%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS233+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 : n018.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 07:46:20 AM UTC 2026
% Result : Theorem 81.45s 11.70s
% Output : CNFRefutation 81.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 10 unt; 0 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 78 ( 31 ~; 28 |; 13 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 40 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm,axiom,
! [Ax,C] :
( ! [I1] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ),
file('theBenchmark.p',thm) ).
fof(csa,axiom,
! [Ax,C] :
( ? [I1] :
( model(I1,not(C))
& model(I1,Ax) )
<=> status(Ax,C,csa) ),
file('theBenchmark.p',csa) ).
fof(nevera,axiom,
! [S1,S2] :
( ! [Ax,C] :
( status(Ax,C,S1)
=> ~ status(Ax,C,S2) )
<=> nevera(S1,S2) ),
file('theBenchmark.p',nevera) ).
fof(not,axiom,
! [I,F] :
( model(I,F)
<=> ~ model(I,not(F)) ),
file('theBenchmark.p',not) ).
fof(nevera_csa_thm,conjecture,
nevera(csa,thm),
file('theBenchmark.p',nevera_csa_thm) ).
fof(nevera_csa_thm_neg,negated_conjecture,
~ nevera(csa,thm),
inference(assume_negation,[status(cth)],[nevera_csa_thm]) ).
fof(nnf_23,plain,
! [S1,S2] :
( ( ~ nevera(S1,S2)
| ! [Ax,C] :
( ~ status(Ax,C,S2)
| ~ status(Ax,C,S1) ) )
& ( nevera(S1,S2)
| ? [X0,X1] :
( status(X0,X1,S2)
& status(X0,X1,S1) ) ) ),
inference(fof_nnf,[status(thm)],[nevera]) ).
fof(sk_nevera_sk,plain,
! [S1,S2] :
( ( ~ nevera(S1,S2)
| ! [Ax,C] :
( ~ status(Ax,C,S2)
| ~ status(Ax,C,S1) ) )
& ( nevera(S1,S2)
| ( status(sK0(S1,S2),sK1(S1,S2),S2)
& status(sK0(S1,S2),sK1(S1,S2),S1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0(S1,S2)),skolemize(X1,sK1(S1,S2))],[nnf_23]) ).
fof(sk_nevera,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ nevera(VAR_2,VAR_3)
| ~ status(VAR_0,VAR_1,VAR_3)
| ~ status(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1] :
( nevera(VAR_0,VAR_1)
| status(sK0(VAR_0,VAR_1),sK1(VAR_0,VAR_1),VAR_1) )
& ! [VAR_0,VAR_1] :
( nevera(VAR_0,VAR_1)
| status(sK0(VAR_0,VAR_1),sK1(VAR_0,VAR_1),VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_nevera_sk]) ).
cnf(c_43,plain,
( nevera(A,B)
| status(sK0(A,B),sK1(A,B),B) ),
inference(split_conjunct,[status(thm)],[sk_nevera]) ).
cnf(c_45,negated_conjecture,
~ nevera(csa,thm),
inference(clausify,[status(thm)],[nevera_csa_thm_neg]) ).
cnf(c_46,plain,
( nevera(A,B)
| status(sK0(A,B),sK1(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_nevera]) ).
cnf(c_75,plain,
( ~ model(A,not(B))
| ~ model(A,B) ),
inference(clausify,[status(thm)],[not]) ).
fof(nnf_17,plain,
! [Ax,C] :
( ( ~ status(Ax,C,csa)
| ? [I1] :
( model(I1,not(C))
& model(I1,Ax) ) )
& ( status(Ax,C,csa)
| ! [X0] :
( ~ model(X0,not(C))
| ~ model(X0,Ax) ) ) ),
inference(fof_nnf,[status(thm)],[csa]) ).
fof(sk_csa_sk,plain,
! [Ax,C] :
( ( ~ status(Ax,C,csa)
| ( model(sK2(Ax,C),not(C))
& model(sK2(Ax,C),Ax) ) )
& ( status(Ax,C,csa)
| ! [X0] :
( ~ model(X0,not(C))
| ~ model(X0,Ax) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(I1,sK2(Ax,C))],[nnf_17]) ).
fof(sk_csa,plain,
( ! [VAR_0,VAR_1] :
( ~ status(VAR_0,VAR_1,csa)
| model(sK2(VAR_0,VAR_1),not(VAR_1)) )
& ! [VAR_0,VAR_1] :
( ~ status(VAR_0,VAR_1,csa)
| model(sK2(VAR_0,VAR_1),VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( status(VAR_1,VAR_2,csa)
| ~ model(VAR_0,not(VAR_2))
| ~ model(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_csa_sk]) ).
cnf(c_84,plain,
( ~ status(A,B,csa)
| model(sK2(A,B),not(B)) ),
inference(split_conjunct,[status(thm)],[sk_csa]) ).
cnf(c_85,plain,
( ~ status(A,B,csa)
| model(sK2(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_csa]) ).
cnf(c_133,plain,
( ~ status(B,C,thm)
| model(A,C)
| ~ model(A,B) ),
inference(clausify,[status(thm)],[thm]) ).
cnf(c_152,negated_conjecture,
status(sK0(csa,thm),sK1(csa,thm),thm),
inference(resolve,[status(thm)],[c_43,c_45]) ).
cnf(c_154,negated_conjecture,
status(sK0(csa,thm),sK1(csa,thm),csa),
inference(resolve,[status(thm)],[c_46,c_45]) ).
cnf(c_567,plain,
( model(A,sK1(csa,thm))
| ~ model(A,sK0(csa,thm)) ),
inference(resolve,[status(thm)],[c_152,c_133]) ).
cnf(c_596,plain,
model(sK2(sK0(csa,thm),sK1(csa,thm)),sK0(csa,thm)),
inference(resolve,[status(thm)],[c_154,c_85]) ).
cnf(c_597,plain,
model(sK2(sK0(csa,thm),sK1(csa,thm)),not(sK1(csa,thm))),
inference(resolve,[status(thm)],[c_154,c_84]) ).
cnf(c_29689,plain,
model(sK2(sK0(csa,thm),sK1(csa,thm)),sK1(csa,thm)),
inference(resolve,[status(thm)],[c_596,c_567]) ).
cnf(c_29779,plain,
~ model(sK2(sK0(csa,thm),sK1(csa,thm)),sK1(csa,thm)),
inference(resolve,[status(thm)],[c_597,c_75]) ).
cnf(c_29778,plain,
$false,
inference(resolve,[status(thm)],[c_29689,c_29779]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS233+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n018.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 19:50:06 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 2696257 was started by sandbox on n018,
% 0.18/0.45 % Fri Sep 25 19:50:06 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.47
% 0.18/0.47 % From the command line: assign(max_seconds, 300).
% 81.45/11.70
% 81.45/11.70 % given #500 (A,wt=14): 257 model(f30(A,not(B)),A) | status(A,not(B),sca) | model(C,B). [resolve(96,b,74,b)].
% 81.45/11.70
% 81.45/11.70 % given #1000 (A,wt=15): 358 -model(A,B) | -model(f15(B,c7),c7) | model(c8,B) | status(B,c7,wec). [resolve(123,c,68,a)].
% 81.45/11.70
% 81.45/11.70 % given #1500 (A,wt=27): 510 model(f3(f50(sap,A),f51(sap,A)),f50(sap,A)) | -status(B,C,sap) | -status(B,C,A) | status(f50(sap,A),f51(sap,A),A). [resolve(145,b,51,c)].
% 81.45/11.70
% 81.45/11.70 % SZS status Theorem for theBenchmark
% 81.45/11.70
% 81.45/11.70 % Proof 1 at 7.44 (+ 3.68) seconds.
% 81.45/11.70 % Length of proof is 19.
% 81.45/11.70 % Level of proof is 5.
% 81.45/11.70 % Maximum clause weight is 12.000.
% 81.45/11.70 % Given clauses 1868.
% 81.45/11.70
% 81.45/11.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------