%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC100-1 : 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 : n001.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 08:56:49 AM UTC 2026
% Result : Unsatisfiable 80.36s 11.63s
% Output : CNFRefutation 80.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 22
% Syntax : Number of formulae : 104 ( 37 unt; 0 def)
% Number of atoms : 235 ( 74 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 252 ( 121 ~; 131 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_14,axiom,
( neq(sk2,nil)
| nil != sk1 ),
file('theBenchmark.p',co1_14) ).
cnf(c_53,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(clausify,[status(thm)],[co1_14]) ).
cnf(c_54,plain,
( neq(sk2,nil)
| sk1 != nil ),
inference(copy,[status(thm)],[c_53]) ).
fof(co1_13,axiom,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ),
file('theBenchmark.p',co1_13) ).
cnf(c_55,plain,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_56,plain,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil)
| sk2 = nil ),
inference(copy,[status(thm)],[c_55]) ).
fof(co1_11,axiom,
( nil != sk3
| nil = sk4 ),
file('theBenchmark.p',co1_11) ).
cnf(c_59,plain,
( nil != sk3
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_11]) ).
cnf(c_22776,plain,
( nil != sk3
| sk4 = nil ),
inference(copy,[status(thm)],[c_59]) ).
cnf(c_60,plain,
( sk3 != nil
| sk4 = nil ),
inference(copy,[status(thm)],[c_22776]) ).
fof(co1_8,axiom,
app(sk3,sk5) = sk4,
file('theBenchmark.p',co1_8) ).
cnf(c_63,plain,
app(sk3,sk5) = sk4,
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
ssList(sk5),
file('theBenchmark.p',co1_7) ).
cnf(c_64,plain,
ssList(sk5),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_65,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
cnf(c_66,plain,
sk3 = sk1,
inference(copy,[status(thm)],[c_65]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_67,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_68,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_67]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_69,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_70,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(co1_2,axiom,
ssList(sk2),
file('theBenchmark.p',co1_2) ).
cnf(c_71,plain,
ssList(sk2),
inference(clausify,[status(thm)],[co1_2]) ).
fof(co1_1,axiom,
ssList(sk1),
file('theBenchmark.p',co1_1) ).
cnf(c_72,plain,
ssList(sk1),
inference(clausify,[status(thm)],[co1_1]) ).
fof(clause152,axiom,
! [VAR_0,VAR_1,VAR_2] :
( segmentP(VAR_0,VAR_2)
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| ~ ssList(VAR_2)
| ~ segmentP(VAR_1,VAR_2)
| ~ segmentP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause152) ).
cnf(c_98,plain,
( segmentP(A,C)
| ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ~ segmentP(B,C)
| ~ segmentP(A,B) ),
inference(clausify,[status(thm)],[clause152]) ).
fof(clause137,axiom,
! [VAR_0,VAR_1,VAR_2] :
( frontsegP(app(VAR_0,VAR_2),VAR_1)
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| ~ ssList(VAR_2)
| ~ frontsegP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause137) ).
cnf(c_112,plain,
( frontsegP(app(A,C),B)
| ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ~ frontsegP(A,B) ),
inference(clausify,[status(thm)],[clause137]) ).
fof(clause127,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| ~ ssList(VAR_1)
| ~ ssList(VAR_0)
| ~ segmentP(VAR_1,VAR_0)
| ~ segmentP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause127) ).
cnf(c_122,plain,
( B = A
| ~ ssList(B)
| ~ ssList(A)
| ~ segmentP(B,A)
| ~ segmentP(A,B) ),
inference(clausify,[status(thm)],[clause127]) ).
fof(clause118,axiom,
! [VAR_0,VAR_1] :
( nil = VAR_0
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| app(VAR_0,VAR_1) != nil ),
file('theBenchmark.p',clause118) ).
cnf(c_130,plain,
( nil = A
| ~ ssList(A)
| ~ ssList(B)
| app(A,B) != nil ),
inference(clausify,[status(thm)],[clause118]) ).
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_133,plain,
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(A,B)
| A != B ),
inference(clausify,[status(thm)],[clause115]) ).
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_148,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause79,axiom,
! [VAR_0] :
( segmentP(nil,VAR_0)
| ~ ssList(VAR_0)
| nil != VAR_0 ),
file('theBenchmark.p',clause79) ).
cnf(c_162,plain,
( segmentP(nil,A)
| ~ ssList(A)
| nil != A ),
inference(clausify,[status(thm)],[clause79]) ).
fof(clause61,axiom,
! [VAR_0] :
( frontsegP(VAR_0,VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause61) ).
cnf(c_172,plain,
( frontsegP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause61]) ).
fof(clause57,axiom,
! [VAR_0] :
( segmentP(VAR_0,VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause57) ).
cnf(c_176,plain,
( segmentP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause57]) ).
fof(clause56,axiom,
! [VAR_0] :
( segmentP(VAR_0,nil)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause56) ).
cnf(c_177,plain,
( segmentP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause56]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_225,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_384,plain,
( frontsegP(app(A,B),A)
| ~ ssList(A)
| ~ ssList(B)
| ~ frontsegP(A,A) ),
inference(factor,[status(thm)],[c_112]) ).
cnf(c_838,plain,
app(sk1,sk5) = sk4,
inference(paramod,[status(thm)],[c_66,c_63]) ).
cnf(c_1087,plain,
( nil = A
| ~ ssList(A)
| app(A,sk5) != nil ),
inference(resolve,[status(thm)],[c_130,c_64]) ).
cnf(c_1108,plain,
( sk1 = A
| neq(sk1,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_148,c_72]) ).
cnf(c_22777,plain,
( segmentP(nil,sk1)
| nil != sk1 ),
inference(resolve,[status(thm)],[c_162,c_72]) ).
cnf(c_1133,plain,
( segmentP(nil,sk1)
| sk1 != nil ),
inference(copy,[status(thm)],[c_22777]) ).
cnf(c_22778,plain,
( segmentP(nil,sk4)
| nil != sk4 ),
inference(resolve,[status(thm)],[c_162,c_69]) ).
cnf(c_1136,plain,
( segmentP(nil,sk4)
| sk4 != nil ),
inference(copy,[status(thm)],[c_22778]) ).
cnf(c_1158,plain,
frontsegP(sk1,sk1),
inference(resolve,[status(thm)],[c_172,c_72]) ).
cnf(c_1180,plain,
segmentP(sk3,sk3),
inference(resolve,[status(thm)],[c_176,c_70]) ).
cnf(c_1181,plain,
segmentP(sk4,sk4),
inference(resolve,[status(thm)],[c_176,c_69]) ).
cnf(c_1184,plain,
segmentP(sk2,nil),
inference(resolve,[status(thm)],[c_177,c_71]) ).
cnf(c_1185,plain,
segmentP(sk3,nil),
inference(resolve,[status(thm)],[c_177,c_70]) ).
cnf(c_4937,plain,
app(sk1,sk5) = sk2,
inference(paramod,[status(thm)],[c_68,c_838]) ).
cnf(c_22779,plain,
( frontsegP(app(sk1,A),sk1)
| ~ ssList(sk1)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_1158,c_384]) ).
cnf(c_4974,plain,
( frontsegP(app(sk1,A),sk1)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_72,c_22779]) ).
cnf(c_5256,plain,
segmentP(sk1,sk3),
inference(paramod,[status(thm)],[c_66,c_1180]) ).
cnf(c_5265,plain,
segmentP(sk4,sk2),
inference(paramod,[status(thm)],[c_68,c_1181]) ).
cnf(c_22780,plain,
( sk2 = nil
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ segmentP(nil,sk2) ),
inference(resolve,[status(thm)],[c_1184,c_122]) ).
cnf(c_22781,plain,
( sk2 = nil
| ~ ssList(sk2)
| ~ segmentP(nil,sk2) ),
inference(resolve,[status(thm)],[c_225,c_22780]) ).
cnf(c_5643,plain,
( sk2 = nil
| ~ segmentP(nil,sk2) ),
inference(resolve,[status(thm)],[c_71,c_22781]) ).
cnf(c_22782,plain,
( sk3 = nil
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ segmentP(nil,sk3) ),
inference(resolve,[status(thm)],[c_1185,c_122]) ).
cnf(c_22783,plain,
( sk3 = nil
| ~ ssList(sk3)
| ~ segmentP(nil,sk3) ),
inference(resolve,[status(thm)],[c_225,c_22782]) ).
cnf(c_5656,plain,
( sk3 = nil
| ~ segmentP(nil,sk3) ),
inference(resolve,[status(thm)],[c_70,c_22783]) ).
cnf(c_22784,plain,
( segmentP(A,sk3)
| ~ ssList(A)
| ~ ssList(sk1)
| ~ ssList(sk3)
| ~ segmentP(A,sk1) ),
inference(resolve,[status(thm)],[c_5256,c_98]) ).
cnf(c_22785,plain,
( segmentP(A,sk3)
| ~ ssList(A)
| ~ ssList(sk1)
| ~ segmentP(A,sk1) ),
inference(resolve,[status(thm)],[c_70,c_22784]) ).
cnf(c_6805,plain,
( segmentP(A,sk3)
| ~ ssList(A)
| ~ segmentP(A,sk1) ),
inference(resolve,[status(thm)],[c_72,c_22785]) ).
cnf(c_22786,plain,
( segmentP(A,sk2)
| ~ ssList(A)
| ~ ssList(sk4)
| ~ ssList(sk2)
| ~ segmentP(A,sk4) ),
inference(resolve,[status(thm)],[c_5265,c_98]) ).
cnf(c_22787,plain,
( segmentP(A,sk2)
| ~ ssList(A)
| ~ ssList(sk4)
| ~ segmentP(A,sk4) ),
inference(resolve,[status(thm)],[c_71,c_22786]) ).
cnf(c_7152,plain,
( segmentP(A,sk2)
| ~ ssList(A)
| ~ segmentP(A,sk4) ),
inference(resolve,[status(thm)],[c_69,c_22787]) ).
cnf(c_13728,plain,
( sk1 = nil
| neq(sk1,nil) ),
inference(resolve,[status(thm)],[c_1108,c_225]) ).
cnf(c_13756,plain,
( ~ frontsegP(sk2,sk1)
| sk2 = nil
| sk1 = nil ),
inference(resolve,[status(thm)],[c_13728,c_56]) ).
cnf(c_22788,plain,
( nil = sk1
| app(sk1,sk5) != nil ),
inference(resolve,[status(thm)],[c_1087,c_72]) ).
cnf(c_21823,plain,
( sk1 = nil
| app(sk1,sk5) != nil ),
inference(copy,[status(thm)],[c_22788]) ).
cnf(c_21983,plain,
frontsegP(app(sk1,sk5),sk1),
inference(resolve,[status(thm)],[c_4974,c_64]) ).
cnf(c_22058,plain,
frontsegP(sk2,sk1),
inference(paramod,[status(thm)],[c_4937,c_21983]) ).
cnf(c_22059,plain,
( sk2 = nil
| sk1 = nil ),
inference(resolve,[status(thm)],[c_22058,c_13756]) ).
cnf(c_22096,plain,
( segmentP(nil,sk1)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_22059,c_1133]) ).
cnf(c_22789,plain,
( segmentP(nil,sk3)
| ~ ssList(nil)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_22096,c_6805]) ).
cnf(c_22145,plain,
( segmentP(nil,sk3)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_225,c_22789]) ).
cnf(c_22169,plain,
( sk3 = nil
| sk2 = nil ),
inference(resolve,[status(thm)],[c_22145,c_5656]) ).
cnf(c_22226,plain,
( sk4 = nil
| sk2 = nil ),
inference(resolve,[status(thm)],[c_22169,c_60]) ).
cnf(c_22254,plain,
( segmentP(nil,sk4)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_22226,c_1136]) ).
cnf(c_22790,plain,
( segmentP(nil,sk2)
| ~ ssList(nil)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_22254,c_7152]) ).
cnf(c_22257,plain,
( segmentP(nil,sk2)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_225,c_22790]) ).
cnf(c_22791,plain,
( sk2 = nil
| sk2 = nil ),
inference(resolve,[status(thm)],[c_22257,c_5643]) ).
cnf(c_22283,plain,
sk2 = nil,
inference(copy,[status(thm)],[c_22791]) ).
cnf(c_22325,plain,
app(sk1,sk5) = nil,
inference(paramod,[status(thm)],[c_22283,c_4937]) ).
cnf(c_22395,plain,
sk1 = nil,
inference(resolve,[status(thm)],[c_22325,c_21823]) ).
cnf(c_22462,plain,
neq(sk2,nil),
inference(resolve,[status(thm)],[c_22395,c_54]) ).
cnf(c_22792,plain,
( ~ ssList(sk2)
| ~ ssList(nil)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_22462,c_133]) ).
cnf(c_22793,plain,
( ~ ssList(sk2)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_22283,c_22792]) ).
cnf(c_22794,plain,
~ ssList(sk2),
inference(resolve,[status(thm)],[c_225,c_22793]) ).
cnf(c_22775,plain,
$false,
inference(resolve,[status(thm)],[c_71,c_22794]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC100-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n001.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 12:20:58 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 1769589 was started by sandbox on n001,
% 0.11/0.37 % Sat Sep 26 12:20:58 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 80.36/11.63
% 80.36/11.63 % given #500 (I,wt=38): 562 app(app(A,cons(B,A)),cons(C,D)) != D | -ssList(D) | -ssList(A) | -ssItem(C) | -ssItem(B) | lt(B,C) | lt(C,B) | -lt(skaf59(D),skaf60(D)). [factor(302,c,d)].
% 80.36/11.63
% 80.36/11.63 % given #1000 (W,wt=8): 2998 segmentP(skaf76(A),nil). [resolve(214,a,177,a)].
% 80.36/11.63
% 80.36/11.63 % given #1500 (T,wt=9): 12349 frontsegP(app(sk1,sk3),sk1). [para(66(a,1),6431(a,2))].
% 80.36/11.63
% 80.36/11.63 % given #2000 (F,wt=13): 19330 cons(skac2,cons(skac3,sk4)) != nil. [resolve(19035,a,3424,b)].
% 80.36/11.63
% 80.36/11.63 % SZS status Unsatisfiable for theBenchmark
% 80.36/11.63
% 80.36/11.63 % Proof 1 at 2.27 (+ 0.86) seconds.
% 80.36/11.63 % Length of proof is 63.
% 80.36/11.63 % Level of proof is 16.
% 80.36/11.63 % Maximum clause weight is 18.000.
% 80.36/11.63 % Given clauses 2403.
% 80.36/11.63
% 80.36/11.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------