%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC208+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 : n005.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 08:57:10 AM UTC 2026
% Result : Theorem 2.34s 0.80s
% Output : CNFRefutation 2.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 89 ( 34 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 87 ( 20 ~; 26 |; 33 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 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 8 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ~ frontsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| neq(U,nil)
| ~ neq(V,nil)
| 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)
=> ( ( ( ~ frontsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| neq(U,nil)
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( frontsegP(X,W)
& neq(W,nil) )
| ( nil = W
& nil = X ) )
& ~ neq(U,nil)
& neq(V,nil)
& 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,
( ( ( frontsegP(sK1,sK0)
& neq(sK0,nil) )
| ( nil = sK0
& nil = sK1 ) )
& ~ neq(sK2,nil)
& neq(sK3,nil)
& sK0 = sK2
& sK1 = sK3
& ssList(sK1)
& ssList(sK0)
& ssList(sK3)
& ssList(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK0,sK1]),skolemize(U,sK2),skolemize(V,sK3),skolemize(W,sK0),skolemize(X,sK1)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( frontsegP(sK1,sK0)
| nil = sK0 )
& ( neq(sK0,nil)
| nil = sK0 )
& ( frontsegP(sK1,sK0)
| nil = sK1 )
& ( neq(sK0,nil)
| nil = sK1 )
& ~ neq(sK2,nil)
& neq(sK3,nil)
& sK0 = sK2
& sK1 = sK3
& ssList(sK1)
& ssList(sK0)
& ssList(sK3)
& ssList(sK2) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_192,negated_conjecture,
( neq(sK0,nil)
| nil = sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( neq(sK0,nil)
| sK0 = nil ),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_196,negated_conjecture,
( neq(sK0,nil)
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
( neq(sK0,nil)
| sK1 = nil ),
inference(copy,[status(thm)],[c_196]) ).
cnf(c_198,negated_conjecture,
~ neq(sK2,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
neq(sK3,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_200,negated_conjecture,
sK0 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
sK1 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_1047,negated_conjecture,
( neq(sK0,nil)
| sK3 = nil ),
inference(paramod,[status(thm)],[c_201,c_197]) ).
cnf(c_1048,negated_conjecture,
( neq(sK2,nil)
| sK3 = nil ),
inference(paramod,[status(thm)],[c_200,c_1047]) ).
cnf(c_550,negated_conjecture,
sK3 = nil,
inference(resolve,[status(thm)],[c_198,c_1048]) ).
cnf(c_1049,negated_conjecture,
( neq(sK0,nil)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_200,c_193]) ).
cnf(c_1050,negated_conjecture,
( neq(sK2,nil)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_200,c_1049]) ).
cnf(c_551,negated_conjecture,
sK2 = nil,
inference(resolve,[status(thm)],[c_198,c_1050]) ).
cnf(c_1044,negated_conjecture,
neq(nil,nil),
inference(paramod,[status(thm)],[c_550,c_199]) ).
cnf(c_1051,negated_conjecture,
~ neq(nil,nil),
inference(paramod,[status(thm)],[c_551,c_198]) ).
cnf(c_1046,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1044,c_1051]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC208+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 12:31:01 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2139198 was started by sandbox2 on n005,
% 0.09/0.36 % Sat Sep 26 12:31:01 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.40
% 0.14/0.40 % From the command line: assign(max_seconds, 300).
% 2.34/0.80
% 2.34/0.80 % SZS status Theorem for theBenchmark
% 2.34/0.80
% 2.34/0.80 % Proof 1 at 0.35 (+ 0.03) seconds.
% 2.34/0.80 % Length of proof is 13.
% 2.34/0.80 % Level of proof is 5.
% 2.34/0.80 % Maximum clause weight is 11.000.
% 2.34/0.80 % Given clauses 0.
% 2.34/0.80
% 2.34/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------