%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC019-1 : 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 : n006.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 08:56:33 AM UTC 2026
% Result : Unsatisfiable 37.21s 5.13s
% Output : CNFRefutation 37.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 17 unt; 0 def)
% Number of atoms : 67 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 74 ( 42 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 12 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_9,axiom,
( nil != sk1
| nil != sk2 ),
file('theBenchmark.p',co1_9) ).
cnf(c_51,plain,
( nil != sk1
| nil != sk2 ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_14278,plain,
( nil != sk1
| sk2 != nil ),
inference(copy,[status(thm)],[c_51]) ).
cnf(c_52,plain,
( sk1 != nil
| sk2 != nil ),
inference(copy,[status(thm)],[c_14278]) ).
fof(co1_8,axiom,
! [VAR_0] :
( ~ frontsegP(sk1,VAR_0)
| ~ frontsegP(sk2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',co1_8) ).
cnf(c_53,plain,
( ~ frontsegP(sk1,A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
sk4 = sk3,
file('theBenchmark.p',co1_7) ).
cnf(c_54,plain,
sk4 = sk3,
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_55,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_56,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_57,plain,
sk2 = sk3,
inference(paramod,[status(thm)],[c_54,c_56]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_58,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
cnf(c_59,plain,
ssList(sk3),
inference(paramod,[status(thm)],[c_54,c_58]) ).
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_137,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause61,axiom,
! [VAR_0] :
( frontsegP(VAR_0,VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause61) ).
cnf(c_161,plain,
( frontsegP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause61]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_214,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_14279,plain,
( ~ frontsegP(sk1,A)
| ~ frontsegP(sk3,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_57,c_53]) ).
cnf(c_14280,plain,
( ~ frontsegP(sk3,A)
| ~ frontsegP(sk3,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_55,c_14279]) ).
cnf(c_318,plain,
( ~ frontsegP(sk3,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_14280]) ).
cnf(c_14281,plain,
( sk1 != nil
| sk3 != nil ),
inference(paramod,[status(thm)],[c_57,c_52]) ).
cnf(c_14282,plain,
( sk3 != nil
| sk3 != nil ),
inference(paramod,[status(thm)],[c_55,c_14281]) ).
cnf(c_319,plain,
sk3 != nil,
inference(copy,[status(thm)],[c_14282]) ).
cnf(c_989,plain,
( sk3 = A
| neq(sk3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_137,c_59]) ).
cnf(c_1009,plain,
frontsegP(sk3,sk3),
inference(resolve,[status(thm)],[c_161,c_59]) ).
cnf(c_14283,plain,
( ~ frontsegP(sk3,sk3)
| ~ neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_318,c_59]) ).
cnf(c_7700,plain,
~ neq(sk3,nil),
inference(resolve,[status(thm)],[c_1009,c_14283]) ).
cnf(c_14284,plain,
( sk3 = nil
| neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_989,c_214]) ).
cnf(c_14285,plain,
sk3 = nil,
inference(resolve,[status(thm)],[c_7700,c_14284]) ).
cnf(c_14277,plain,
$false,
inference(resolve,[status(thm)],[c_319,c_14285]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC019-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n006.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 12:04:14 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 1202735 was started by sandbox on n006,
% 0.11/0.37 % Sat Sep 26 12:04:14 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 37.21/5.13
% 37.21/5.13 % given #500 (I,wt=52): 561 app(app(A,cons(B,C)),cons(B,C)) != D | -ssList(C) | -ssList(A) | -ssItem(B) | -ssList(D) | lt(B,B) | app(app(skaf61(D),cons(skaf59(D),skaf62(D))),cons(skaf60(D),skaf63(D))) = D. [factor(296,d,e),merge(g)].
% 37.21/5.13
% 37.21/5.13 % given #1000 (T,wt=9): 2006 leq(skaf44(A),skaf44(A)). [resolve(175,a,160,a)].
% 37.21/5.13
% 37.21/5.13 % SZS status Unsatisfiable for theBenchmark
% 37.21/5.13
% 37.21/5.13 % Proof 1 at 3.56 (+ 1.13) seconds.
% 37.21/5.13 % Length of proof is 18.
% 37.21/5.13 % Level of proof is 4.
% 37.21/5.13 % Maximum clause weight is 13.000.
% 37.21/5.13 % Given clauses 1250.
% 37.21/5.13
% 37.21/5.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------