%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS203+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 07:46:18 AM UTC 2026
% Result : Theorem 1.69s 0.68s
% Output : CNFRefutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 18 unt; 0 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 118 ( 47 ~; 38 |; 27 &)
% ( 4 <=>; 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 93 ( 6 sgn 45 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sat,axiom,
! [Ax,C] :
( ? [I1] :
( model(I1,C)
& model(I1,Ax) )
<=> status(Ax,C,sat) ),
file('theBenchmark.p',sat) ).
fof(thm,axiom,
! [Ax,C] :
( ! [I1] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ),
file('theBenchmark.p',thm) ).
fof(tac,axiom,
! [Ax,C] :
( ( ! [I2] : model(I2,C)
& ? [I1] : model(I1,Ax) )
<=> status(Ax,C,tac) ),
file('theBenchmark.p',tac) ).
fof(nota,axiom,
! [S1,S2] :
( ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) )
<=> nota(S1,S2) ),
file('theBenchmark.p',nota) ).
fof(tautology,axiom,
? [F] :
! [I] : model(I,F),
file('theBenchmark.p',tautology) ).
fof(mixed_pair,axiom,
? [Ax,C] :
( ? [I4] : ~ model(I4,C)
& ? [I3] :
( model(I3,C)
& ~ model(I3,Ax) )
& ! [I2] :
( model(I2,Ax)
=> model(I2,C) )
& ? [I1] : model(I1,Ax) ),
file('theBenchmark.p',mixed_pair) ).
fof(nota_sat_thm,conjecture,
nota(sat,thm),
file('theBenchmark.p',nota_sat_thm) ).
fof(nota_sat_thm_neg,negated_conjecture,
~ nota(sat,thm),
inference(assume_negation,[status(cth)],[nota_sat_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(sat,thm),
inference(clausify,[status(thm)],[nota_sat_thm_neg]) ).
cnf(c_55,negated_conjecture,
( status(A,B,thm)
| ~ status(A,B,sat) ),
inference(resolve,[status(thm)],[c_43,c_41]) ).
fof(nnf_31,plain,
? [Ax,C] :
( ? [I4] : ~ model(I4,C)
& ? [I3] :
( model(I3,C)
& ~ model(I3,Ax) )
& ! [I2] :
( model(I2,C)
| ~ model(I2,Ax) )
& ? [I1] : model(I1,Ax) ),
inference(fof_nnf,[status(thm)],[mixed_pair]) ).
fof(sk_mixed_pair,plain,
( ~ model(sK0,sK1)
& model(sK10,sK1)
& ~ model(sK10,sK2)
& ! [I2] :
( model(I2,sK1)
| ~ model(I2,sK2) )
& model(sK3,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK2,sK1,sK10,sK0]),skolemize(Ax,sK2),skolemize(C,sK1),skolemize(I1,sK3),skolemize(I3,sK10),skolemize(I4,sK0)],[nnf_31]) ).
cnf(c_63,plain,
~ model(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_mixed_pair]) ).
cnf(c_66,plain,
( model(A,sK1)
| ~ model(A,sK2) ),
inference(split_conjunct,[status(thm)],[sk_mixed_pair]) ).
cnf(c_67,plain,
model(sK3,sK2),
inference(split_conjunct,[status(thm)],[sk_mixed_pair]) ).
fof(nnf_27,plain,
? [F] :
! [I] : model(I,F),
inference(fof_nnf,[status(thm)],[tautology]) ).
fof(sk_tautology,plain,
! [I] : model(I,sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(F,sK4)],[nnf_27]) ).
cnf(c_74,plain,
model(A,sK4),
inference(split_conjunct,[status(thm)],[sk_tautology]) ).
fof(nnf_7,plain,
! [Ax,C] :
( ( ~ status(Ax,C,tac)
| ( ! [I2] : model(I2,C)
& ? [I1] : model(I1,Ax) ) )
& ( status(Ax,C,tac)
| ? [X0] : ~ model(X0,C)
| ! [X1] : ~ model(X1,Ax) ) ),
inference(fof_nnf,[status(thm)],[tac]) ).
fof(sk_tac_sk,plain,
! [Ax,C] :
( ( ~ status(Ax,C,tac)
| ( ! [I2] : model(I2,C)
& model(sK5(Ax,C),Ax) ) )
& ( status(Ax,C,tac)
| ~ model(sK6(Ax,C),C)
| ! [X1] : ~ model(X1,Ax) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK5]),skolemize(X0,sK6(Ax,C)),skolemize(I1,sK5(Ax,C))],[nnf_7]) ).
fof(sk_tac,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ status(VAR_2,VAR_1,tac)
| model(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( ~ status(VAR_0,VAR_1,tac)
| model(sK5(VAR_0,VAR_1),VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( status(VAR_1,VAR_2,tac)
| ~ model(sK6(VAR_1,VAR_2),VAR_2)
| ~ model(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_tac_sk]) ).
cnf(c_127,plain,
( ~ status(A,B,tac)
| model(sK5(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_tac]) ).
cnf(c_128,plain,
( status(B,C,tac)
| ~ model(sK6(B,C),C)
| ~ model(A,B) ),
inference(split_conjunct,[status(thm)],[sk_tac]) ).
cnf(c_134,plain,
( ~ status(B,C,thm)
| model(A,C)
| ~ model(A,B) ),
inference(clausify,[status(thm)],[thm]) ).
fof(nnf_4,plain,
! [Ax,C] :
( ( ~ status(Ax,C,sat)
| ? [I1] :
( model(I1,C)
& model(I1,Ax) ) )
& ( status(Ax,C,sat)
| ! [X0] :
( ~ model(X0,C)
| ~ model(X0,Ax) ) ) ),
inference(fof_nnf,[status(thm)],[sat]) ).
fof(sk_sat_sk,plain,
! [Ax,C] :
( ( ~ status(Ax,C,sat)
| ( model(sK7(Ax,C),C)
& model(sK7(Ax,C),Ax) ) )
& ( status(Ax,C,sat)
| ! [X0] :
( ~ model(X0,C)
| ~ model(X0,Ax) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(I1,sK7(Ax,C))],[nnf_4]) ).
fof(sk_sat,plain,
( ! [VAR_0,VAR_1] :
( ~ status(VAR_0,VAR_1,sat)
| model(sK7(VAR_0,VAR_1),VAR_1) )
& ! [VAR_0,VAR_1] :
( ~ status(VAR_0,VAR_1,sat)
| model(sK7(VAR_0,VAR_1),VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( status(VAR_1,VAR_2,sat)
| ~ model(VAR_0,VAR_2)
| ~ model(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_sat_sk]) ).
cnf(c_138,plain,
( ~ status(A,B,sat)
| model(sK7(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_sat]) ).
cnf(c_139,plain,
( status(B,C,sat)
| ~ model(A,C)
| ~ model(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sat]) ).
cnf(c_169,plain,
( status(B,B,sat)
| ~ model(A,B) ),
inference(factor,[status(thm)],[c_139]) ).
cnf(c_399,plain,
( status(B,sK4,tac)
| ~ model(A,B) ),
inference(resolve,[status(thm)],[c_128,c_74]) ).
cnf(c_435,plain,
( status(sK4,B,sat)
| ~ model(A,B) ),
inference(resolve,[status(thm)],[c_139,c_74]) ).
cnf(c_614,plain,
status(sK2,sK2,sat),
inference(resolve,[status(thm)],[c_169,c_67]) ).
cnf(c_1102,plain,
model(sK7(sK2,sK2),sK2),
inference(resolve,[status(thm)],[c_614,c_138]) ).
cnf(c_1613,plain,
status(sK2,sK4,tac),
inference(resolve,[status(thm)],[c_399,c_1102]) ).
cnf(c_1691,plain,
model(sK5(sK2,sK4),sK2),
inference(resolve,[status(thm)],[c_1613,c_127]) ).
cnf(c_1864,plain,
model(sK5(sK2,sK4),sK1),
inference(resolve,[status(thm)],[c_1691,c_66]) ).
cnf(c_1967,plain,
status(sK4,sK1,sat),
inference(resolve,[status(thm)],[c_435,c_1864]) ).
cnf(c_2011,plain,
status(sK4,sK1,thm),
inference(resolve,[status(thm)],[c_1967,c_55]) ).
cnf(c_2151,plain,
( model(A,sK1)
| ~ model(A,sK4) ),
inference(resolve,[status(thm)],[c_2011,c_134]) ).
cnf(c_2149,plain,
model(A,sK1),
inference(resolve,[status(thm)],[c_74,c_2151]) ).
cnf(c_2150,plain,
$false,
inference(resolve,[status(thm)],[c_2149,c_63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS203+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 19:47:24 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 3280138 was started by sandbox2 on n026,
% 0.10/0.37 % Fri Sep 25 19:47:24 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 1.69/0.68
% 1.69/0.68 % SZS status Theorem for theBenchmark
% 1.69/0.68
% 1.69/0.68 % Proof 1 at 0.21 (+ 0.06) seconds.
% 1.69/0.68 % Length of proof is 31.
% 1.69/0.68 % Level of proof is 11.
% 1.69/0.68 % Maximum clause weight is 12.000.
% 1.69/0.68 % Given clauses 213.
% 1.69/0.68
% 1.69/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------