%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC118-1 : 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 : n012.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 08:56:53 AM UTC 2026
% Result : Unsatisfiable 15.75s 2.35s
% Output : CNFRefutation 15.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 49 ( 22 unt; 0 def)
% Number of atoms : 95 ( 39 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 102 ( 56 ~; 46 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_15,axiom,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
file('theBenchmark.p',co1_15) ).
cnf(c_51,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(clausify,[status(thm)],[co1_15]) ).
fof(co1_14,axiom,
( nil != sk1
| nil != sk2 ),
file('theBenchmark.p',co1_14) ).
cnf(c_52,plain,
( nil != sk1
| nil != sk2 ),
inference(clausify,[status(thm)],[co1_14]) ).
cnf(c_6781,plain,
( nil != sk1
| sk2 != nil ),
inference(copy,[status(thm)],[c_52]) ).
cnf(c_53,plain,
( sk1 != nil
| sk2 != nil ),
inference(copy,[status(thm)],[c_6781]) ).
fof(co1_13,axiom,
( nil != sk3
| nil = sk4 ),
file('theBenchmark.p',co1_13) ).
cnf(c_54,plain,
( nil != sk3
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_6782,plain,
( nil != sk3
| sk4 = nil ),
inference(copy,[status(thm)],[c_54]) ).
cnf(c_55,plain,
( sk3 != nil
| sk4 = nil ),
inference(copy,[status(thm)],[c_6782]) ).
fof(co1_9,axiom,
app(app(sk5,sk3),sk6) = sk4,
file('theBenchmark.p',co1_9) ).
cnf(c_59,plain,
app(app(sk5,sk3),sk6) = sk4,
inference(clausify,[status(thm)],[co1_9]) ).
fof(co1_8,axiom,
ssList(sk6),
file('theBenchmark.p',co1_8) ).
cnf(c_60,plain,
ssList(sk6),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
ssList(sk5),
file('theBenchmark.p',co1_7) ).
cnf(c_61,plain,
ssList(sk5),
inference(clausify,[status(thm)],[co1_7]) ).
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]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_64,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_65,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
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_75,plain,
( segmentP(D,B)
| ~ ssList(D)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != D ),
inference(clausify,[status(thm)],[clause173]) ).
fof(clause100,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| neq(VAR_1,VAR_0)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause100) ).
cnf(c_143,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_220,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_6783,plain,
( sk1 != nil
| sk4 != nil ),
inference(paramod,[status(thm)],[c_63,c_53]) ).
cnf(c_328,plain,
( sk3 != nil
| sk4 != nil ),
inference(paramod,[status(thm)],[c_62,c_6783]) ).
cnf(c_6784,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk3,nil) ),
inference(paramod,[status(thm)],[c_62,c_51]) ).
cnf(c_6785,plain,
( ~ segmentP(sk4,sk1)
| ~ neq(sk3,nil) ),
inference(paramod,[status(thm)],[c_63,c_6784]) ).
cnf(c_329,plain,
( ~ segmentP(sk4,sk3)
| ~ neq(sk3,nil) ),
inference(paramod,[status(thm)],[c_62,c_6785]) ).
cnf(c_6786,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssList(sk6) ),
inference(resolve,[status(thm)],[c_75,c_59]) ).
cnf(c_6787,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ ssList(sk5) ),
inference(resolve,[status(thm)],[c_60,c_6786]) ).
cnf(c_6788,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_61,c_6787]) ).
cnf(c_6789,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk4) ),
inference(resolve,[status(thm)],[c_65,c_6788]) ).
cnf(c_879,plain,
segmentP(sk4,sk3),
inference(resolve,[status(thm)],[c_64,c_6789]) ).
cnf(c_880,plain,
~ neq(sk3,nil),
inference(resolve,[status(thm)],[c_879,c_329]) ).
cnf(c_1243,plain,
( sk3 = A
| neq(sk3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_143,c_65]) ).
cnf(c_6790,plain,
( sk3 = nil
| neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_1243,c_220]) ).
cnf(c_6633,plain,
sk3 = nil,
inference(resolve,[status(thm)],[c_880,c_6790]) ).
cnf(c_6791,plain,
( nil != nil
| sk4 != nil ),
inference(paramod,[status(thm)],[c_6633,c_328]) ).
cnf(c_6777,plain,
sk4 != nil,
inference(copy,[status(thm)],[c_6791]) ).
cnf(c_6792,plain,
( nil != nil
| sk4 = nil ),
inference(paramod,[status(thm)],[c_6633,c_55]) ).
cnf(c_6793,plain,
sk4 = nil,
inference(copy,[status(thm)],[c_6792]) ).
cnf(c_6780,plain,
$false,
inference(resolve,[status(thm)],[c_6777,c_6793]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC118-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sat Sep 26 12:17:04 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.29 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.29 % Process 560006 was started by sandbox2 on n012,
% 0.02/0.29 % Sat Sep 26 12:17:04 2026
% 0.02/0.29 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.02/0.30
% 0.02/0.30 % From the command line: assign(max_seconds, 300).
% 15.75/2.35
% 15.75/2.35 % given #500 (I,wt=52): 555 app(app(A,cons(B,A)),cons(C,A)) != D | -ssList(A) | -ssItem(C) | -ssItem(B) | -ssList(D) | lt(B,C) | lt(C,B) | -lt(skaf59(D),skaf60(D)). [factor(295,b,c)].
% 15.75/2.35
% 15.75/2.35 % SZS status Unsatisfiable for theBenchmark
% 15.75/2.35
% 15.75/2.35 % Proof 1 at 1.39 (+ 0.53) seconds.
% 15.75/2.35 % Length of proof is 23.
% 15.75/2.35 % Level of proof is 5.
% 15.75/2.35 % Maximum clause weight is 35.000.
% 15.75/2.35 % Given clauses 932.
% 15.75/2.35
% 15.75/2.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------