%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS181+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 : n015.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 07:46:16 AM UTC 2026
% Result : Theorem 0.14s 15.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 61 ( 25 ~; 18 |; 13 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 28 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(isa,axiom,
! [S1,S2] :
( ! [Ax,C] :
( status(Ax,C,S1)
=> status(Ax,C,S2) )
<=> isa(S1,S2) ),
file('theBenchmark.p',isa) ).
fof(nota,axiom,
! [S1,S2] :
( ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) )
<=> nota(S1,S2) ),
file('theBenchmark.p',nota) ).
fof(nota_isa_nota,conjecture,
! [S1,S2,S3] :
( ( nota(S1,S3)
& isa(S1,S2) )
=> nota(S2,S3) ),
file('theBenchmark.p',nota_isa_nota) ).
fof(nota_isa_nota_neg,negated_conjecture,
~ ! [S1,S2,S3] :
( ( nota(S1,S3)
& isa(S1,S2) )
=> nota(S2,S3) ),
inference(assume_negation,[status(cth)],[nota_isa_nota]) ).
cnf(c_18,plain,
( ~ isa(C,D)
| status(A,B,D)
| ~ status(A,B,C) ),
inference(clausify,[status(thm)],[isa]) ).
fof(nnf_14,plain,
? [S1,S2,S3] :
( ~ nota(S2,S3)
& nota(S1,S3)
& isa(S1,S2) ),
inference(fof_nnf,[status(thm)],[nota_isa_nota_neg]) ).
fof(sk_nota_isa_nota_neg,plain,
( ~ nota(sK1,sK4)
& nota(sK0,sK4)
& isa(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK4]),skolemize(S1,sK0),skolemize(S2,sK1),skolemize(S3,sK4)],[nnf_14]) ).
cnf(c_19,negated_conjecture,
isa(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_nota_isa_nota_neg]) ).
fof(nnf_3,plain,
! [S1,S2] :
( ( ~ nota(S1,S2)
| ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) ) )
& ( nota(S1,S2)
| ! [X0,X1] :
( status(X0,X1,S2)
| ~ status(X0,X1,S1) ) ) ),
inference(fof_nnf,[status(thm)],[nota]) ).
fof(sk_nota_sk,plain,
! [S1,S2] :
( ( ~ nota(S1,S2)
| ( ~ status(sK2(S1,S2),sK3(S1,S2),S2)
& status(sK2(S1,S2),sK3(S1,S2),S1) ) )
& ( nota(S1,S2)
| ! [X0,X1] :
( status(X0,X1,S2)
| ~ status(X0,X1,S1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(Ax,sK2(S1,S2)),skolemize(C,sK3(S1,S2))],[nnf_3]) ).
fof(sk_nota,plain,
( ! [VAR_0,VAR_1] :
( ~ nota(VAR_0,VAR_1)
| ~ status(sK2(VAR_0,VAR_1),sK3(VAR_0,VAR_1),VAR_1) )
& ! [VAR_0,VAR_1] :
( ~ nota(VAR_0,VAR_1)
| status(sK2(VAR_0,VAR_1),sK3(VAR_0,VAR_1),VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( nota(VAR_2,VAR_3)
| status(VAR_0,VAR_1,VAR_3)
| ~ status(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_nota_sk]) ).
cnf(c_22,plain,
( ~ nota(A,B)
| status(sK2(A,B),sK3(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_nota]) ).
cnf(c_23,plain,
( nota(C,D)
| status(A,B,D)
| ~ status(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_nota]) ).
cnf(c_24,plain,
( ~ nota(A,B)
| ~ status(sK2(A,B),sK3(A,B),B) ),
inference(split_conjunct,[status(thm)],[sk_nota]) ).
cnf(c_25,negated_conjecture,
nota(sK0,sK4),
inference(split_conjunct,[status(thm)],[sk_nota_isa_nota_neg]) ).
cnf(c_26,negated_conjecture,
~ nota(sK1,sK4),
inference(split_conjunct,[status(thm)],[sk_nota_isa_nota_neg]) ).
cnf(c_38,negated_conjecture,
( status(A,B,sK4)
| ~ status(A,B,sK1) ),
inference(resolve,[status(thm)],[c_26,c_23]) ).
cnf(c_39,negated_conjecture,
status(sK2(sK0,sK4),sK3(sK0,sK4),sK0),
inference(resolve,[status(thm)],[c_25,c_22]) ).
cnf(c_40,negated_conjecture,
~ status(sK2(sK0,sK4),sK3(sK0,sK4),sK4),
inference(resolve,[status(thm)],[c_25,c_24]) ).
cnf(c_62,negated_conjecture,
( status(A,B,sK1)
| ~ status(A,B,sK0) ),
inference(resolve,[status(thm)],[c_18,c_19]) ).
cnf(c_73,negated_conjecture,
~ status(sK2(sK0,sK4),sK3(sK0,sK4),sK1),
inference(resolve,[status(thm)],[c_38,c_40]) ).
cnf(c_91,negated_conjecture,
status(sK2(sK0,sK4),sK3(sK0,sK4),sK1),
inference(resolve,[status(thm)],[c_62,c_39]) ).
cnf(c_90,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_73,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS181+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/15.38 % Computer : n015.cluster.edu
% 0.09/15.38 % Model : x86_64 x86_64
% 0.09/15.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/15.38 % Memory : 8046.5625MB
% 0.09/15.38 % OS : Linux 6.8.0-71-generic
% 0.09/15.38 % CPULimit : 300
% 0.09/15.38 % WCLimit : 300
% 0.09/15.38 % DateTime : Fri Sep 25 19:46:43 UTC 2026
% 0.09/15.39 % CPUTime :
% 0.09/15.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/15.39 % Process 2088714 was started by sandbox2 on n015,
% 0.09/15.39 % Fri Sep 25 19:46:43 2026
% 0.09/15.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/15.40
% 0.14/15.40 % From the command line: assign(max_seconds, 300).
% 0.14/15.41
% 0.14/15.41 % SZS status Theorem for theBenchmark
% 0.14/15.41
% 0.14/15.41 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.14/15.41 % Length of proof is 16.
% 0.14/15.41 % Level of proof is 4.
% 0.14/15.41 % Maximum clause weight is 8.000.
% 0.14/15.41 % Given clauses 29.
% 0.14/15.41
% 0.14/15.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------