%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS187+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 : n026.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 0.23s 0.94s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 66 ( 24 ~; 24 |; 13 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 4 sgn 39 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm,axiom,
! [Ax,C] :
( ! [I1] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ),
file('theBenchmark.p',thm) ).
fof(tac,axiom,
! [Ax,C] :
( ( ! [I2] : model(I2,C)
& ? [I1] : model(I1,Ax) )
<=> status(Ax,C,tac) ),
file('theBenchmark.p',tac) ).
fof(isa,axiom,
! [S1,S2] :
( ! [Ax,C] :
( status(Ax,C,S1)
=> status(Ax,C,S2) )
<=> isa(S1,S2) ),
file('theBenchmark.p',isa) ).
fof(isa_tac_thm,conjecture,
isa(tac,thm),
file('theBenchmark.p',isa_tac_thm) ).
fof(isa_tac_thm_neg,negated_conjecture,
~ isa(tac,thm),
inference(assume_negation,[status(cth)],[isa_tac_thm]) ).
fof(nnf_21,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_21]) ).
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_37,plain,
( isa(A,B)
| ~ status(sK0(A,B),sK1(A,B),B) ),
inference(split_conjunct,[status(thm)],[sk_isa]) ).
cnf(c_39,negated_conjecture,
~ isa(tac,thm),
inference(clausify,[status(thm)],[isa_tac_thm_neg]) ).
cnf(c_40,plain,
( isa(A,B)
| status(sK0(A,B),sK1(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_isa]) ).
cnf(c_125,plain,
( ~ status(C,B,tac)
| model(A,B) ),
inference(clausify,[status(thm)],[tac]) ).
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_134,plain,
( status(A,B,thm)
| ~ model(sK2(A,B),B) ),
inference(split_conjunct,[status(thm)],[sk_thm]) ).
cnf(c_150,negated_conjecture,
~ status(sK0(tac,thm),sK1(tac,thm),thm),
inference(resolve,[status(thm)],[c_37,c_39]) ).
cnf(c_152,negated_conjecture,
status(sK0(tac,thm),sK1(tac,thm),tac),
inference(resolve,[status(thm)],[c_40,c_39]) ).
cnf(c_557,plain,
model(A,sK1(tac,thm)),
inference(resolve,[status(thm)],[c_152,c_125]) ).
cnf(c_1355,plain,
status(A,sK1(tac,thm),thm),
inference(resolve,[status(thm)],[c_557,c_134]) ).
cnf(c_1356,plain,
$false,
inference(resolve,[status(thm)],[c_1355,c_150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS187+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.65 % Computer : n026.cluster.edu
% 0.20/0.65 % Model : x86_64 x86_64
% 0.20/0.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.65 % Memory : 8046.5625MB
% 0.20/0.65 % OS : Linux 6.8.0-71-generic
% 0.20/0.65 % CPULimit : 300
% 0.20/0.65 % WCLimit : 300
% 0.20/0.65 % DateTime : Fri Sep 25 19:45:25 UTC 2026
% 0.20/0.66 % CPUTime :
% 0.20/0.66 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.66 % Process 3277236 was started by sandbox on n026,
% 0.20/0.66 % Fri Sep 25 19:45:25 2026
% 0.20/0.66 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.20/0.68
% 0.20/0.68 % From the command line: assign(max_seconds, 300).
% 0.23/0.94
% 0.23/0.94 % SZS status Theorem for theBenchmark
% 0.23/0.94
% 0.23/0.94 % Proof 1 at 0.18 (+ 0.06) seconds.
% 0.23/0.94 % Length of proof is 14.
% 0.23/0.94 % Level of proof is 5.
% 0.23/0.94 % Maximum clause weight is 9.000.
% 0.23/0.94 % Given clauses 166.
% 0.23/0.94
% 0.23/0.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------