%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS260+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 : n008.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 0.12s 0.47s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 14 unt; 0 def)
% Number of atoms : 129 ( 0 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 153 ( 58 ~; 52 |; 37 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 100 ( 10 sgn 54 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm,axiom,
! [Ax,C] :
( ! [I1] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ),
file('theBenchmark.p',thm) ).
fof(wec,axiom,
! [Ax,C] :
( ( ? [I3] :
( ~ model(I3,Ax)
& model(I3,C) )
& ! [I2] :
( model(I2,Ax)
=> model(I2,C) )
& ? [I1] : model(I1,Ax) )
<=> status(Ax,C,wec) ),
file('theBenchmark.p',wec) ).
fof(mighta,axiom,
! [S1,S2] :
( ? [Ax,C] :
( status(Ax,C,S2)
& status(Ax,C,S1) )
<=> mighta(S1,S2) ),
file('theBenchmark.p',mighta) ).
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(mighta_wec_thm,conjecture,
mighta(wec,thm),
file('theBenchmark.p',mighta_wec_thm) ).
fof(mighta_wec_thm_neg,negated_conjecture,
~ mighta(wec,thm),
inference(assume_negation,[status(cth)],[mighta_wec_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(wec,thm),
inference(clausify,[status(thm)],[mighta_wec_thm_neg]) ).
cnf(c_57,negated_conjecture,
( ~ status(A,B,thm)
| ~ status(A,B,wec) ),
inference(resolve,[status(thm)],[c_37,c_35]) ).
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(sK9,sK1)
& ~ model(sK9,sK2)
& ! [I2] :
( model(I2,sK1)
| ~ model(I2,sK2) )
& model(sK3,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK2,sK1,sK9,sK0]),skolemize(Ax,sK2),skolemize(C,sK1),skolemize(I1,sK3),skolemize(I3,sK9),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_8,plain,
! [Ax,C] :
( ( ~ status(Ax,C,wec)
| ( ? [I3] :
( ~ model(I3,Ax)
& model(I3,C) )
& ! [I2] :
( model(I2,C)
| ~ model(I2,Ax) )
& ? [I1] : model(I1,Ax) ) )
& ( status(Ax,C,wec)
| ! [X0] :
( model(X0,Ax)
| ~ model(X0,C) )
| ? [X1] :
( ~ model(X1,C)
& model(X1,Ax) )
| ! [X2] : ~ model(X2,Ax) ) ),
inference(fof_nnf,[status(thm)],[wec]) ).
fof(sk_wec_sk,plain,
! [Ax,C] :
( ( ~ status(Ax,C,wec)
| ( ~ model(sK11(Ax,C),Ax)
& model(sK11(Ax,C),C)
& ! [I2] :
( model(I2,C)
| ~ model(I2,Ax) )
& model(sK10(Ax,C),Ax) ) )
& ( status(Ax,C,wec)
| ! [X0] :
( model(X0,Ax)
| ~ model(X0,C) )
| ( ~ model(sK5(Ax,C),C)
& model(sK5(Ax,C),Ax) )
| ! [X2] : ~ model(X2,Ax) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK10,sK11]),skolemize(X1,sK5(Ax,C)),skolemize(I1,sK10(Ax,C)),skolemize(I3,sK11(Ax,C))],[nnf_8]) ).
fof(sk_wec,plain,
( ! [VAR_0,VAR_1] :
( ~ status(VAR_0,VAR_1,wec)
| ~ model(sK11(VAR_0,VAR_1),VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ status(VAR_0,VAR_1,wec)
| model(sK11(VAR_0,VAR_1),VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ status(VAR_1,VAR_2,wec)
| model(VAR_0,VAR_2)
| ~ model(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( ~ status(VAR_0,VAR_1,wec)
| model(sK10(VAR_0,VAR_1),VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( status(VAR_1,VAR_2,wec)
| model(VAR_3,VAR_1)
| ~ model(VAR_3,VAR_2)
| ~ model(sK5(VAR_1,VAR_2),VAR_2)
| ~ model(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( status(VAR_1,VAR_2,wec)
| model(VAR_3,VAR_1)
| ~ model(VAR_3,VAR_2)
| model(sK5(VAR_1,VAR_2),VAR_1)
| ~ model(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_wec_sk]) ).
cnf(c_124,plain,
( status(B,C,wec)
| model(D,B)
| ~ model(D,C)
| ~ model(sK5(B,C),C)
| ~ model(A,B) ),
inference(split_conjunct,[status(thm)],[sk_wec]) ).
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(sK6(Ax,C),C)
& model(sK6(Ax,C),Ax) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6(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(sK6(VAR_0,VAR_1),VAR_1) )
& ! [VAR_0,VAR_1] :
( status(VAR_0,VAR_1,thm)
| model(sK6(VAR_0,VAR_1),VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_thm_sk]) ).
cnf(c_135,plain,
( status(A,B,thm)
| ~ model(sK6(A,B),B) ),
inference(split_conjunct,[status(thm)],[sk_thm]) ).
cnf(c_172,plain,
model(sK3,sK1),
inference(resolve,[status(thm)],[c_67,c_66]) ).
cnf(c_1373,plain,
( status(B,sK4,wec)
| model(C,B)
| ~ model(C,sK4)
| ~ model(A,B) ),
inference(resolve,[status(thm)],[c_124,c_74]) ).
cnf(c_353,plain,
( status(B,sK4,wec)
| model(C,B)
| ~ model(A,B) ),
inference(resolve,[status(thm)],[c_74,c_1373]) ).
cnf(c_417,plain,
status(A,sK4,thm),
inference(resolve,[status(thm)],[c_135,c_74]) ).
cnf(c_680,plain,
~ status(A,sK4,wec),
inference(resolve,[status(thm)],[c_417,c_57]) ).
cnf(c_687,plain,
( model(C,B)
| ~ model(A,B) ),
inference(resolve,[status(thm)],[c_680,c_353]) ).
cnf(c_1371,plain,
model(A,sK1),
inference(resolve,[status(thm)],[c_687,c_172]) ).
cnf(c_1372,plain,
$false,
inference(resolve,[status(thm)],[c_1371,c_63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS260+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n008.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 19:50:54 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 1732164 was started by sandbox on n008,
% 0.07/0.35 % Fri Sep 25 19:50:54 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.37
% 0.07/0.37 % From the command line: assign(max_seconds, 300).
% 0.12/0.47
% 0.12/0.47 % SZS status Theorem for theBenchmark
% 0.12/0.47
% 0.12/0.47 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.12/0.47 % Length of proof is 22.
% 0.12/0.47 % Level of proof is 6.
% 0.12/0.47 % Maximum clause weight is 28.000.
% 0.12/0.47 % Given clauses 177.
% 0.12/0.47
% 0.12/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------