%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS202+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 : n019.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 1.56s 0.69s
% Output : CNFRefutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 14 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 52 ( 21 ~; 12 |; 13 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 48 ( 5 sgn 13 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(esa,axiom,
! [Ax,C] :
( ( ? [I1] : model(I1,Ax)
<=> ? [I2] : model(I2,C) )
<=> status(Ax,C,esa) ),
file('theBenchmark.p',esa) ).
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(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_esa_thm,conjecture,
nota(esa,thm),
file('theBenchmark.p',nota_esa_thm) ).
fof(nota_esa_thm_neg,negated_conjecture,
~ nota(esa,thm),
inference(assume_negation,[status(cth)],[nota_esa_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(esa,thm),
inference(clausify,[status(thm)],[nota_esa_thm_neg]) ).
cnf(c_55,negated_conjecture,
( status(A,B,thm)
| ~ status(A,B,esa) ),
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(sK0,sK1)
& model(sK7,sK1)
& ~ model(sK7,sK2)
& ! [I2] :
( model(I2,sK1)
| ~ model(I2,sK2) )
& model(sK3,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK2,sK1,sK7,sK0]),skolemize(Ax,sK2),skolemize(C,sK1),skolemize(I1,sK3),skolemize(I3,sK7),skolemize(I4,sK0)],[nnf_31]) ).
cnf(c_63,plain,
~ model(sK0,sK1),
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]) ).
fof(nnf_27,plain,
? [F] :
! [I] : model(I,F),
inference(fof_nnf,[status(thm)],[tautology]) ).
fof(sk_tautology,plain,
! [I] : model(I,sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(F,sK4)],[nnf_27]) ).
cnf(c_74,plain,
model(A,sK4),
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_142,plain,
( status(B,D,esa)
| ~ model(C,D)
| ~ model(A,B) ),
inference(clausify,[status(thm)],[esa]) ).
cnf(c_172,plain,
model(sK3,sK1),
inference(resolve,[status(thm)],[c_67,c_66]) ).
cnf(c_453,plain,
( status(sK4,B,esa)
| ~ model(A,B) ),
inference(resolve,[status(thm)],[c_142,c_74]) ).
cnf(c_2024,plain,
status(sK4,sK1,esa),
inference(resolve,[status(thm)],[c_453,c_172]) ).
cnf(c_2045,plain,
status(sK4,sK1,thm),
inference(resolve,[status(thm)],[c_2024,c_55]) ).
cnf(c_2167,plain,
( model(A,sK1)
| ~ model(A,sK4) ),
inference(resolve,[status(thm)],[c_2045,c_134]) ).
cnf(c_2165,plain,
model(A,sK1),
inference(resolve,[status(thm)],[c_74,c_2167]) ).
cnf(c_2166,plain,
$false,
inference(resolve,[status(thm)],[c_2165,c_63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS202+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n019.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 19:44:48 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 3504604 was started by sandbox2 on n019,
% 0.18/0.44 % Fri Sep 25 19:44:48 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).
% 1.56/0.69
% 1.56/0.69 % SZS status Theorem for theBenchmark
% 1.56/0.69
% 1.56/0.69 % Proof 1 at 0.16 (+ 0.05) seconds.
% 1.56/0.69 % Length of proof is 21.
% 1.56/0.69 % Level of proof is 6.
% 1.56/0.69 % Maximum clause weight is 15.000.
% 1.56/0.69 % Given clauses 260.
% 1.56/0.69
% 1.56/0.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------