%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC204-1 : 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 : n014.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 08:57:09 AM UTC 2026
% Result : Unsatisfiable 51.15s 7.87s
% Output : CNFRefutation 51.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 89 ( 31 unt; 0 def)
% Number of atoms : 206 ( 93 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 229 ( 112 ~; 117 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_12,axiom,
( ~ neq(sk4,nil)
| ~ neq(sk1,nil) ),
file('theBenchmark.p',co1_12) ).
cnf(c_51,plain,
( ~ neq(sk4,nil)
| ~ neq(sk1,nil) ),
inference(clausify,[status(thm)],[co1_12]) ).
fof(co1_11,axiom,
! [VAR_0,VAR_1] :
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| app(sk3,VAR_1) != VAR_0
| tl(sk4) != VAR_1
| ~ ssList(VAR_1)
| sk4 = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',co1_11) ).
cnf(c_52,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| app(sk3,B) != A
| tl(sk4) != B
| ~ ssList(B)
| sk4 = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[co1_11]) ).
fof(co1_7,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('theBenchmark.p',co1_7) ).
cnf(c_56,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_57,plain,
neq(sk2,nil),
inference(copy,[status(thm)],[c_56]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_58,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_59,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_60,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_61,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
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_124,plain,
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(A,B)
| A != B ),
inference(clausify,[status(thm)],[clause115]) ).
fof(clause104,axiom,
! [VAR_0] :
( nil = VAR_0
| cons(hd(VAR_0),tl(VAR_0)) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause104) ).
cnf(c_135,plain,
( nil = A
| cons(hd(A),tl(A)) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause104]) ).
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_139,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause99,axiom,
! [VAR_0,VAR_1] :
( ~ ssList(VAR_1)
| ~ ssItem(VAR_0)
| cons(VAR_0,VAR_1) != VAR_1 ),
file('theBenchmark.p',clause99) ).
cnf(c_140,plain,
( ~ ssList(B)
| ~ ssItem(A)
| cons(A,B) != B ),
inference(clausify,[status(thm)],[clause99]) ).
fof(clause78,axiom,
! [VAR_0] :
( nil = VAR_0
| ssItem(hd(VAR_0))
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause78) ).
cnf(c_154,plain,
( nil = A
| ssItem(hd(A))
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause78]) ).
fof(clause77,axiom,
! [VAR_0] :
( nil = VAR_0
| ssList(tl(VAR_0))
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause77) ).
cnf(c_155,plain,
( nil = A
| ssList(tl(A))
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause77]) ).
fof(clause74,axiom,
! [VAR_0] :
( app(nil,VAR_0) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause74) ).
cnf(c_156,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause74]) ).
fof(clause73,axiom,
! [VAR_0] :
( app(VAR_0,nil) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause73) ).
cnf(c_157,plain,
( app(A,nil) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause73]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_216,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_320,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| app(sk3,A) != A
| tl(sk4) != A
| sk4 = A
| ~ ssList(A) ),
inference(factor,[status(thm)],[c_52]) ).
cnf(c_322,plain,
( ~ neq(sk4,nil)
| ~ neq(sk3,nil) ),
inference(paramod,[status(thm)],[c_58,c_51]) ).
cnf(c_323,plain,
neq(sk4,nil),
inference(paramod,[status(thm)],[c_59,c_57]) ).
cnf(c_587,plain,
~ neq(sk3,nil),
inference(resolve,[status(thm)],[c_323,c_322]) ).
cnf(c_588,plain,
( ~ neq(nil,sk4)
| app(sk3,A) != A
| tl(sk4) != A
| sk4 = A
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_323,c_320]) ).
cnf(c_589,plain,
( ~ neq(nil,sk4)
| app(sk3,B) != A
| tl(sk4) != B
| ~ ssList(B)
| sk4 = A
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_323,c_52]) ).
cnf(c_15568,plain,
( ~ ssList(A)
| ~ neq(A,sk3)
| A != sk3 ),
inference(resolve,[status(thm)],[c_124,c_61]) ).
cnf(c_1138,plain,
( ~ ssList(A)
| ~ neq(A,sk3)
| sk3 != A ),
inference(copy,[status(thm)],[c_15568]) ).
cnf(c_15569,plain,
( A = sk3
| neq(A,sk3)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_139,c_61]) ).
cnf(c_1152,plain,
( sk3 = A
| neq(A,sk3)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_15569]) ).
cnf(c_15570,plain,
( A = sk4
| neq(A,sk4)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_139,c_60]) ).
cnf(c_1153,plain,
( sk4 = A
| neq(A,sk4)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_15570]) ).
cnf(c_1154,plain,
( sk3 = A
| neq(sk3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_139,c_61]) ).
cnf(c_1157,plain,
( ~ ssItem(A)
| cons(A,sk4) != sk4 ),
inference(resolve,[status(thm)],[c_140,c_60]) ).
cnf(c_15571,plain,
( nil = sk4
| ssItem(hd(sk4)) ),
inference(resolve,[status(thm)],[c_154,c_60]) ).
cnf(c_1190,plain,
( sk4 = nil
| ssItem(hd(sk4)) ),
inference(copy,[status(thm)],[c_15571]) ).
cnf(c_15572,plain,
( nil = sk4
| ssList(tl(sk4)) ),
inference(resolve,[status(thm)],[c_155,c_60]) ).
cnf(c_1192,plain,
( sk4 = nil
| ssList(tl(sk4)) ),
inference(copy,[status(thm)],[c_15572]) ).
cnf(c_1195,plain,
app(sk3,nil) = sk3,
inference(resolve,[status(thm)],[c_157,c_61]) ).
cnf(c_15573,plain,
( ~ ssList(sk4)
| ~ ssList(nil)
| sk4 != nil ),
inference(resolve,[status(thm)],[c_323,c_124]) ).
cnf(c_15574,plain,
( ~ ssList(sk4)
| sk4 != nil ),
inference(resolve,[status(thm)],[c_216,c_15573]) ).
cnf(c_7875,plain,
sk4 != nil,
inference(resolve,[status(thm)],[c_60,c_15574]) ).
cnf(c_7876,plain,
ssList(tl(sk4)),
inference(resolve,[status(thm)],[c_7875,c_1192]) ).
cnf(c_7877,plain,
ssItem(hd(sk4)),
inference(resolve,[status(thm)],[c_7875,c_1190]) ).
cnf(c_15575,plain,
( ~ neq(nil,sk4)
| app(sk3,tl(sk4)) != tl(sk4)
| sk4 = tl(sk4)
| ~ ssList(tl(sk4)) ),
inference(xxres,[status(thm)],[c_588]) ).
cnf(c_15576,plain,
( ~ neq(nil,sk4)
| app(sk3,tl(sk4)) != tl(sk4)
| tl(sk4) = sk4
| ~ ssList(tl(sk4)) ),
inference(copy,[status(thm)],[c_15575]) ).
cnf(c_9592,plain,
( ~ neq(nil,sk4)
| app(sk3,tl(sk4)) != tl(sk4)
| tl(sk4) = sk4 ),
inference(resolve,[status(thm)],[c_7876,c_15576]) ).
cnf(c_10491,plain,
app(nil,tl(sk4)) = tl(sk4),
inference(resolve,[status(thm)],[c_7876,c_156]) ).
cnf(c_15577,plain,
( nil = tl(sk4)
| cons(hd(tl(sk4)),tl(tl(sk4))) = tl(sk4) ),
inference(resolve,[status(thm)],[c_7876,c_135]) ).
cnf(c_10512,plain,
( tl(sk4) = nil
| cons(hd(tl(sk4)),tl(tl(sk4))) = tl(sk4) ),
inference(copy,[status(thm)],[c_15577]) ).
cnf(c_15578,plain,
( ~ neq(nil,sk4)
| tl(sk4) != nil
| ~ ssList(nil)
| sk4 = sk3
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_1195,c_589]) ).
cnf(c_15579,plain,
( ~ neq(nil,sk4)
| tl(sk4) != nil
| ~ ssList(nil)
| sk3 = sk4
| ~ ssList(sk3) ),
inference(copy,[status(thm)],[c_15578]) ).
cnf(c_15580,plain,
( ~ neq(nil,sk4)
| tl(sk4) != nil
| ~ ssList(nil)
| sk3 = sk4 ),
inference(resolve,[status(thm)],[c_61,c_15579]) ).
cnf(c_12709,plain,
( ~ neq(nil,sk4)
| tl(sk4) != nil
| sk3 = sk4 ),
inference(resolve,[status(thm)],[c_216,c_15580]) ).
cnf(c_12928,plain,
( ~ neq(sk4,sk3)
| sk3 != sk4 ),
inference(resolve,[status(thm)],[c_1138,c_60]) ).
cnf(c_13456,plain,
cons(hd(sk4),sk4) != sk4,
inference(resolve,[status(thm)],[c_1157,c_7877]) ).
cnf(c_14548,plain,
( sk3 = sk4
| neq(sk4,sk3) ),
inference(resolve,[status(thm)],[c_1152,c_60]) ).
cnf(c_15581,plain,
( ~ neq(sk4,nil)
| neq(sk4,sk3) ),
inference(paramod,[status(thm)],[c_14548,c_587]) ).
cnf(c_14626,plain,
neq(sk4,sk3),
inference(resolve,[status(thm)],[c_323,c_15581]) ).
cnf(c_14627,plain,
sk3 != sk4,
inference(resolve,[status(thm)],[c_14626,c_12928]) ).
cnf(c_14628,plain,
( ~ neq(nil,sk4)
| tl(sk4) != nil ),
inference(resolve,[status(thm)],[c_14627,c_12709]) ).
cnf(c_15582,plain,
( sk4 = nil
| neq(nil,sk4) ),
inference(resolve,[status(thm)],[c_1153,c_216]) ).
cnf(c_14726,plain,
neq(nil,sk4),
inference(resolve,[status(thm)],[c_7875,c_15582]) ).
cnf(c_14757,plain,
tl(sk4) != nil,
inference(resolve,[status(thm)],[c_14726,c_14628]) ).
cnf(c_14785,plain,
( app(sk3,tl(sk4)) != tl(sk4)
| tl(sk4) = sk4 ),
inference(resolve,[status(thm)],[c_14726,c_9592]) ).
cnf(c_14796,plain,
cons(hd(tl(sk4)),tl(tl(sk4))) = tl(sk4),
inference(resolve,[status(thm)],[c_14757,c_10512]) ).
cnf(c_15583,plain,
( sk3 = nil
| neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_1154,c_216]) ).
cnf(c_14809,plain,
sk3 = nil,
inference(resolve,[status(thm)],[c_587,c_15583]) ).
cnf(c_15584,plain,
( app(nil,tl(sk4)) != tl(sk4)
| tl(sk4) = sk4 ),
inference(paramod,[status(thm)],[c_14809,c_14785]) ).
cnf(c_15585,plain,
( tl(sk4) != tl(sk4)
| tl(sk4) = sk4 ),
inference(paramod,[status(thm)],[c_10491,c_15584]) ).
cnf(c_14841,plain,
tl(sk4) = sk4,
inference(copy,[status(thm)],[c_15585]) ).
cnf(c_15586,plain,
cons(hd(sk4),tl(tl(sk4))) = tl(sk4),
inference(paramod,[status(thm)],[c_14841,c_14796]) ).
cnf(c_15587,plain,
cons(hd(sk4),tl(sk4)) = tl(sk4),
inference(paramod,[status(thm)],[c_14841,c_15586]) ).
cnf(c_15588,plain,
cons(hd(sk4),sk4) = tl(sk4),
inference(paramod,[status(thm)],[c_14841,c_15587]) ).
cnf(c_15589,plain,
cons(hd(sk4),sk4) = sk4,
inference(paramod,[status(thm)],[c_14841,c_15588]) ).
cnf(c_15567,plain,
$false,
inference(resolve,[status(thm)],[c_13456,c_15589]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC204-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n014.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 12:30:32 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 3150584 was started by sandbox2 on n014,
% 0.15/0.43 % Sat Sep 26 12:30:32 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.44
% 0.15/0.44 % From the command line: assign(max_seconds, 300).
% 51.15/7.87
% 51.15/7.87 % given #500 (I,wt=55): 566 app(app(A,cons(B,C)),cons(D,A)) != A | -ssList(A) | -ssList(C) | -ssItem(D) | -ssItem(B) | lt(B,D) | lt(D,B) | app(app(skaf61(A),cons(skaf59(A),skaf62(A))),cons(skaf60(A),skaf63(A))) = A. [factor(299,b,f)].
% 51.15/7.87
% 51.15/7.87 % given #1000 (T,wt=9): 1374 segmentP(skaf43(A,B),nil). [resolve(172,a,168,a)].
% 51.15/7.87
% 51.15/7.87 % SZS status Unsatisfiable for theBenchmark
% 51.15/7.87
% 51.15/7.87 % Proof 1 at 5.55 (+ 1.79) seconds.
% 51.15/7.87 % Length of proof is 51.
% 51.15/7.87 % Level of proof is 9.
% 51.15/7.87 % Maximum clause weight is 26.000.
% 51.15/7.87 % Given clauses 1351.
% 51.15/7.87
% 51.15/7.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------