%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC384-1 : 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 : n006.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 24.08s 21.89s
% Output : CNFRefutation 24.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 58 ( 22 unt; 0 def)
% Number of atoms : 120 ( 38 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 122 ( 60 ~; 62 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_7,axiom,
neq(sk2,nil),
file('theBenchmark.p',co1_7) ).
cnf(c_30,plain,
neq(sk2,nil),
inference(clausify,[status(thm)],[co1_7]) ).
fof(clause115,axiom,
! [VAR_0,VAR_1] :
( ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| ~ neq(VAR_0,VAR_1)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',clause115) ).
cnf(c_31,plain,
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(A,B)
| A != B ),
inference(clausify,[status(thm)],[clause115]) ).
cnf(c_34,plain,
( ~ ssList(sk2)
| ~ ssList(nil)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_31,c_30]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_52,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
fof(clause116,axiom,
! [VAR_0,VAR_1] :
( singletonP(VAR_1)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0)
| cons(VAR_0,nil) != VAR_1 ),
file('theBenchmark.p',clause116) ).
cnf(c_142,plain,
( singletonP(B)
| ~ ssList(B)
| ~ ssItem(A)
| cons(A,nil) != B ),
inference(clausify,[status(thm)],[clause116]) ).
fof(clause173,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( segmentP(VAR_3,VAR_1)
| ~ ssList(VAR_3)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0)
| ~ ssList(VAR_2)
| app(app(VAR_0,VAR_1),VAR_2) != VAR_3 ),
file('theBenchmark.p',clause173) ).
cnf(c_193,plain,
( segmentP(D,B)
| ~ ssList(D)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != D ),
inference(clausify,[status(thm)],[clause173]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_203,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_204,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_205,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_206,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_8,axiom,
( nil = sk4
| ssItem(sk5) ),
file('theBenchmark.p',co1_8) ).
cnf(c_207,plain,
( nil = sk4
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_208,plain,
( sk4 = nil
| ssItem(sk5) ),
inference(copy,[status(thm)],[c_207]) ).
fof(co1_10,axiom,
( nil = sk4
| ssList(sk6) ),
file('theBenchmark.p',co1_10) ).
cnf(c_211,plain,
( nil = sk4
| ssList(sk6) ),
inference(clausify,[status(thm)],[co1_10]) ).
cnf(c_212,plain,
( sk4 = nil
| ssList(sk6) ),
inference(copy,[status(thm)],[c_211]) ).
fof(co1_11,axiom,
( nil = sk4
| ssList(sk7) ),
file('theBenchmark.p',co1_11) ).
cnf(c_213,plain,
( nil = sk4
| ssList(sk7) ),
inference(clausify,[status(thm)],[co1_11]) ).
cnf(c_214,plain,
( sk4 = nil
| ssList(sk7) ),
inference(copy,[status(thm)],[c_213]) ).
fof(co1_12,axiom,
( nil = sk4
| cons(sk5,nil) = sk3 ),
file('theBenchmark.p',co1_12) ).
cnf(c_215,plain,
( nil = sk4
| cons(sk5,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_12]) ).
cnf(c_216,plain,
( sk4 = nil
| cons(sk5,nil) = sk3 ),
inference(copy,[status(thm)],[c_215]) ).
fof(co1_13,axiom,
( nil = sk4
| app(app(sk6,sk3),sk7) = sk4 ),
file('theBenchmark.p',co1_13) ).
cnf(c_217,plain,
( nil = sk4
| app(app(sk6,sk3),sk7) = sk4 ),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_218,plain,
( sk4 = nil
| app(app(sk6,sk3),sk7) = sk4 ),
inference(copy,[status(thm)],[c_217]) ).
fof(co1_22,axiom,
( ~ segmentP(sk2,sk1)
| ~ singletonP(sk1) ),
file('theBenchmark.p',co1_22) ).
cnf(c_235,plain,
( ~ segmentP(sk2,sk1)
| ~ singletonP(sk1) ),
inference(clausify,[status(thm)],[co1_22]) ).
cnf(c_9736,plain,
( ~ segmentP(sk2,sk1)
| ~ singletonP(sk3) ),
inference(paramod,[status(thm)],[c_206,c_235]) ).
cnf(c_9737,plain,
( ~ segmentP(sk4,sk1)
| ~ singletonP(sk3) ),
inference(paramod,[status(thm)],[c_205,c_9736]) ).
cnf(c_236,plain,
( ~ segmentP(sk4,sk3)
| ~ singletonP(sk3) ),
inference(paramod,[status(thm)],[c_206,c_9737]) ).
cnf(c_9738,plain,
( ~ ssList(sk2)
| ~ ssList(nil)
| sk4 != nil ),
inference(paramod,[status(thm)],[c_205,c_34]) ).
cnf(c_9739,plain,
( ~ ssList(sk4)
| ~ ssList(nil)
| sk4 != nil ),
inference(paramod,[status(thm)],[c_205,c_9738]) ).
cnf(c_9740,plain,
( ~ ssList(sk4)
| sk4 != nil ),
inference(resolve,[status(thm)],[c_52,c_9739]) ).
cnf(c_321,plain,
sk4 != nil,
inference(resolve,[status(thm)],[c_204,c_9740]) ).
cnf(c_541,plain,
app(app(sk6,sk3),sk7) = sk4,
inference(resolve,[status(thm)],[c_321,c_218]) ).
cnf(c_542,plain,
cons(sk5,nil) = sk3,
inference(resolve,[status(thm)],[c_321,c_216]) ).
cnf(c_543,plain,
ssList(sk7),
inference(resolve,[status(thm)],[c_321,c_214]) ).
cnf(c_544,plain,
ssList(sk6),
inference(resolve,[status(thm)],[c_321,c_212]) ).
cnf(c_545,plain,
ssItem(sk5),
inference(resolve,[status(thm)],[c_321,c_208]) ).
cnf(c_9741,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_541,c_193]) ).
cnf(c_9742,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ ssList(sk6) ),
inference(resolve,[status(thm)],[c_543,c_9741]) ).
cnf(c_9743,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_544,c_9742]) ).
cnf(c_9744,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk4) ),
inference(resolve,[status(thm)],[c_203,c_9743]) ).
cnf(c_9712,plain,
segmentP(sk4,sk3),
inference(resolve,[status(thm)],[c_204,c_9744]) ).
cnf(c_9731,plain,
~ singletonP(sk3),
inference(resolve,[status(thm)],[c_9712,c_236]) ).
cnf(c_9745,plain,
( singletonP(sk3)
| ~ ssList(sk3)
| ~ ssItem(sk5) ),
inference(resolve,[status(thm)],[c_542,c_142]) ).
cnf(c_9746,plain,
( singletonP(sk3)
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_545,c_9745]) ).
cnf(c_9747,plain,
singletonP(sk3),
inference(resolve,[status(thm)],[c_203,c_9746]) ).
cnf(c_9735,plain,
$false,
inference(resolve,[status(thm)],[c_9731,c_9747]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC384-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/15.36 % Computer : n006.cluster.edu
% 0.05/15.36 % Model : x86_64 x86_64
% 0.05/15.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/15.36 % Memory : 8046.5625MB
% 0.05/15.36 % OS : Linux 6.8.0-71-generic
% 0.05/15.36 % CPULimit : 300
% 0.05/15.36 % WCLimit : 300
% 0.05/15.36 % DateTime : Sat Sep 26 12:55:56 UTC 2026
% 0.05/15.36 % CPUTime :
% 0.05/15.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/15.37 % Process 1311246 was started by sandbox on n006,
% 0.05/15.37 % Sat Sep 26 12:55:56 2026
% 0.05/15.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.05/15.38
% 0.05/15.38 % From the command line: assign(max_seconds, 300).
% 24.08/21.89
% 24.08/21.89 % SZS status Unsatisfiable for theBenchmark
% 24.08/21.89
% 24.08/21.89 % Proof 1 at 2.49 (+ 0.55) seconds.
% 24.08/21.89 % Length of proof is 31.
% 24.08/21.89 % Level of proof is 6.
% 24.08/21.89 % Maximum clause weight is 26.000.
% 24.08/21.89 % Given clauses 456.
% 24.08/21.89
% 24.08/21.89 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------