%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS235+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 : n007.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 07:46:21 AM UTC 2026
% Result : Theorem 93.23s 13.23s
% Output : CNFRefutation 93.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 10 unt; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 102 ( 39 ~; 36 |; 21 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 47 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm,axiom,
! [Ax,C] :
( ! [I1] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ),
file('theBenchmark.p',thm) ).
fof(noc,axiom,
! [Ax,C] :
( ( ? [I2] :
( model(I2,not(C))
& model(I2,Ax) )
& ? [I1] :
( model(I1,C)
& model(I1,Ax) ) )
<=> status(Ax,C,noc) ),
file('theBenchmark.p',noc) ).
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_noc_thm,conjecture,
nevera(noc,thm),
file('theBenchmark.p',nevera_noc_thm) ).
fof(nevera_noc_thm_neg,negated_conjecture,
~ nevera(noc,thm),
inference(assume_negation,[status(cth)],[nevera_noc_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(noc,thm),
inference(clausify,[status(thm)],[nevera_noc_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_19,plain,
! [Ax,C] :
( ( ~ status(Ax,C,noc)
| ( ? [I2] :
( model(I2,not(C))
& model(I2,Ax) )
& ? [I1] :
( model(I1,C)
& model(I1,Ax) ) ) )
& ( status(Ax,C,noc)
| ! [X0] :
( ~ model(X0,not(C))
| ~ model(X0,Ax) )
| ! [X1] :
( ~ model(X1,C)
| ~ model(X1,Ax) ) ) ),
inference(fof_nnf,[status(thm)],[noc]) ).
fof(sk_noc_sk,plain,
! [Ax,C] :
( ( ~ status(Ax,C,noc)
| ( model(sK2(Ax,C),not(C))
& model(sK2(Ax,C),Ax)
& model(sK3(Ax,C),C)
& model(sK3(Ax,C),Ax) ) )
& ( status(Ax,C,noc)
| ! [X0] :
( ~ model(X0,not(C))
| ~ model(X0,Ax) )
| ! [X1] :
( ~ model(X1,C)
| ~ model(X1,Ax) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK2]),skolemize(I1,sK3(Ax,C)),skolemize(I2,sK2(Ax,C))],[nnf_19]) ).
fof(sk_noc,plain,
( ! [VAR_0,VAR_1] :
( ~ status(VAR_0,VAR_1,noc)
| model(sK2(VAR_0,VAR_1),not(VAR_1)) )
& ! [VAR_0,VAR_1] :
( ~ status(VAR_0,VAR_1,noc)
| model(sK2(VAR_0,VAR_1),VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ status(VAR_0,VAR_1,noc)
| model(sK3(VAR_0,VAR_1),VAR_1) )
& ! [VAR_0,VAR_1] :
( ~ status(VAR_0,VAR_1,noc)
| model(sK3(VAR_0,VAR_1),VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( status(VAR_1,VAR_2,noc)
| ~ model(VAR_3,not(VAR_2))
| ~ model(VAR_3,VAR_1)
| ~ model(VAR_0,VAR_2)
| ~ model(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_noc_sk]) ).
cnf(c_76,plain,
( ~ status(A,B,noc)
| model(sK2(A,B),not(B)) ),
inference(split_conjunct,[status(thm)],[sk_noc]) ).
cnf(c_77,plain,
( ~ status(A,B,noc)
| model(sK2(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_noc]) ).
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(noc,thm),sK1(noc,thm),thm),
inference(resolve,[status(thm)],[c_43,c_45]) ).
cnf(c_154,negated_conjecture,
status(sK0(noc,thm),sK1(noc,thm),noc),
inference(resolve,[status(thm)],[c_46,c_45]) ).
cnf(c_567,plain,
( model(A,sK1(noc,thm))
| ~ model(A,sK0(noc,thm)) ),
inference(resolve,[status(thm)],[c_152,c_133]) ).
cnf(c_598,plain,
model(sK2(sK0(noc,thm),sK1(noc,thm)),sK0(noc,thm)),
inference(resolve,[status(thm)],[c_154,c_77]) ).
cnf(c_599,plain,
model(sK2(sK0(noc,thm),sK1(noc,thm)),not(sK1(noc,thm))),
inference(resolve,[status(thm)],[c_154,c_76]) ).
cnf(c_29779,plain,
model(sK2(sK0(noc,thm),sK1(noc,thm)),sK1(noc,thm)),
inference(resolve,[status(thm)],[c_598,c_567]) ).
cnf(c_29836,plain,
~ model(sK2(sK0(noc,thm),sK1(noc,thm)),sK1(noc,thm)),
inference(resolve,[status(thm)],[c_599,c_75]) ).
cnf(c_29835,plain,
$false,
inference(resolve,[status(thm)],[c_29779,c_29836]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KRS235+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n007.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 19:45:54 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.40 % Process 1718148 was started by sandbox2 on n007,
% 0.14/0.40 % Fri Sep 25 19:45:54 2026
% 0.14/0.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.41
% 0.18/0.41 % From the command line: assign(max_seconds, 300).
% 93.23/13.23
% 93.23/13.23 % 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)].
% 93.23/13.23
% 93.23/13.23 % 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)].
% 93.23/13.23
% 93.23/13.23 % 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)].
% 93.23/13.23
% 93.23/13.23 % SZS status Theorem for theBenchmark
% 93.23/13.23
% 93.23/13.23 % Proof 1 at 8.36 (+ 4.23) seconds.
% 93.23/13.23 % Length of proof is 19.
% 93.23/13.23 % Level of proof is 5.
% 93.23/13.23 % Maximum clause weight is 12.000.
% 93.23/13.23 % Given clauses 1878.
% 93.23/13.23
% 93.23/13.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------