%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC110-1 : 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 : n018.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 08:56:52 AM UTC 2026
% Result : Unsatisfiable 23.04s 3.71s
% Output : CNFRefutation 23.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 16
% Syntax : Number of formulae : 68 ( 25 unt; 0 def)
% Number of atoms : 152 ( 63 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 169 ( 85 ~; 84 |; 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 : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_14,axiom,
( neq(sk2,nil)
| nil != sk1 ),
file('theBenchmark.p',co1_14) ).
cnf(c_55,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(clausify,[status(thm)],[co1_14]) ).
cnf(c_56,plain,
( neq(sk2,nil)
| sk1 != nil ),
inference(copy,[status(thm)],[c_55]) ).
fof(co1_13,axiom,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ),
file('theBenchmark.p',co1_13) ).
cnf(c_57,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_58,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil)
| sk2 = nil ),
inference(copy,[status(thm)],[c_57]) ).
fof(co1_12,axiom,
( neq(sk2,nil)
| nil = sk2 ),
file('theBenchmark.p',co1_12) ).
cnf(c_59,plain,
( neq(sk2,nil)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_12]) ).
cnf(c_60,plain,
( neq(sk2,nil)
| sk2 = nil ),
inference(copy,[status(thm)],[c_59]) ).
fof(co1_11,axiom,
( nil != sk3
| nil = sk4 ),
file('theBenchmark.p',co1_11) ).
cnf(c_61,plain,
( nil != sk3
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_11]) ).
cnf(c_18243,plain,
( nil != sk3
| sk4 = nil ),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_62,plain,
( sk3 != nil
| sk4 = nil ),
inference(copy,[status(thm)],[c_18243]) ).
fof(co1_8,axiom,
app(sk3,sk5) = sk4,
file('theBenchmark.p',co1_8) ).
cnf(c_64,plain,
app(sk3,sk5) = sk4,
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
ssList(sk5),
file('theBenchmark.p',co1_7) ).
cnf(c_65,plain,
ssList(sk5),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_66,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
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]) ).
cnf(c_70,plain,
ssList(sk2),
inference(paramod,[status(thm)],[c_68,c_69]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_71,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_80,plain,
( segmentP(D,B)
| ~ ssList(D)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != D ),
inference(clausify,[status(thm)],[clause173]) ).
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(clause74,axiom,
! [VAR_0] :
( app(nil,VAR_0) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause74) ).
cnf(c_165,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause74]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_225,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_18244,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk3,nil)
| sk2 = nil ),
inference(paramod,[status(thm)],[c_66,c_58]) ).
cnf(c_333,plain,
( ~ segmentP(sk2,sk3)
| ~ neq(sk3,nil)
| sk2 = nil ),
inference(paramod,[status(thm)],[c_66,c_18244]) ).
cnf(c_334,plain,
( neq(sk2,nil)
| sk3 != nil ),
inference(paramod,[status(thm)],[c_66,c_56]) ).
cnf(c_336,plain,
app(sk3,sk5) = sk2,
inference(paramod,[status(thm)],[c_68,c_64]) ).
cnf(c_337,plain,
( sk3 != nil
| sk2 = nil ),
inference(paramod,[status(thm)],[c_68,c_62]) ).
cnf(c_920,plain,
( segmentP(sk2,B)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != sk2 ),
inference(resolve,[status(thm)],[c_80,c_70]) ).
cnf(c_1338,plain,
( sk3 = A
| neq(sk3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_148,c_71]) ).
cnf(c_1398,plain,
app(nil,sk3) = sk3,
inference(resolve,[status(thm)],[c_165,c_71]) ).
cnf(c_18245,plain,
( nil = sk3
| ~ ssList(sk3)
| ~ ssList(sk5)
| sk2 != nil ),
inference(paramod,[status(thm)],[c_336,c_130]) ).
cnf(c_18246,plain,
( sk3 = nil
| ~ ssList(sk3)
| ~ ssList(sk5)
| sk2 != nil ),
inference(copy,[status(thm)],[c_18245]) ).
cnf(c_18247,plain,
( sk3 = nil
| ~ ssList(sk3)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_65,c_18246]) ).
cnf(c_8378,plain,
( sk3 = nil
| sk2 != nil ),
inference(resolve,[status(thm)],[c_71,c_18247]) ).
cnf(c_12593,plain,
( neq(sk2,nil)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_8378,c_60]) ).
cnf(c_18248,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(resolve,[status(thm)],[c_12593,c_334]) ).
cnf(c_13121,plain,
neq(sk2,nil),
inference(copy,[status(thm)],[c_18248]) ).
cnf(c_18249,plain,
( ~ ssList(sk2)
| ~ ssList(nil)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_13121,c_133]) ).
cnf(c_18250,plain,
( ~ ssList(sk2)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_225,c_18249]) ).
cnf(c_13122,plain,
sk2 != nil,
inference(resolve,[status(thm)],[c_70,c_18250]) ).
cnf(c_13145,plain,
sk3 != nil,
inference(resolve,[status(thm)],[c_13122,c_337]) ).
cnf(c_13146,plain,
( ~ segmentP(sk2,sk3)
| ~ neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_13122,c_333]) ).
cnf(c_18251,plain,
( segmentP(sk2,sk3)
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(A)
| app(sk3,A) != sk2 ),
inference(paramod,[status(thm)],[c_1398,c_920]) ).
cnf(c_18252,plain,
( segmentP(sk2,sk3)
| ~ ssList(sk3)
| ~ ssList(A)
| app(sk3,A) != sk2 ),
inference(resolve,[status(thm)],[c_225,c_18251]) ).
cnf(c_14593,plain,
( segmentP(sk2,sk3)
| ~ ssList(A)
| app(sk3,A) != sk2 ),
inference(resolve,[status(thm)],[c_71,c_18252]) ).
cnf(c_18253,plain,
( sk3 = nil
| neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_1338,c_225]) ).
cnf(c_18162,plain,
neq(sk3,nil),
inference(resolve,[status(thm)],[c_13145,c_18253]) ).
cnf(c_18192,plain,
~ segmentP(sk2,sk3),
inference(resolve,[status(thm)],[c_18162,c_13146]) ).
cnf(c_18202,plain,
( ~ ssList(A)
| app(sk3,A) != sk2 ),
inference(resolve,[status(thm)],[c_18192,c_14593]) ).
cnf(c_18254,plain,
~ ssList(sk5),
inference(resolve,[status(thm)],[c_18202,c_336]) ).
cnf(c_18242,plain,
$false,
inference(resolve,[status(thm)],[c_65,c_18254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC110-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 12:18:38 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 420013 was started by sandbox on n018,
% 0.08/0.36 % Sat Sep 26 12:18:38 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 23.04/3.71
% 23.04/3.71 % given #500 (I,wt=40): 569 app(app(A,cons(B,C)),cons(D,A)) != C | -ssList(A) | -ssList(C) | -ssItem(D) | -ssItem(B) | lt(B,D) | lt(D,B) | -lt(skaf59(C),skaf60(C)). [factor(301,c,f)].
% 23.04/3.71
% 23.04/3.71 % given #1000 (T,wt=8): 6886 segmentP(skaf80(A),nil). [resolve(218,a,177,a)].
% 23.04/3.71
% 23.04/3.71 % given #1500 (F,wt=12): 13075 skaf53(A) != sk5 | -neq(skaf53(A),sk5). [resolve(1312,c,191,a),flip(a)].
% 23.04/3.71
% 23.04/3.71 % SZS status Unsatisfiable for theBenchmark
% 23.04/3.71
% 23.04/3.71 % Proof 1 at 2.53 (+ 0.76) seconds.
% 23.04/3.71 % Length of proof is 40.
% 23.04/3.71 % Level of proof is 11.
% 23.04/3.71 % Maximum clause weight is 26.000.
% 23.04/3.71 % Given clauses 1741.
% 23.04/3.71
% 23.04/3.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------