%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC205-1 : 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 : n017.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 34.50s 10.10s
% Output : CNFRefutation 30.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 21 unt; 0 def)
% Number of atoms : 55 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 26 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 9 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_9,axiom,
( nil != sk3
| nil = sk4 ),
file('theBenchmark.p',co1_9) ).
cnf(c_53,plain,
( nil != sk3
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_15235,plain,
( nil != sk3
| sk4 = nil ),
inference(copy,[status(thm)],[c_53]) ).
cnf(c_54,plain,
( sk3 != nil
| sk4 = nil ),
inference(copy,[status(thm)],[c_15235]) ).
fof(co1_8,axiom,
~ neq(sk1,nil),
file('theBenchmark.p',co1_8) ).
cnf(c_55,plain,
~ neq(sk1,nil),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
neq(sk2,nil),
file('theBenchmark.p',co1_7) ).
cnf(c_56,plain,
neq(sk2,nil),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_57,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_58,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_59,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_1,axiom,
ssList(sk1),
file('theBenchmark.p',co1_1) ).
cnf(c_62,plain,
ssList(sk1),
inference(clausify,[status(thm)],[co1_1]) ).
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_123,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_138,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_215,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_827,plain,
neq(sk4,nil),
inference(paramod,[status(thm)],[c_58,c_56]) ).
cnf(c_1051,plain,
( sk1 = A
| neq(sk1,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_138,c_62]) ).
cnf(c_15236,plain,
( ~ ssList(sk4)
| ~ ssList(nil)
| sk4 != nil ),
inference(resolve,[status(thm)],[c_827,c_123]) ).
cnf(c_15237,plain,
( ~ ssList(sk4)
| sk4 != nil ),
inference(resolve,[status(thm)],[c_215,c_15236]) ).
cnf(c_11243,plain,
sk4 != nil,
inference(resolve,[status(thm)],[c_59,c_15237]) ).
cnf(c_11256,plain,
sk3 != nil,
inference(resolve,[status(thm)],[c_11243,c_54]) ).
cnf(c_15238,plain,
( sk1 = nil
| neq(sk1,nil) ),
inference(resolve,[status(thm)],[c_1051,c_215]) ).
cnf(c_15199,plain,
sk1 = nil,
inference(resolve,[status(thm)],[c_55,c_15238]) ).
cnf(c_15239,plain,
nil = sk3,
inference(paramod,[status(thm)],[c_15199,c_57]) ).
cnf(c_15240,plain,
sk3 = nil,
inference(copy,[status(thm)],[c_15239]) ).
cnf(c_15234,plain,
$false,
inference(resolve,[status(thm)],[c_11256,c_15240]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC205-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.65 % Computer : n017.cluster.edu
% 0.16/5.65 % Model : x86_64 x86_64
% 0.16/5.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.65 % Memory : 8046.5625MB
% 0.16/5.65 % OS : Linux 6.8.0-71-generic
% 0.16/5.65 % CPULimit : 300
% 0.16/5.65 % WCLimit : 300
% 0.16/5.65 % DateTime : Sat Sep 26 12:26:09 UTC 2026
% 0.16/5.65 % CPUTime :
% 0.16/5.65 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.65 % Process 702371 was started by sandbox2 on n017,
% 0.16/5.65 % Sat Sep 26 12:26:09 2026
% 0.16/5.65 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.67
% 0.16/5.67 % From the command line: assign(max_seconds, 300).
% 34.50/10.10
% 34.50/10.10 % given #500 (I,wt=70): 562 app(app(A,cons(B,C)),cons(D,A)) != C | -ssList(A) | -ssList(C) | -ssItem(D) | -ssItem(B) | lt(B,D) | lt(D,B) | app(app(skaf61(C),cons(skaf59(C),skaf62(C))),cons(skaf60(C),skaf63(C))) = C. [factor(298,c,f)].
% 34.50/10.10
% 34.50/10.10 % SZS status Unsatisfiable for theBenchmark
% 34.50/10.10
% 34.50/10.10 % Proof 1 at 3.89 (+ 0.49) seconds.
% 34.50/10.10 % Length of proof is 17.
% 34.50/10.10 % Level of proof is 4.
% 34.50/10.10 % Maximum clause weight is 15.000.
% 34.50/10.10 % Given clauses 943.
% 34.50/10.10
% 34.50/10.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------