%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS178+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 : n014.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 07:46:15 AM UTC 2026
% Result : Theorem 0.17s 10.42s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 8 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 35 ( 15 ~; 12 |; 6 &)
% ( 1 <=>; 1 =>; 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 : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 22 !; 3 ?)
% 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_reflexive,conjecture,
! [S1] : isa(S1,S1),
file('theBenchmark.p',isa_reflexive) ).
fof(isa_reflexive_neg,negated_conjecture,
~ ! [S1] : isa(S1,S1),
inference(assume_negation,[status(cth)],[isa_reflexive]) ).
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(sK0(S1,S2),sK1(S1,S2),S2)
& status(sK0(S1,S2),sK1(S1,S2),S1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0(S1,S2)),skolemize(X1,sK1(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(sK0(VAR_0,VAR_1),sK1(VAR_0,VAR_1),VAR_1) )
& ! [VAR_0,VAR_1] :
( isa(VAR_0,VAR_1)
| status(sK0(VAR_0,VAR_1),sK1(VAR_0,VAR_1),VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_isa_sk]) ).
cnf(c_18,plain,
( isa(A,B)
| ~ status(sK0(A,B),sK1(A,B),B) ),
inference(split_conjunct,[status(thm)],[sk_isa]) ).
fof(nnf_14,plain,
? [S1] : ~ isa(S1,S1),
inference(fof_nnf,[status(thm)],[isa_reflexive_neg]) ).
fof(sk_isa_reflexive_neg,plain,
~ isa(sK2,sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(S1,sK2)],[nnf_14]) ).
cnf(c_20,negated_conjecture,
~ isa(sK2,sK2),
inference(split_conjunct,[status(thm)],[sk_isa_reflexive_neg]) ).
cnf(c_21,plain,
( isa(A,B)
| status(sK0(A,B),sK1(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_isa]) ).
cnf(c_58,negated_conjecture,
~ status(sK0(sK2,sK2),sK1(sK2,sK2),sK2),
inference(resolve,[status(thm)],[c_18,c_20]) ).
cnf(c_60,negated_conjecture,
status(sK0(sK2,sK2),sK1(sK2,sK2),sK2),
inference(resolve,[status(thm)],[c_21,c_20]) ).
cnf(c_61,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_58,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS178+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/10.39 % Computer : n014.cluster.edu
% 0.12/10.39 % Model : x86_64 x86_64
% 0.12/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.39 % Memory : 8046.5625MB
% 0.12/10.39 % OS : Linux 6.8.0-71-generic
% 0.12/10.39 % CPULimit : 300
% 0.12/10.39 % WCLimit : 300
% 0.12/10.39 % DateTime : Fri Sep 25 19:43:28 UTC 2026
% 0.12/10.40 % CPUTime :
% 0.17/10.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/10.40 % Process 939913 was started by sandbox2 on n014,
% 0.17/10.40 % Fri Sep 25 19:43:28 2026
% 0.17/10.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/10.41
% 0.17/10.41 % From the command line: assign(max_seconds, 300).
% 0.17/10.42
% 0.17/10.42 % SZS status Theorem for theBenchmark
% 0.17/10.42
% 0.17/10.42 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/10.42 % Length of proof is 8.
% 0.17/10.42 % Level of proof is 3.
% 0.17/10.42 % Maximum clause weight is 8.000.
% 0.17/10.42 % Given clauses 0.
% 0.17/10.42
% 0.17/10.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------