%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC057-1 : 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 : n019.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 08:56:41 AM UTC 2026
% Result : Unsatisfiable 87.05s 12.55s
% Output : CNFRefutation 87.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of formulae : 85 ( 26 unt; 0 def)
% Number of atoms : 197 ( 66 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 214 ( 102 ~; 112 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 41 ( 4 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_14,axiom,
( frontsegP(sk4,sk3)
| nil = sk3 ),
file('theBenchmark.p',co1_14) ).
cnf(c_51,plain,
( frontsegP(sk4,sk3)
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_14]) ).
cnf(c_52,plain,
( frontsegP(sk4,sk3)
| sk3 = nil ),
inference(copy,[status(thm)],[c_51]) ).
fof(co1_13,axiom,
( neq(sk3,nil)
| nil = sk3 ),
file('theBenchmark.p',co1_13) ).
cnf(c_53,plain,
( neq(sk3,nil)
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_54,plain,
( neq(sk3,nil)
| sk3 = nil ),
inference(copy,[status(thm)],[c_53]) ).
fof(co1_11,axiom,
( neq(sk3,nil)
| nil = sk4 ),
file('theBenchmark.p',co1_11) ).
cnf(c_57,plain,
( neq(sk3,nil)
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_11]) ).
cnf(c_58,plain,
( neq(sk3,nil)
| sk4 = nil ),
inference(copy,[status(thm)],[c_57]) ).
fof(co1_9,axiom,
( neq(sk2,nil)
| nil != sk1 ),
file('theBenchmark.p',co1_9) ).
cnf(c_61,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_62,plain,
( neq(sk2,nil)
| sk1 != nil ),
inference(copy,[status(thm)],[c_61]) ).
fof(co1_8,axiom,
! [VAR_0] :
( ~ segmentP(sk1,VAR_0)
| ~ segmentP(sk2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil = sk2 ),
file('theBenchmark.p',co1_8) ).
cnf(c_63,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_64,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sk2 = nil ),
inference(copy,[status(thm)],[c_63]) ).
fof(co1_7,axiom,
( neq(sk2,nil)
| nil = sk2 ),
file('theBenchmark.p',co1_7) ).
cnf(c_65,plain,
( neq(sk2,nil)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_66,plain,
( neq(sk2,nil)
| sk2 = nil ),
inference(copy,[status(thm)],[c_65]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_67,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_68,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_69,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_68]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_70,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
cnf(c_71,plain,
ssList(sk2),
inference(paramod,[status(thm)],[c_69,c_70]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_72,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_81,plain,
( segmentP(D,B)
| ~ ssList(D)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != D ),
inference(clausify,[status(thm)],[clause173]) ).
fof(clause132,axiom,
! [VAR_0,VAR_1] :
( app(VAR_1,skaf45(VAR_0,VAR_1)) = VAR_0
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| ~ frontsegP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause132) ).
cnf(c_118,plain,
( app(B,skaf45(A,B)) = A
| ~ ssList(A)
| ~ ssList(B)
| ~ frontsegP(A,B) ),
inference(clausify,[status(thm)],[clause132]) ).
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_134,plain,
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(A,B)
| A != B ),
inference(clausify,[status(thm)],[clause115]) ).
fof(clause84,axiom,
! [VAR_0] :
( nil = VAR_0
| ~ ssList(VAR_0)
| ~ frontsegP(nil,VAR_0) ),
file('theBenchmark.p',clause84) ).
cnf(c_158,plain,
( nil = A
| ~ ssList(A)
| ~ frontsegP(nil,A) ),
inference(clausify,[status(thm)],[clause84]) ).
fof(clause74,axiom,
! [VAR_0] :
( app(nil,VAR_0) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause74) ).
cnf(c_166,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_177,plain,
( segmentP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause57]) ).
fof(clause51,axiom,
! [VAR_0,VAR_1] : ssList(skaf45(VAR_0,VAR_1)),
file('theBenchmark.p',clause51) ).
cnf(c_183,plain,
ssList(skaf45(A,B)),
inference(clausify,[status(thm)],[clause51]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_226,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_330,plain,
( ~ segmentP(sk3,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sk2 = nil ),
inference(paramod,[status(thm)],[c_67,c_64]) ).
cnf(c_331,plain,
( neq(sk2,nil)
| sk3 != nil ),
inference(paramod,[status(thm)],[c_67,c_62]) ).
cnf(c_333,plain,
( neq(sk3,nil)
| sk2 = nil ),
inference(paramod,[status(thm)],[c_69,c_58]) ).
cnf(c_335,plain,
( frontsegP(sk2,sk3)
| sk3 = nil ),
inference(paramod,[status(thm)],[c_69,c_52]) ).
cnf(c_14562,plain,
( ~ ssList(A)
| ~ neq(A,A)
| A != A ),
inference(factor,[status(thm)],[c_134]) ).
cnf(c_400,plain,
( ~ ssList(A)
| ~ neq(A,A) ),
inference(copy,[status(thm)],[c_14562]) ).
cnf(c_895,plain,
( segmentP(sk2,B)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != sk2 ),
inference(resolve,[status(thm)],[c_81,c_71]) ).
cnf(c_14563,plain,
( nil = sk3
| ~ frontsegP(nil,sk3) ),
inference(resolve,[status(thm)],[c_158,c_72]) ).
cnf(c_1211,plain,
( sk3 = nil
| ~ frontsegP(nil,sk3) ),
inference(copy,[status(thm)],[c_14563]) ).
cnf(c_1236,plain,
app(nil,sk3) = sk3,
inference(resolve,[status(thm)],[c_166,c_72]) ).
cnf(c_1248,plain,
segmentP(sk3,sk3),
inference(resolve,[status(thm)],[c_177,c_72]) ).
cnf(c_7950,plain,
( neq(sk3,nil)
| neq(sk2,nil) ),
inference(resolve,[status(thm)],[c_331,c_54]) ).
cnf(c_14564,plain,
( ~ segmentP(sk3,sk3)
| ~ segmentP(sk2,sk3)
| ~ ssList(sk3)
| sk2 = nil
| sk2 = nil ),
inference(resolve,[status(thm)],[c_333,c_330]) ).
cnf(c_14565,plain,
( ~ segmentP(sk3,sk3)
| ~ segmentP(sk2,sk3)
| ~ ssList(sk3)
| sk2 = nil ),
inference(copy,[status(thm)],[c_14564]) ).
cnf(c_14566,plain,
( ~ segmentP(sk3,sk3)
| ~ segmentP(sk2,sk3)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_72,c_14565]) ).
cnf(c_7999,plain,
( ~ segmentP(sk2,sk3)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_1248,c_14566]) ).
cnf(c_14567,plain,
( app(sk3,skaf45(sk2,sk3)) = sk2
| ~ ssList(sk2)
| ~ ssList(sk3)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_335,c_118]) ).
cnf(c_14568,plain,
( app(sk3,skaf45(sk2,sk3)) = sk2
| ~ ssList(sk2)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_72,c_14567]) ).
cnf(c_8047,plain,
( app(sk3,skaf45(sk2,sk3)) = sk2
| sk3 = nil ),
inference(resolve,[status(thm)],[c_71,c_14568]) ).
cnf(c_8052,plain,
( frontsegP(nil,sk3)
| sk3 = nil
| neq(sk2,nil) ),
inference(paramod,[status(thm)],[c_66,c_335]) ).
cnf(c_9421,plain,
~ neq(nil,nil),
inference(resolve,[status(thm)],[c_400,c_226]) ).
cnf(c_14569,plain,
( neq(sk3,nil)
| neq(nil,nil)
| neq(sk3,nil) ),
inference(paramod,[status(thm)],[c_333,c_7950]) ).
cnf(c_14570,plain,
( neq(nil,nil)
| neq(sk3,nil) ),
inference(copy,[status(thm)],[c_14569]) ).
cnf(c_12311,plain,
neq(sk3,nil),
inference(resolve,[status(thm)],[c_9421,c_14570]) ).
cnf(c_14571,plain,
( ~ ssList(sk3)
| ~ ssList(nil)
| sk3 != nil ),
inference(resolve,[status(thm)],[c_12311,c_134]) ).
cnf(c_14572,plain,
( ~ ssList(sk3)
| sk3 != nil ),
inference(resolve,[status(thm)],[c_226,c_14571]) ).
cnf(c_12316,plain,
sk3 != nil,
inference(resolve,[status(thm)],[c_72,c_14572]) ).
cnf(c_12325,plain,
( frontsegP(nil,sk3)
| neq(sk2,nil) ),
inference(resolve,[status(thm)],[c_12316,c_8052]) ).
cnf(c_12329,plain,
app(sk3,skaf45(sk2,sk3)) = sk2,
inference(resolve,[status(thm)],[c_12316,c_8047]) ).
cnf(c_12335,plain,
~ frontsegP(nil,sk3),
inference(resolve,[status(thm)],[c_12316,c_1211]) ).
cnf(c_12349,plain,
neq(sk2,nil),
inference(resolve,[status(thm)],[c_12335,c_12325]) ).
cnf(c_14573,plain,
( ~ ssList(sk2)
| ~ ssList(nil)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_12349,c_134]) ).
cnf(c_14574,plain,
( ~ ssList(sk2)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_226,c_14573]) ).
cnf(c_12360,plain,
sk2 != nil,
inference(resolve,[status(thm)],[c_71,c_14574]) ).
cnf(c_12365,plain,
~ segmentP(sk2,sk3),
inference(resolve,[status(thm)],[c_12360,c_7999]) ).
cnf(c_14575,plain,
( segmentP(sk2,sk3)
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(A)
| app(sk3,A) != sk2 ),
inference(paramod,[status(thm)],[c_1236,c_895]) ).
cnf(c_14576,plain,
( segmentP(sk2,sk3)
| ~ ssList(sk3)
| ~ ssList(A)
| app(sk3,A) != sk2 ),
inference(resolve,[status(thm)],[c_226,c_14575]) ).
cnf(c_14577,plain,
( segmentP(sk2,sk3)
| ~ ssList(A)
| app(sk3,A) != sk2 ),
inference(resolve,[status(thm)],[c_72,c_14576]) ).
cnf(c_13151,plain,
( ~ ssList(A)
| app(sk3,A) != sk2 ),
inference(resolve,[status(thm)],[c_12365,c_14577]) ).
cnf(c_14560,plain,
app(sk3,skaf45(A,B)) != sk2,
inference(resolve,[status(thm)],[c_13151,c_183]) ).
cnf(c_14561,plain,
$false,
inference(resolve,[status(thm)],[c_14560,c_12329]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC057-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n019.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 12:09:04 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 1254328 was started by sandbox2 on n019,
% 0.16/0.43 % Sat Sep 26 12:09:04 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 87.05/12.55
% 87.05/12.55 % given #500 (I,wt=37): 571 app(app(A,cons(B,A)),cons(B,C)) != D | -ssList(C) | -ssList(A) | -ssItem(B) | -ssList(D) | lt(B,B) | -lt(skaf59(D),skaf60(D)). [factor(304,d,e),merge(g)].
% 87.05/12.55
% 87.05/12.55 % given #1000 (F,wt=9): 9436 -neq(skaf61(A),skaf61(A)). [resolve(400,b,200,a)].
% 87.05/12.55
% 87.05/12.55 % SZS status Unsatisfiable for theBenchmark
% 87.05/12.55
% 87.05/12.55 % Proof 1 at 2.97 (+ 0.98) seconds.
% 87.05/12.55 % Length of proof is 51.
% 87.05/12.55 % Level of proof is 12.
% 87.05/12.55 % Maximum clause weight is 26.000.
% 87.05/12.55 % Given clauses 1265.
% 87.05/12.55
% 87.05/12.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------