%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC006-1 : 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 : n014.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 08:56:30 AM UTC 2026
% Result : Unsatisfiable 20.17s 3.06s
% Output : CNFRefutation 20.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 16 unt; 0 def)
% Number of atoms : 49 ( 18 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 59 ( 34 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_202,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_203,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_7,axiom,
! [VAR_0,VAR_1,VAR_2] :
( app(VAR_0,VAR_2) != sk1
| app(app(VAR_0,VAR_1),VAR_2) != sk2
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',co1_7) ).
cnf(c_204,plain,
( app(A,C) != sk1
| app(app(A,B),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_8025,plain,
( app(A,C) != sk1
| app(app(A,B),C) != sk4
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_202,c_204]) ).
cnf(c_205,plain,
( app(A,C) != sk3
| app(app(A,B),C) != sk4
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_203,c_8025]) ).
fof(co1_8,axiom,
ssList(sk5),
file('theBenchmark.p',co1_8) ).
cnf(c_206,plain,
ssList(sk5),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_9,axiom,
ssList(sk6),
file('theBenchmark.p',co1_9) ).
cnf(c_207,plain,
ssList(sk6),
inference(clausify,[status(thm)],[co1_9]) ).
fof(co1_10,axiom,
ssList(sk7),
file('theBenchmark.p',co1_10) ).
cnf(c_208,plain,
ssList(sk7),
inference(clausify,[status(thm)],[co1_10]) ).
fof(co1_11,axiom,
app(app(sk5,sk6),sk7) = sk4,
file('theBenchmark.p',co1_11) ).
cnf(c_209,plain,
app(app(sk5,sk6),sk7) = sk4,
inference(clausify,[status(thm)],[co1_11]) ).
fof(co1_12,axiom,
app(sk5,sk7) = sk3,
file('theBenchmark.p',co1_12) ).
cnf(c_210,plain,
app(sk5,sk7) = sk3,
inference(clausify,[status(thm)],[co1_12]) ).
cnf(c_8026,plain,
( app(sk5,sk7) != sk3
| ~ ssList(sk7)
| ~ ssList(sk6)
| ~ ssList(sk5) ),
inference(resolve,[status(thm)],[c_209,c_205]) ).
cnf(c_8027,plain,
( sk3 != sk3
| ~ ssList(sk7)
| ~ ssList(sk6)
| ~ ssList(sk5) ),
inference(paramod,[status(thm)],[c_210,c_8026]) ).
cnf(c_8028,plain,
( ~ ssList(sk7)
| ~ ssList(sk6)
| ~ ssList(sk5) ),
inference(copy,[status(thm)],[c_8027]) ).
cnf(c_8029,plain,
( ~ ssList(sk7)
| ~ ssList(sk6) ),
inference(resolve,[status(thm)],[c_206,c_8028]) ).
cnf(c_8030,plain,
~ ssList(sk7),
inference(resolve,[status(thm)],[c_207,c_8029]) ).
cnf(c_8024,plain,
$false,
inference(resolve,[status(thm)],[c_208,c_8030]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC006-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n014.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 12:02:46 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 3093734 was started by sandbox2 on n014,
% 0.19/0.45 % Sat Sep 26 12:02:46 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.47
% 0.19/0.47 % From the command line: assign(max_seconds, 300).
% 20.17/3.06
% 20.17/3.06 % SZS status Unsatisfiable for theBenchmark
% 20.17/3.06
% 20.17/3.06 % Proof 1 at 1.93 (+ 0.39) seconds.
% 20.17/3.06 % Length of proof is 10.
% 20.17/3.06 % Level of proof is 2.
% 20.17/3.06 % Maximum clause weight is 26.000.
% 20.17/3.06 % Given clauses 166.
% 20.17/3.06
% 20.17/3.06 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------