%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC185-1 : 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 : n016.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 08:57:06 AM UTC 2026
% Result : Unsatisfiable 68.94s 25.32s
% Output : CNFRefutation 68.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 15 unt; 0 def)
% Number of atoms : 67 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 88 ( 50 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_204,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
cnf(c_205,plain,
sk3 = sk1,
inference(copy,[status(thm)],[c_204]) ).
fof(co1_7,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ memberP(VAR_1,VAR_0)
| app(app(VAR_1,cons(VAR_0,nil)),VAR_2) != sk3
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_7) ).
cnf(c_206,plain,
( ~ memberP(B,A)
| app(app(B,cons(A,nil)),C) != sk3
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_207,plain,
( ~ memberP(B,A)
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_205,c_206]) ).
fof(co1_8,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ memberP(VAR_2,VAR_0)
| app(app(VAR_1,cons(VAR_0,nil)),VAR_2) != sk3
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_8) ).
cnf(c_208,plain,
( ~ memberP(C,A)
| app(app(B,cons(A,nil)),C) != sk3
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_209,plain,
( ~ memberP(C,A)
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_205,c_208]) ).
fof(co1_9,axiom,
ssItem(sk5),
file('theBenchmark.p',co1_9) ).
cnf(c_210,plain,
ssItem(sk5),
inference(clausify,[status(thm)],[co1_9]) ).
fof(co1_10,axiom,
ssList(sk6),
file('theBenchmark.p',co1_10) ).
cnf(c_211,plain,
ssList(sk6),
inference(clausify,[status(thm)],[co1_10]) ).
fof(co1_11,axiom,
ssList(sk7),
file('theBenchmark.p',co1_11) ).
cnf(c_212,plain,
ssList(sk7),
inference(clausify,[status(thm)],[co1_11]) ).
fof(co1_12,axiom,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
file('theBenchmark.p',co1_12) ).
cnf(c_213,plain,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
inference(clausify,[status(thm)],[co1_12]) ).
fof(co1_13,axiom,
( memberP(sk7,sk5)
| memberP(sk6,sk5) ),
file('theBenchmark.p',co1_13) ).
cnf(c_214,plain,
( memberP(sk7,sk5)
| memberP(sk6,sk5) ),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_7937,plain,
( ~ memberP(sk7,sk5)
| ~ ssList(sk7)
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(resolve,[status(thm)],[c_213,c_209]) ).
cnf(c_7938,plain,
( ~ memberP(sk7,sk5)
| ~ ssList(sk7)
| ~ ssList(sk6) ),
inference(resolve,[status(thm)],[c_210,c_7937]) ).
cnf(c_7939,plain,
( ~ memberP(sk7,sk5)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_211,c_7938]) ).
cnf(c_7922,plain,
~ memberP(sk7,sk5),
inference(resolve,[status(thm)],[c_212,c_7939]) ).
cnf(c_7940,plain,
( ~ memberP(sk6,sk5)
| ~ ssList(sk7)
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(resolve,[status(thm)],[c_213,c_207]) ).
cnf(c_7941,plain,
( ~ memberP(sk6,sk5)
| ~ ssList(sk7)
| ~ ssList(sk6) ),
inference(resolve,[status(thm)],[c_210,c_7940]) ).
cnf(c_7942,plain,
( ~ memberP(sk6,sk5)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_211,c_7941]) ).
cnf(c_7923,plain,
~ memberP(sk6,sk5),
inference(resolve,[status(thm)],[c_212,c_7942]) ).
cnf(c_7943,plain,
memberP(sk7,sk5),
inference(resolve,[status(thm)],[c_7923,c_214]) ).
cnf(c_7936,plain,
$false,
inference(resolve,[status(thm)],[c_7922,c_7943]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC185-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.13/15.66 % CPULimit : 300
% 0.13/15.66 % WCLimit : 300
% 0.13/15.66 % DateTime : Sat Sep 26 12:27:17 UTC 2026
% 0.13/15.66 % CPUTime :
% 0.13/15.67 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/15.67 % Process 2130705 was started by sandbox on n005,
% 0.13/15.67 % Sat Sep 26 12:27:17 2026
% 0.13/15.67 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/15.68
% 0.13/15.68 % From the command line: assign(max_seconds, 300).
% 68.94/25.32
% 68.94/25.32 % SZS status Unsatisfiable for theBenchmark
% 68.94/25.32
% 68.94/25.32 % Proof 1 at 1.33 (+ 0.23) seconds.
% 68.94/25.32 % Length of proof is 14.
% 68.94/25.32 % Level of proof is 4.
% 68.94/25.32 % Maximum clause weight is 28.000.
% 68.94/25.32 % Given clauses 167.
% 68.94/25.32
% 68.94/25.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------