%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS136+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 07:46:07 AM UTC 2026
% Result : Theorem 0.18s 5.68s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 5 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 72 ( 31 ~; 30 |; 8 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 12 ( 2 sgn 6 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_0,axiom,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
file('theBenchmark.p',axiom_0) ).
fof(axiom_1,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ),
file('theBenchmark.p',axiom_1) ).
fof(the_axiom,conjecture,
( ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('theBenchmark.p',the_axiom) ).
fof(the_axiom_neg,negated_conjecture,
~ ( ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(assume_negation,[status(cth)],[the_axiom]) ).
fof(nnf_3,plain,
( ? [X] :
( ( xsd_integer(X)
| ~ xsd_string(X) )
& ( ~ xsd_integer(X)
| xsd_string(X) ) )
| ? [X0] :
( cowlNothing(X0)
| ~ cowlThing(X0) ) ),
inference(fof_nnf,[status(thm)],[the_axiom_neg]) ).
fof(sk_the_axiom_neg_sk,plain,
( ( ( xsd_integer(sK1)
| ~ xsd_string(sK1) )
& ( ~ xsd_integer(sK1)
| xsd_string(sK1) ) )
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X,sK1)],[nnf_3]) ).
fof(sk_the_axiom_neg,plain,
( ( xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_the_axiom_neg_sk]) ).
cnf(c_4,negated_conjecture,
( ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_5,plain,
cowlThing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_6,negated_conjecture,
( xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_7,plain,
~ cowlNothing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_8,negated_conjecture,
( ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_9,negated_conjecture,
( xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_10,negated_conjecture,
( ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_11,negated_conjecture,
( xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_7,c_9]) ).
cnf(c_12,plain,
( ~ xsd_integer(A)
| ~ xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_13,plain,
( xsd_integer(A)
| xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_14,negated_conjecture,
( xsd_integer(sK1)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_13,c_11]) ).
cnf(c_15,negated_conjecture,
xsd_integer(sK1),
inference(copy,[status(thm)],[c_14]) ).
cnf(c_16,negated_conjecture,
( ~ xsd_integer(sK1)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_12,c_10]) ).
cnf(c_18,negated_conjecture,
~ xsd_integer(sK1),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_17,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_15,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS136+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.66 % Computer : n016.cluster.edu
% 0.18/5.66 % Model : x86_64 x86_64
% 0.18/5.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.66 % Memory : 8046.5625MB
% 0.18/5.66 % OS : Linux 6.8.0-71-generic
% 0.18/5.66 % CPULimit : 300
% 0.18/5.66 % WCLimit : 300
% 0.18/5.66 % DateTime : Fri Sep 25 19:46:07 UTC 2026
% 0.18/5.66 % CPUTime :
% 0.18/5.66 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.66 % Process 3130659 was started by sandbox2 on n016,
% 0.18/5.66 % Fri Sep 25 19:46:07 2026
% 0.18/5.66 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/5.67
% 0.18/5.67 % From the command line: assign(max_seconds, 300).
% 0.18/5.68
% 0.18/5.68 % SZS status Theorem for theBenchmark
% 0.18/5.68
% 0.18/5.68 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/5.68 % Length of proof is 17.
% 0.18/5.68 % Level of proof is 6.
% 0.18/5.68 % Maximum clause weight is 2.000.
% 0.18/5.68 % Given clauses 0.
% 0.18/5.68
% 0.18/5.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------