%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC381-1 : 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 08:57:39 AM UTC 2026
% Result : Unsatisfiable 12.13s 7.33s
% Output : CNFRefutation 12.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 11 unt; 0 def)
% Number of atoms : 58 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 62 ( 34 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_16,axiom,
( ~ neq(sk4,nil)
| memberP(sk4,sk5) ),
file('theBenchmark.p',co1_16) ).
cnf(c_51,plain,
( ~ neq(sk4,nil)
| memberP(sk4,sk5) ),
inference(clausify,[status(thm)],[co1_16]) ).
fof(co1_15,axiom,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk3 ),
file('theBenchmark.p',co1_15) ).
cnf(c_52,plain,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_15]) ).
fof(co1_14,axiom,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('theBenchmark.p',co1_14) ).
cnf(c_53,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_14]) ).
fof(co1_13,axiom,
! [VAR_0] :
( ~ neq(sk4,nil)
| ~ memberP(sk2,VAR_0)
| cons(VAR_0,nil) != sk1
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_13) ).
cnf(c_54,plain,
( ~ neq(sk4,nil)
| ~ memberP(sk2,A)
| cons(A,nil) != sk1
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_13]) ).
fof(co1_7,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('theBenchmark.p',co1_7) ).
cnf(c_60,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_61,plain,
neq(sk2,nil),
inference(copy,[status(thm)],[c_60]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_62,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_63,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_64,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_63]) ).
cnf(c_7903,plain,
( ~ neq(sk4,nil)
| ~ memberP(sk2,A)
| cons(A,nil) != sk3
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_62,c_54]) ).
cnf(c_7904,plain,
( ~ neq(sk2,nil)
| ~ memberP(sk2,A)
| cons(A,nil) != sk3
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_64,c_7903]) ).
cnf(c_325,plain,
( ~ memberP(sk2,A)
| cons(A,nil) != sk3
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_61,c_7904]) ).
cnf(c_7905,plain,
( ~ neq(sk2,nil)
| ssItem(sk5) ),
inference(paramod,[status(thm)],[c_64,c_53]) ).
cnf(c_326,plain,
ssItem(sk5),
inference(resolve,[status(thm)],[c_61,c_7905]) ).
cnf(c_7906,plain,
( ~ neq(sk2,nil)
| cons(sk5,nil) = sk3 ),
inference(paramod,[status(thm)],[c_64,c_52]) ).
cnf(c_327,plain,
cons(sk5,nil) = sk3,
inference(resolve,[status(thm)],[c_61,c_7906]) ).
cnf(c_7907,plain,
( ~ neq(sk4,nil)
| memberP(sk2,sk5) ),
inference(paramod,[status(thm)],[c_64,c_51]) ).
cnf(c_7908,plain,
( ~ neq(sk2,nil)
| memberP(sk2,sk5) ),
inference(paramod,[status(thm)],[c_64,c_7907]) ).
cnf(c_328,plain,
memberP(sk2,sk5),
inference(resolve,[status(thm)],[c_61,c_7908]) ).
cnf(c_7909,plain,
( ~ memberP(sk2,sk5)
| cons(sk5,nil) != sk3 ),
inference(resolve,[status(thm)],[c_326,c_325]) ).
cnf(c_7910,plain,
( ~ memberP(sk2,sk5)
| sk3 != sk3 ),
inference(paramod,[status(thm)],[c_327,c_7909]) ).
cnf(c_7911,plain,
~ memberP(sk2,sk5),
inference(copy,[status(thm)],[c_7910]) ).
cnf(c_7902,plain,
$false,
inference(resolve,[status(thm)],[c_328,c_7911]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC381-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.55 % Computer : n016.cluster.edu
% 0.10/5.55 % Model : x86_64 x86_64
% 0.10/5.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.55 % Memory : 8046.5625MB
% 0.10/5.55 % OS : Linux 6.8.0-71-generic
% 0.10/5.55 % CPULimit : 300
% 0.10/5.55 % WCLimit : 300
% 0.10/5.55 % DateTime : Sat Sep 26 13:00:21 UTC 2026
% 0.10/5.55 % CPUTime :
% 0.10/5.55 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.55 % Process 921391 was started by sandbox on n016,
% 0.10/5.55 % Sat Sep 26 13:00:21 2026
% 0.10/5.55 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.56
% 0.10/5.56 % From the command line: assign(max_seconds, 300).
% 12.13/7.33
% 12.13/7.33 % SZS status Unsatisfiable for theBenchmark
% 12.13/7.33
% 12.13/7.33 % Proof 1 at 1.35 (+ 0.38) seconds.
% 12.13/7.33 % Length of proof is 14.
% 12.13/7.33 % Level of proof is 3.
% 12.13/7.33 % Maximum clause weight is 17.000.
% 12.13/7.33 % Given clauses 266.
% 12.13/7.33
% 12.13/7.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------