%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC349+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 : n012.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 08:57:33 AM UTC 2026
% Result : Theorem 7.31s 6.54s
% Output : CNFRefutation 7.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 10 unt; 0 def)
% Number of atoms : 50 ( 17 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 48 ( 14 ~; 9 |; 16 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 14 ( 0 sgn 9 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax45,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,nil) ),
file('theBenchmark.p',ax45) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( frontsegP(V,U)
| ~ neq(V,nil)
| U != W
| V != X
| nil != W ) ) ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( frontsegP(V,U)
| ~ neq(V,nil)
| U != W
| V != X
| nil != W ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_271,plain,
( frontsegP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax45]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ~ frontsegP(V,U)
& neq(V,nil)
& W = U
& X = V
& nil = W
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg,plain,
( ~ frontsegP(sK0,sK2)
& neq(sK0,nil)
& sK1 = sK2
& sK3 = sK0
& nil = sK1
& ssList(sK3)
& ssList(sK1)
& ssList(sK0)
& ssList(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1,sK3]),skolemize(U,sK2),skolemize(V,sK0),skolemize(W,sK1),skolemize(X,sK3)],[nnf_87]) ).
cnf(c_329,negated_conjecture,
ssList(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_332,negated_conjecture,
nil = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_333,negated_conjecture,
sK1 = nil,
inference(copy,[status(thm)],[c_332]) ).
cnf(c_335,negated_conjecture,
sK1 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2013,negated_conjecture,
nil = sK2,
inference(paramod,[status(thm)],[c_333,c_335]) ).
cnf(c_336,negated_conjecture,
sK2 = nil,
inference(copy,[status(thm)],[c_2013]) ).
cnf(c_337,negated_conjecture,
~ frontsegP(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_338,negated_conjecture,
~ frontsegP(sK0,nil),
inference(paramod,[status(thm)],[c_336,c_337]) ).
cnf(c_2014,negated_conjecture,
frontsegP(sK0,nil),
inference(resolve,[status(thm)],[c_329,c_271]) ).
cnf(c_2012,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_338,c_2014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC349+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.56 % Computer : n012.cluster.edu
% 0.08/5.56 % Model : x86_64 x86_64
% 0.08/5.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.56 % Memory : 8046.5625MB
% 0.08/5.56 % OS : Linux 6.8.0-71-generic
% 0.08/5.56 % CPULimit : 300
% 0.08/5.56 % WCLimit : 300
% 0.08/5.56 % DateTime : Sat Sep 26 12:51:56 UTC 2026
% 0.08/5.56 % CPUTime :
% 0.08/5.56 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.56 % Process 639737 was started by sandbox2 on n012,
% 0.08/5.56 % Sat Sep 26 12:51:56 2026
% 0.08/5.56 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/5.59
% 0.08/5.59 % From the command line: assign(max_seconds, 300).
% 7.31/6.54
% 7.31/6.54 % SZS status Theorem for theBenchmark
% 7.31/6.54
% 7.31/6.54 % Proof 1 at 0.86 (+ 0.07) seconds.
% 7.31/6.54 % Length of proof is 11.
% 7.31/6.54 % Level of proof is 5.
% 7.31/6.54 % Maximum clause weight is 7.000.
% 7.31/6.54 % Given clauses 157.
% 7.31/6.54
% 7.31/6.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------