%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS130+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 : 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 07:46:06 AM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 5 unt; 0 def)
% Number of atoms : 203 ( 0 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 226 ( 67 ~; 138 |; 14 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 27 ( 5 sgn 12 !; 6 ?)
% 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(axiom_2,axiom,
! [X] :
( cNothing(X)
=> ~ ? [Y] : rp(X,Y) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cNothing(X)
=> ? [Y0] : rp(X,Y0) ),
file('theBenchmark.p',axiom_3) ).
fof(the_axiom,conjecture,
( ! [X] :
( cNothing(X)
<=> cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('theBenchmark.p',the_axiom) ).
fof(the_axiom_neg,negated_conjecture,
~ ( ! [X] :
( cNothing(X)
<=> cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(assume_negation,[status(cth)],[the_axiom]) ).
fof(nnf_5,plain,
( ? [X] :
( ( ~ cowlNothing(X)
| ~ cNothing(X) )
& ( cowlNothing(X)
| cNothing(X) ) )
| ? [X1] :
( ( xsd_integer(X1)
| ~ xsd_string(X1) )
& ( ~ xsd_integer(X1)
| xsd_string(X1) ) )
| ? [X0] :
( cowlNothing(X0)
| ~ cowlThing(X0) ) ),
inference(fof_nnf,[status(thm)],[the_axiom_neg]) ).
fof(sk_the_axiom_neg_sk,plain,
( ( ( ~ cowlNothing(sK2)
| ~ cNothing(sK2) )
& ( cowlNothing(sK2)
| cNothing(sK2) ) )
| ( ( 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,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X,sK2)],[nnf_5]) ).
fof(sk_the_axiom_neg,plain,
( ( ~ cowlNothing(sK2)
| ~ cNothing(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( cowlNothing(sK2)
| cNothing(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ~ cowlNothing(sK2)
| ~ cNothing(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( cowlNothing(sK2)
| cNothing(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_the_axiom_neg_sk]) ).
cnf(c_6,negated_conjecture,
( cowlNothing(sK2)
| cNothing(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_7,plain,
cowlThing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_9,negated_conjecture,
( cowlNothing(sK2)
| cNothing(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_12,negated_conjecture,
( cowlNothing(sK2)
| cNothing(sK2)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_9,c_7]) ).
cnf(c_14,negated_conjecture,
( cowlNothing(sK2)
| cNothing(sK2)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_15,plain,
( xsd_integer(A)
| xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_16,plain,
( ~ xsd_integer(A)
| ~ xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_17,plain,
( ~ rp(A,B)
| ~ cNothing(A) ),
inference(clausify,[status(thm)],[axiom_2]) ).
cnf(c_18,negated_conjecture,
( cowlNothing(sK2)
| cNothing(sK2)
| xsd_integer(sK1)
| cowlNothing(sK0)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_15,c_12]) ).
cnf(c_19,negated_conjecture,
( cowlNothing(sK2)
| cNothing(sK2)
| ~ xsd_integer(sK1)
| cowlNothing(sK0)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_16,c_14]) ).
fof(nnf_4,plain,
! [X] :
( ? [Y0] : rp(X,Y0)
| ~ cNothing(X) ),
inference(fof_nnf,[status(thm)],[axiom_3]) ).
fof(sk_axiom_3,plain,
! [X] :
( rp(X,sK3(X))
| ~ cNothing(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(Y0,sK3(X))],[nnf_4]) ).
cnf(c_20,plain,
( rp(A,sK3(A))
| ~ cNothing(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
cnf(c_21,negated_conjecture,
( cowlNothing(sK2)
| ~ xsd_integer(sK1)
| cowlNothing(sK0)
| ~ xsd_integer(sK1)
| ~ rp(sK2,A) ),
inference(resolve,[status(thm)],[c_17,c_19]) ).
cnf(c_22,negated_conjecture,
( cowlNothing(sK2)
| xsd_integer(sK1)
| cowlNothing(sK0)
| xsd_integer(sK1)
| rp(sK2,sK3(sK2)) ),
inference(resolve,[status(thm)],[c_20,c_18]) ).
cnf(c_23,negated_conjecture,
( cowlNothing(sK2)
| ~ xsd_integer(sK1)
| cowlNothing(sK0)
| ~ xsd_integer(sK1)
| rp(sK2,sK3(sK2)) ),
inference(resolve,[status(thm)],[c_20,c_19]) ).
cnf(c_24,negated_conjecture,
( cowlNothing(sK2)
| xsd_integer(sK1)
| cowlNothing(sK0)
| xsd_integer(sK1)
| ~ rp(sK2,A) ),
inference(resolve,[status(thm)],[c_17,c_18]) ).
cnf(c_25,negated_conjecture,
( cowlNothing(sK2)
| xsd_integer(sK1)
| cowlNothing(sK0)
| xsd_integer(sK1)
| cowlNothing(sK2)
| xsd_integer(sK1)
| cowlNothing(sK0)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_24,c_22]) ).
cnf(c_32,negated_conjecture,
( cowlNothing(sK2)
| xsd_integer(sK1)
| cowlNothing(sK0)
| xsd_integer(sK1)
| cowlNothing(sK2)
| cowlNothing(sK0)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_25]) ).
cnf(c_33,negated_conjecture,
( cowlNothing(sK2)
| xsd_integer(sK1)
| cowlNothing(sK0)
| cowlNothing(sK2)
| cowlNothing(sK0)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_34,negated_conjecture,
( cowlNothing(sK2)
| xsd_integer(sK1)
| cowlNothing(sK2)
| cowlNothing(sK0)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_33]) ).
cnf(c_35,negated_conjecture,
( cowlNothing(sK2)
| cowlNothing(sK2)
| cowlNothing(sK0)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_34]) ).
cnf(c_26,negated_conjecture,
( cowlNothing(sK2)
| cowlNothing(sK0)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_35]) ).
cnf(c_27,negated_conjecture,
( cowlNothing(sK2)
| ~ xsd_integer(sK1)
| cowlNothing(sK0)
| ~ xsd_integer(sK1)
| cowlNothing(sK2)
| ~ xsd_integer(sK1)
| cowlNothing(sK0)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_21,c_23]) ).
cnf(c_36,negated_conjecture,
( cowlNothing(sK2)
| ~ xsd_integer(sK1)
| cowlNothing(sK0)
| ~ xsd_integer(sK1)
| cowlNothing(sK2)
| cowlNothing(sK0)
| ~ xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_27]) ).
cnf(c_37,negated_conjecture,
( cowlNothing(sK2)
| ~ xsd_integer(sK1)
| cowlNothing(sK0)
| cowlNothing(sK2)
| cowlNothing(sK0)
| ~ xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_36]) ).
cnf(c_38,negated_conjecture,
( cowlNothing(sK2)
| ~ xsd_integer(sK1)
| cowlNothing(sK2)
| cowlNothing(sK0)
| ~ xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_37]) ).
cnf(c_39,negated_conjecture,
( cowlNothing(sK2)
| cowlNothing(sK2)
| cowlNothing(sK0)
| ~ xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_38]) ).
cnf(c_28,negated_conjecture,
( cowlNothing(sK2)
| cowlNothing(sK0)
| ~ xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_39]) ).
cnf(c_29,plain,
~ cowlNothing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_40,negated_conjecture,
( cowlNothing(sK2)
| ~ xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_29,c_28]) ).
cnf(c_30,negated_conjecture,
~ xsd_integer(sK1),
inference(resolve,[status(thm)],[c_29,c_40]) ).
cnf(c_41,negated_conjecture,
( cowlNothing(sK2)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_30,c_26]) ).
cnf(c_42,negated_conjecture,
cowlNothing(sK2),
inference(resolve,[status(thm)],[c_29,c_41]) ).
cnf(c_31,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_29,c_42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KRS130+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n026.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 19:43:26 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 3273087 was started by sandbox2 on n026,
% 0.16/0.44 % Fri Sep 25 19:43:26 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 0.16/0.46
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46
% 0.16/0.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.46 % Length of proof is 27.
% 0.16/0.46 % Level of proof is 8.
% 0.16/0.46 % Maximum clause weight is 6.000.
% 0.16/0.46 % Given clauses 0.
% 0.16/0.46
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------