%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS157+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 07:46:10 AM UTC 2026
% Result : Theorem 0.13s 5.71s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 15 unt; 0 def)
% Number of atoms : 288 ( 0 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 425 ( 195 ~; 195 |; 28 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 23 ( 2 sgn 10 !; 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(axiom_121,axiom,
! [X] :
( cC216(X)
<=> ( cC214xcomp(X)
& cC64(X) ) ),
file('theBenchmark.p',axiom_121) ).
fof(axiom_132,axiom,
! [X] :
( cC30(X)
<=> ( cC14(X)
& cC28(X) ) ),
file('theBenchmark.p',axiom_132) ).
fof(axiom_148,axiom,
! [X] :
( cC46(X)
<=> ( cC44(X)
& cC30(X) ) ),
file('theBenchmark.p',axiom_148) ).
fof(axiom_201,axiom,
! [X] :
( cTEST(X)
<=> ( cC46(X)
& cC216(X) ) ),
file('theBenchmark.p',axiom_201) ).
fof(the_axiom,conjecture,
( cC30(iV3102)
& cowlThing(iV3102)
& cC28(iV3102)
& cC46(iV3102)
& cC64(iV3102)
& cC216(iV3102)
& cC44(iV3102)
& cC14(iV3102)
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('theBenchmark.p',the_axiom) ).
fof(the_axiom_neg,negated_conjecture,
~ ( cC30(iV3102)
& cowlThing(iV3102)
& cC28(iV3102)
& cC46(iV3102)
& cC64(iV3102)
& cC216(iV3102)
& cC44(iV3102)
& cC14(iV3102)
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(assume_negation,[status(cth)],[the_axiom]) ).
cnf(c_213,plain,
cowlThing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_214,plain,
~ cowlNothing(A),
inference(clausify,[status(thm)],[axiom_0]) ).
cnf(c_215,plain,
( ~ xsd_integer(A)
| ~ xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_216,plain,
( xsd_integer(A)
| xsd_string(A) ),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_514,plain,
( cC64(A)
| ~ cC216(A) ),
inference(clausify,[status(thm)],[axiom_121]) ).
cnf(c_541,plain,
( cC28(A)
| ~ cC30(A) ),
inference(clausify,[status(thm)],[axiom_132]) ).
cnf(c_542,plain,
( cC14(A)
| ~ cC30(A) ),
inference(clausify,[status(thm)],[axiom_132]) ).
cnf(c_581,plain,
( cC30(A)
| ~ cC46(A) ),
inference(clausify,[status(thm)],[axiom_148]) ).
cnf(c_582,plain,
( cC44(A)
| ~ cC46(A) ),
inference(clausify,[status(thm)],[axiom_148]) ).
cnf(c_716,plain,
( cC216(A)
| ~ cTEST(A) ),
inference(clausify,[status(thm)],[axiom_201]) ).
cnf(c_717,plain,
( cC46(A)
| ~ cTEST(A) ),
inference(clausify,[status(thm)],[axiom_201]) ).
fof(axiom_202,axiom,
cTEST(iV3102),
file('theBenchmark.p',axiom_202) ).
cnf(c_719,plain,
cTEST(iV3102),
inference(clausify,[status(thm)],[axiom_202]) ).
fof(nnf_208,plain,
( ~ cC30(iV3102)
| ~ cowlThing(iV3102)
| ~ cC28(iV3102)
| ~ cC46(iV3102)
| ~ cC64(iV3102)
| ~ cC216(iV3102)
| ~ cC44(iV3102)
| ~ cC14(iV3102)
| ? [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,
( ~ cC30(iV3102)
| ~ cowlThing(iV3102)
| ~ cC28(iV3102)
| ~ cC46(iV3102)
| ~ cC64(iV3102)
| ~ cC216(iV3102)
| ~ cC44(iV3102)
| ~ cC14(iV3102)
| ( ( 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_208]) ).
fof(sk_the_axiom_neg,plain,
( ( ~ cC30(iV3102)
| ~ cowlThing(iV3102)
| ~ cC28(iV3102)
| ~ cC46(iV3102)
| ~ cC64(iV3102)
| ~ cC216(iV3102)
| ~ cC44(iV3102)
| ~ cC14(iV3102)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) )
& ( ~ cC30(iV3102)
| ~ cowlThing(iV3102)
| ~ cC28(iV3102)
| ~ cC46(iV3102)
| ~ cC64(iV3102)
| ~ cC216(iV3102)
| ~ cC44(iV3102)
| ~ cC14(iV3102)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_the_axiom_neg_sk]) ).
cnf(c_735,negated_conjecture,
( ~ cC30(iV3102)
| ~ cowlThing(iV3102)
| ~ cC28(iV3102)
| ~ cC46(iV3102)
| ~ cC64(iV3102)
| ~ cC216(iV3102)
| ~ cC44(iV3102)
| ~ cC14(iV3102)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_760,negated_conjecture,
( ~ cC30(iV3102)
| ~ cowlThing(iV3102)
| ~ cC28(iV3102)
| ~ cC46(iV3102)
| ~ cC64(iV3102)
| ~ cC216(iV3102)
| ~ cC44(iV3102)
| ~ cC14(iV3102)
| ~ xsd_integer(sK1)
| xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_213,c_735]) ).
cnf(c_761,negated_conjecture,
( ~ cC30(iV3102)
| ~ cowlThing(iV3102)
| ~ cC28(iV3102)
| ~ cC46(iV3102)
| ~ cC64(iV3102)
| ~ cC216(iV3102)
| ~ cC44(iV3102)
| ~ cC14(iV3102)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_214,c_760]) ).
cnf(c_736,negated_conjecture,
( ~ cC30(iV3102)
| ~ cC28(iV3102)
| ~ cC46(iV3102)
| ~ cC64(iV3102)
| ~ cC216(iV3102)
| ~ cC44(iV3102)
| ~ cC14(iV3102)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_213,c_761]) ).
cnf(c_737,negated_conjecture,
( ~ cC30(iV3102)
| ~ cowlThing(iV3102)
| ~ cC28(iV3102)
| ~ cC46(iV3102)
| ~ cC64(iV3102)
| ~ cC216(iV3102)
| ~ cC44(iV3102)
| ~ cC14(iV3102)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0)
| ~ cowlThing(sK0) ),
inference(split_conjunct,[status(thm)],[sk_the_axiom_neg]) ).
cnf(c_762,negated_conjecture,
( ~ cC30(iV3102)
| ~ cowlThing(iV3102)
| ~ cC28(iV3102)
| ~ cC46(iV3102)
| ~ cC64(iV3102)
| ~ cC216(iV3102)
| ~ cC44(iV3102)
| ~ cC14(iV3102)
| xsd_integer(sK1)
| ~ xsd_string(sK1)
| cowlNothing(sK0) ),
inference(resolve,[status(thm)],[c_213,c_737]) ).
cnf(c_763,negated_conjecture,
( ~ cC30(iV3102)
| ~ cowlThing(iV3102)
| ~ cC28(iV3102)
| ~ cC46(iV3102)
| ~ cC64(iV3102)
| ~ cC216(iV3102)
| ~ cC44(iV3102)
| ~ cC14(iV3102)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_214,c_762]) ).
cnf(c_738,negated_conjecture,
( ~ cC30(iV3102)
| ~ cC28(iV3102)
| ~ cC46(iV3102)
| ~ cC64(iV3102)
| ~ cC216(iV3102)
| ~ cC44(iV3102)
| ~ cC14(iV3102)
| xsd_integer(sK1)
| ~ xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_213,c_763]) ).
cnf(c_764,negated_conjecture,
( xsd_integer(sK1)
| ~ cC30(iV3102)
| ~ cC28(iV3102)
| ~ cC46(iV3102)
| ~ cC64(iV3102)
| ~ cC216(iV3102)
| ~ cC44(iV3102)
| ~ cC14(iV3102)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_738,c_216]) ).
cnf(c_740,negated_conjecture,
( ~ cC30(iV3102)
| ~ cC28(iV3102)
| ~ cC46(iV3102)
| ~ cC64(iV3102)
| ~ cC216(iV3102)
| ~ cC44(iV3102)
| ~ cC14(iV3102)
| xsd_integer(sK1) ),
inference(copy,[status(thm)],[c_764]) ).
cnf(c_743,plain,
cC46(iV3102),
inference(resolve,[status(thm)],[c_719,c_717]) ).
cnf(c_744,plain,
cC216(iV3102),
inference(resolve,[status(thm)],[c_719,c_716]) ).
cnf(c_765,negated_conjecture,
( ~ cC30(iV3102)
| ~ cC28(iV3102)
| ~ cC46(iV3102)
| ~ cC64(iV3102)
| ~ cC44(iV3102)
| ~ cC14(iV3102)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_744,c_740]) ).
cnf(c_745,negated_conjecture,
( ~ cC30(iV3102)
| ~ cC28(iV3102)
| ~ cC64(iV3102)
| ~ cC44(iV3102)
| ~ cC14(iV3102)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_743,c_765]) ).
cnf(c_766,negated_conjecture,
( ~ cC30(iV3102)
| ~ cC28(iV3102)
| ~ cC46(iV3102)
| ~ cC64(iV3102)
| ~ cC44(iV3102)
| ~ cC14(iV3102)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_744,c_736]) ).
cnf(c_746,negated_conjecture,
( ~ cC30(iV3102)
| ~ cC28(iV3102)
| ~ cC64(iV3102)
| ~ cC44(iV3102)
| ~ cC14(iV3102)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_743,c_766]) ).
cnf(c_747,plain,
cC44(iV3102),
inference(resolve,[status(thm)],[c_743,c_582]) ).
cnf(c_748,plain,
cC30(iV3102),
inference(resolve,[status(thm)],[c_743,c_581]) ).
cnf(c_767,negated_conjecture,
( ~ cC30(iV3102)
| ~ cC28(iV3102)
| ~ cC64(iV3102)
| ~ cC14(iV3102)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_747,c_746]) ).
cnf(c_749,negated_conjecture,
( ~ cC28(iV3102)
| ~ cC64(iV3102)
| ~ cC14(iV3102)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_748,c_767]) ).
cnf(c_768,negated_conjecture,
( ~ cC30(iV3102)
| ~ cC28(iV3102)
| ~ cC64(iV3102)
| ~ cC14(iV3102)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_747,c_745]) ).
cnf(c_750,negated_conjecture,
( ~ cC28(iV3102)
| ~ cC64(iV3102)
| ~ cC14(iV3102)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_748,c_768]) ).
cnf(c_751,plain,
cC64(iV3102),
inference(resolve,[status(thm)],[c_744,c_514]) ).
cnf(c_752,negated_conjecture,
( ~ cC28(iV3102)
| ~ cC14(iV3102)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_751,c_750]) ).
cnf(c_753,negated_conjecture,
( ~ cC28(iV3102)
| ~ cC14(iV3102)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_751,c_749]) ).
cnf(c_754,plain,
cC14(iV3102),
inference(resolve,[status(thm)],[c_748,c_542]) ).
cnf(c_755,plain,
cC28(iV3102),
inference(resolve,[status(thm)],[c_748,c_541]) ).
cnf(c_769,negated_conjecture,
( ~ cC28(iV3102)
| ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_754,c_753]) ).
cnf(c_756,negated_conjecture,
( ~ xsd_integer(sK1)
| xsd_string(sK1) ),
inference(resolve,[status(thm)],[c_755,c_769]) ).
cnf(c_770,negated_conjecture,
( ~ cC28(iV3102)
| xsd_integer(sK1) ),
inference(resolve,[status(thm)],[c_754,c_752]) ).
cnf(c_757,negated_conjecture,
xsd_integer(sK1),
inference(resolve,[status(thm)],[c_755,c_770]) ).
cnf(c_758,negated_conjecture,
xsd_string(sK1),
inference(resolve,[status(thm)],[c_757,c_756]) ).
cnf(c_771,negated_conjecture,
~ xsd_integer(sK1),
inference(resolve,[status(thm)],[c_758,c_215]) ).
cnf(c_759,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_757,c_771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS157+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.54 % Computer : n010.cluster.edu
% 0.08/5.54 % Model : x86_64 x86_64
% 0.08/5.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.54 % Memory : 8046.5625MB
% 0.08/5.54 % OS : Linux 6.8.0-71-generic
% 0.08/5.54 % CPULimit : 300
% 0.08/5.54 % WCLimit : 300
% 0.08/5.54 % DateTime : Fri Sep 25 19:42:21 UTC 2026
% 0.08/5.54 % CPUTime :
% 0.08/5.54 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.54 % Process 1490903 was started by sandbox on n010,
% 0.08/5.54 % Fri Sep 25 19:42:21 2026
% 0.08/5.54 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/5.59
% 0.08/5.59 % From the command line: assign(max_seconds, 300).
% 0.08/5.59
% 0.08/5.59 % SInE: 217 to sos, 2 to usable, of 219 axioms (tolerance 2.00, depth 0 fixpoint).
% 0.13/5.71
% 0.13/5.71 % SZS status Theorem for theBenchmark
% 0.13/5.71
% 0.13/5.71 % Proof 1 at 0.08 (+ 0.02) seconds.
% 0.13/5.71 % Length of proof is 41.
% 0.13/5.71 % Level of proof is 9.
% 0.13/5.71 % Maximum clause weight is 107.000.
% 0.13/5.71 % Given clauses 91.
% 0.13/5.71
% 0.13/5.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------