%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS201+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 : 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 07:46:18 AM UTC 2026
% Result : Theorem 1.24s 0.60s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 14 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 18 ~; 8 |; 4 &)
% ( 4 <=>; 2 =>; 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; 6 con; 0-1 aty)
% Number of variables : 45 ( 8 sgn 12 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sap,axiom,
! [Ax,C] :
( ( ? [I1] : model(I1,Ax)
=> ? [I2] : model(I2,C) )
<=> status(Ax,C,sap) ),
file('theBenchmark.p',sap) ).
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(not,axiom,
! [I,F] :
( model(I,F)
<=> ~ model(I,not(F)) ),
file('theBenchmark.p',not) ).
fof(satisfiable,axiom,
? [F] :
( ? [I2] : ~ model(I2,F)
& ? [I1] : model(I1,F) ),
file('theBenchmark.p',satisfiable) ).
fof(contradiction,axiom,
? [F] :
! [I] : ~ model(I,F),
file('theBenchmark.p',contradiction) ).
fof(nota_sap_thm,conjecture,
nota(sap,thm),
file('theBenchmark.p',nota_sap_thm) ).
fof(nota_sap_thm_neg,negated_conjecture,
~ nota(sap,thm),
inference(assume_negation,[status(cth)],[nota_sap_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(sap,thm),
inference(clausify,[status(thm)],[nota_sap_thm_neg]) ).
cnf(c_55,negated_conjecture,
( status(A,B,thm)
| ~ status(A,B,sap) ),
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_28,plain,
? [F] :
( ? [I2] : ~ model(I2,F)
& ? [I1] : model(I1,F) ),
inference(fof_nnf,[status(thm)],[satisfiable]) ).
fof(sk_satisfiable,plain,
( ~ model(sK1,sK2)
& model(sK3,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK2,sK1]),skolemize(F,sK2),skolemize(I1,sK3),skolemize(I2,sK1)],[nnf_28]) ).
cnf(c_72,plain,
~ model(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_satisfiable]) ).
cnf(c_73,plain,
model(sK3,sK2),
inference(split_conjunct,[status(thm)],[sk_satisfiable]) ).
cnf(c_75,plain,
( model(A,not(B))
| model(A,B) ),
inference(clausify,[status(thm)],[not]) ).
cnf(c_134,plain,
( ~ status(B,C,thm)
| model(A,C)
| ~ model(A,B) ),
inference(clausify,[status(thm)],[thm]) ).
cnf(c_145,plain,
( status(C,B,sap)
| ~ model(A,B) ),
inference(clausify,[status(thm)],[sap]) ).
cnf(c_174,plain,
model(A,not(sK0)),
inference(resolve,[status(thm)],[c_75,c_71]) ).
cnf(c_699,plain,
status(A,sK2,sap),
inference(resolve,[status(thm)],[c_145,c_73]) ).
cnf(c_1117,plain,
status(A,sK2,thm),
inference(resolve,[status(thm)],[c_699,c_55]) ).
cnf(c_2265,plain,
( model(A,sK2)
| ~ model(A,B) ),
inference(resolve,[status(thm)],[c_1117,c_134]) ).
cnf(c_2412,plain,
model(A,sK2),
inference(resolve,[status(thm)],[c_2265,c_174]) ).
cnf(c_2413,plain,
$false,
inference(resolve,[status(thm)],[c_2412,c_72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS201+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 19:44:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3924162 was started by sandbox on n004,
% 0.10/0.37 % Fri Sep 25 19:44:52 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 1.24/0.60
% 1.24/0.60 % SZS status Theorem for theBenchmark
% 1.24/0.60
% 1.24/0.60 % Proof 1 at 0.15 (+ 0.03) seconds.
% 1.24/0.60 % Length of proof is 22.
% 1.24/0.60 % Level of proof is 6.
% 1.24/0.60 % Maximum clause weight is 17.000.
% 1.24/0.60 % Given clauses 187.
% 1.24/0.60
% 1.24/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------