%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC044+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 : 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 08:56:39 AM UTC 2026
% Result : Theorem 4.37s 0.95s
% Output : CNFRefutation 4.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 13 unt; 0 def)
% Number of atoms : 59 ( 28 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 55 ( 17 ~; 12 |; 16 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 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(ax52,axiom,
! [U] :
( ssList(U)
=> ( rearsegP(nil,U)
<=> nil = U ) ),
file('theBenchmark.p',ax52) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( nil = U
| ~ rearsegP(X,W)
| U != W
| V != X
| nil != V ) ) ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( nil = U
| ~ rearsegP(X,W)
| U != W
| V != X
| nil != V ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_278,plain,
( nil = A
| ~ rearsegP(nil,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax52]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( nil != U
& rearsegP(X,W)
& W = U
& X = V
& nil = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg,plain,
( nil != sK0
& rearsegP(sK2,sK3)
& sK3 = sK0
& sK2 = sK1
& nil = 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]) ).
cnf(c_327,negated_conjecture,
ssList(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_331,negated_conjecture,
nil = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_332,negated_conjecture,
sK1 = nil,
inference(copy,[status(thm)],[c_331]) ).
cnf(c_333,negated_conjecture,
sK2 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_334,negated_conjecture,
sK2 = nil,
inference(paramod,[status(thm)],[c_332,c_333]) ).
cnf(c_335,negated_conjecture,
sK3 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_336,negated_conjecture,
rearsegP(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2000,negated_conjecture,
rearsegP(nil,sK3),
inference(paramod,[status(thm)],[c_334,c_336]) ).
cnf(c_337,negated_conjecture,
rearsegP(nil,sK0),
inference(paramod,[status(thm)],[c_335,c_2000]) ).
cnf(c_338,negated_conjecture,
nil != sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_339,negated_conjecture,
sK0 != nil,
inference(copy,[status(thm)],[c_338]) ).
cnf(c_2001,negated_conjecture,
( nil = sK0
| ~ rearsegP(nil,sK0) ),
inference(resolve,[status(thm)],[c_327,c_278]) ).
cnf(c_2002,negated_conjecture,
( sK0 = nil
| ~ rearsegP(nil,sK0) ),
inference(copy,[status(thm)],[c_2001]) ).
cnf(c_2003,negated_conjecture,
sK0 = nil,
inference(resolve,[status(thm)],[c_337,c_2002]) ).
cnf(c_1999,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_339,c_2003]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC044+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 12:07:19 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.30 % Process 539014 was started by sandbox on n012,
% 0.03/0.30 % Sat Sep 26 12:07:19 2026
% 0.03/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.31
% 0.03/0.31 % From the command line: assign(max_seconds, 300).
% 4.37/0.95
% 4.37/0.95 % SZS status Theorem for theBenchmark
% 4.37/0.95
% 4.37/0.95 % Proof 1 at 0.54 (+ 0.04) seconds.
% 4.37/0.95 % Length of proof is 14.
% 4.37/0.95 % Level of proof is 5.
% 4.37/0.95 % Maximum clause weight is 10.000.
% 4.37/0.95 % Given clauses 157.
% 4.37/0.95
% 4.37/0.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------