%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS216+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 : n008.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 5.36s 1.12s
% Output : CNFRefutation 5.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 16 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 59 ( 26 ~; 20 |; 8 &)
% ( 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; 4 con; 0-2 aty)
% Number of variables : 61 ( 5 sgn 33 !; 8 ?)
% 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(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(contradiction,axiom,
? [F] :
! [I] : ~ model(I,F),
file('theBenchmark.p',contradiction) ).
fof(nota_uns_thm,conjecture,
nota(uns,thm),
file('theBenchmark.p',nota_uns_thm) ).
fof(nota_uns_thm_neg,negated_conjecture,
~ nota(uns,thm),
inference(assume_negation,[status(cth)],[nota_uns_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(uns,thm),
inference(clausify,[status(thm)],[nota_uns_thm_neg]) ).
cnf(c_55,negated_conjecture,
( status(A,B,thm)
| ~ status(A,B,uns) ),
inference(resolve,[status(thm)],[c_43,c_41]) ).
fof(nnf_29,plain,
? [F] :
! [I] : ~ model(I,F),
inference(fof_nnf,[status(thm)],[contradiction]) ).
fof(sk_contradiction,plain,
! [I] : ~ model(I,sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(F,sK0)],[nnf_29]) ).
cnf(c_71,plain,
~ model(A,sK0),
inference(split_conjunct,[status(thm)],[sk_contradiction]) ).
fof(nnf_27,plain,
? [F] :
! [I] : model(I,F),
inference(fof_nnf,[status(thm)],[tautology]) ).
fof(sk_tautology,plain,
! [I] : model(I,sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(F,sK1)],[nnf_27]) ).
cnf(c_74,plain,
model(A,sK1),
inference(split_conjunct,[status(thm)],[sk_tautology]) ).
cnf(c_75,plain,
( model(A,not(B))
| model(A,B) ),
inference(clausify,[status(thm)],[not]) ).
fof(nnf_18,plain,
! [Ax,C] :
( ( ~ status(Ax,C,uns)
| ( ! [I2] : model(I2,not(C))
& ! [I1] : model(I1,Ax) ) )
& ( status(Ax,C,uns)
| ? [X0] : ~ model(X0,not(C))
| ? [X1] : ~ model(X1,Ax) ) ),
inference(fof_nnf,[status(thm)],[uns]) ).
fof(sk_uns_sk,plain,
! [Ax,C] :
( ( ~ status(Ax,C,uns)
| ( ! [I2] : model(I2,not(C))
& ! [I1] : model(I1,Ax) ) )
& ( status(Ax,C,uns)
| ~ model(sK3(Ax,C),not(C))
| ~ model(sK2(Ax,C),Ax) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X1,sK2(Ax,C)),skolemize(X0,sK3(Ax,C))],[nnf_18]) ).
fof(sk_uns,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ status(VAR_2,VAR_1,uns)
| model(VAR_0,not(VAR_1)) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ status(VAR_1,VAR_2,uns)
| model(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( status(VAR_0,VAR_1,uns)
| ~ model(sK3(VAR_0,VAR_1),not(VAR_1))
| ~ model(sK2(VAR_0,VAR_1),VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_uns_sk]) ).
cnf(c_84,plain,
( status(A,B,uns)
| ~ model(sK3(A,B),not(B))
| ~ model(sK2(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_uns]) ).
cnf(c_134,plain,
( ~ status(B,C,thm)
| model(A,C)
| ~ model(A,B) ),
inference(clausify,[status(thm)],[thm]) ).
cnf(c_174,plain,
model(A,not(sK0)),
inference(resolve,[status(thm)],[c_75,c_71]) ).
cnf(c_223,plain,
( status(sK1,A,uns)
| ~ model(sK3(sK1,A),not(A)) ),
inference(resolve,[status(thm)],[c_84,c_74]) ).
cnf(c_612,plain,
( ~ status(sK1,B,thm)
| model(A,B) ),
inference(resolve,[status(thm)],[c_134,c_74]) ).
cnf(c_3939,plain,
status(sK1,sK0,uns),
inference(resolve,[status(thm)],[c_223,c_174]) ).
cnf(c_4064,plain,
status(sK1,sK0,thm),
inference(resolve,[status(thm)],[c_3939,c_55]) ).
cnf(c_4070,plain,
model(A,sK0),
inference(resolve,[status(thm)],[c_4064,c_612]) ).
cnf(c_4069,plain,
$false,
inference(resolve,[status(thm)],[c_71,c_4070]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS216+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n008.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % 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 19:46:54 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.36 % Process 1715873 was started by sandbox on n008,
% 0.02/0.36 % Fri Sep 25 19:46:54 2026
% 0.02/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.37
% 0.02/0.37 % From the command line: assign(max_seconds, 300).
% 5.36/1.12
% 5.36/1.12 % SZS status Theorem for theBenchmark
% 5.36/1.12
% 5.36/1.12 % Proof 1 at 0.62 (+ 0.11) seconds.
% 5.36/1.12 % Length of proof is 21.
% 5.36/1.12 % Level of proof is 5.
% 5.36/1.12 % Maximum clause weight is 19.000.
% 5.36/1.12 % Given clauses 377.
% 5.36/1.12
% 5.36/1.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------