%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC037-1 : 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 : 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 08:56:37 AM UTC 2026
% Result : Unsatisfiable 5.60s 1.22s
% Output : CNFRefutation 5.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 20 unt; 0 def)
% Number of atoms : 69 ( 38 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 58 ( 28 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 6 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_14,axiom,
( nil = sk3
| neq(sk5,nil) ),
file('theBenchmark.p',co1_14) ).
cnf(c_31,plain,
( nil = sk3
| neq(sk5,nil) ),
inference(clausify,[status(thm)],[co1_14]) ).
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_32,plain,
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(A,B)
| A != B ),
inference(clausify,[status(thm)],[clause115]) ).
cnf(c_35,plain,
( nil = sk3
| ~ ssList(sk5)
| ~ ssList(nil)
| sk5 != nil ),
inference(resolve,[status(thm)],[c_32,c_31]) ).
cnf(c_36,plain,
( sk3 = nil
| ~ ssList(sk5)
| ~ ssList(nil)
| sk5 != nil ),
inference(copy,[status(thm)],[c_35]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_59,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
fof(clause80,axiom,
! [VAR_0] :
( nil = VAR_0
| ~ ssList(VAR_0)
| ~ segmentP(nil,VAR_0) ),
file('theBenchmark.p',clause80) ).
cnf(c_123,plain,
( nil = A
| ~ ssList(A)
| ~ segmentP(nil,A) ),
inference(clausify,[status(thm)],[clause80]) ).
fof(co1_5,axiom,
nil = sk2,
file('theBenchmark.p',co1_5) ).
cnf(c_212,plain,
nil = sk2,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_213,plain,
sk2 = nil,
inference(copy,[status(thm)],[c_212]) ).
fof(co1_6,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_6) ).
cnf(c_214,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_6]) ).
cnf(c_7238,plain,
nil = sk4,
inference(paramod,[status(thm)],[c_213,c_214]) ).
cnf(c_215,plain,
sk4 = nil,
inference(copy,[status(thm)],[c_7238]) ).
fof(co1_7,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_7) ).
cnf(c_216,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_8,axiom,
nil != sk1,
file('theBenchmark.p',co1_8) ).
cnf(c_217,plain,
nil != sk1,
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_7239,plain,
nil != sk3,
inference(paramod,[status(thm)],[c_216,c_217]) ).
cnf(c_218,plain,
sk3 != nil,
inference(copy,[status(thm)],[c_7239]) ).
fof(co1_10,axiom,
( nil = sk3
| ssList(sk5) ),
file('theBenchmark.p',co1_10) ).
cnf(c_220,plain,
( nil = sk3
| ssList(sk5) ),
inference(clausify,[status(thm)],[co1_10]) ).
cnf(c_7240,plain,
( sk3 = nil
| ssList(sk5) ),
inference(copy,[status(thm)],[c_220]) ).
cnf(c_221,plain,
ssList(sk5),
inference(resolve,[status(thm)],[c_218,c_7240]) ).
fof(co1_15,axiom,
( nil = sk3
| segmentP(sk4,sk5) ),
file('theBenchmark.p',co1_15) ).
cnf(c_224,plain,
( nil = sk3
| segmentP(sk4,sk5) ),
inference(clausify,[status(thm)],[co1_15]) ).
cnf(c_7241,plain,
( nil = sk3
| segmentP(nil,sk5) ),
inference(paramod,[status(thm)],[c_215,c_224]) ).
cnf(c_7242,plain,
( sk3 = nil
| segmentP(nil,sk5) ),
inference(copy,[status(thm)],[c_7241]) ).
cnf(c_225,plain,
segmentP(nil,sk5),
inference(resolve,[status(thm)],[c_218,c_7242]) ).
cnf(c_7243,plain,
( sk3 = nil
| ~ ssList(sk5)
| sk5 != nil ),
inference(resolve,[status(thm)],[c_59,c_36]) ).
cnf(c_7244,plain,
( sk3 = nil
| sk5 != nil ),
inference(resolve,[status(thm)],[c_221,c_7243]) ).
cnf(c_312,plain,
sk5 != nil,
inference(resolve,[status(thm)],[c_218,c_7244]) ).
cnf(c_7245,plain,
( nil = sk5
| ~ segmentP(nil,sk5) ),
inference(resolve,[status(thm)],[c_221,c_123]) ).
cnf(c_7246,plain,
( sk5 = nil
| ~ segmentP(nil,sk5) ),
inference(copy,[status(thm)],[c_7245]) ).
cnf(c_7247,plain,
sk5 = nil,
inference(resolve,[status(thm)],[c_225,c_7246]) ).
cnf(c_7237,plain,
$false,
inference(resolve,[status(thm)],[c_312,c_7247]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC037-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 12:06:25 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 1208553 was started by sandbox2 on n006,
% 0.11/0.38 % Sat Sep 26 12:06:25 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 5.60/1.22
% 5.60/1.22 % SZS status Unsatisfiable for theBenchmark
% 5.60/1.22
% 5.60/1.22 % Proof 1 at 0.65 (+ 0.14) seconds.
% 5.60/1.22 % Length of proof is 19.
% 5.60/1.22 % Level of proof is 4.
% 5.60/1.22 % Maximum clause weight is 12.000.
% 5.60/1.22 % Given clauses 163.
% 5.60/1.22
% 5.60/1.22 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------