%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS180+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 : n005.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 07:46:16 AM UTC 2026
% Result : Theorem 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 5 unt; 0 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 111 ( 46 ~; 43 |; 13 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 6 sgn 38 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(isa,axiom,
! [S1,S2] :
( ! [Ax,C] :
( status(Ax,C,S1)
=> status(Ax,C,S2) )
<=> isa(S1,S2) ),
file('theBenchmark.p',isa) ).
fof(nota,axiom,
! [S1,S2] :
( ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) )
<=> nota(S1,S2) ),
file('theBenchmark.p',nota) ).
fof(nevera,axiom,
! [S1,S2] :
( ! [Ax,C] :
( status(Ax,C,S1)
=> ~ status(Ax,C,S2) )
<=> nevera(S1,S2) ),
file('theBenchmark.p',nevera) ).
fof(xora,axiom,
! [S1,S2] :
( ! [Ax,C] :
~ ( status(Ax,C,S1)
<=> status(Ax,C,S2) )
<=> xora(S1,S2) ),
file('theBenchmark.p',xora) ).
fof(isa_exclusive,conjecture,
! [S1,S2] :
? [Ax,C] :
( status(Ax,C,S1)
=> ~ ( ( xora(S1,S2)
| nevera(S1,S2)
| nota(S1,S2) )
& isa(S1,S2) ) ),
file('theBenchmark.p',isa_exclusive) ).
fof(isa_exclusive_neg,negated_conjecture,
~ ! [S1,S2] :
? [Ax,C] :
( status(Ax,C,S1)
=> ~ ( ( xora(S1,S2)
| nevera(S1,S2)
| nota(S1,S2) )
& isa(S1,S2) ) ),
inference(assume_negation,[status(cth)],[isa_exclusive]) ).
cnf(c_18,plain,
( ~ isa(C,D)
| status(A,B,D)
| ~ status(A,B,C) ),
inference(clausify,[status(thm)],[isa]) ).
fof(nnf_14,plain,
? [S1,S2] :
! [Ax,C] :
( ( xora(S1,S2)
| nevera(S1,S2)
| nota(S1,S2) )
& isa(S1,S2)
& status(Ax,C,S1) ),
inference(fof_nnf,[status(thm)],[isa_exclusive_neg]) ).
fof(sk_isa_exclusive_neg,plain,
! [Ax,C] :
( ( xora(sK0,sK1)
| nevera(sK0,sK1)
| nota(sK0,sK1) )
& isa(sK0,sK1)
& status(Ax,C,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(S1,sK0),skolemize(S2,sK1)],[nnf_14]) ).
cnf(c_19,negated_conjecture,
isa(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_isa_exclusive_neg]) ).
fof(nnf_3,plain,
! [S1,S2] :
( ( ~ nota(S1,S2)
| ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) ) )
& ( nota(S1,S2)
| ! [X0,X1] :
( status(X0,X1,S2)
| ~ status(X0,X1,S1) ) ) ),
inference(fof_nnf,[status(thm)],[nota]) ).
fof(sk_nota_sk,plain,
! [S1,S2] :
( ( ~ nota(S1,S2)
| ( ~ status(sK2(S1,S2),sK3(S1,S2),S2)
& status(sK2(S1,S2),sK3(S1,S2),S1) ) )
& ( nota(S1,S2)
| ! [X0,X1] :
( status(X0,X1,S2)
| ~ status(X0,X1,S1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(Ax,sK2(S1,S2)),skolemize(C,sK3(S1,S2))],[nnf_3]) ).
fof(sk_nota,plain,
( ! [VAR_0,VAR_1] :
( ~ nota(VAR_0,VAR_1)
| ~ status(sK2(VAR_0,VAR_1),sK3(VAR_0,VAR_1),VAR_1) )
& ! [VAR_0,VAR_1] :
( ~ nota(VAR_0,VAR_1)
| status(sK2(VAR_0,VAR_1),sK3(VAR_0,VAR_1),VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( nota(VAR_2,VAR_3)
| status(VAR_0,VAR_1,VAR_3)
| ~ status(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_nota_sk]) ).
cnf(c_24,plain,
( ~ nota(A,B)
| ~ status(sK2(A,B),sK3(A,B),B) ),
inference(split_conjunct,[status(thm)],[sk_nota]) ).
cnf(c_25,negated_conjecture,
( xora(sK0,sK1)
| nevera(sK0,sK1)
| nota(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_isa_exclusive_neg]) ).
cnf(c_26,plain,
( ~ nevera(C,D)
| ~ status(A,B,D)
| ~ status(A,B,C) ),
inference(clausify,[status(thm)],[nevera]) ).
cnf(c_27,negated_conjecture,
( ~ status(sK2(sK0,sK1),sK3(sK0,sK1),sK1)
| xora(sK0,sK1)
| nevera(sK0,sK1) ),
inference(resolve,[status(thm)],[c_25,c_24]) ).
cnf(c_34,negated_conjecture,
( ~ status(sK2(sK0,sK1),sK3(sK0,sK1),sK1)
| xora(sK0,sK1)
| ~ status(A,B,sK1)
| ~ status(A,B,sK0) ),
inference(resolve,[status(thm)],[c_26,c_27]) ).
cnf(c_36,plain,
( ~ xora(C,D)
| ~ status(A,B,D)
| ~ status(A,B,C) ),
inference(clausify,[status(thm)],[xora]) ).
cnf(c_37,negated_conjecture,
( ~ status(sK2(sK0,sK1),sK3(sK0,sK1),sK1)
| ~ status(C,D,sK1)
| ~ status(C,D,sK0)
| ~ status(A,B,sK1)
| ~ status(A,B,sK0) ),
inference(resolve,[status(thm)],[c_36,c_34]) ).
cnf(c_46,negated_conjecture,
status(A,B,sK0),
inference(split_conjunct,[status(thm)],[sk_isa_exclusive_neg]) ).
cnf(c_64,negated_conjecture,
( status(A,B,sK1)
| ~ status(A,B,sK0) ),
inference(resolve,[status(thm)],[c_18,c_19]) ).
cnf(c_65,negated_conjecture,
status(A,B,sK1),
inference(resolve,[status(thm)],[c_46,c_64]) ).
cnf(c_71,plain,
( ~ status(sK2(sK0,sK1),sK3(sK0,sK1),sK1)
| ~ status(A,B,sK1)
| ~ status(A,B,sK1)
| ~ status(A,B,sK0) ),
inference(factor,[status(thm)],[c_37]) ).
cnf(c_72,plain,
( ~ status(sK2(sK0,sK1),sK3(sK0,sK1),sK1)
| ~ status(A,B,sK1)
| ~ status(A,B,sK0) ),
inference(copy,[status(thm)],[c_71]) ).
cnf(c_73,negated_conjecture,
( ~ status(sK2(sK0,sK1),sK3(sK0,sK1),sK1)
| ~ status(A,B,sK1) ),
inference(resolve,[status(thm)],[c_46,c_72]) ).
cnf(c_74,negated_conjecture,
~ status(sK2(sK0,sK1),sK3(sK0,sK1),sK1),
inference(resolve,[status(thm)],[c_65,c_73]) ).
cnf(c_70,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_65,c_74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS180+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 19:43:03 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 14548 was started by sandbox2 on n005,
% 0.08/0.36 % Fri Sep 25 19:43:03 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.08/0.38
% 0.08/0.38 % SZS status Theorem for theBenchmark
% 0.08/0.38
% 0.08/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.38 % Length of proof is 18.
% 0.08/0.38 % Level of proof is 5.
% 0.08/0.38 % Maximum clause weight is 24.000.
% 0.08/0.38 % Given clauses 0.
% 0.08/0.38
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------