%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS265+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 07:46:23 AM UTC 2026
% Result : Theorem 1.22s 0.66s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 11 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 62 ( 27 ~; 21 |; 10 &)
% ( 3 <=>; 1 =>; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 4 sgn 34 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm,axiom,
! [Ax,C] :
( ! [I1] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ),
file('theBenchmark.p',thm) ).
fof(cax,axiom,
! [Ax,C] :
( ~ ? [I1] : model(I1,Ax)
<=> status(Ax,C,cax) ),
file('theBenchmark.p',cax) ).
fof(mighta,axiom,
! [S1,S2] :
( ? [Ax,C] :
( status(Ax,C,S2)
& status(Ax,C,S1) )
<=> mighta(S1,S2) ),
file('theBenchmark.p',mighta) ).
fof(contradiction,axiom,
? [F] :
! [I] : ~ model(I,F),
file('theBenchmark.p',contradiction) ).
fof(mighta_cax_thm,conjecture,
mighta(cax,thm),
file('theBenchmark.p',mighta_cax_thm) ).
fof(mighta_cax_thm_neg,negated_conjecture,
~ mighta(cax,thm),
inference(assume_negation,[status(cth)],[mighta_cax_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(cax,thm),
inference(clausify,[status(thm)],[mighta_cax_thm_neg]) ).
cnf(c_57,negated_conjecture,
( ~ status(A,B,thm)
| ~ status(A,B,cax) ),
inference(resolve,[status(thm)],[c_37,c_35]) ).
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_13,plain,
! [Ax,C] :
( ( ~ status(Ax,C,cax)
| ! [I1] : ~ model(I1,Ax) )
& ( status(Ax,C,cax)
| ? [X0] : model(X0,Ax) ) ),
inference(fof_nnf,[status(thm)],[cax]) ).
fof(sk_cax_sk,plain,
! [Ax,C] :
( ( ~ status(Ax,C,cax)
| ! [I1] : ~ model(I1,Ax) )
& ( status(Ax,C,cax)
| model(sK1(Ax,C),Ax) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1(Ax,C))],[nnf_13]) ).
fof(sk_cax,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ status(VAR_1,VAR_2,cax)
| ~ model(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( status(VAR_0,VAR_1,cax)
| model(sK1(VAR_0,VAR_1),VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_cax_sk]) ).
cnf(c_99,plain,
( status(A,B,cax)
| model(sK1(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_cax]) ).
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(sK2(Ax,C),C)
& model(sK2(Ax,C),Ax) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2(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(sK2(VAR_0,VAR_1),VAR_1) )
& ! [VAR_0,VAR_1] :
( status(VAR_0,VAR_1,thm)
| model(sK2(VAR_0,VAR_1),VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_thm_sk]) ).
cnf(c_136,plain,
( status(A,B,thm)
| model(sK2(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_thm]) ).
cnf(c_296,plain,
status(sK0,A,cax),
inference(resolve,[status(thm)],[c_99,c_71]) ).
cnf(c_521,plain,
status(sK0,A,thm),
inference(resolve,[status(thm)],[c_136,c_71]) ).
cnf(c_1063,negated_conjecture,
~ status(sK0,A,thm),
inference(resolve,[status(thm)],[c_296,c_57]) ).
cnf(c_1062,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_521,c_1063]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KRS265+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 19:48:39 UTC 2026
% 0.18/0.41 % CPUTime :
% 0.18/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.41 % Process 1727767 was started by sandbox2 on n007,
% 0.18/0.41 % Fri Sep 25 19:48:39 2026
% 0.18/0.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.43
% 0.18/0.43 % From the command line: assign(max_seconds, 300).
% 1.22/0.66
% 1.22/0.66 % SZS status Theorem for theBenchmark
% 1.22/0.66
% 1.22/0.66 % Proof 1 at 0.17 (+ 0.04) seconds.
% 1.22/0.66 % Length of proof is 14.
% 1.22/0.66 % Level of proof is 3.
% 1.22/0.66 % Maximum clause weight is 19.000.
% 1.22/0.66 % Given clauses 122.
% 1.22/0.66
% 1.22/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------