sk5) ),
inference(paramod,[status(thm)],[c_62,c_52]) ).
cnf(c_324,plain,
ssItem(sk5),
inference(resolve,[status(thm)],[c_59,c_7902]) ).
cnf(c_7903,plain,
( ~ neq(sk4,nil)
| app(sk3,cons(sk5,nil)) = sk2 ),
inference(paramod,[status(thm)],[c_62,c_51]) ).
cnf(c_7904,plain,
( ~ neq(sk2,nil)
| app(sk3,cons(sk5,nil)) = sk2 ),
inference(paramod,[status(thm)],[c_62,c_7903]) ).
cnf(c_325,plain,
app(sk3,cons(sk5,nil)) = sk2,
inference(resolve,[status(thm)],[c_59,c_7904]) ).
cnf(c_7905,plain,
app(sk3,cons(sk5,nil)) != sk2,
inference(resolve,[status(thm)],[c_324,c_323]) ).
cnf(c_7906,plain,
sk2 != sk2,
inference(paramod,[status(thm)],[c_325,c_7905]) ).
cnf(c_7899,plain,
$false,
inference(copy,[status(thm)],[c_7906]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC097-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n013.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sat Sep 26 12:14:27 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 2704446 was started by sandbox on n013,
% 0.09/5.37 % Sat Sep 26 12:14:27 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.37
% 0.09/5.37 % From the command line: assign(max_seconds, 300).
% 7.44/6.34
% 7.44/6.34 % SZS status Unsatisfiable for theBenchmark
% 7.44/6.34
% 7.44/6.34 % Proof 1 at 0.75 (+ 0.20) seconds.
% 7.44/6.34 % Length of proof is 12.
% 7.44/6.34 % Level of proof is 3.
% 7.44/6.34 % Maximum clause weight is 18.000.
% 7.44/6.34 % Given clauses 266.
% 7.44/6.34
% 7.44/6.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------