%------------------------------------------------------------------------------
% 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/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 : Theorem 9.47s 1.80s
% Output : CNFRefutation 9.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 46 ( 16 unt; 0 def)
% Number of atoms : 167 ( 54 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 201 ( 80 ~; 73 |; 36 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 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 : 29 ( 0 sgn 15 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax49,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,U) ),
file('theBenchmark.p',ax49) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ? [Y] :
( rearsegP(U,Y)
& rearsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| X != W
| U != W
| V != X ) ) ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ? [Y] :
( rearsegP(U,Y)
& rearsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| X != W
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ! [Y] :
( ~ rearsegP(U,Y)
| ~ rearsegP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& X = W
& W = U
& X = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg_sk,plain,
( ( ( ! [Y] :
( ~ rearsegP(sK0,Y)
| ~ rearsegP(sK1,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(sK1,nil) )
| ( nil != sK0
& nil = sK1 ) )
& sK2 = sK3
& sK3 = sK0
& sK2 = sK1
& ssList(sK2)
& ssList(sK3)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK3,sK2]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK3),skolemize(X,sK2)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ! [VAR_0] :
( ~ rearsegP(sK0,VAR_0)
| ~ rearsegP(sK1,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil != sK0 )
& ( neq(sK1,nil)
| nil != sK0 )
& ! [VAR_0] :
( ~ rearsegP(sK0,VAR_0)
| ~ rearsegP(sK1,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil = sK1 )
& ( neq(sK1,nil)
| nil = sK1 )
& sK2 = sK3
& sK3 = sK0
& sK2 = sK1
& ssList(sK2)
& ssList(sK3)
& ssList(sK1)
& ssList(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_192,negated_conjecture,
( neq(sK1,nil)
| nil != sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( neq(sK1,nil)
| sK0 != nil ),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_194,negated_conjecture,
( ~ rearsegP(sK0,A)
| ~ rearsegP(sK1,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
( ~ rearsegP(sK0,A)
| ~ rearsegP(sK1,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sK1 = nil ),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_196,negated_conjecture,
( neq(sK1,nil)
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
( neq(sK1,nil)
| sK1 = nil ),
inference(copy,[status(thm)],[c_196]) ).
cnf(c_198,negated_conjecture,
sK2 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
sK3 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_200,negated_conjecture,
sK2 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2227,negated_conjecture,
sK3 = sK1,
inference(paramod,[status(thm)],[c_198,c_200]) ).
cnf(c_2228,negated_conjecture,
sK0 = sK1,
inference(paramod,[status(thm)],[c_199,c_2227]) ).
cnf(c_201,negated_conjecture,
sK1 = sK0,
inference(copy,[status(thm)],[c_2228]) ).
cnf(c_202,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2229,negated_conjecture,
ssList(sK3),
inference(paramod,[status(thm)],[c_198,c_202]) ).
cnf(c_203,negated_conjecture,
ssList(sK0),
inference(paramod,[status(thm)],[c_199,c_2229]) ).
cnf(c_257,plain,
( rearsegP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax49]) ).
cnf(c_304,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_2230,negated_conjecture,
( neq(sK1,nil)
| sK0 = nil ),
inference(paramod,[status(thm)],[c_201,c_197]) ).
cnf(c_551,negated_conjecture,
( neq(sK0,nil)
| sK0 = nil ),
inference(paramod,[status(thm)],[c_201,c_2230]) ).
cnf(c_2231,negated_conjecture,
( ~ rearsegP(sK0,A)
| ~ rearsegP(sK1,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sK0 = nil ),
inference(paramod,[status(thm)],[c_201,c_195]) ).
cnf(c_2232,negated_conjecture,
( ~ rearsegP(sK0,A)
| ~ rearsegP(sK0,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sK0 = nil ),
inference(paramod,[status(thm)],[c_201,c_2231]) ).
cnf(c_552,negated_conjecture,
( ~ rearsegP(sK0,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sK0 = nil ),
inference(copy,[status(thm)],[c_2232]) ).
cnf(c_553,negated_conjecture,
( neq(sK0,nil)
| sK0 != nil ),
inference(paramod,[status(thm)],[c_201,c_193]) ).
cnf(c_1730,plain,
rearsegP(sK0,sK0),
inference(resolve,[status(thm)],[c_257,c_203]) ).
cnf(c_2233,negated_conjecture,
( ~ neq(sK0,sK1)
| ~ ssList(sK1)
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_304,c_201]) ).
cnf(c_2234,negated_conjecture,
( ~ neq(sK0,sK1)
| ~ ssList(sK0)
| ~ ssList(sK0) ),
inference(paramod,[status(thm)],[c_201,c_2233]) ).
cnf(c_2235,negated_conjecture,
( ~ neq(sK0,sK0)
| ~ ssList(sK0)
| ~ ssList(sK0) ),
inference(paramod,[status(thm)],[c_201,c_2234]) ).
cnf(c_2236,negated_conjecture,
( ~ neq(sK0,sK0)
| ~ ssList(sK0) ),
inference(copy,[status(thm)],[c_2235]) ).
cnf(c_1882,negated_conjecture,
~ neq(sK0,sK0),
inference(resolve,[status(thm)],[c_203,c_2236]) ).
cnf(c_2237,negated_conjecture,
( sK0 = nil
| ~ rearsegP(sK0,sK0)
| ~ ssList(sK0)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_552,c_551]) ).
cnf(c_2238,negated_conjecture,
( ~ rearsegP(sK0,sK0)
| ~ ssList(sK0)
| sK0 = nil ),
inference(copy,[status(thm)],[c_2237]) ).
cnf(c_2239,negated_conjecture,
( ~ rearsegP(sK0,sK0)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_203,c_2238]) ).
cnf(c_2223,negated_conjecture,
sK0 = nil,
inference(resolve,[status(thm)],[c_1730,c_2239]) ).
cnf(c_2240,negated_conjecture,
~ neq(nil,sK0),
inference(paramod,[status(thm)],[c_2223,c_1882]) ).
cnf(c_2224,negated_conjecture,
~ neq(nil,nil),
inference(paramod,[status(thm)],[c_2223,c_2240]) ).
cnf(c_2241,negated_conjecture,
( neq(sK0,nil)
| nil != nil ),
inference(paramod,[status(thm)],[c_2223,c_553]) ).
cnf(c_2242,negated_conjecture,
( neq(nil,nil)
| nil != nil ),
inference(paramod,[status(thm)],[c_2223,c_2241]) ).
cnf(c_2243,negated_conjecture,
neq(nil,nil),
inference(copy,[status(thm)],[c_2242]) ).
cnf(c_2226,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2224,c_2243]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC047+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.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 12:08:14 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 57505 was started by sandbox2 on n009,
% 0.08/0.36 % Sat Sep 26 12:08:14 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.39
% 0.08/0.39 % From the command line: assign(max_seconds, 300).
% 9.47/1.80
% 9.47/1.80 % SZS status Theorem for theBenchmark
% 9.47/1.80
% 9.47/1.80 % Proof 1 at 1.06 (+ 0.11) seconds.
% 9.47/1.80 % Length of proof is 25.
% 9.47/1.80 % Level of proof is 6.
% 9.47/1.80 % Maximum clause weight is 16.000.
% 9.47/1.80 % Given clauses 352.
% 9.47/1.80
% 9.47/1.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------