%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC365+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 : n008.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 2.97s 0.88s
% Output : CNFRefutation 2.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 6 unt; 0 def)
% Number of atoms : 80 ( 22 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 93 ( 28 ~; 23 |; 34 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 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)
=> ( ( ( ~ rearsegP(X,W)
| ~ neq(W,nil) )
& neq(X,nil) )
| ( nil = X
& nil != W )
| rearsegP(V,U)
| ~ 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)
=> ( ( ( ~ rearsegP(X,W)
| ~ neq(W,nil) )
& neq(X,nil) )
| ( nil = X
& nil != W )
| rearsegP(V,U)
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( rearsegP(X,W)
& neq(W,nil) )
| ~ neq(X,nil) )
& ( nil != X
| nil = W )
& ~ rearsegP(V,U)
& 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,
( ( ( rearsegP(sK0,sK1)
& neq(sK1,nil) )
| ~ neq(sK0,nil) )
& ( nil != sK0
| nil = sK1 )
& ~ rearsegP(sK2,sK3)
& neq(sK2,nil)
& sK1 = sK3
& sK0 = sK2
& ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK2,sK1,sK0]),skolemize(U,sK3),skolemize(V,sK2),skolemize(W,sK1),skolemize(X,sK0)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( rearsegP(sK0,sK1)
| ~ neq(sK0,nil) )
& ( neq(sK1,nil)
| ~ neq(sK0,nil) )
& ( nil != sK0
| nil = sK1 )
& ~ rearsegP(sK2,sK3)
& neq(sK2,nil)
& sK1 = sK3
& sK0 = sK2
& ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_190,negated_conjecture,
( rearsegP(sK0,sK1)
| ~ neq(sK0,nil) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_194,negated_conjecture,
~ rearsegP(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
neq(sK2,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
sK1 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
sK0 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_549,negated_conjecture,
( rearsegP(sK0,sK1)
| ~ neq(sK2,nil) ),
inference(paramod,[status(thm)],[c_197,c_190]) ).
cnf(c_550,negated_conjecture,
( rearsegP(sK2,sK1)
| ~ neq(sK2,nil) ),
inference(paramod,[status(thm)],[c_197,c_549]) ).
cnf(c_551,negated_conjecture,
( rearsegP(sK2,sK3)
| ~ neq(sK2,nil) ),
inference(paramod,[status(thm)],[c_196,c_550]) ).
cnf(c_552,negated_conjecture,
rearsegP(sK2,sK3),
inference(resolve,[status(thm)],[c_195,c_551]) ).
cnf(c_548,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_194,c_552]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC365+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.39 % Computer : n008.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 12:54:09 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.40 % Process 3715488 was started by sandbox2 on n008,
% 0.12/0.40 % Sat Sep 26 12:54:09 2026
% 0.12/0.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 2.97/0.88
% 2.97/0.88 % SZS status Theorem for theBenchmark
% 2.97/0.88
% 2.97/0.88 % Proof 1 at 0.41 (+ 0.01) seconds.
% 2.97/0.88 % Length of proof is 7.
% 2.97/0.88 % Level of proof is 2.
% 2.97/0.88 % Maximum clause weight is 6.000.
% 2.97/0.88 % Given clauses 0.
% 2.97/0.88
% 2.97/0.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------