%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS217+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 07:46:19 AM UTC 2026
% Result : Theorem 3.80s 0.93s
% Output : CNFRefutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 12 unt; 0 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 71 ( 29 ~; 20 |; 16 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-1 aty)
% Number of variables : 45 ( 0 sgn 12 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm,axiom,
! [Ax,C] :
( ! [I1] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ),
file('theBenchmark.p',thm) ).
fof(noc,axiom,
! [Ax,C] :
( ( ? [I2] :
( model(I2,not(C))
& model(I2,Ax) )
& ? [I1] :
( model(I1,C)
& model(I1,Ax) ) )
<=> status(Ax,C,noc) ),
file('theBenchmark.p',noc) ).
fof(nota,axiom,
! [S1,S2] :
( ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) )
<=> nota(S1,S2) ),
file('theBenchmark.p',nota) ).
fof(not,axiom,
! [I,F] :
( model(I,F)
<=> ~ model(I,not(F)) ),
file('theBenchmark.p',not) ).
fof(mixed_pair,axiom,
? [Ax,C] :
( ? [I4] : ~ model(I4,C)
& ? [I3] :
( model(I3,C)
& ~ model(I3,Ax) )
& ! [I2] :
( model(I2,Ax)
=> model(I2,C) )
& ? [I1] : model(I1,Ax) ),
file('theBenchmark.p',mixed_pair) ).
fof(nota_noc_thm,conjecture,
nota(noc,thm),
file('theBenchmark.p',nota_noc_thm) ).
fof(nota_noc_thm_neg,negated_conjecture,
~ nota(noc,thm),
inference(assume_negation,[status(cth)],[nota_noc_thm]) ).
cnf(c_41,plain,
( nota(C,D)
| status(A,B,D)
| ~ status(A,B,C) ),
inference(clausify,[status(thm)],[nota]) ).
cnf(c_43,negated_conjecture,
~ nota(noc,thm),
inference(clausify,[status(thm)],[nota_noc_thm_neg]) ).
cnf(c_55,negated_conjecture,
( status(A,B,thm)
| ~ status(A,B,noc) ),
inference(resolve,[status(thm)],[c_43,c_41]) ).
fof(nnf_31,plain,
? [Ax,C] :
( ? [I4] : ~ model(I4,C)
& ? [I3] :
( model(I3,C)
& ~ model(I3,Ax) )
& ! [I2] :
( model(I2,C)
| ~ model(I2,Ax) )
& ? [I1] : model(I1,Ax) ),
inference(fof_nnf,[status(thm)],[mixed_pair]) ).
fof(sk_mixed_pair,plain,
( ~ model(sK6,sK1)
& model(sK0,sK1)
& ~ model(sK0,sK2)
& ! [I2] :
( model(I2,sK1)
| ~ model(I2,sK2) )
& model(sK3,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK2,sK1,sK0,sK6]),skolemize(Ax,sK2),skolemize(C,sK1),skolemize(I1,sK3),skolemize(I3,sK0),skolemize(I4,sK6)],[nnf_31]) ).
cnf(c_64,plain,
model(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_mixed_pair]) ).
cnf(c_65,plain,
~ model(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_mixed_pair]) ).
cnf(c_66,plain,
( model(A,sK1)
| ~ model(A,sK2) ),
inference(split_conjunct,[status(thm)],[sk_mixed_pair]) ).
cnf(c_67,plain,
model(sK3,sK2),
inference(split_conjunct,[status(thm)],[sk_mixed_pair]) ).
cnf(c_75,plain,
( model(A,not(B))
| model(A,B) ),
inference(clausify,[status(thm)],[not]) ).
cnf(c_81,plain,
( status(B,C,noc)
| ~ model(D,not(C))
| ~ model(D,B)
| ~ model(A,C)
| ~ model(A,B) ),
inference(clausify,[status(thm)],[noc]) ).
cnf(c_134,plain,
( ~ status(B,C,thm)
| model(A,C)
| ~ model(A,B) ),
inference(clausify,[status(thm)],[thm]) ).
cnf(c_172,plain,
model(sK3,sK1),
inference(resolve,[status(thm)],[c_67,c_66]) ).
cnf(c_177,plain,
model(sK0,not(sK2)),
inference(resolve,[status(thm)],[c_75,c_65]) ).
cnf(c_197,plain,
( status(A,sK2,noc)
| ~ model(B,not(sK2))
| ~ model(B,A)
| ~ model(sK3,A) ),
inference(resolve,[status(thm)],[c_81,c_67]) ).
cnf(c_2785,plain,
( status(sK1,sK2,noc)
| ~ model(sK0,not(sK2))
| ~ model(sK3,sK1) ),
inference(resolve,[status(thm)],[c_197,c_64]) ).
cnf(c_2786,plain,
( status(sK1,sK2,noc)
| ~ model(sK0,not(sK2)) ),
inference(resolve,[status(thm)],[c_172,c_2785]) ).
cnf(c_2612,plain,
status(sK1,sK2,noc),
inference(resolve,[status(thm)],[c_177,c_2786]) ).
cnf(c_2755,plain,
status(sK1,sK2,thm),
inference(resolve,[status(thm)],[c_2612,c_55]) ).
cnf(c_2766,plain,
( model(A,sK2)
| ~ model(A,sK1) ),
inference(resolve,[status(thm)],[c_2755,c_134]) ).
cnf(c_2787,plain,
model(sK0,sK2),
inference(resolve,[status(thm)],[c_2766,c_64]) ).
cnf(c_2784,plain,
$false,
inference(resolve,[status(thm)],[c_65,c_2787]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS217+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 19:41:18 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 3002762 was started by sandbox2 on n017,
% 0.11/0.37 % Fri Sep 25 19:41:18 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 3.80/0.93
% 3.80/0.93 % SZS status Theorem for theBenchmark
% 3.80/0.93
% 3.80/0.93 % Proof 1 at 0.39 (+ 0.08) seconds.
% 3.80/0.93 % Length of proof is 23.
% 3.80/0.93 % Level of proof is 6.
% 3.80/0.93 % Maximum clause weight is 27.000.
% 3.80/0.93 % Given clauses 199.
% 3.80/0.93
% 3.80/0.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------