%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS200+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 : n014.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 07:46:18 AM UTC 2026
% Result : Theorem 0.23s 0.61s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 12 unt; 0 def)
% Number of atoms : 39 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 15 ~; 7 |; 4 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 41 ( 8 sgn 10 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(unp,axiom,
! [Ax,C] :
( ( ~ ? [I1] : model(I1,Ax)
=> ~ ? [I2] : model(I2,C) )
<=> status(Ax,C,unp) ),
file('theBenchmark.p',unp) ).
fof(thm,axiom,
! [Ax,C] :
( ! [I1] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ),
file('theBenchmark.p',thm) ).
fof(nota,axiom,
! [S1,S2] :
( ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) )
<=> nota(S1,S2) ),
file('theBenchmark.p',nota) ).
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_unp_thm,conjecture,
nota(unp,thm),
file('theBenchmark.p',nota_unp_thm) ).
fof(nota_unp_thm_neg,negated_conjecture,
~ nota(unp,thm),
inference(assume_negation,[status(cth)],[nota_unp_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(unp,thm),
inference(clausify,[status(thm)],[nota_unp_thm_neg]) ).
cnf(c_55,negated_conjecture,
( status(A,B,thm)
| ~ status(A,B,unp) ),
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_134,plain,
( ~ status(B,C,thm)
| model(A,C)
| ~ model(A,B) ),
inference(clausify,[status(thm)],[thm]) ).
cnf(c_149,plain,
( status(B,C,unp)
| ~ model(A,B) ),
inference(clausify,[status(thm)],[unp]) ).
cnf(c_530,plain,
status(sK2,A,unp),
inference(resolve,[status(thm)],[c_149,c_74]) ).
cnf(c_837,plain,
status(sK2,A,thm),
inference(resolve,[status(thm)],[c_530,c_55]) ).
cnf(c_1328,plain,
( model(A,B)
| ~ model(A,sK2) ),
inference(resolve,[status(thm)],[c_837,c_134]) ).
cnf(c_1326,plain,
model(A,B),
inference(resolve,[status(thm)],[c_74,c_1328]) ).
cnf(c_1327,plain,
$false,
inference(resolve,[status(thm)],[c_1326,c_72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS200+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n014.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 : Fri Sep 25 19:44:03 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 941695 was started by sandbox2 on n014,
% 0.18/0.44 % Fri Sep 25 19:44:03 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 0.23/0.61
% 0.23/0.61 % SZS status Theorem for theBenchmark
% 0.23/0.61
% 0.23/0.61 % Proof 1 at 0.10 (+ 0.02) seconds.
% 0.23/0.61 % Length of proof is 17.
% 0.23/0.61 % Level of proof is 5.
% 0.23/0.61 % Maximum clause weight is 10.000.
% 0.23/0.61 % Given clauses 165.
% 0.23/0.61
% 0.23/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------