%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC367+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 : n004.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 08:57:36 AM UTC 2026
% Result : Theorem 15.35s 2.49s
% Output : CNFRefutation 15.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 11 unt; 0 def)
% Number of atoms : 96 ( 37 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 87 ( 20 ~; 28 |; 30 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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(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)
=> ( ( ( ~ rearsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| rearsegP(V,U)
| 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)
=> ( ( ( ~ rearsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| rearsegP(V,U)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_233,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_277,plain,
( rearsegP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax49]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( rearsegP(X,W)
& neq(W,nil) )
| ( nil = W
& nil = X ) )
& ~ rearsegP(V,U)
& 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,
( ( ( rearsegP(sK0,sK2)
& neq(sK2,nil) )
| ( nil = sK2
& nil = sK0 ) )
& ~ rearsegP(sK1,sK3)
& sK2 = sK3
& sK0 = sK1
& ssList(sK0)
& ssList(sK2)
& ssList(sK1)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK1,sK2,sK0]),skolemize(U,sK3),skolemize(V,sK1),skolemize(W,sK2),skolemize(X,sK0)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( rearsegP(sK0,sK2)
| nil = sK2 )
& ( neq(sK2,nil)
| nil = sK2 )
& ( rearsegP(sK0,sK2)
| nil = sK0 )
& ( neq(sK2,nil)
| nil = sK0 )
& ~ rearsegP(sK1,sK3)
& sK2 = sK3
& sK0 = sK1
& ssList(sK0)
& ssList(sK2)
& ssList(sK1)
& ssList(sK3) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_333,negated_conjecture,
sK0 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_334,negated_conjecture,
sK2 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_335,negated_conjecture,
~ rearsegP(sK1,sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_336,negated_conjecture,
( rearsegP(sK0,sK2)
| nil = sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_1857,negated_conjecture,
( rearsegP(sK0,sK2)
| nil = sK1 ),
inference(paramod,[status(thm)],[c_333,c_336]) ).
cnf(c_1858,negated_conjecture,
( rearsegP(sK1,sK2)
| nil = sK1 ),
inference(paramod,[status(thm)],[c_333,c_1857]) ).
cnf(c_1859,negated_conjecture,
( rearsegP(sK1,sK3)
| nil = sK1 ),
inference(paramod,[status(thm)],[c_334,c_1858]) ).
cnf(c_1860,negated_conjecture,
( rearsegP(sK1,sK3)
| sK1 = nil ),
inference(copy,[status(thm)],[c_1859]) ).
cnf(c_337,negated_conjecture,
sK1 = nil,
inference(resolve,[status(thm)],[c_335,c_1860]) ).
cnf(c_338,negated_conjecture,
( rearsegP(sK0,sK2)
| nil = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_1861,negated_conjecture,
( rearsegP(sK0,sK2)
| nil = sK3 ),
inference(paramod,[status(thm)],[c_334,c_338]) ).
cnf(c_1862,negated_conjecture,
( rearsegP(sK1,sK2)
| nil = sK3 ),
inference(paramod,[status(thm)],[c_333,c_1861]) ).
cnf(c_1863,negated_conjecture,
( rearsegP(nil,sK2)
| nil = sK3 ),
inference(paramod,[status(thm)],[c_337,c_1862]) ).
cnf(c_1864,negated_conjecture,
( rearsegP(nil,sK3)
| nil = sK3 ),
inference(paramod,[status(thm)],[c_334,c_1863]) ).
cnf(c_339,negated_conjecture,
( rearsegP(nil,sK3)
| sK3 = nil ),
inference(copy,[status(thm)],[c_1864]) ).
cnf(c_621,negated_conjecture,
~ rearsegP(nil,sK3),
inference(paramod,[status(thm)],[c_337,c_335]) ).
cnf(c_1076,negated_conjecture,
sK3 = nil,
inference(resolve,[status(thm)],[c_621,c_339]) ).
cnf(c_1479,negated_conjecture,
~ rearsegP(nil,nil),
inference(paramod,[status(thm)],[c_1076,c_621]) ).
cnf(c_1865,plain,
rearsegP(nil,nil),
inference(resolve,[status(thm)],[c_277,c_233]) ).
cnf(c_1856,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1479,c_1865]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC367+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n004.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 12:53:21 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 1756525 was started by sandbox2 on n004,
% 0.18/0.44 % Sat Sep 26 12:53:21 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.48
% 0.18/0.48 % From the command line: assign(max_seconds, 300).
% 15.35/2.49
% 15.35/2.49 % SZS status Theorem for theBenchmark
% 15.35/2.49
% 15.35/2.49 % Proof 1 at 1.65 (+ 0.12) seconds.
% 15.35/2.49 % Length of proof is 15.
% 15.35/2.49 % Level of proof is 6.
% 15.35/2.49 % Maximum clause weight is 8.000.
% 15.35/2.49 % Given clauses 107.
% 15.35/2.49
% 15.35/2.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------