%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS268+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 : n002.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 07:46:24 AM UTC 2026
% Result : Theorem 0.16s 5.95s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 13 unt; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 100 ( 41 ~; 34 |; 21 &)
% ( 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 80 ( 8 sgn 44 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm,axiom,
! [Ax,C] :
( ! [I1] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ),
file('theBenchmark.p',thm) ).
fof(wca,axiom,
! [Ax,C] :
( ( ? [I3] : ~ model(I3,C)
& ? [I2] : model(I2,C)
& ~ ? [I1] : model(I1,Ax) )
<=> status(Ax,C,wca) ),
file('theBenchmark.p',wca) ).
fof(mighta,axiom,
! [S1,S2] :
( ? [Ax,C] :
( status(Ax,C,S2)
& status(Ax,C,S1) )
<=> mighta(S1,S2) ),
file('theBenchmark.p',mighta) ).
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(mighta_wca_thm,conjecture,
mighta(wca,thm),
file('theBenchmark.p',mighta_wca_thm) ).
fof(mighta_wca_thm_neg,negated_conjecture,
~ mighta(wca,thm),
inference(assume_negation,[status(cth)],[mighta_wca_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(wca,thm),
inference(clausify,[status(thm)],[mighta_wca_thm_neg]) ).
cnf(c_57,negated_conjecture,
( ~ status(A,B,thm)
| ~ status(A,B,wca) ),
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_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]) ).
fof(nnf_16,plain,
! [Ax,C] :
( ( ~ status(Ax,C,wca)
| ( ? [I3] : ~ model(I3,C)
& ? [I2] : model(I2,C)
& ! [I1] : ~ model(I1,Ax) ) )
& ( status(Ax,C,wca)
| ! [X0] : model(X0,C)
| ! [X1] : ~ model(X1,C)
| ? [X2] : model(X2,Ax) ) ),
inference(fof_nnf,[status(thm)],[wca]) ).
fof(sk_wca_sk,plain,
! [Ax,C] :
( ( ~ status(Ax,C,wca)
| ( ~ model(sK9(Ax,C),C)
& model(sK8(Ax,C),C)
& ! [I1] : ~ model(I1,Ax) ) )
& ( status(Ax,C,wca)
| ! [X0] : model(X0,C)
| ! [X1] : ~ model(X1,C)
| model(sK4(Ax,C),Ax) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK8,sK9]),skolemize(X2,sK4(Ax,C)),skolemize(I2,sK8(Ax,C)),skolemize(I3,sK9(Ax,C))],[nnf_16]) ).
fof(sk_wca,plain,
( ! [VAR_0,VAR_1] :
( ~ status(VAR_0,VAR_1,wca)
| ~ model(sK9(VAR_0,VAR_1),VAR_1) )
& ! [VAR_0,VAR_1] :
( ~ status(VAR_0,VAR_1,wca)
| model(sK8(VAR_0,VAR_1),VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ status(VAR_1,VAR_2,wca)
| ~ model(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( status(VAR_0,VAR_1,wca)
| model(VAR_3,VAR_1)
| ~ model(VAR_2,VAR_1)
| model(sK4(VAR_0,VAR_1),VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_wca_sk]) ).
cnf(c_91,plain,
( status(A,B,wca)
| model(D,B)
| ~ model(C,B)
| model(sK4(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_wca]) ).
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(sK5(Ax,C),C)
& model(sK5(Ax,C),Ax) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X0,sK5(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(sK5(VAR_0,VAR_1),VAR_1) )
& ! [VAR_0,VAR_1] :
( status(VAR_0,VAR_1,thm)
| model(sK5(VAR_0,VAR_1),VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_thm_sk]) ).
cnf(c_136,plain,
( status(A,B,thm)
| model(sK5(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_thm]) ).
cnf(c_253,plain,
( status(A,sK2,wca)
| model(B,sK2)
| model(sK4(A,sK2),A) ),
inference(resolve,[status(thm)],[c_91,c_73]) ).
cnf(c_658,plain,
status(sK0,A,thm),
inference(resolve,[status(thm)],[c_136,c_71]) ).
cnf(c_1312,plain,
~ status(sK0,A,wca),
inference(resolve,[status(thm)],[c_658,c_57]) ).
cnf(c_5210,plain,
( status(sK0,sK2,wca)
| model(A,sK2) ),
inference(resolve,[status(thm)],[c_253,c_71]) ).
cnf(c_5208,plain,
model(A,sK2),
inference(resolve,[status(thm)],[c_1312,c_5210]) ).
cnf(c_5209,plain,
$false,
inference(resolve,[status(thm)],[c_5208,c_72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS268+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/5.38 % Computer : n002.cluster.edu
% 0.13/5.38 % Model : x86_64 x86_64
% 0.13/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.38 % Memory : 8046.5625MB
% 0.13/5.38 % OS : Linux 6.8.0-71-generic
% 0.13/5.38 % CPULimit : 300
% 0.13/5.38 % WCLimit : 300
% 0.13/5.38 % DateTime : Fri Sep 25 19:53:25 UTC 2026
% 0.13/5.39 % CPUTime :
% 0.13/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/5.39 % Process 4004925 was started by sandbox2 on n002,
% 0.13/5.39 % Fri Sep 25 19:53:25 2026
% 0.13/5.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/5.39
% 0.13/5.39 % From the command line: assign(max_seconds, 300).
% 0.16/5.95
% 0.16/5.95 % SZS status Theorem for theBenchmark
% 0.16/5.95
% 0.16/5.95 % Proof 1 at 0.44 (+ 0.07) seconds.
% 0.16/5.95 % Length of proof is 19.
% 0.16/5.95 % Level of proof is 5.
% 0.16/5.95 % Maximum clause weight is 19.000.
% 0.16/5.95 % Given clauses 439.
% 0.16/5.95
% 0.16/5.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------