%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS179+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 : n009.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 0.15s 0.38s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 52 ( 20 ~; 16 |; 12 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 26 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(isa,axiom,
! [S1,S2] :
( ! [Ax,C] :
( status(Ax,C,S1)
=> status(Ax,C,S2) )
<=> isa(S1,S2) ),
file('theBenchmark.p',isa) ).
fof(isa_transitive,conjecture,
! [S1,S2,S3] :
( ( isa(S2,S3)
& isa(S1,S2) )
=> isa(S1,S3) ),
file('theBenchmark.p',isa_transitive) ).
fof(isa_transitive_neg,negated_conjecture,
~ ! [S1,S2,S3] :
( ( isa(S2,S3)
& isa(S1,S2) )
=> isa(S1,S3) ),
inference(assume_negation,[status(cth)],[isa_transitive]) ).
fof(nnf_14,plain,
? [S1,S2,S3] :
( ~ isa(S1,S3)
& isa(S2,S3)
& isa(S1,S2) ),
inference(fof_nnf,[status(thm)],[isa_transitive_neg]) ).
fof(sk_isa_transitive_neg,plain,
( ~ isa(sK2,sK1)
& isa(sK0,sK1)
& isa(sK2,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1]),skolemize(S1,sK2),skolemize(S2,sK0),skolemize(S3,sK1)],[nnf_14]) ).
cnf(c_18,negated_conjecture,
isa(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_isa_transitive_neg]) ).
cnf(c_19,negated_conjecture,
~ isa(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_isa_transitive_neg]) ).
cnf(c_20,negated_conjecture,
isa(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_isa_transitive_neg]) ).
fof(nnf_2,plain,
! [S1,S2] :
( ( ~ isa(S1,S2)
| ! [Ax,C] :
( status(Ax,C,S2)
| ~ status(Ax,C,S1) ) )
& ( isa(S1,S2)
| ? [X0,X1] :
( ~ status(X0,X1,S2)
& status(X0,X1,S1) ) ) ),
inference(fof_nnf,[status(thm)],[isa]) ).
fof(sk_isa_sk,plain,
! [S1,S2] :
( ( ~ isa(S1,S2)
| ! [Ax,C] :
( status(Ax,C,S2)
| ~ status(Ax,C,S1) ) )
& ( isa(S1,S2)
| ( ~ status(sK3(S1,S2),sK4(S1,S2),S2)
& status(sK3(S1,S2),sK4(S1,S2),S1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3(S1,S2)),skolemize(X1,sK4(S1,S2))],[nnf_2]) ).
fof(sk_isa,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ isa(VAR_2,VAR_3)
| status(VAR_0,VAR_1,VAR_3)
| ~ status(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1] :
( isa(VAR_0,VAR_1)
| ~ status(sK3(VAR_0,VAR_1),sK4(VAR_0,VAR_1),VAR_1) )
& ! [VAR_0,VAR_1] :
( isa(VAR_0,VAR_1)
| status(sK3(VAR_0,VAR_1),sK4(VAR_0,VAR_1),VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_isa_sk]) ).
cnf(c_21,plain,
( ~ isa(C,D)
| status(A,B,D)
| ~ status(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_isa]) ).
cnf(c_22,plain,
( isa(A,B)
| ~ status(sK3(A,B),sK4(A,B),B) ),
inference(split_conjunct,[status(thm)],[sk_isa]) ).
cnf(c_23,plain,
( isa(A,B)
| status(sK3(A,B),sK4(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_isa]) ).
cnf(c_59,negated_conjecture,
( status(A,B,sK0)
| ~ status(A,B,sK2) ),
inference(resolve,[status(thm)],[c_21,c_20]) ).
cnf(c_60,negated_conjecture,
( status(A,B,sK1)
| ~ status(A,B,sK0) ),
inference(resolve,[status(thm)],[c_21,c_18]) ).
cnf(c_62,negated_conjecture,
~ status(sK3(sK2,sK1),sK4(sK2,sK1),sK1),
inference(resolve,[status(thm)],[c_22,c_19]) ).
cnf(c_64,negated_conjecture,
status(sK3(sK2,sK1),sK4(sK2,sK1),sK2),
inference(resolve,[status(thm)],[c_23,c_19]) ).
cnf(c_79,negated_conjecture,
~ status(sK3(sK2,sK1),sK4(sK2,sK1),sK0),
inference(resolve,[status(thm)],[c_60,c_62]) ).
cnf(c_83,negated_conjecture,
status(sK3(sK2,sK1),sK4(sK2,sK1),sK0),
inference(resolve,[status(thm)],[c_64,c_59]) ).
cnf(c_82,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_79,c_83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS179+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n009.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Fri Sep 25 19:43:29 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 2377935 was started by sandbox on n009,
% 0.11/0.36 % Fri Sep 25 19:43:29 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.36
% 0.11/0.36 % From the command line: assign(max_seconds, 300).
% 0.15/0.38
% 0.15/0.38 % SZS status Theorem for theBenchmark
% 0.15/0.38
% 0.15/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/0.38 % Length of proof is 14.
% 0.15/0.38 % Level of proof is 4.
% 0.15/0.38 % Maximum clause weight is 8.000.
% 0.15/0.38 % Given clauses 31.
% 0.15/0.38
% 0.15/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------