%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS234+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 : n026.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 07:46:20 AM UTC 2026
% Result : Theorem 0.25s 0.65s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 10 unt; 0 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 52 ( 21 ~; 18 |; 7 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 51 ( 8 sgn 29 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm,axiom,
! [Ax,C] :
( ! [I1] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ),
file('theBenchmark.p',thm) ).
fof(uns,axiom,
! [Ax,C] :
( ( ! [I2] : model(I2,not(C))
& ! [I1] : model(I1,Ax) )
<=> status(Ax,C,uns) ),
file('theBenchmark.p',uns) ).
fof(nevera,axiom,
! [S1,S2] :
( ! [Ax,C] :
( status(Ax,C,S1)
=> ~ status(Ax,C,S2) )
<=> nevera(S1,S2) ),
file('theBenchmark.p',nevera) ).
fof(not,axiom,
! [I,F] :
( model(I,F)
<=> ~ model(I,not(F)) ),
file('theBenchmark.p',not) ).
fof(nevera_uns_thm,conjecture,
nevera(uns,thm),
file('theBenchmark.p',nevera_uns_thm) ).
fof(nevera_uns_thm_neg,negated_conjecture,
~ nevera(uns,thm),
inference(assume_negation,[status(cth)],[nevera_uns_thm]) ).
fof(nnf_23,plain,
! [S1,S2] :
( ( ~ nevera(S1,S2)
| ! [Ax,C] :
( ~ status(Ax,C,S2)
| ~ status(Ax,C,S1) ) )
& ( nevera(S1,S2)
| ? [X0,X1] :
( status(X0,X1,S2)
& status(X0,X1,S1) ) ) ),
inference(fof_nnf,[status(thm)],[nevera]) ).
fof(sk_nevera_sk,plain,
! [S1,S2] :
( ( ~ nevera(S1,S2)
| ! [Ax,C] :
( ~ status(Ax,C,S2)
| ~ status(Ax,C,S1) ) )
& ( nevera(S1,S2)
| ( status(sK0(S1,S2),sK1(S1,S2),S2)
& status(sK0(S1,S2),sK1(S1,S2),S1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0(S1,S2)),skolemize(X1,sK1(S1,S2))],[nnf_23]) ).
fof(sk_nevera,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ nevera(VAR_2,VAR_3)
| ~ status(VAR_0,VAR_1,VAR_3)
| ~ status(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1] :
( nevera(VAR_0,VAR_1)
| status(sK0(VAR_0,VAR_1),sK1(VAR_0,VAR_1),VAR_1) )
& ! [VAR_0,VAR_1] :
( nevera(VAR_0,VAR_1)
| status(sK0(VAR_0,VAR_1),sK1(VAR_0,VAR_1),VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_nevera_sk]) ).
cnf(c_43,plain,
( nevera(A,B)
| status(sK0(A,B),sK1(A,B),B) ),
inference(split_conjunct,[status(thm)],[sk_nevera]) ).
cnf(c_45,negated_conjecture,
~ nevera(uns,thm),
inference(clausify,[status(thm)],[nevera_uns_thm_neg]) ).
cnf(c_46,plain,
( nevera(A,B)
| status(sK0(A,B),sK1(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_nevera]) ).
cnf(c_75,plain,
( ~ model(A,not(B))
| ~ model(A,B) ),
inference(clausify,[status(thm)],[not]) ).
cnf(c_81,plain,
( ~ status(C,B,uns)
| model(A,not(B)) ),
inference(clausify,[status(thm)],[uns]) ).
cnf(c_82,plain,
( ~ status(B,C,uns)
| model(A,B) ),
inference(clausify,[status(thm)],[uns]) ).
cnf(c_133,plain,
( ~ status(B,C,thm)
| model(A,C)
| ~ model(A,B) ),
inference(clausify,[status(thm)],[thm]) ).
cnf(c_152,negated_conjecture,
status(sK0(uns,thm),sK1(uns,thm),thm),
inference(resolve,[status(thm)],[c_43,c_45]) ).
cnf(c_154,negated_conjecture,
status(sK0(uns,thm),sK1(uns,thm),uns),
inference(resolve,[status(thm)],[c_46,c_45]) ).
cnf(c_567,plain,
( model(A,sK1(uns,thm))
| ~ model(A,sK0(uns,thm)) ),
inference(resolve,[status(thm)],[c_152,c_133]) ).
cnf(c_596,plain,
model(A,sK0(uns,thm)),
inference(resolve,[status(thm)],[c_154,c_82]) ).
cnf(c_597,plain,
model(A,not(sK1(uns,thm))),
inference(resolve,[status(thm)],[c_154,c_81]) ).
cnf(c_608,plain,
model(A,sK1(uns,thm)),
inference(resolve,[status(thm)],[c_596,c_567]) ).
cnf(c_1633,plain,
~ model(A,sK1(uns,thm)),
inference(resolve,[status(thm)],[c_597,c_75]) ).
cnf(c_1632,plain,
$false,
inference(resolve,[status(thm)],[c_608,c_1633]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS234+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n026.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 19:50:40 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 3289999 was started by sandbox2 on n026,
% 0.18/0.44 % Fri Sep 25 19:50:40 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).
% 0.25/0.65
% 0.25/0.65 % SZS status Theorem for theBenchmark
% 0.25/0.65
% 0.25/0.65 % Proof 1 at 0.12 (+ 0.05) seconds.
% 0.25/0.65 % Length of proof is 19.
% 0.25/0.65 % Level of proof is 5.
% 0.25/0.65 % Maximum clause weight is 10.000.
% 0.25/0.65 % Given clauses 178.
% 0.25/0.65
% 0.25/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------