%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC131-1 : 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 : n020.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 08:56:56 AM UTC 2026
% Result : Unsatisfiable 30.26s 4.80s
% Output : CNFRefutation 30.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 17 unt; 0 def)
% Number of atoms : 35 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 12 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 6 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause7,axiom,
cyclefreeP(nil),
file('theBenchmark.p',clause7) ).
cnf(c_39,plain,
cyclefreeP(nil),
inference(clausify,[status(thm)],[clause7]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_40,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
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_120,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(co1_2,axiom,
ssList(sk2),
file('theBenchmark.p',co1_2) ).
cnf(c_199,plain,
ssList(sk2),
inference(clausify,[status(thm)],[co1_2]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_202,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_203,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_202]) ).
fof(co1_7,axiom,
~ neq(sk4,nil),
file('theBenchmark.p',co1_7) ).
cnf(c_206,plain,
~ neq(sk4,nil),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_8,axiom,
~ cyclefreeP(sk2),
file('theBenchmark.p',co1_8) ).
cnf(c_207,plain,
~ cyclefreeP(sk2),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_14164,plain,
( A = nil
| neq(A,nil)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_120,c_40]) ).
cnf(c_4672,plain,
( nil = A
| neq(A,nil)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_14164]) ).
cnf(c_6819,plain,
~ neq(sk2,nil),
inference(paramod,[status(thm)],[c_203,c_206]) ).
cnf(c_14165,plain,
( nil = sk2
| neq(sk2,nil) ),
inference(resolve,[status(thm)],[c_4672,c_199]) ).
cnf(c_14166,plain,
( sk2 = nil
| neq(sk2,nil) ),
inference(copy,[status(thm)],[c_14165]) ).
cnf(c_14117,plain,
sk2 = nil,
inference(resolve,[status(thm)],[c_6819,c_14166]) ).
cnf(c_14167,plain,
~ cyclefreeP(nil),
inference(paramod,[status(thm)],[c_14117,c_207]) ).
cnf(c_14163,plain,
$false,
inference(resolve,[status(thm)],[c_39,c_14167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC131-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.40 % Computer : n020.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.40 % CPULimit : 300
% 0.16/0.40 % WCLimit : 300
% 0.16/0.40 % DateTime : Sat Sep 26 12:20:19 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.41 % Process 1529874 was started by sandbox2 on n020,
% 0.16/0.41 % Sat Sep 26 12:20:19 2026
% 0.16/0.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.42
% 0.16/0.42 % From the command line: assign(max_seconds, 300).
% 30.26/4.80
% 30.26/4.80 % given #500 (I,wt=50): 552 app(app(A,cons(B,C)),cons(D,C)) != C | -ssList(C) | -ssList(A) | -ssItem(D) | -ssItem(B) | lt(B,D) | lt(D,B) | -lt(skaf59(C),skaf60(C)). [factor(377,b,f)].
% 30.26/4.80
% 30.26/4.80 % SZS status Unsatisfiable for theBenchmark
% 30.26/4.80
% 30.26/4.80 % Proof 1 at 3.83 (+ 0.49) seconds.
% 30.26/4.80 % Length of proof is 12.
% 30.26/4.80 % Level of proof is 4.
% 30.26/4.80 % Maximum clause weight is 15.000.
% 30.26/4.80 % Given clauses 807.
% 30.26/4.80
% 30.26/4.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------