%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS258+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 : n013.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 07:46:22 AM UTC 2026
% Result : Theorem 0.13s 0.51s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 11 unt; 0 def)
% Number of atoms : 96 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 114 ( 44 ~; 45 |; 20 &)
% ( 4 <=>; 1 =>; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 70 ( 4 sgn 46 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm,axiom,
! [Ax,C] :
( ! [I1] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ),
file('theBenchmark.p',thm) ).
fof(eqv,axiom,
! [Ax,C] :
( ( ! [I2] :
( model(I2,Ax)
<=> model(I2,C) )
& ? [I1] : model(I1,Ax) )
<=> status(Ax,C,eqv) ),
file('theBenchmark.p',eqv) ).
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(mighta_eqv_thm,conjecture,
mighta(eqv,thm),
file('theBenchmark.p',mighta_eqv_thm) ).
fof(mighta_eqv_thm_neg,negated_conjecture,
~ mighta(eqv,thm),
inference(assume_negation,[status(cth)],[mighta_eqv_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(eqv,thm),
inference(clausify,[status(thm)],[mighta_eqv_thm_neg]) ).
cnf(c_57,negated_conjecture,
( ~ status(A,B,thm)
| ~ status(A,B,eqv) ),
inference(resolve,[status(thm)],[c_37,c_35]) ).
fof(nnf_27,plain,
? [F] :
! [I] : model(I,F),
inference(fof_nnf,[status(thm)],[tautology]) ).
fof(sk_tautology,plain,
! [I] : model(I,sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(F,sK0)],[nnf_27]) ).
cnf(c_74,plain,
model(A,sK0),
inference(split_conjunct,[status(thm)],[sk_tautology]) ).
fof(nnf_6,plain,
! [Ax,C] :
( ( ~ status(Ax,C,eqv)
| ( ! [I2] :
( ( ~ model(I2,C)
| model(I2,Ax) )
& ( model(I2,C)
| ~ model(I2,Ax) ) )
& ? [I1] : model(I1,Ax) ) )
& ( status(Ax,C,eqv)
| ? [X0] :
( ( ~ model(X0,C)
| ~ model(X0,Ax) )
& ( model(X0,C)
| model(X0,Ax) ) )
| ! [X1] : ~ model(X1,Ax) ) ),
inference(fof_nnf,[status(thm)],[eqv]) ).
fof(sk_eqv_sk,plain,
! [Ax,C] :
( ( ~ status(Ax,C,eqv)
| ( ! [I2] :
( ( ~ model(I2,C)
| model(I2,Ax) )
& ( model(I2,C)
| ~ model(I2,Ax) ) )
& model(sK5(Ax,C),Ax) ) )
& ( status(Ax,C,eqv)
| ( ( ~ model(sK1(Ax,C),C)
| ~ model(sK1(Ax,C),Ax) )
& ( model(sK1(Ax,C),C)
| model(sK1(Ax,C),Ax) ) )
| ! [X1] : ~ model(X1,Ax) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK5]),skolemize(X0,sK1(Ax,C)),skolemize(I1,sK5(Ax,C))],[nnf_6]) ).
fof(sk_eqv,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ status(VAR_1,VAR_2,eqv)
| ~ model(VAR_0,VAR_2)
| model(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ status(VAR_1,VAR_2,eqv)
| model(VAR_0,VAR_2)
| ~ model(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( ~ status(VAR_0,VAR_1,eqv)
| model(sK5(VAR_0,VAR_1),VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( status(VAR_1,VAR_2,eqv)
| ~ model(sK1(VAR_1,VAR_2),VAR_2)
| ~ model(sK1(VAR_1,VAR_2),VAR_1)
| ~ model(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( status(VAR_1,VAR_2,eqv)
| model(sK1(VAR_1,VAR_2),VAR_2)
| model(sK1(VAR_1,VAR_2),VAR_1)
| ~ model(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_eqv_sk]) ).
cnf(c_132,plain,
( status(B,C,eqv)
| ~ model(sK1(B,C),C)
| ~ model(sK1(B,C),B)
| ~ model(A,B) ),
inference(split_conjunct,[status(thm)],[sk_eqv]) ).
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_135,plain,
( status(A,B,thm)
| ~ model(sK2(A,B),B) ),
inference(split_conjunct,[status(thm)],[sk_thm]) ).
cnf(c_661,plain,
( status(A,A,eqv)
| ~ model(sK1(A,A),A)
| ~ model(sK1(A,A),A) ),
inference(factor,[status(thm)],[c_132]) ).
cnf(c_167,plain,
( status(A,A,eqv)
| ~ model(sK1(A,A),A) ),
inference(copy,[status(thm)],[c_661]) ).
cnf(c_417,plain,
status(A,sK0,thm),
inference(resolve,[status(thm)],[c_135,c_74]) ).
cnf(c_609,plain,
status(sK0,sK0,eqv),
inference(resolve,[status(thm)],[c_167,c_74]) ).
cnf(c_659,plain,
~ status(A,sK0,eqv),
inference(resolve,[status(thm)],[c_417,c_57]) ).
cnf(c_660,plain,
$false,
inference(resolve,[status(thm)],[c_659,c_609]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS258+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n013.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Fri Sep 25 19:49:51 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 1053350 was started by sandbox2 on n013,
% 0.09/0.35 % Fri Sep 25 19:49:51 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.51
% 0.13/0.51 % SZS status Theorem for theBenchmark
% 0.13/0.51
% 0.13/0.51 % Proof 1 at 0.10 (+ 0.02) seconds.
% 0.13/0.51 % Length of proof is 16.
% 0.13/0.51 % Level of proof is 4.
% 0.13/0.51 % Maximum clause weight is 17.000.
% 0.13/0.51 % Given clauses 120.
% 0.13/0.51
% 0.13/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------