%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC047-1 : 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 : n001.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 08:56:39 AM UTC 2026
% Result : Unsatisfiable 5.43s 1.12s
% Output : CNFRefutation 5.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 43 ( 24 unt; 0 def)
% Number of atoms : 82 ( 29 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 79 ( 40 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 9 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_10,axiom,
( neq(sk2,nil)
| nil != sk1 ),
file('theBenchmark.p',co1_10) ).
cnf(c_53,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(clausify,[status(thm)],[co1_10]) ).
cnf(c_54,plain,
( neq(sk2,nil)
| sk1 != nil ),
inference(copy,[status(thm)],[c_53]) ).
fof(co1_9,axiom,
! [VAR_0] :
( ~ rearsegP(sk1,VAR_0)
| ~ rearsegP(sk2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil = sk2 ),
file('theBenchmark.p',co1_9) ).
cnf(c_55,plain,
( ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_56,plain,
( ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sk2 = nil ),
inference(copy,[status(thm)],[c_55]) ).
fof(co1_8,axiom,
( neq(sk2,nil)
| nil = sk2 ),
file('theBenchmark.p',co1_8) ).
cnf(c_57,plain,
( neq(sk2,nil)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_58,plain,
( neq(sk2,nil)
| sk2 = nil ),
inference(copy,[status(thm)],[c_57]) ).
fof(co1_7,axiom,
sk4 = sk3,
file('theBenchmark.p',co1_7) ).
cnf(c_59,plain,
sk4 = sk3,
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_60,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
cnf(c_61,plain,
sk3 = sk1,
inference(copy,[status(thm)],[c_60]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_62,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_63,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_62]) ).
fof(co1_2,axiom,
ssList(sk2),
file('theBenchmark.p',co1_2) ).
cnf(c_66,plain,
ssList(sk2),
inference(clausify,[status(thm)],[co1_2]) ).
fof(co1_1,axiom,
ssList(sk1),
file('theBenchmark.p',co1_1) ).
cnf(c_67,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_128,plain,
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(A,B)
| A != B ),
inference(clausify,[status(thm)],[clause115]) ).
fof(clause59,axiom,
! [VAR_0] :
( rearsegP(VAR_0,VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause59) ).
cnf(c_169,plain,
( rearsegP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause59]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_220,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_8546,plain,
( ~ rearsegP(sk1,sk2)
| ~ rearsegP(sk2,sk2)
| ~ ssList(sk2)
| sk2 = nil
| sk2 = nil ),
inference(resolve,[status(thm)],[c_58,c_56]) ).
cnf(c_8547,plain,
( ~ rearsegP(sk1,sk2)
| ~ rearsegP(sk2,sk2)
| ~ ssList(sk2)
| sk2 = nil ),
inference(copy,[status(thm)],[c_8546]) ).
cnf(c_831,plain,
( ~ rearsegP(sk1,sk2)
| ~ rearsegP(sk2,sk2)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_66,c_8547]) ).
cnf(c_832,plain,
sk4 = sk1,
inference(paramod,[status(thm)],[c_61,c_59]) ).
cnf(c_1098,plain,
rearsegP(sk1,sk1),
inference(resolve,[status(thm)],[c_169,c_67]) ).
cnf(c_1099,plain,
rearsegP(sk2,sk2),
inference(resolve,[status(thm)],[c_169,c_66]) ).
cnf(c_1102,plain,
( ~ rearsegP(sk1,sk2)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_1099,c_831]) ).
cnf(c_4780,plain,
sk1 = sk2,
inference(paramod,[status(thm)],[c_832,c_63]) ).
cnf(c_6163,plain,
rearsegP(sk1,sk2),
inference(paramod,[status(thm)],[c_4780,c_1098]) ).
cnf(c_6166,plain,
sk2 = nil,
inference(resolve,[status(thm)],[c_6163,c_1102]) ).
cnf(c_8241,plain,
sk1 = nil,
inference(paramod,[status(thm)],[c_6166,c_4780]) ).
cnf(c_8264,plain,
neq(sk2,nil),
inference(resolve,[status(thm)],[c_8241,c_54]) ).
cnf(c_8548,plain,
( ~ ssList(sk2)
| ~ ssList(nil)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_8264,c_128]) ).
cnf(c_8549,plain,
( ~ ssList(sk2)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_6166,c_8548]) ).
cnf(c_8550,plain,
~ ssList(sk2),
inference(resolve,[status(thm)],[c_220,c_8549]) ).
cnf(c_8545,plain,
$false,
inference(resolve,[status(thm)],[c_66,c_8550]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC047-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n001.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 12:13:58 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 1754750 was started by sandbox on n001,
% 0.08/0.36 % Sat Sep 26 12:13:58 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 5.43/1.12
% 5.43/1.12 % given #500 (I,wt=35): 561 app(app(A,cons(B,C)),cons(B,D)) != A | -ssList(D) | -ssList(C) | -ssList(A) | -ssItem(B) | lt(B,B) | -lt(skaf59(A),skaf60(A)). [factor(300,e,f),merge(g)].
% 5.43/1.12
% 5.43/1.12 % SZS status Unsatisfiable for theBenchmark
% 5.43/1.12
% 5.43/1.12 % Proof 1 at 0.59 (+ 0.15) seconds.
% 5.43/1.12 % Length of proof is 27.
% 5.43/1.12 % Level of proof is 8.
% 5.43/1.12 % Maximum clause weight is 16.000.
% 5.43/1.12 % Given clauses 943.
% 5.43/1.12
% 5.43/1.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------