%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC065-1 : 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 : n007.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 08:56:43 AM UTC 2026
% Result : Unsatisfiable 62.83s 8.36s
% Output : CNFRefutation 62.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 72 ( 26 unt; 0 def)
% Number of atoms : 169 ( 64 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 195 ( 98 ~; 97 |; 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 : 36 ( 0 sgn 13 !; 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,
! [VAR_0] :
( ~ segmentP(sk1,VAR_0)
| ~ segmentP(sk2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil = sk2 ),
file('theBenchmark.p',co1_13) ).
cnf(c_57,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_58,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| 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_18068,plain,
( nil != sk3
| sk4 = nil ),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_62,plain,
( sk3 != nil
| sk4 = nil ),
inference(copy,[status(thm)],[c_18068]) ).
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(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(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_225,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_333,plain,
( ~ segmentP(sk3,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sk2 = nil ),
inference(paramod,[status(thm)],[c_66,c_58]) ).
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_1416,plain,
segmentP(sk3,sk3),
inference(resolve,[status(thm)],[c_176,c_71]) ).
cnf(c_18069,plain,
( ~ segmentP(sk3,sk3)
| ~ segmentP(sk2,sk3)
| ~ neq(sk3,nil)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_333,c_71]) ).
cnf(c_8397,plain,
( ~ segmentP(sk2,sk3)
| ~ neq(sk3,nil)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_1416,c_18069]) ).
cnf(c_18070,plain,
( nil = sk3
| ~ ssList(sk3)
| ~ ssList(sk5)
| sk2 != nil ),
inference(paramod,[status(thm)],[c_336,c_130]) ).
cnf(c_18071,plain,
( sk3 = nil
| ~ ssList(sk3)
| ~ ssList(sk5)
| sk2 != nil ),
inference(copy,[status(thm)],[c_18070]) ).
cnf(c_18072,plain,
( sk3 = nil
| ~ ssList(sk3)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_65,c_18071]) ).
cnf(c_8441,plain,
( sk3 = nil
| sk2 != nil ),
inference(resolve,[status(thm)],[c_71,c_18072]) ).
cnf(c_12654,plain,
( neq(sk2,nil)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_8441,c_60]) ).
cnf(c_18073,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(resolve,[status(thm)],[c_12654,c_334]) ).
cnf(c_13163,plain,
neq(sk2,nil),
inference(copy,[status(thm)],[c_18073]) ).
cnf(c_18074,plain,
( ~ ssList(sk2)
| ~ ssList(nil)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_13163,c_133]) ).
cnf(c_18075,plain,
( ~ ssList(sk2)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_225,c_18074]) ).
cnf(c_13276,plain,
sk2 != nil,
inference(resolve,[status(thm)],[c_70,c_18075]) ).
cnf(c_13286,plain,
( ~ segmentP(sk2,sk3)
| ~ neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_13276,c_8397]) ).
cnf(c_13331,plain,
sk3 != nil,
inference(resolve,[status(thm)],[c_13276,c_337]) ).
cnf(c_18076,plain,
( segmentP(sk2,sk3)
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(A)
| app(sk3,A) != sk2 ),
inference(paramod,[status(thm)],[c_1398,c_920]) ).
cnf(c_18077,plain,
( segmentP(sk2,sk3)
| ~ ssList(sk3)
| ~ ssList(A)
| app(sk3,A) != sk2 ),
inference(resolve,[status(thm)],[c_225,c_18076]) ).
cnf(c_14640,plain,
( segmentP(sk2,sk3)
| ~ ssList(A)
| app(sk3,A) != sk2 ),
inference(resolve,[status(thm)],[c_71,c_18077]) ).
cnf(c_18078,plain,
( sk3 = nil
| neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_1338,c_225]) ).
cnf(c_18014,plain,
neq(sk3,nil),
inference(resolve,[status(thm)],[c_13331,c_18078]) ).
cnf(c_18044,plain,
~ segmentP(sk2,sk3),
inference(resolve,[status(thm)],[c_18014,c_13286]) ).
cnf(c_18054,plain,
( ~ ssList(A)
| app(sk3,A) != sk2 ),
inference(resolve,[status(thm)],[c_18044,c_14640]) ).
cnf(c_18079,plain,
~ ssList(sk5),
inference(resolve,[status(thm)],[c_18054,c_336]) ).
cnf(c_18067,plain,
$false,
inference(resolve,[status(thm)],[c_65,c_18079]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC065-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 12:08:10 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 3677821 was started by sandbox2 on n007,
% 0.08/0.36 % Sat Sep 26 12:08:10 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 62.83/8.36
% 62.83/8.36 % 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)].
% 62.83/8.36
% 62.83/8.36 % given #1000 (T,wt=8): 6886 segmentP(skaf80(A),nil). [resolve(218,a,177,a)].
% 62.83/8.36
% 62.83/8.36 % given #1500 (F,wt=12): 13100 skaf71(A) != sk5 | -neq(skaf71(A),sk5). [resolve(1312,c,209,a),flip(a)].
% 62.83/8.36
% 62.83/8.36 % SZS status Unsatisfiable for theBenchmark
% 62.83/8.36
% 62.83/8.36 % Proof 1 at 5.65 (+ 1.76) seconds.
% 62.83/8.36 % Length of proof is 43.
% 62.83/8.36 % Level of proof is 11.
% 62.83/8.36 % Maximum clause weight is 26.000.
% 62.83/8.36 % Given clauses 1708.
% 62.83/8.36
% 62.83/8.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------