%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS215+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 3.37s 0.82s
% Output : CNFRefutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 10 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 16 ~; 14 |; 5 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 52 ( 9 sgn 12 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm,axiom,
! [Ax,C] :
( ! [I1] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ),
file('theBenchmark.p',thm) ).
fof(csa,axiom,
! [Ax,C] :
( ? [I1] :
( model(I1,not(C))
& model(I1,Ax) )
<=> status(Ax,C,csa) ),
file('theBenchmark.p',csa) ).
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(tautology,axiom,
? [F] :
! [I] : model(I,F),
file('theBenchmark.p',tautology) ).
fof(satisfiable,axiom,
? [F] :
( ? [I2] : ~ model(I2,F)
& ? [I1] : model(I1,F) ),
file('theBenchmark.p',satisfiable) ).
fof(nota_csa_thm,conjecture,
nota(csa,thm),
file('theBenchmark.p',nota_csa_thm) ).
fof(nota_csa_thm_neg,negated_conjecture,
~ nota(csa,thm),
inference(assume_negation,[status(cth)],[nota_csa_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(csa,thm),
inference(clausify,[status(thm)],[nota_csa_thm_neg]) ).
cnf(c_55,negated_conjecture,
( status(A,B,thm)
| ~ status(A,B,csa) ),
inference(resolve,[status(thm)],[c_43,c_41]) ).
fof(nnf_28,plain,
? [F] :
( ? [I2] : ~ model(I2,F)
& ? [I1] : model(I1,F) ),
inference(fof_nnf,[status(thm)],[satisfiable]) ).
fof(sk_satisfiable,plain,
( ~ model(sK0,sK1)
& model(sK5,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK1,sK0]),skolemize(F,sK1),skolemize(I1,sK5),skolemize(I2,sK0)],[nnf_28]) ).
cnf(c_72,plain,
~ model(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_satisfiable]) ).
fof(nnf_27,plain,
? [F] :
! [I] : model(I,F),
inference(fof_nnf,[status(thm)],[tautology]) ).
fof(sk_tautology,plain,
! [I] : model(I,sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(F,sK2)],[nnf_27]) ).
cnf(c_74,plain,
model(A,sK2),
inference(split_conjunct,[status(thm)],[sk_tautology]) ).
cnf(c_75,plain,
( model(A,not(B))
| model(A,B) ),
inference(clausify,[status(thm)],[not]) ).
cnf(c_87,plain,
( status(B,C,csa)
| ~ model(A,not(C))
| ~ model(A,B) ),
inference(clausify,[status(thm)],[csa]) ).
cnf(c_134,plain,
( ~ status(B,C,thm)
| model(A,C)
| ~ model(A,B) ),
inference(clausify,[status(thm)],[thm]) ).
cnf(c_228,plain,
( status(sK2,B,csa)
| ~ model(A,not(B)) ),
inference(resolve,[status(thm)],[c_87,c_74]) ).
cnf(c_2400,plain,
( model(B,A)
| status(sK2,A,csa) ),
inference(resolve,[status(thm)],[c_228,c_75]) ).
cnf(c_3360,plain,
( status(sK2,B,thm)
| model(A,B) ),
inference(resolve,[status(thm)],[c_2400,c_55]) ).
cnf(c_3557,plain,
( model(C,B)
| ~ model(C,sK2)
| model(A,B) ),
inference(resolve,[status(thm)],[c_3360,c_134]) ).
cnf(c_3544,plain,
( model(C,B)
| model(A,B) ),
inference(resolve,[status(thm)],[c_74,c_3557]) ).
cnf(c_3555,plain,
model(A,B),
inference(factor,[status(thm)],[c_3544]) ).
cnf(c_3556,plain,
$false,
inference(resolve,[status(thm)],[c_3555,c_72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS215+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 19:47:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3614373 was started by sandbox on n020,
% 0.09/0.36 % Fri Sep 25 19:47:03 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 3.37/0.82
% 3.37/0.82 % SZS status Theorem for theBenchmark
% 3.37/0.82
% 3.37/0.82 % Proof 1 at 0.35 (+ 0.09) seconds.
% 3.37/0.82 % Length of proof is 21.
% 3.37/0.82 % Level of proof is 7.
% 3.37/0.82 % Maximum clause weight is 21.000.
% 3.37/0.82 % Given clauses 361.
% 3.37/0.82
% 3.37/0.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------