%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS254+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 : n004.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 07:46:22 AM UTC 2026
% Result : Theorem 0.09s 0.48s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 12 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 56 ( 23 ~; 15 |; 13 &)
% ( 3 <=>; 2 =>; 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 : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 53 ( 6 sgn 23 !; 15 ?)
% 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(mighta,axiom,
! [S1,S2] :
( ? [Ax,C] :
( status(Ax,C,S2)
& status(Ax,C,S1) )
<=> mighta(S1,S2) ),
file('theBenchmark.p',mighta) ).
fof(tautology,axiom,
? [F] :
! [I] : model(I,F),
file('theBenchmark.p',tautology) ).
fof(non_thm_spt,axiom,
? [I1,Ax,C] :
( ? [I2] : model(I2,C)
& ~ model(I1,C)
& model(I1,Ax) ),
file('theBenchmark.p',non_thm_spt) ).
fof(mighta_unp_thm,conjecture,
mighta(unp,thm),
file('theBenchmark.p',mighta_unp_thm) ).
fof(mighta_unp_thm_neg,negated_conjecture,
~ mighta(unp,thm),
inference(assume_negation,[status(cth)],[mighta_unp_thm]) ).
cnf(c_35,plain,
( mighta(C,D)
| ~ status(A,B,D)
| ~ status(A,B,C) ),
inference(clausify,[status(thm)],[mighta]) ).
cnf(c_37,negated_conjecture,
~ mighta(unp,thm),
inference(clausify,[status(thm)],[mighta_unp_thm_neg]) ).
cnf(c_57,negated_conjecture,
( ~ status(A,B,thm)
| ~ status(A,B,unp) ),
inference(resolve,[status(thm)],[c_37,c_35]) ).
fof(nnf_32,plain,
? [I1,Ax,C] :
( ? [I2] : model(I2,C)
& ~ model(I1,C)
& model(I1,Ax) ),
inference(fof_nnf,[status(thm)],[non_thm_spt]) ).
fof(sk_non_thm_spt,plain,
( model(sK0,sK1)
& ~ model(sK6,sK1)
& model(sK6,sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK1,sK0]),skolemize(I1,sK6),skolemize(Ax,sK7),skolemize(C,sK1),skolemize(I2,sK0)],[nnf_32]) ).
cnf(c_60,plain,
model(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_non_thm_spt]) ).
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]) ).
fof(nnf_5,plain,
! [Ax,C] :
( ( ~ status(Ax,C,thm)
| ! [I1] :
( model(I1,C)
| ~ model(I1,Ax) ) )
& ( status(Ax,C,thm)
| ? [X0] :
( ~ model(X0,C)
& model(X0,Ax) ) ) ),
inference(fof_nnf,[status(thm)],[thm]) ).
fof(sk_thm_sk,plain,
! [Ax,C] :
( ( ~ status(Ax,C,thm)
| ! [I1] :
( model(I1,C)
| ~ model(I1,Ax) ) )
& ( status(Ax,C,thm)
| ( ~ model(sK3(Ax,C),C)
& model(sK3(Ax,C),Ax) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3(Ax,C))],[nnf_5]) ).
fof(sk_thm,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ status(VAR_1,VAR_2,thm)
| model(VAR_0,VAR_2)
| ~ model(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( status(VAR_0,VAR_1,thm)
| ~ model(sK3(VAR_0,VAR_1),VAR_1) )
& ! [VAR_0,VAR_1] :
( status(VAR_0,VAR_1,thm)
| model(sK3(VAR_0,VAR_1),VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_thm_sk]) ).
cnf(c_135,plain,
( status(A,B,thm)
| ~ model(sK3(A,B),B) ),
inference(split_conjunct,[status(thm)],[sk_thm]) ).
cnf(c_149,plain,
( status(B,C,unp)
| ~ model(A,B) ),
inference(clausify,[status(thm)],[unp]) ).
cnf(c_517,plain,
status(A,sK2,thm),
inference(resolve,[status(thm)],[c_135,c_74]) ).
cnf(c_678,plain,
status(sK1,A,unp),
inference(resolve,[status(thm)],[c_149,c_60]) ).
cnf(c_804,plain,
~ status(A,sK2,unp),
inference(resolve,[status(thm)],[c_517,c_57]) ).
cnf(c_805,plain,
$false,
inference(resolve,[status(thm)],[c_804,c_678]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS254+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.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
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 19:50:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3936008 was started by sandbox2 on n004,
% 0.09/0.36 % Fri Sep 25 19:50:06 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.48
% 0.09/0.48 % SZS status Theorem for theBenchmark
% 0.09/0.48
% 0.09/0.48 % Proof 1 at 0.07 (+ 0.03) seconds.
% 0.09/0.48 % Length of proof is 17.
% 0.09/0.48 % Level of proof is 4.
% 0.09/0.48 % Maximum clause weight is 19.000.
% 0.09/0.48 % Given clauses 126.
% 0.09/0.48
% 0.09/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------